Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.44389 | −0.833633 | −0.416816 | − | 0.908991i | \(-0.636854\pi\) | ||||
−0.416816 | + | 0.908991i | \(0.636854\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.880270 | −0.393669 | −0.196834 | − | 0.980437i | \(-0.563066\pi\) | ||||
−0.196834 | + | 0.980437i | \(0.563066\pi\) | |||||||
\(6\) | −1.44389 | −0.589467 | ||||||||
\(7\) | −5.04870 | −1.90823 | −0.954114 | − | 0.299444i | \(-0.903199\pi\) | ||||
−0.954114 | + | 0.299444i | \(0.903199\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.915168 | −0.305056 | ||||||||
\(10\) | −0.880270 | −0.278366 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.44389 | −0.416816 | ||||||||
\(13\) | 1.58937 | 0.440813 | 0.220407 | − | 0.975408i | \(-0.429262\pi\) | ||||
0.220407 | + | 0.975408i | \(0.429262\pi\) | |||||||
\(14\) | −5.04870 | −1.34932 | ||||||||
\(15\) | 1.27102 | 0.328175 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.33984 | −0.810029 | −0.405015 | − | 0.914310i | \(-0.632734\pi\) | ||||
−0.405015 | + | 0.914310i | \(0.632734\pi\) | |||||||
\(18\) | −0.915168 | −0.215707 | ||||||||
\(19\) | −2.18701 | −0.501734 | −0.250867 | − | 0.968022i | \(-0.580716\pi\) | ||||
−0.250867 | + | 0.968022i | \(0.580716\pi\) | |||||||
\(20\) | −0.880270 | −0.196834 | ||||||||
\(21\) | 7.28978 | 1.59076 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 0.594770 | 0.124018 | 0.0620091 | − | 0.998076i | \(-0.480249\pi\) | ||||
0.0620091 | + | 0.998076i | \(0.480249\pi\) | |||||||
\(24\) | −1.44389 | −0.294734 | ||||||||
\(25\) | −4.22513 | −0.845025 | ||||||||
\(26\) | 1.58937 | 0.311702 | ||||||||
\(27\) | 5.65309 | 1.08794 | ||||||||
\(28\) | −5.04870 | −0.954114 | ||||||||
\(29\) | 6.81432 | 1.26539 | 0.632693 | − | 0.774402i | \(-0.281949\pi\) | ||||
0.632693 | + | 0.774402i | \(0.281949\pi\) | |||||||
\(30\) | 1.27102 | 0.232055 | ||||||||
\(31\) | −8.51050 | −1.52853 | −0.764265 | − | 0.644902i | \(-0.776898\pi\) | ||||
−0.764265 | + | 0.644902i | \(0.776898\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.44389 | −0.251350 | ||||||||
\(34\) | −3.33984 | −0.572777 | ||||||||
\(35\) | 4.44421 | 0.751209 | ||||||||
\(36\) | −0.915168 | −0.152528 | ||||||||
\(37\) | −11.5469 | −1.89830 | −0.949151 | − | 0.314822i | \(-0.898055\pi\) | ||||
−0.949151 | + | 0.314822i | \(0.898055\pi\) | |||||||
\(38\) | −2.18701 | −0.354780 | ||||||||
\(39\) | −2.29489 | −0.367476 | ||||||||
\(40\) | −0.880270 | −0.139183 | ||||||||
\(41\) | −0.0999763 | −0.0156137 | −0.00780684 | − | 0.999970i | \(-0.502485\pi\) | ||||
−0.00780684 | + | 0.999970i | \(0.502485\pi\) | |||||||
\(42\) | 7.28978 | 1.12484 | ||||||||
\(43\) | −7.64379 | −1.16567 | −0.582833 | − | 0.812592i | \(-0.698056\pi\) | ||||
−0.582833 | + | 0.812592i | \(0.698056\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0.805595 | 0.120091 | ||||||||
\(46\) | 0.594770 | 0.0876941 | ||||||||
\(47\) | 10.6610 | 1.55507 | 0.777533 | − | 0.628842i | \(-0.216471\pi\) | ||||
0.777533 | + | 0.628842i | \(0.216471\pi\) | |||||||
\(48\) | −1.44389 | −0.208408 | ||||||||
\(49\) | 18.4893 | 2.64133 | ||||||||
\(50\) | −4.22513 | −0.597523 | ||||||||
\(51\) | 4.82237 | 0.675267 | ||||||||
\(52\) | 1.58937 | 0.220407 | ||||||||
\(53\) | −8.79832 | −1.20854 | −0.604271 | − | 0.796779i | \(-0.706536\pi\) | ||||
−0.604271 | + | 0.796779i | \(0.706536\pi\) | |||||||
\(54\) | 5.65309 | 0.769288 | ||||||||
\(55\) | −0.880270 | −0.118696 | ||||||||
\(56\) | −5.04870 | −0.674660 | ||||||||
\(57\) | 3.15781 | 0.418262 | ||||||||
\(58\) | 6.81432 | 0.894764 | ||||||||
\(59\) | 12.2524 | 1.59512 | 0.797562 | − | 0.603237i | \(-0.206123\pi\) | ||||
0.797562 | + | 0.603237i | \(0.206123\pi\) | |||||||
\(60\) | 1.27102 | 0.164088 | ||||||||
\(61\) | −6.41861 | −0.821819 | −0.410909 | − | 0.911676i | \(-0.634789\pi\) | ||||
−0.410909 | + | 0.911676i | \(0.634789\pi\) | |||||||
\(62\) | −8.51050 | −1.08083 | ||||||||
\(63\) | 4.62041 | 0.582117 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.39908 | −0.173534 | ||||||||
\(66\) | −1.44389 | −0.177731 | ||||||||
\(67\) | 2.66780 | 0.325923 | 0.162962 | − | 0.986632i | \(-0.447895\pi\) | ||||
0.162962 | + | 0.986632i | \(0.447895\pi\) | |||||||
\(68\) | −3.33984 | −0.405015 | ||||||||
\(69\) | −0.858786 | −0.103386 | ||||||||
\(70\) | 4.44421 | 0.531185 | ||||||||
\(71\) | 8.78579 | 1.04268 | 0.521341 | − | 0.853349i | \(-0.325432\pi\) | ||||
0.521341 | + | 0.853349i | \(0.325432\pi\) | |||||||
\(72\) | −0.915168 | −0.107854 | ||||||||
\(73\) | 0.0781045 | 0.00914144 | 0.00457072 | − | 0.999990i | \(-0.498545\pi\) | ||||
0.00457072 | + | 0.999990i | \(0.498545\pi\) | |||||||
\(74\) | −11.5469 | −1.34230 | ||||||||
\(75\) | 6.10064 | 0.704441 | ||||||||
\(76\) | −2.18701 | −0.250867 | ||||||||
\(77\) | −5.04870 | −0.575352 | ||||||||
\(78\) | −2.29489 | −0.259845 | ||||||||
\(79\) | −0.149095 | −0.0167745 | −0.00838724 | − | 0.999965i | \(-0.502670\pi\) | ||||
−0.00838724 | + | 0.999965i | \(0.502670\pi\) | |||||||
\(80\) | −0.880270 | −0.0984171 | ||||||||
\(81\) | −5.41696 | −0.601885 | ||||||||
\(82\) | −0.0999763 | −0.0110405 | ||||||||
\(83\) | 6.73880 | 0.739680 | 0.369840 | − | 0.929096i | \(-0.379413\pi\) | ||||
0.369840 | + | 0.929096i | \(0.379413\pi\) | |||||||
\(84\) | 7.28978 | 0.795381 | ||||||||
\(85\) | 2.93996 | 0.318883 | ||||||||
\(86\) | −7.64379 | −0.824251 | ||||||||
\(87\) | −9.83915 | −1.05487 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −13.1212 | −1.39084 | −0.695421 | − | 0.718602i | \(-0.744782\pi\) | ||||
−0.695421 | + | 0.718602i | \(0.744782\pi\) | |||||||
\(90\) | 0.805595 | 0.0849172 | ||||||||
\(91\) | −8.02427 | −0.841172 | ||||||||
\(92\) | 0.594770 | 0.0620091 | ||||||||
\(93\) | 12.2883 | 1.27423 | ||||||||
\(94\) | 10.6610 | 1.09960 | ||||||||
\(95\) | 1.92516 | 0.197517 | ||||||||
\(96\) | −1.44389 | −0.147367 | ||||||||
\(97\) | 7.38017 | 0.749342 | 0.374671 | − | 0.927158i | \(-0.377756\pi\) | ||||
0.374671 | + | 0.927158i | \(0.377756\pi\) | |||||||
\(98\) | 18.4893 | 1.86770 | ||||||||
\(99\) | −0.915168 | −0.0919779 | ||||||||
\(100\) | −4.22513 | −0.422513 | ||||||||
\(101\) | 10.4210 | 1.03692 | 0.518462 | − | 0.855101i | \(-0.326505\pi\) | ||||
0.518462 | + | 0.855101i | \(0.326505\pi\) | |||||||
\(102\) | 4.82237 | 0.477486 | ||||||||
\(103\) | −1.04881 | −0.103342 | −0.0516710 | − | 0.998664i | \(-0.516455\pi\) | ||||
−0.0516710 | + | 0.998664i | \(0.516455\pi\) | |||||||
\(104\) | 1.58937 | 0.155851 | ||||||||
\(105\) | −6.41698 | −0.626233 | ||||||||
\(106\) | −8.79832 | −0.854568 | ||||||||
\(107\) | 14.8629 | 1.43685 | 0.718425 | − | 0.695604i | \(-0.244863\pi\) | ||||
0.718425 | + | 0.695604i | \(0.244863\pi\) | |||||||
\(108\) | 5.65309 | 0.543969 | ||||||||
\(109\) | 9.52282 | 0.912121 | 0.456060 | − | 0.889949i | \(-0.349260\pi\) | ||||
0.456060 | + | 0.889949i | \(0.349260\pi\) | |||||||
\(110\) | −0.880270 | −0.0839304 | ||||||||
\(111\) | 16.6725 | 1.58249 | ||||||||
\(112\) | −5.04870 | −0.477057 | ||||||||
\(113\) | 17.4354 | 1.64018 | 0.820091 | − | 0.572233i | \(-0.193923\pi\) | ||||
0.820091 | + | 0.572233i | \(0.193923\pi\) | |||||||
\(114\) | 3.15781 | 0.295756 | ||||||||
\(115\) | −0.523558 | −0.0488221 | ||||||||
\(116\) | 6.81432 | 0.632693 | ||||||||
\(117\) | −1.45455 | −0.134473 | ||||||||
\(118\) | 12.2524 | 1.12792 | ||||||||
\(119\) | 16.8618 | 1.54572 | ||||||||
\(120\) | 1.27102 | 0.116027 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −6.41861 | −0.581114 | ||||||||
\(123\) | 0.144355 | 0.0130161 | ||||||||
\(124\) | −8.51050 | −0.764265 | ||||||||
\(125\) | 8.12060 | 0.726328 | ||||||||
\(126\) | 4.62041 | 0.411619 | ||||||||
\(127\) | 14.9631 | 1.32776 | 0.663882 | − | 0.747838i | \(-0.268908\pi\) | ||||
0.663882 | + | 0.747838i | \(0.268908\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 11.0368 | 0.971738 | ||||||||
\(130\) | −1.39908 | −0.122707 | ||||||||
\(131\) | 19.4126 | 1.69609 | 0.848043 | − | 0.529928i | \(-0.177781\pi\) | ||||
0.848043 | + | 0.529928i | \(0.177781\pi\) | |||||||
\(132\) | −1.44389 | −0.125675 | ||||||||
\(133\) | 11.0415 | 0.957424 | ||||||||
\(134\) | 2.66780 | 0.230463 | ||||||||
\(135\) | −4.97624 | −0.428287 | ||||||||
\(136\) | −3.33984 | −0.286389 | ||||||||
\(137\) | −4.81891 | −0.411707 | −0.205854 | − | 0.978583i | \(-0.565997\pi\) | ||||
−0.205854 | + | 0.978583i | \(0.565997\pi\) | |||||||
\(138\) | −0.858786 | −0.0731047 | ||||||||
\(139\) | −16.7243 | −1.41854 | −0.709269 | − | 0.704938i | \(-0.750975\pi\) | ||||
−0.709269 | + | 0.704938i | \(0.750975\pi\) | |||||||
\(140\) | 4.44421 | 0.375605 | ||||||||
\(141\) | −15.3933 | −1.29635 | ||||||||
\(142\) | 8.78579 | 0.737287 | ||||||||
\(143\) | 1.58937 | 0.132910 | ||||||||
\(144\) | −0.915168 | −0.0762640 | ||||||||
\(145\) | −5.99844 | −0.498143 | ||||||||
\(146\) | 0.0781045 | 0.00646397 | ||||||||
\(147\) | −26.6966 | −2.20190 | ||||||||
\(148\) | −11.5469 | −0.949151 | ||||||||
\(149\) | −14.6284 | −1.19840 | −0.599201 | − | 0.800599i | \(-0.704515\pi\) | ||||
−0.599201 | + | 0.800599i | \(0.704515\pi\) | |||||||
\(150\) | 6.10064 | 0.498115 | ||||||||
\(151\) | 22.0137 | 1.79145 | 0.895725 | − | 0.444608i | \(-0.146657\pi\) | ||||
0.895725 | + | 0.444608i | \(0.146657\pi\) | |||||||
\(152\) | −2.18701 | −0.177390 | ||||||||
\(153\) | 3.05651 | 0.247104 | ||||||||
\(154\) | −5.04870 | −0.406835 | ||||||||
\(155\) | 7.49153 | 0.601734 | ||||||||
\(156\) | −2.29489 | −0.183738 | ||||||||
\(157\) | −6.74428 | −0.538252 | −0.269126 | − | 0.963105i | \(-0.586735\pi\) | ||||
−0.269126 | + | 0.963105i | \(0.586735\pi\) | |||||||
\(158\) | −0.149095 | −0.0118614 | ||||||||
\(159\) | 12.7038 | 1.00748 | ||||||||
\(160\) | −0.880270 | −0.0695914 | ||||||||
\(161\) | −3.00282 | −0.236655 | ||||||||
\(162\) | −5.41696 | −0.425597 | ||||||||
\(163\) | −7.86399 | −0.615955 | −0.307977 | − | 0.951394i | \(-0.599652\pi\) | ||||
−0.307977 | + | 0.951394i | \(0.599652\pi\) | |||||||
\(164\) | −0.0999763 | −0.00780684 | ||||||||
\(165\) | 1.27102 | 0.0989485 | ||||||||
\(166\) | 6.73880 | 0.523032 | ||||||||
\(167\) | 12.2190 | 0.945534 | 0.472767 | − | 0.881187i | \(-0.343255\pi\) | ||||
0.472767 | + | 0.881187i | \(0.343255\pi\) | |||||||
\(168\) | 7.28978 | 0.562419 | ||||||||
\(169\) | −10.4739 | −0.805684 | ||||||||
\(170\) | 2.93996 | 0.225484 | ||||||||
\(171\) | 2.00148 | 0.153057 | ||||||||
\(172\) | −7.64379 | −0.582833 | ||||||||
\(173\) | −2.73513 | −0.207948 | −0.103974 | − | 0.994580i | \(-0.533156\pi\) | ||||
−0.103974 | + | 0.994580i | \(0.533156\pi\) | |||||||
\(174\) | −9.83915 | −0.745904 | ||||||||
\(175\) | 21.3314 | 1.61250 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −17.6911 | −1.32975 | ||||||||
\(178\) | −13.1212 | −0.983474 | ||||||||
\(179\) | 9.45338 | 0.706579 | 0.353289 | − | 0.935514i | \(-0.385063\pi\) | ||||
0.353289 | + | 0.935514i | \(0.385063\pi\) | |||||||
\(180\) | 0.805595 | 0.0600455 | ||||||||
\(181\) | 19.1365 | 1.42240 | 0.711202 | − | 0.702988i | \(-0.248151\pi\) | ||||
0.711202 | + | 0.702988i | \(0.248151\pi\) | |||||||
\(182\) | −8.02427 | −0.594798 | ||||||||
\(183\) | 9.26780 | 0.685095 | ||||||||
\(184\) | 0.594770 | 0.0438471 | ||||||||
\(185\) | 10.1644 | 0.747301 | ||||||||
\(186\) | 12.2883 | 0.901019 | ||||||||
\(187\) | −3.33984 | −0.244233 | ||||||||
\(188\) | 10.6610 | 0.777533 | ||||||||
\(189\) | −28.5407 | −2.07603 | ||||||||
\(190\) | 1.92516 | 0.139666 | ||||||||
\(191\) | 17.2098 | 1.24526 | 0.622628 | − | 0.782518i | \(-0.286065\pi\) | ||||
0.622628 | + | 0.782518i | \(0.286065\pi\) | |||||||
\(192\) | −1.44389 | −0.104204 | ||||||||
\(193\) | −6.91213 | −0.497546 | −0.248773 | − | 0.968562i | \(-0.580027\pi\) | ||||
−0.248773 | + | 0.968562i | \(0.580027\pi\) | |||||||
\(194\) | 7.38017 | 0.529865 | ||||||||
\(195\) | 2.02012 | 0.144664 | ||||||||
\(196\) | 18.4893 | 1.32067 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | −0.915168 | −0.0650382 | ||||||||
\(199\) | −5.37847 | −0.381269 | −0.190635 | − | 0.981661i | \(-0.561055\pi\) | ||||
−0.190635 | + | 0.981661i | \(0.561055\pi\) | |||||||
\(200\) | −4.22513 | −0.298761 | ||||||||
\(201\) | −3.85202 | −0.271700 | ||||||||
\(202\) | 10.4210 | 0.733216 | ||||||||
\(203\) | −34.4034 | −2.41465 | ||||||||
\(204\) | 4.82237 | 0.337634 | ||||||||
\(205\) | 0.0880061 | 0.00614661 | ||||||||
\(206\) | −1.04881 | −0.0730738 | ||||||||
\(207\) | −0.544315 | −0.0378325 | ||||||||
\(208\) | 1.58937 | 0.110203 | ||||||||
\(209\) | −2.18701 | −0.151279 | ||||||||
\(210\) | −6.41698 | −0.442813 | ||||||||
\(211\) | −26.6202 | −1.83261 | −0.916305 | − | 0.400480i | \(-0.868843\pi\) | ||||
−0.916305 | + | 0.400480i | \(0.868843\pi\) | |||||||
\(212\) | −8.79832 | −0.604271 | ||||||||
\(213\) | −12.6858 | −0.869214 | ||||||||
\(214\) | 14.8629 | 1.01601 | ||||||||
\(215\) | 6.72859 | 0.458886 | ||||||||
\(216\) | 5.65309 | 0.384644 | ||||||||
\(217\) | 42.9669 | 2.91678 | ||||||||
\(218\) | 9.52282 | 0.644967 | ||||||||
\(219\) | −0.112775 | −0.00762061 | ||||||||
\(220\) | −0.880270 | −0.0593478 | ||||||||
\(221\) | −5.30825 | −0.357072 | ||||||||
\(222\) | 16.6725 | 1.11899 | ||||||||
\(223\) | −15.6479 | −1.04786 | −0.523930 | − | 0.851761i | \(-0.675535\pi\) | ||||
−0.523930 | + | 0.851761i | \(0.675535\pi\) | |||||||
\(224\) | −5.04870 | −0.337330 | ||||||||
\(225\) | 3.86670 | 0.257780 | ||||||||
\(226\) | 17.4354 | 1.15978 | ||||||||
\(227\) | −13.3236 | −0.884317 | −0.442158 | − | 0.896937i | \(-0.645787\pi\) | ||||
−0.442158 | + | 0.896937i | \(0.645787\pi\) | |||||||
\(228\) | 3.15781 | 0.209131 | ||||||||
\(229\) | 14.7794 | 0.976648 | 0.488324 | − | 0.872663i | \(-0.337609\pi\) | ||||
0.488324 | + | 0.872663i | \(0.337609\pi\) | |||||||
\(230\) | −0.523558 | −0.0345224 | ||||||||
\(231\) | 7.28978 | 0.479633 | ||||||||
\(232\) | 6.81432 | 0.447382 | ||||||||
\(233\) | −13.5300 | −0.886380 | −0.443190 | − | 0.896428i | \(-0.646153\pi\) | ||||
−0.443190 | + | 0.896428i | \(0.646153\pi\) | |||||||
\(234\) | −1.45455 | −0.0950866 | ||||||||
\(235\) | −9.38455 | −0.612180 | ||||||||
\(236\) | 12.2524 | 0.797562 | ||||||||
\(237\) | 0.215277 | 0.0139838 | ||||||||
\(238\) | 16.8618 | 1.09299 | ||||||||
\(239\) | −3.32174 | −0.214866 | −0.107433 | − | 0.994212i | \(-0.534263\pi\) | ||||
−0.107433 | + | 0.994212i | \(0.534263\pi\) | |||||||
\(240\) | 1.27102 | 0.0820438 | ||||||||
\(241\) | −1.44506 | −0.0930846 | −0.0465423 | − | 0.998916i | \(-0.514820\pi\) | ||||
−0.0465423 | + | 0.998916i | \(0.514820\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −9.13775 | −0.586187 | ||||||||
\(244\) | −6.41861 | −0.410909 | ||||||||
\(245\) | −16.2756 | −1.03981 | ||||||||
\(246\) | 0.144355 | 0.00920375 | ||||||||
\(247\) | −3.47598 | −0.221171 | ||||||||
\(248\) | −8.51050 | −0.540417 | ||||||||
\(249\) | −9.73012 | −0.616621 | ||||||||
\(250\) | 8.12060 | 0.513592 | ||||||||
\(251\) | −0.391010 | −0.0246803 | −0.0123402 | − | 0.999924i | \(-0.503928\pi\) | ||||
−0.0123402 | + | 0.999924i | \(0.503928\pi\) | |||||||
\(252\) | 4.62041 | 0.291058 | ||||||||
\(253\) | 0.594770 | 0.0373929 | ||||||||
\(254\) | 14.9631 | 0.938870 | ||||||||
\(255\) | −4.24499 | −0.265831 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.9484 | −1.49386 | −0.746931 | − | 0.664902i | \(-0.768473\pi\) | ||||
−0.746931 | + | 0.664902i | \(0.768473\pi\) | |||||||
\(258\) | 11.0368 | 0.687123 | ||||||||
\(259\) | 58.2969 | 3.62239 | ||||||||
\(260\) | −1.39908 | −0.0867671 | ||||||||
\(261\) | −6.23625 | −0.386014 | ||||||||
\(262\) | 19.4126 | 1.19931 | ||||||||
\(263\) | 3.06283 | 0.188862 | 0.0944312 | − | 0.995531i | \(-0.469897\pi\) | ||||
0.0944312 | + | 0.995531i | \(0.469897\pi\) | |||||||
\(264\) | −1.44389 | −0.0888656 | ||||||||
\(265\) | 7.74489 | 0.475765 | ||||||||
\(266\) | 11.0415 | 0.677001 | ||||||||
\(267\) | 18.9456 | 1.15945 | ||||||||
\(268\) | 2.66780 | 0.162962 | ||||||||
\(269\) | 23.6940 | 1.44465 | 0.722325 | − | 0.691553i | \(-0.243073\pi\) | ||||
0.722325 | + | 0.691553i | \(0.243073\pi\) | |||||||
\(270\) | −4.97624 | −0.302845 | ||||||||
\(271\) | 29.5632 | 1.79584 | 0.897919 | − | 0.440160i | \(-0.145078\pi\) | ||||
0.897919 | + | 0.440160i | \(0.145078\pi\) | |||||||
\(272\) | −3.33984 | −0.202507 | ||||||||
\(273\) | 11.5862 | 0.701228 | ||||||||
\(274\) | −4.81891 | −0.291121 | ||||||||
\(275\) | −4.22513 | −0.254785 | ||||||||
\(276\) | −0.858786 | −0.0516928 | ||||||||
\(277\) | −31.3643 | −1.88450 | −0.942250 | − | 0.334910i | \(-0.891294\pi\) | ||||
−0.942250 | + | 0.334910i | \(0.891294\pi\) | |||||||
\(278\) | −16.7243 | −1.00306 | ||||||||
\(279\) | 7.78854 | 0.466288 | ||||||||
\(280\) | 4.44421 | 0.265593 | ||||||||
\(281\) | 6.32290 | 0.377193 | 0.188596 | − | 0.982055i | \(-0.439606\pi\) | ||||
0.188596 | + | 0.982055i | \(0.439606\pi\) | |||||||
\(282\) | −15.3933 | −0.916661 | ||||||||
\(283\) | −12.5026 | −0.743203 | −0.371601 | − | 0.928392i | \(-0.621191\pi\) | ||||
−0.371601 | + | 0.928392i | \(0.621191\pi\) | |||||||
\(284\) | 8.78579 | 0.521341 | ||||||||
\(285\) | −2.77973 | −0.164657 | ||||||||
\(286\) | 1.58937 | 0.0939817 | ||||||||
\(287\) | 0.504750 | 0.0297944 | ||||||||
\(288\) | −0.915168 | −0.0539268 | ||||||||
\(289\) | −5.84549 | −0.343852 | ||||||||
\(290\) | −5.99844 | −0.352240 | ||||||||
\(291\) | −10.6562 | −0.624676 | ||||||||
\(292\) | 0.0781045 | 0.00457072 | ||||||||
\(293\) | −19.6350 | −1.14709 | −0.573543 | − | 0.819175i | \(-0.694432\pi\) | ||||
−0.573543 | + | 0.819175i | \(0.694432\pi\) | |||||||
\(294\) | −26.6966 | −1.55698 | ||||||||
\(295\) | −10.7854 | −0.627950 | ||||||||
\(296\) | −11.5469 | −0.671151 | ||||||||
\(297\) | 5.65309 | 0.328026 | ||||||||
\(298\) | −14.6284 | −0.847398 | ||||||||
\(299\) | 0.945313 | 0.0546689 | ||||||||
\(300\) | 6.10064 | 0.352220 | ||||||||
\(301\) | 38.5912 | 2.22436 | ||||||||
\(302\) | 22.0137 | 1.26675 | ||||||||
\(303\) | −15.0468 | −0.864414 | ||||||||
\(304\) | −2.18701 | −0.125434 | ||||||||
\(305\) | 5.65011 | 0.323524 | ||||||||
\(306\) | 3.05651 | 0.174729 | ||||||||
\(307\) | 19.4170 | 1.10819 | 0.554094 | − | 0.832454i | \(-0.313065\pi\) | ||||
0.554094 | + | 0.832454i | \(0.313065\pi\) | |||||||
\(308\) | −5.04870 | −0.287676 | ||||||||
\(309\) | 1.51437 | 0.0861493 | ||||||||
\(310\) | 7.49153 | 0.425491 | ||||||||
\(311\) | −9.47098 | −0.537050 | −0.268525 | − | 0.963273i | \(-0.586536\pi\) | ||||
−0.268525 | + | 0.963273i | \(0.586536\pi\) | |||||||
\(312\) | −2.29489 | −0.129923 | ||||||||
\(313\) | 14.4608 | 0.817374 | 0.408687 | − | 0.912675i | \(-0.365987\pi\) | ||||
0.408687 | + | 0.912675i | \(0.365987\pi\) | |||||||
\(314\) | −6.74428 | −0.380602 | ||||||||
\(315\) | −4.06720 | −0.229161 | ||||||||
\(316\) | −0.149095 | −0.00838724 | ||||||||
\(317\) | 15.6786 | 0.880600 | 0.440300 | − | 0.897851i | \(-0.354872\pi\) | ||||
0.440300 | + | 0.897851i | \(0.354872\pi\) | |||||||
\(318\) | 12.7038 | 0.712396 | ||||||||
\(319\) | 6.81432 | 0.381528 | ||||||||
\(320\) | −0.880270 | −0.0492086 | ||||||||
\(321\) | −21.4604 | −1.19781 | ||||||||
\(322\) | −3.00282 | −0.167340 | ||||||||
\(323\) | 7.30426 | 0.406420 | ||||||||
\(324\) | −5.41696 | −0.300942 | ||||||||
\(325\) | −6.71531 | −0.372498 | ||||||||
\(326\) | −7.86399 | −0.435546 | ||||||||
\(327\) | −13.7499 | −0.760374 | ||||||||
\(328\) | −0.0999763 | −0.00552027 | ||||||||
\(329\) | −53.8241 | −2.96742 | ||||||||
\(330\) | 1.27102 | 0.0699672 | ||||||||
\(331\) | −16.6573 | −0.915567 | −0.457784 | − | 0.889064i | \(-0.651357\pi\) | ||||
−0.457784 | + | 0.889064i | \(0.651357\pi\) | |||||||
\(332\) | 6.73880 | 0.369840 | ||||||||
\(333\) | 10.5674 | 0.579088 | ||||||||
\(334\) | 12.2190 | 0.668594 | ||||||||
\(335\) | −2.34838 | −0.128306 | ||||||||
\(336\) | 7.28978 | 0.397690 | ||||||||
\(337\) | 32.3648 | 1.76303 | 0.881513 | − | 0.472160i | \(-0.156526\pi\) | ||||
0.881513 | + | 0.472160i | \(0.156526\pi\) | |||||||
\(338\) | −10.4739 | −0.569704 | ||||||||
\(339\) | −25.1748 | −1.36731 | ||||||||
\(340\) | 2.93996 | 0.159442 | ||||||||
\(341\) | −8.51050 | −0.460869 | ||||||||
\(342\) | 2.00148 | 0.108228 | ||||||||
\(343\) | −58.0061 | −3.13204 | ||||||||
\(344\) | −7.64379 | −0.412125 | ||||||||
\(345\) | 0.755963 | 0.0406997 | ||||||||
\(346\) | −2.73513 | −0.147042 | ||||||||
\(347\) | −19.4041 | −1.04167 | −0.520835 | − | 0.853658i | \(-0.674379\pi\) | ||||
−0.520835 | + | 0.853658i | \(0.674379\pi\) | |||||||
\(348\) | −9.83915 | −0.527434 | ||||||||
\(349\) | 9.64496 | 0.516283 | 0.258141 | − | 0.966107i | \(-0.416890\pi\) | ||||
0.258141 | + | 0.966107i | \(0.416890\pi\) | |||||||
\(350\) | 21.3314 | 1.14021 | ||||||||
\(351\) | 8.98488 | 0.479577 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 21.6340 | 1.15146 | 0.575731 | − | 0.817639i | \(-0.304718\pi\) | ||||
0.575731 | + | 0.817639i | \(0.304718\pi\) | |||||||
\(354\) | −17.6911 | −0.940273 | ||||||||
\(355\) | −7.73387 | −0.410471 | ||||||||
\(356\) | −13.1212 | −0.695421 | ||||||||
\(357\) | −24.3467 | −1.28856 | ||||||||
\(358\) | 9.45338 | 0.499627 | ||||||||
\(359\) | 3.30685 | 0.174529 | 0.0872645 | − | 0.996185i | \(-0.472187\pi\) | ||||
0.0872645 | + | 0.996185i | \(0.472187\pi\) | |||||||
\(360\) | 0.805595 | 0.0424586 | ||||||||
\(361\) | −14.2170 | −0.748263 | ||||||||
\(362\) | 19.1365 | 1.00579 | ||||||||
\(363\) | −1.44389 | −0.0757848 | ||||||||
\(364\) | −8.02427 | −0.420586 | ||||||||
\(365\) | −0.0687530 | −0.00359870 | ||||||||
\(366\) | 9.26780 | 0.484436 | ||||||||
\(367\) | 6.97451 | 0.364067 | 0.182033 | − | 0.983292i | \(-0.441732\pi\) | ||||
0.182033 | + | 0.983292i | \(0.441732\pi\) | |||||||
\(368\) | 0.594770 | 0.0310046 | ||||||||
\(369\) | 0.0914952 | 0.00476305 | ||||||||
\(370\) | 10.1644 | 0.528422 | ||||||||
\(371\) | 44.4200 | 2.30617 | ||||||||
\(372\) | 12.2883 | 0.637117 | ||||||||
\(373\) | −27.4676 | −1.42222 | −0.711108 | − | 0.703083i | \(-0.751806\pi\) | ||||
−0.711108 | + | 0.703083i | \(0.751806\pi\) | |||||||
\(374\) | −3.33984 | −0.172699 | ||||||||
\(375\) | −11.7253 | −0.605491 | ||||||||
\(376\) | 10.6610 | 0.549799 | ||||||||
\(377\) | 10.8305 | 0.557799 | ||||||||
\(378\) | −28.5407 | −1.46798 | ||||||||
\(379\) | −1.24602 | −0.0640040 | −0.0320020 | − | 0.999488i | \(-0.510188\pi\) | ||||
−0.0320020 | + | 0.999488i | \(0.510188\pi\) | |||||||
\(380\) | 1.92516 | 0.0987585 | ||||||||
\(381\) | −21.6052 | −1.10687 | ||||||||
\(382\) | 17.2098 | 0.880528 | ||||||||
\(383\) | −15.2911 | −0.781340 | −0.390670 | − | 0.920531i | \(-0.627757\pi\) | ||||
−0.390670 | + | 0.920531i | \(0.627757\pi\) | |||||||
\(384\) | −1.44389 | −0.0736834 | ||||||||
\(385\) | 4.44421 | 0.226498 | ||||||||
\(386\) | −6.91213 | −0.351818 | ||||||||
\(387\) | 6.99535 | 0.355594 | ||||||||
\(388\) | 7.38017 | 0.374671 | ||||||||
\(389\) | 12.1854 | 0.617823 | 0.308912 | − | 0.951091i | \(-0.400035\pi\) | ||||
0.308912 | + | 0.951091i | \(0.400035\pi\) | |||||||
\(390\) | 2.02012 | 0.102293 | ||||||||
\(391\) | −1.98644 | −0.100458 | ||||||||
\(392\) | 18.4893 | 0.933852 | ||||||||
\(393\) | −28.0297 | −1.41391 | ||||||||
\(394\) | 1.00000 | 0.0503793 | ||||||||
\(395\) | 0.131244 | 0.00660359 | ||||||||
\(396\) | −0.915168 | −0.0459889 | ||||||||
\(397\) | −33.6081 | −1.68674 | −0.843372 | − | 0.537330i | \(-0.819433\pi\) | ||||
−0.843372 | + | 0.537330i | \(0.819433\pi\) | |||||||
\(398\) | −5.37847 | −0.269598 | ||||||||
\(399\) | −15.9428 | −0.798140 | ||||||||
\(400\) | −4.22513 | −0.211256 | ||||||||
\(401\) | −27.5483 | −1.37570 | −0.687849 | − | 0.725854i | \(-0.741445\pi\) | ||||
−0.687849 | + | 0.725854i | \(0.741445\pi\) | |||||||
\(402\) | −3.85202 | −0.192121 | ||||||||
\(403\) | −13.5264 | −0.673796 | ||||||||
\(404\) | 10.4210 | 0.518462 | ||||||||
\(405\) | 4.76839 | 0.236943 | ||||||||
\(406\) | −34.4034 | −1.70741 | ||||||||
\(407\) | −11.5469 | −0.572359 | ||||||||
\(408\) | 4.82237 | 0.238743 | ||||||||
\(409\) | 24.6144 | 1.21710 | 0.608552 | − | 0.793514i | \(-0.291751\pi\) | ||||
0.608552 | + | 0.793514i | \(0.291751\pi\) | |||||||
\(410\) | 0.0880061 | 0.00434631 | ||||||||
\(411\) | 6.95800 | 0.343213 | ||||||||
\(412\) | −1.04881 | −0.0516710 | ||||||||
\(413\) | −61.8585 | −3.04386 | ||||||||
\(414\) | −0.544315 | −0.0267516 | ||||||||
\(415\) | −5.93196 | −0.291189 | ||||||||
\(416\) | 1.58937 | 0.0779255 | ||||||||
\(417\) | 24.1481 | 1.18254 | ||||||||
\(418\) | −2.18701 | −0.106970 | ||||||||
\(419\) | 16.9172 | 0.826459 | 0.413230 | − | 0.910627i | \(-0.364401\pi\) | ||||
0.413230 | + | 0.910627i | \(0.364401\pi\) | |||||||
\(420\) | −6.41698 | −0.313116 | ||||||||
\(421\) | 19.7096 | 0.960588 | 0.480294 | − | 0.877107i | \(-0.340530\pi\) | ||||
0.480294 | + | 0.877107i | \(0.340530\pi\) | |||||||
\(422\) | −26.6202 | −1.29585 | ||||||||
\(423\) | −9.75660 | −0.474382 | ||||||||
\(424\) | −8.79832 | −0.427284 | ||||||||
\(425\) | 14.1112 | 0.684495 | ||||||||
\(426\) | −12.6858 | −0.614627 | ||||||||
\(427\) | 32.4056 | 1.56822 | ||||||||
\(428\) | 14.8629 | 0.718425 | ||||||||
\(429\) | −2.29489 | −0.110798 | ||||||||
\(430\) | 6.72859 | 0.324482 | ||||||||
\(431\) | −18.7848 | −0.904834 | −0.452417 | − | 0.891807i | \(-0.649438\pi\) | ||||
−0.452417 | + | 0.891807i | \(0.649438\pi\) | |||||||
\(432\) | 5.65309 | 0.271984 | ||||||||
\(433\) | 8.72681 | 0.419384 | 0.209692 | − | 0.977768i | \(-0.432754\pi\) | ||||
0.209692 | + | 0.977768i | \(0.432754\pi\) | |||||||
\(434\) | 42.9669 | 2.06248 | ||||||||
\(435\) | 8.66111 | 0.415268 | ||||||||
\(436\) | 9.52282 | 0.456060 | ||||||||
\(437\) | −1.30077 | −0.0622242 | ||||||||
\(438\) | −0.112775 | −0.00538858 | ||||||||
\(439\) | 7.05658 | 0.336792 | 0.168396 | − | 0.985719i | \(-0.446141\pi\) | ||||
0.168396 | + | 0.985719i | \(0.446141\pi\) | |||||||
\(440\) | −0.880270 | −0.0419652 | ||||||||
\(441\) | −16.9209 | −0.805755 | ||||||||
\(442\) | −5.30825 | −0.252488 | ||||||||
\(443\) | 25.2265 | 1.19855 | 0.599275 | − | 0.800543i | \(-0.295456\pi\) | ||||
0.599275 | + | 0.800543i | \(0.295456\pi\) | |||||||
\(444\) | 16.6725 | 0.791243 | ||||||||
\(445\) | 11.5502 | 0.547531 | ||||||||
\(446\) | −15.6479 | −0.740949 | ||||||||
\(447\) | 21.1218 | 0.999028 | ||||||||
\(448\) | −5.04870 | −0.238528 | ||||||||
\(449\) | 13.3348 | 0.629306 | 0.314653 | − | 0.949207i | \(-0.398112\pi\) | ||||
0.314653 | + | 0.949207i | \(0.398112\pi\) | |||||||
\(450\) | 3.86670 | 0.182278 | ||||||||
\(451\) | −0.0999763 | −0.00470770 | ||||||||
\(452\) | 17.4354 | 0.820091 | ||||||||
\(453\) | −31.7855 | −1.49341 | ||||||||
\(454\) | −13.3236 | −0.625306 | ||||||||
\(455\) | 7.06352 | 0.331143 | ||||||||
\(456\) | 3.15781 | 0.147878 | ||||||||
\(457\) | −15.9201 | −0.744709 | −0.372354 | − | 0.928091i | \(-0.621449\pi\) | ||||
−0.372354 | + | 0.928091i | \(0.621449\pi\) | |||||||
\(458\) | 14.7794 | 0.690594 | ||||||||
\(459\) | −18.8804 | −0.881262 | ||||||||
\(460\) | −0.523558 | −0.0244110 | ||||||||
\(461\) | 12.5893 | 0.586342 | 0.293171 | − | 0.956060i | \(-0.405290\pi\) | ||||
0.293171 | + | 0.956060i | \(0.405290\pi\) | |||||||
\(462\) | 7.28978 | 0.339151 | ||||||||
\(463\) | 33.6257 | 1.56272 | 0.781360 | − | 0.624080i | \(-0.214526\pi\) | ||||
0.781360 | + | 0.624080i | \(0.214526\pi\) | |||||||
\(464\) | 6.81432 | 0.316347 | ||||||||
\(465\) | −10.8170 | −0.501626 | ||||||||
\(466\) | −13.5300 | −0.626765 | ||||||||
\(467\) | 25.4854 | 1.17932 | 0.589662 | − | 0.807650i | \(-0.299261\pi\) | ||||
0.589662 | + | 0.807650i | \(0.299261\pi\) | |||||||
\(468\) | −1.45455 | −0.0672364 | ||||||||
\(469\) | −13.4689 | −0.621936 | ||||||||
\(470\) | −9.38455 | −0.432877 | ||||||||
\(471\) | 9.73803 | 0.448705 | ||||||||
\(472\) | 12.2524 | 0.563961 | ||||||||
\(473\) | −7.64379 | −0.351462 | ||||||||
\(474\) | 0.215277 | 0.00988802 | ||||||||
\(475\) | 9.24039 | 0.423978 | ||||||||
\(476\) | 16.8618 | 0.772860 | ||||||||
\(477\) | 8.05195 | 0.368673 | ||||||||
\(478\) | −3.32174 | −0.151933 | ||||||||
\(479\) | 22.4360 | 1.02513 | 0.512563 | − | 0.858649i | \(-0.328696\pi\) | ||||
0.512563 | + | 0.858649i | \(0.328696\pi\) | |||||||
\(480\) | 1.27102 | 0.0580137 | ||||||||
\(481\) | −18.3524 | −0.836796 | ||||||||
\(482\) | −1.44506 | −0.0658208 | ||||||||
\(483\) | 4.33575 | 0.197283 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −6.49654 | −0.294993 | ||||||||
\(486\) | −9.13775 | −0.414497 | ||||||||
\(487\) | 21.2895 | 0.964721 | 0.482361 | − | 0.875973i | \(-0.339779\pi\) | ||||
0.482361 | + | 0.875973i | \(0.339779\pi\) | |||||||
\(488\) | −6.41861 | −0.290557 | ||||||||
\(489\) | 11.3548 | 0.513480 | ||||||||
\(490\) | −16.2756 | −0.735256 | ||||||||
\(491\) | −22.0437 | −0.994820 | −0.497410 | − | 0.867516i | \(-0.665716\pi\) | ||||
−0.497410 | + | 0.867516i | \(0.665716\pi\) | |||||||
\(492\) | 0.144355 | 0.00650804 | ||||||||
\(493\) | −22.7587 | −1.02500 | ||||||||
\(494\) | −3.47598 | −0.156392 | ||||||||
\(495\) | 0.805595 | 0.0362088 | ||||||||
\(496\) | −8.51050 | −0.382133 | ||||||||
\(497\) | −44.3568 | −1.98967 | ||||||||
\(498\) | −9.73012 | −0.436017 | ||||||||
\(499\) | −34.1956 | −1.53081 | −0.765404 | − | 0.643550i | \(-0.777461\pi\) | ||||
−0.765404 | + | 0.643550i | \(0.777461\pi\) | |||||||
\(500\) | 8.12060 | 0.363164 | ||||||||
\(501\) | −17.6429 | −0.788228 | ||||||||
\(502\) | −0.391010 | −0.0174516 | ||||||||
\(503\) | −4.99014 | −0.222499 | −0.111250 | − | 0.993792i | \(-0.535485\pi\) | ||||
−0.111250 | + | 0.993792i | \(0.535485\pi\) | |||||||
\(504\) | 4.62041 | 0.205809 | ||||||||
\(505\) | −9.17325 | −0.408204 | ||||||||
\(506\) | 0.594770 | 0.0264408 | ||||||||
\(507\) | 15.1232 | 0.671645 | ||||||||
\(508\) | 14.9631 | 0.663882 | ||||||||
\(509\) | 8.12393 | 0.360087 | 0.180043 | − | 0.983659i | \(-0.442376\pi\) | ||||
0.180043 | + | 0.983659i | \(0.442376\pi\) | |||||||
\(510\) | −4.24499 | −0.187971 | ||||||||
\(511\) | −0.394326 | −0.0174439 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −12.3634 | −0.545856 | ||||||||
\(514\) | −23.9484 | −1.05632 | ||||||||
\(515\) | 0.923232 | 0.0406825 | ||||||||
\(516\) | 11.0368 | 0.485869 | ||||||||
\(517\) | 10.6610 | 0.468870 | ||||||||
\(518\) | 58.2969 | 2.56142 | ||||||||
\(519\) | 3.94924 | 0.173353 | ||||||||
\(520\) | −1.39908 | −0.0613536 | ||||||||
\(521\) | 36.4451 | 1.59669 | 0.798343 | − | 0.602202i | \(-0.205710\pi\) | ||||
0.798343 | + | 0.602202i | \(0.205710\pi\) | |||||||
\(522\) | −6.23625 | −0.272953 | ||||||||
\(523\) | 5.87211 | 0.256770 | 0.128385 | − | 0.991724i | \(-0.459021\pi\) | ||||
0.128385 | + | 0.991724i | \(0.459021\pi\) | |||||||
\(524\) | 19.4126 | 0.848043 | ||||||||
\(525\) | −30.8003 | −1.34423 | ||||||||
\(526\) | 3.06283 | 0.133546 | ||||||||
\(527\) | 28.4237 | 1.23815 | ||||||||
\(528\) | −1.44389 | −0.0628374 | ||||||||
\(529\) | −22.6462 | −0.984619 | ||||||||
\(530\) | 7.74489 | 0.336417 | ||||||||
\(531\) | −11.2130 | −0.486602 | ||||||||
\(532\) | 11.0415 | 0.478712 | ||||||||
\(533\) | −0.158900 | −0.00688271 | ||||||||
\(534\) | 18.9456 | 0.819856 | ||||||||
\(535\) | −13.0834 | −0.565643 | ||||||||
\(536\) | 2.66780 | 0.115231 | ||||||||
\(537\) | −13.6497 | −0.589027 | ||||||||
\(538\) | 23.6940 | 1.02152 | ||||||||
\(539\) | 18.4893 | 0.796392 | ||||||||
\(540\) | −4.97624 | −0.214143 | ||||||||
\(541\) | −18.6061 | −0.799939 | −0.399969 | − | 0.916528i | \(-0.630979\pi\) | ||||
−0.399969 | + | 0.916528i | \(0.630979\pi\) | |||||||
\(542\) | 29.5632 | 1.26985 | ||||||||
\(543\) | −27.6311 | −1.18576 | ||||||||
\(544\) | −3.33984 | −0.143194 | ||||||||
\(545\) | −8.38265 | −0.359073 | ||||||||
\(546\) | 11.5862 | 0.495843 | ||||||||
\(547\) | 10.7066 | 0.457780 | 0.228890 | − | 0.973452i | \(-0.426490\pi\) | ||||
0.228890 | + | 0.973452i | \(0.426490\pi\) | |||||||
\(548\) | −4.81891 | −0.205854 | ||||||||
\(549\) | 5.87411 | 0.250701 | ||||||||
\(550\) | −4.22513 | −0.180160 | ||||||||
\(551\) | −14.9030 | −0.634888 | ||||||||
\(552\) | −0.858786 | −0.0365524 | ||||||||
\(553\) | 0.752735 | 0.0320095 | ||||||||
\(554\) | −31.3643 | −1.33254 | ||||||||
\(555\) | −14.6763 | −0.622975 | ||||||||
\(556\) | −16.7243 | −0.709269 | ||||||||
\(557\) | −16.9689 | −0.718994 | −0.359497 | − | 0.933146i | \(-0.617052\pi\) | ||||
−0.359497 | + | 0.933146i | \(0.617052\pi\) | |||||||
\(558\) | 7.78854 | 0.329715 | ||||||||
\(559\) | −12.1488 | −0.513841 | ||||||||
\(560\) | 4.44421 | 0.187802 | ||||||||
\(561\) | 4.82237 | 0.203601 | ||||||||
\(562\) | 6.32290 | 0.266715 | ||||||||
\(563\) | −1.21078 | −0.0510285 | −0.0255142 | − | 0.999674i | \(-0.508122\pi\) | ||||
−0.0255142 | + | 0.999674i | \(0.508122\pi\) | |||||||
\(564\) | −15.3933 | −0.648177 | ||||||||
\(565\) | −15.3478 | −0.645688 | ||||||||
\(566\) | −12.5026 | −0.525524 | ||||||||
\(567\) | 27.3486 | 1.14853 | ||||||||
\(568\) | 8.78579 | 0.368644 | ||||||||
\(569\) | 8.01404 | 0.335966 | 0.167983 | − | 0.985790i | \(-0.446275\pi\) | ||||
0.167983 | + | 0.985790i | \(0.446275\pi\) | |||||||
\(570\) | −2.77973 | −0.116430 | ||||||||
\(571\) | −4.48484 | −0.187685 | −0.0938424 | − | 0.995587i | \(-0.529915\pi\) | ||||
−0.0938424 | + | 0.995587i | \(0.529915\pi\) | |||||||
\(572\) | 1.58937 | 0.0664551 | ||||||||
\(573\) | −24.8491 | −1.03809 | ||||||||
\(574\) | 0.504750 | 0.0210679 | ||||||||
\(575\) | −2.51298 | −0.104799 | ||||||||
\(576\) | −0.915168 | −0.0381320 | ||||||||
\(577\) | −7.35900 | −0.306359 | −0.153180 | − | 0.988198i | \(-0.548951\pi\) | ||||
−0.153180 | + | 0.988198i | \(0.548951\pi\) | |||||||
\(578\) | −5.84549 | −0.243140 | ||||||||
\(579\) | 9.98038 | 0.414771 | ||||||||
\(580\) | −5.99844 | −0.249071 | ||||||||
\(581\) | −34.0222 | −1.41148 | ||||||||
\(582\) | −10.6562 | −0.441713 | ||||||||
\(583\) | −8.79832 | −0.364389 | ||||||||
\(584\) | 0.0781045 | 0.00323199 | ||||||||
\(585\) | 1.28039 | 0.0529377 | ||||||||
\(586\) | −19.6350 | −0.811113 | ||||||||
\(587\) | 32.9009 | 1.35797 | 0.678983 | − | 0.734154i | \(-0.262421\pi\) | ||||
0.678983 | + | 0.734154i | \(0.262421\pi\) | |||||||
\(588\) | −26.6966 | −1.10095 | ||||||||
\(589\) | 18.6125 | 0.766916 | ||||||||
\(590\) | −10.7854 | −0.444028 | ||||||||
\(591\) | −1.44389 | −0.0593939 | ||||||||
\(592\) | −11.5469 | −0.474575 | ||||||||
\(593\) | 23.3548 | 0.959067 | 0.479534 | − | 0.877524i | \(-0.340806\pi\) | ||||
0.479534 | + | 0.877524i | \(0.340806\pi\) | |||||||
\(594\) | 5.65309 | 0.231949 | ||||||||
\(595\) | −14.8429 | −0.608502 | ||||||||
\(596\) | −14.6284 | −0.599201 | ||||||||
\(597\) | 7.76594 | 0.317839 | ||||||||
\(598\) | 0.945313 | 0.0386567 | ||||||||
\(599\) | −25.0587 | −1.02387 | −0.511936 | − | 0.859024i | \(-0.671071\pi\) | ||||
−0.511936 | + | 0.859024i | \(0.671071\pi\) | |||||||
\(600\) | 6.10064 | 0.249057 | ||||||||
\(601\) | 0.112766 | 0.00459984 | 0.00229992 | − | 0.999997i | \(-0.499268\pi\) | ||||
0.00229992 | + | 0.999997i | \(0.499268\pi\) | |||||||
\(602\) | 38.5912 | 1.57286 | ||||||||
\(603\) | −2.44148 | −0.0994249 | ||||||||
\(604\) | 22.0137 | 0.895725 | ||||||||
\(605\) | −0.880270 | −0.0357881 | ||||||||
\(606\) | −15.0468 | −0.611233 | ||||||||
\(607\) | −24.0781 | −0.977300 | −0.488650 | − | 0.872480i | \(-0.662511\pi\) | ||||
−0.488650 | + | 0.872480i | \(0.662511\pi\) | |||||||
\(608\) | −2.18701 | −0.0886950 | ||||||||
\(609\) | 49.6749 | 2.01293 | ||||||||
\(610\) | 5.65011 | 0.228766 | ||||||||
\(611\) | 16.9443 | 0.685493 | ||||||||
\(612\) | 3.05651 | 0.123552 | ||||||||
\(613\) | −25.2776 | −1.02095 | −0.510477 | − | 0.859892i | \(-0.670531\pi\) | ||||
−0.510477 | + | 0.859892i | \(0.670531\pi\) | |||||||
\(614\) | 19.4170 | 0.783607 | ||||||||
\(615\) | −0.127072 | −0.00512402 | ||||||||
\(616\) | −5.04870 | −0.203418 | ||||||||
\(617\) | 12.3561 | 0.497438 | 0.248719 | − | 0.968576i | \(-0.419991\pi\) | ||||
0.248719 | + | 0.968576i | \(0.419991\pi\) | |||||||
\(618\) | 1.51437 | 0.0609167 | ||||||||
\(619\) | 3.51032 | 0.141091 | 0.0705457 | − | 0.997509i | \(-0.477526\pi\) | ||||
0.0705457 | + | 0.997509i | \(0.477526\pi\) | |||||||
\(620\) | 7.49153 | 0.300867 | ||||||||
\(621\) | 3.36229 | 0.134924 | ||||||||
\(622\) | −9.47098 | −0.379752 | ||||||||
\(623\) | 66.2448 | 2.65404 | ||||||||
\(624\) | −2.29489 | −0.0918691 | ||||||||
\(625\) | 13.9773 | 0.559092 | ||||||||
\(626\) | 14.4608 | 0.577971 | ||||||||
\(627\) | 3.15781 | 0.126111 | ||||||||
\(628\) | −6.74428 | −0.269126 | ||||||||
\(629\) | 38.5648 | 1.53768 | ||||||||
\(630\) | −4.06720 | −0.162041 | ||||||||
\(631\) | 36.0566 | 1.43539 | 0.717696 | − | 0.696357i | \(-0.245197\pi\) | ||||
0.717696 | + | 0.696357i | \(0.245197\pi\) | |||||||
\(632\) | −0.149095 | −0.00593068 | ||||||||
\(633\) | 38.4368 | 1.52772 | ||||||||
\(634\) | 15.6786 | 0.622678 | ||||||||
\(635\) | −13.1716 | −0.522699 | ||||||||
\(636\) | 12.7038 | 0.503740 | ||||||||
\(637\) | 29.3865 | 1.16433 | ||||||||
\(638\) | 6.81432 | 0.269781 | ||||||||
\(639\) | −8.04048 | −0.318076 | ||||||||
\(640\) | −0.880270 | −0.0347957 | ||||||||
\(641\) | −1.98377 | −0.0783543 | −0.0391772 | − | 0.999232i | \(-0.512474\pi\) | ||||
−0.0391772 | + | 0.999232i | \(0.512474\pi\) | |||||||
\(642\) | −21.4604 | −0.846976 | ||||||||
\(643\) | −11.8958 | −0.469125 | −0.234563 | − | 0.972101i | \(-0.575366\pi\) | ||||
−0.234563 | + | 0.972101i | \(0.575366\pi\) | |||||||
\(644\) | −3.00282 | −0.118327 | ||||||||
\(645\) | −9.71538 | −0.382543 | ||||||||
\(646\) | 7.30426 | 0.287382 | ||||||||
\(647\) | 7.20476 | 0.283248 | 0.141624 | − | 0.989920i | \(-0.454768\pi\) | ||||
0.141624 | + | 0.989920i | \(0.454768\pi\) | |||||||
\(648\) | −5.41696 | −0.212798 | ||||||||
\(649\) | 12.2524 | 0.480948 | ||||||||
\(650\) | −6.71531 | −0.263396 | ||||||||
\(651\) | −62.0397 | −2.43153 | ||||||||
\(652\) | −7.86399 | −0.307977 | ||||||||
\(653\) | 23.9709 | 0.938055 | 0.469028 | − | 0.883184i | \(-0.344604\pi\) | ||||
0.469028 | + | 0.883184i | \(0.344604\pi\) | |||||||
\(654\) | −13.7499 | −0.537666 | ||||||||
\(655\) | −17.0883 | −0.667695 | ||||||||
\(656\) | −0.0999763 | −0.00390342 | ||||||||
\(657\) | −0.0714788 | −0.00278865 | ||||||||
\(658\) | −53.8241 | −2.09828 | ||||||||
\(659\) | −2.27960 | −0.0888005 | −0.0444002 | − | 0.999014i | \(-0.514138\pi\) | ||||
−0.0444002 | + | 0.999014i | \(0.514138\pi\) | |||||||
\(660\) | 1.27102 | 0.0494743 | ||||||||
\(661\) | 1.65178 | 0.0642467 | 0.0321233 | − | 0.999484i | \(-0.489773\pi\) | ||||
0.0321233 | + | 0.999484i | \(0.489773\pi\) | |||||||
\(662\) | −16.6573 | −0.647404 | ||||||||
\(663\) | 7.66456 | 0.297667 | ||||||||
\(664\) | 6.73880 | 0.261516 | ||||||||
\(665\) | −9.71954 | −0.376908 | ||||||||
\(666\) | 10.5674 | 0.409477 | ||||||||
\(667\) | 4.05295 | 0.156931 | ||||||||
\(668\) | 12.2190 | 0.472767 | ||||||||
\(669\) | 22.5939 | 0.873531 | ||||||||
\(670\) | −2.34838 | −0.0907259 | ||||||||
\(671\) | −6.41861 | −0.247788 | ||||||||
\(672\) | 7.28978 | 0.281210 | ||||||||
\(673\) | −4.04331 | −0.155858 | −0.0779291 | − | 0.996959i | \(-0.524831\pi\) | ||||
−0.0779291 | + | 0.996959i | \(0.524831\pi\) | |||||||
\(674\) | 32.3648 | 1.24665 | ||||||||
\(675\) | −23.8850 | −0.919335 | ||||||||
\(676\) | −10.4739 | −0.402842 | ||||||||
\(677\) | −14.1594 | −0.544190 | −0.272095 | − | 0.962270i | \(-0.587717\pi\) | ||||
−0.272095 | + | 0.962270i | \(0.587717\pi\) | |||||||
\(678\) | −25.1748 | −0.966834 | ||||||||
\(679\) | −37.2602 | −1.42992 | ||||||||
\(680\) | 2.93996 | 0.112742 | ||||||||
\(681\) | 19.2378 | 0.737195 | ||||||||
\(682\) | −8.51050 | −0.325884 | ||||||||
\(683\) | 10.3207 | 0.394911 | 0.197456 | − | 0.980312i | \(-0.436732\pi\) | ||||
0.197456 | + | 0.980312i | \(0.436732\pi\) | |||||||
\(684\) | 2.00148 | 0.0765286 | ||||||||
\(685\) | 4.24194 | 0.162076 | ||||||||
\(686\) | −58.0061 | −2.21468 | ||||||||
\(687\) | −21.3398 | −0.814166 | ||||||||
\(688\) | −7.64379 | −0.291417 | ||||||||
\(689\) | −13.9838 | −0.532741 | ||||||||
\(690\) | 0.755963 | 0.0287790 | ||||||||
\(691\) | −15.7126 | −0.597735 | −0.298867 | − | 0.954295i | \(-0.596609\pi\) | ||||
−0.298867 | + | 0.954295i | \(0.596609\pi\) | |||||||
\(692\) | −2.73513 | −0.103974 | ||||||||
\(693\) | 4.62041 | 0.175515 | ||||||||
\(694\) | −19.4041 | −0.736571 | ||||||||
\(695\) | 14.7219 | 0.558434 | ||||||||
\(696\) | −9.83915 | −0.372952 | ||||||||
\(697\) | 0.333905 | 0.0126475 | ||||||||
\(698\) | 9.64496 | 0.365067 | ||||||||
\(699\) | 19.5359 | 0.738915 | ||||||||
\(700\) | 21.3314 | 0.806250 | ||||||||
\(701\) | 21.1227 | 0.797793 | 0.398897 | − | 0.916996i | \(-0.369393\pi\) | ||||
0.398897 | + | 0.916996i | \(0.369393\pi\) | |||||||
\(702\) | 8.98488 | 0.339112 | ||||||||
\(703\) | 25.2532 | 0.952443 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 13.5503 | 0.510334 | ||||||||
\(706\) | 21.6340 | 0.814206 | ||||||||
\(707\) | −52.6122 | −1.97869 | ||||||||
\(708\) | −17.6911 | −0.664874 | ||||||||
\(709\) | −41.6743 | −1.56511 | −0.782555 | − | 0.622582i | \(-0.786084\pi\) | ||||
−0.782555 | + | 0.622582i | \(0.786084\pi\) | |||||||
\(710\) | −7.73387 | −0.290247 | ||||||||
\(711\) | 0.136447 | 0.00511716 | ||||||||
\(712\) | −13.1212 | −0.491737 | ||||||||
\(713\) | −5.06179 | −0.189566 | ||||||||
\(714\) | −24.3467 | −0.911152 | ||||||||
\(715\) | −1.39908 | −0.0523226 | ||||||||
\(716\) | 9.45338 | 0.353289 | ||||||||
\(717\) | 4.79624 | 0.179119 | ||||||||
\(718\) | 3.30685 | 0.123411 | ||||||||
\(719\) | 20.7487 | 0.773794 | 0.386897 | − | 0.922123i | \(-0.373547\pi\) | ||||
0.386897 | + | 0.922123i | \(0.373547\pi\) | |||||||
\(720\) | 0.805595 | 0.0300228 | ||||||||
\(721\) | 5.29510 | 0.197200 | ||||||||
\(722\) | −14.2170 | −0.529102 | ||||||||
\(723\) | 2.08652 | 0.0775984 | ||||||||
\(724\) | 19.1365 | 0.711202 | ||||||||
\(725\) | −28.7913 | −1.06928 | ||||||||
\(726\) | −1.44389 | −0.0535880 | ||||||||
\(727\) | 25.4430 | 0.943629 | 0.471815 | − | 0.881698i | \(-0.343599\pi\) | ||||
0.471815 | + | 0.881698i | \(0.343599\pi\) | |||||||
\(728\) | −8.02427 | −0.297399 | ||||||||
\(729\) | 29.4448 | 1.09055 | ||||||||
\(730\) | −0.0687530 | −0.00254466 | ||||||||
\(731\) | 25.5290 | 0.944224 | ||||||||
\(732\) | 9.26780 | 0.342548 | ||||||||
\(733\) | −23.4763 | −0.867117 | −0.433558 | − | 0.901125i | \(-0.642742\pi\) | ||||
−0.433558 | + | 0.901125i | \(0.642742\pi\) | |||||||
\(734\) | 6.97451 | 0.257434 | ||||||||
\(735\) | 23.5002 | 0.866820 | ||||||||
\(736\) | 0.594770 | 0.0219235 | ||||||||
\(737\) | 2.66780 | 0.0982696 | ||||||||
\(738\) | 0.0914952 | 0.00336798 | ||||||||
\(739\) | 52.5932 | 1.93467 | 0.967337 | − | 0.253495i | \(-0.0815803\pi\) | ||||
0.967337 | + | 0.253495i | \(0.0815803\pi\) | |||||||
\(740\) | 10.1644 | 0.373651 | ||||||||
\(741\) | 5.01894 | 0.184376 | ||||||||
\(742\) | 44.4200 | 1.63071 | ||||||||
\(743\) | 13.1888 | 0.483851 | 0.241925 | − | 0.970295i | \(-0.422221\pi\) | ||||
0.241925 | + | 0.970295i | \(0.422221\pi\) | |||||||
\(744\) | 12.2883 | 0.450510 | ||||||||
\(745\) | 12.8769 | 0.471773 | ||||||||
\(746\) | −27.4676 | −1.00566 | ||||||||
\(747\) | −6.16714 | −0.225644 | ||||||||
\(748\) | −3.33984 | −0.122117 | ||||||||
\(749\) | −75.0382 | −2.74184 | ||||||||
\(750\) | −11.7253 | −0.428147 | ||||||||
\(751\) | 39.8951 | 1.45579 | 0.727896 | − | 0.685687i | \(-0.240498\pi\) | ||||
0.727896 | + | 0.685687i | \(0.240498\pi\) | |||||||
\(752\) | 10.6610 | 0.388766 | ||||||||
\(753\) | 0.564577 | 0.0205743 | ||||||||
\(754\) | 10.8305 | 0.394424 | ||||||||
\(755\) | −19.3780 | −0.705238 | ||||||||
\(756\) | −28.5407 | −1.03802 | ||||||||
\(757\) | −50.5984 | −1.83903 | −0.919516 | − | 0.393053i | \(-0.871419\pi\) | ||||
−0.919516 | + | 0.393053i | \(0.871419\pi\) | |||||||
\(758\) | −1.24602 | −0.0452577 | ||||||||
\(759\) | −0.858786 | −0.0311720 | ||||||||
\(760\) | 1.92516 | 0.0698328 | ||||||||
\(761\) | 1.70332 | 0.0617452 | 0.0308726 | − | 0.999523i | \(-0.490171\pi\) | ||||
0.0308726 | + | 0.999523i | \(0.490171\pi\) | |||||||
\(762\) | −21.6052 | −0.782673 | ||||||||
\(763\) | −48.0778 | −1.74053 | ||||||||
\(764\) | 17.2098 | 0.622628 | ||||||||
\(765\) | −2.69056 | −0.0972773 | ||||||||
\(766\) | −15.2911 | −0.552491 | ||||||||
\(767\) | 19.4736 | 0.703151 | ||||||||
\(768\) | −1.44389 | −0.0521021 | ||||||||
\(769\) | 1.96422 | 0.0708315 | 0.0354158 | − | 0.999373i | \(-0.488724\pi\) | ||||
0.0354158 | + | 0.999373i | \(0.488724\pi\) | |||||||
\(770\) | 4.44421 | 0.160158 | ||||||||
\(771\) | 34.5790 | 1.24533 | ||||||||
\(772\) | −6.91213 | −0.248773 | ||||||||
\(773\) | 54.9197 | 1.97532 | 0.987662 | − | 0.156600i | \(-0.0500535\pi\) | ||||
0.987662 | + | 0.156600i | \(0.0500535\pi\) | |||||||
\(774\) | 6.99535 | 0.251443 | ||||||||
\(775\) | 35.9579 | 1.29165 | ||||||||
\(776\) | 7.38017 | 0.264933 | ||||||||
\(777\) | −84.1745 | −3.01974 | ||||||||
\(778\) | 12.1854 | 0.436867 | ||||||||
\(779\) | 0.218649 | 0.00783392 | ||||||||
\(780\) | 2.02012 | 0.0723319 | ||||||||
\(781\) | 8.78579 | 0.314380 | ||||||||
\(782\) | −1.98644 | −0.0710348 | ||||||||
\(783\) | 38.5219 | 1.37666 | ||||||||
\(784\) | 18.4893 | 0.660333 | ||||||||
\(785\) | 5.93678 | 0.211893 | ||||||||
\(786\) | −28.0297 | −0.999787 | ||||||||
\(787\) | 3.14000 | 0.111929 | 0.0559645 | − | 0.998433i | \(-0.482177\pi\) | ||||
0.0559645 | + | 0.998433i | \(0.482177\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | −4.42241 | −0.157442 | ||||||||
\(790\) | 0.131244 | 0.00466944 | ||||||||
\(791\) | −88.0259 | −3.12984 | ||||||||
\(792\) | −0.915168 | −0.0325191 | ||||||||
\(793\) | −10.2016 | −0.362269 | ||||||||
\(794\) | −33.6081 | −1.19271 | ||||||||
\(795\) | −11.1828 | −0.396613 | ||||||||
\(796\) | −5.37847 | −0.190635 | ||||||||
\(797\) | 1.27330 | 0.0451025 | 0.0225512 | − | 0.999746i | \(-0.492821\pi\) | ||||
0.0225512 | + | 0.999746i | \(0.492821\pi\) | |||||||
\(798\) | −15.9428 | −0.564370 | ||||||||
\(799\) | −35.6060 | −1.25965 | ||||||||
\(800\) | −4.22513 | −0.149381 | ||||||||
\(801\) | 12.0081 | 0.424285 | ||||||||
\(802\) | −27.5483 | −0.972765 | ||||||||
\(803\) | 0.0781045 | 0.00275625 | ||||||||
\(804\) | −3.85202 | −0.135850 | ||||||||
\(805\) | 2.64329 | 0.0931636 | ||||||||
\(806\) | −13.5264 | −0.476446 | ||||||||
\(807\) | −34.2117 | −1.20431 | ||||||||
\(808\) | 10.4210 | 0.366608 | ||||||||
\(809\) | −37.2702 | −1.31035 | −0.655175 | − | 0.755477i | \(-0.727405\pi\) | ||||
−0.655175 | + | 0.755477i | \(0.727405\pi\) | |||||||
\(810\) | 4.76839 | 0.167544 | ||||||||
\(811\) | 13.0739 | 0.459088 | 0.229544 | − | 0.973298i | \(-0.426277\pi\) | ||||
0.229544 | + | 0.973298i | \(0.426277\pi\) | |||||||
\(812\) | −34.4034 | −1.20732 | ||||||||
\(813\) | −42.6862 | −1.49707 | ||||||||
\(814\) | −11.5469 | −0.404719 | ||||||||
\(815\) | 6.92243 | 0.242482 | ||||||||
\(816\) | 4.82237 | 0.168817 | ||||||||
\(817\) | 16.7170 | 0.584855 | ||||||||
\(818\) | 24.6144 | 0.860622 | ||||||||
\(819\) | 7.34356 | 0.256605 | ||||||||
\(820\) | 0.0880061 | 0.00307331 | ||||||||
\(821\) | 49.8139 | 1.73852 | 0.869258 | − | 0.494358i | \(-0.164597\pi\) | ||||
0.869258 | + | 0.494358i | \(0.164597\pi\) | |||||||
\(822\) | 6.95800 | 0.242688 | ||||||||
\(823\) | −35.1735 | −1.22607 | −0.613035 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613035 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(824\) | −1.04881 | −0.0365369 | ||||||||
\(825\) | 6.10064 | 0.212397 | ||||||||
\(826\) | −61.8585 | −2.15233 | ||||||||
\(827\) | −18.6216 | −0.647538 | −0.323769 | − | 0.946136i | \(-0.604950\pi\) | ||||
−0.323769 | + | 0.946136i | \(0.604950\pi\) | |||||||
\(828\) | −0.544315 | −0.0189163 | ||||||||
\(829\) | −27.3746 | −0.950760 | −0.475380 | − | 0.879780i | \(-0.657689\pi\) | ||||
−0.475380 | + | 0.879780i | \(0.657689\pi\) | |||||||
\(830\) | −5.93196 | −0.205901 | ||||||||
\(831\) | 45.2868 | 1.57098 | ||||||||
\(832\) | 1.58937 | 0.0551016 | ||||||||
\(833\) | −61.7513 | −2.13956 | ||||||||
\(834\) | 24.1481 | 0.836182 | ||||||||
\(835\) | −10.7560 | −0.372227 | ||||||||
\(836\) | −2.18701 | −0.0756393 | ||||||||
\(837\) | −48.1106 | −1.66295 | ||||||||
\(838\) | 16.9172 | 0.584395 | ||||||||
\(839\) | −40.6758 | −1.40428 | −0.702142 | − | 0.712037i | \(-0.747773\pi\) | ||||
−0.702142 | + | 0.712037i | \(0.747773\pi\) | |||||||
\(840\) | −6.41698 | −0.221407 | ||||||||
\(841\) | 17.4349 | 0.601204 | ||||||||
\(842\) | 19.7096 | 0.679238 | ||||||||
\(843\) | −9.12960 | −0.314440 | ||||||||
\(844\) | −26.6202 | −0.916305 | ||||||||
\(845\) | 9.21985 | 0.317172 | ||||||||
\(846\) | −9.75660 | −0.335439 | ||||||||
\(847\) | −5.04870 | −0.173475 | ||||||||
\(848\) | −8.79832 | −0.302136 | ||||||||
\(849\) | 18.0524 | 0.619558 | ||||||||
\(850\) | 14.1112 | 0.484011 | ||||||||
\(851\) | −6.86776 | −0.235424 | ||||||||
\(852\) | −12.6858 | −0.434607 | ||||||||
\(853\) | −12.7417 | −0.436268 | −0.218134 | − | 0.975919i | \(-0.569997\pi\) | ||||
−0.218134 | + | 0.975919i | \(0.569997\pi\) | |||||||
\(854\) | 32.4056 | 1.10890 | ||||||||
\(855\) | −1.76184 | −0.0602538 | ||||||||
\(856\) | 14.8629 | 0.508003 | ||||||||
\(857\) | 33.1562 | 1.13260 | 0.566298 | − | 0.824201i | \(-0.308375\pi\) | ||||
0.566298 | + | 0.824201i | \(0.308375\pi\) | |||||||
\(858\) | −2.29489 | −0.0783462 | ||||||||
\(859\) | 44.5782 | 1.52099 | 0.760495 | − | 0.649344i | \(-0.224956\pi\) | ||||
0.760495 | + | 0.649344i | \(0.224956\pi\) | |||||||
\(860\) | 6.72859 | 0.229443 | ||||||||
\(861\) | −0.728806 | −0.0248376 | ||||||||
\(862\) | −18.7848 | −0.639814 | ||||||||
\(863\) | −8.41725 | −0.286527 | −0.143263 | − | 0.989685i | \(-0.545760\pi\) | ||||
−0.143263 | + | 0.989685i | \(0.545760\pi\) | |||||||
\(864\) | 5.65309 | 0.192322 | ||||||||
\(865\) | 2.40765 | 0.0818627 | ||||||||
\(866\) | 8.72681 | 0.296549 | ||||||||
\(867\) | 8.44027 | 0.286647 | ||||||||
\(868\) | 42.9669 | 1.45839 | ||||||||
\(869\) | −0.149095 | −0.00505770 | ||||||||
\(870\) | 8.66111 | 0.293639 | ||||||||
\(871\) | 4.24013 | 0.143671 | ||||||||
\(872\) | 9.52282 | 0.322483 | ||||||||
\(873\) | −6.75410 | −0.228592 | ||||||||
\(874\) | −1.30077 | −0.0439992 | ||||||||
\(875\) | −40.9984 | −1.38600 | ||||||||
\(876\) | −0.112775 | −0.00381030 | ||||||||
\(877\) | 7.74519 | 0.261536 | 0.130768 | − | 0.991413i | \(-0.458256\pi\) | ||||
0.130768 | + | 0.991413i | \(0.458256\pi\) | |||||||
\(878\) | 7.05658 | 0.238148 | ||||||||
\(879\) | 28.3508 | 0.956249 | ||||||||
\(880\) | −0.880270 | −0.0296739 | ||||||||
\(881\) | −6.95411 | −0.234290 | −0.117145 | − | 0.993115i | \(-0.537374\pi\) | ||||
−0.117145 | + | 0.993115i | \(0.537374\pi\) | |||||||
\(882\) | −16.9209 | −0.569755 | ||||||||
\(883\) | −24.5937 | −0.827645 | −0.413822 | − | 0.910358i | \(-0.635807\pi\) | ||||
−0.413822 | + | 0.910358i | \(0.635807\pi\) | |||||||
\(884\) | −5.30825 | −0.178536 | ||||||||
\(885\) | 15.5730 | 0.523480 | ||||||||
\(886\) | 25.2265 | 0.847502 | ||||||||
\(887\) | 18.5173 | 0.621750 | 0.310875 | − | 0.950451i | \(-0.399378\pi\) | ||||
0.310875 | + | 0.950451i | \(0.399378\pi\) | |||||||
\(888\) | 16.6725 | 0.559493 | ||||||||
\(889\) | −75.5443 | −2.53367 | ||||||||
\(890\) | 11.5502 | 0.387163 | ||||||||
\(891\) | −5.41696 | −0.181475 | ||||||||
\(892\) | −15.6479 | −0.523930 | ||||||||
\(893\) | −23.3157 | −0.780230 | ||||||||
\(894\) | 21.1218 | 0.706419 | ||||||||
\(895\) | −8.32152 | −0.278158 | ||||||||
\(896\) | −5.04870 | −0.168665 | ||||||||
\(897\) | −1.36493 | −0.0455738 | ||||||||
\(898\) | 13.3348 | 0.444986 | ||||||||
\(899\) | −57.9932 | −1.93418 | ||||||||
\(900\) | 3.86670 | 0.128890 | ||||||||
\(901\) | 29.3850 | 0.978955 | ||||||||
\(902\) | −0.0999763 | −0.00332885 | ||||||||
\(903\) | −55.7216 | −1.85430 | ||||||||
\(904\) | 17.4354 | 0.579892 | ||||||||
\(905\) | −16.8453 | −0.559956 | ||||||||
\(906\) | −31.7855 | −1.05600 | ||||||||
\(907\) | 32.3280 | 1.07343 | 0.536716 | − | 0.843763i | \(-0.319665\pi\) | ||||
0.536716 | + | 0.843763i | \(0.319665\pi\) | |||||||
\(908\) | −13.3236 | −0.442158 | ||||||||
\(909\) | −9.53693 | −0.316320 | ||||||||
\(910\) | 7.06352 | 0.234153 | ||||||||
\(911\) | −37.4263 | −1.23999 | −0.619995 | − | 0.784606i | \(-0.712865\pi\) | ||||
−0.619995 | + | 0.784606i | \(0.712865\pi\) | |||||||
\(912\) | 3.15781 | 0.104566 | ||||||||
\(913\) | 6.73880 | 0.223022 | ||||||||
\(914\) | −15.9201 | −0.526589 | ||||||||
\(915\) | −8.15816 | −0.269700 | ||||||||
\(916\) | 14.7794 | 0.488324 | ||||||||
\(917\) | −98.0082 | −3.23652 | ||||||||
\(918\) | −18.8804 | −0.623146 | ||||||||
\(919\) | 21.7349 | 0.716969 | 0.358485 | − | 0.933536i | \(-0.383294\pi\) | ||||
0.358485 | + | 0.933536i | \(0.383294\pi\) | |||||||
\(920\) | −0.523558 | −0.0172612 | ||||||||
\(921\) | −28.0361 | −0.923821 | ||||||||
\(922\) | 12.5893 | 0.414606 | ||||||||
\(923\) | 13.9639 | 0.459628 | ||||||||
\(924\) | 7.28978 | 0.239816 | ||||||||
\(925\) | 48.7872 | 1.60411 | ||||||||
\(926\) | 33.6257 | 1.10501 | ||||||||
\(927\) | 0.959834 | 0.0315251 | ||||||||
\(928\) | 6.81432 | 0.223691 | ||||||||
\(929\) | −44.4884 | −1.45962 | −0.729808 | − | 0.683652i | \(-0.760391\pi\) | ||||
−0.729808 | + | 0.683652i | \(0.760391\pi\) | |||||||
\(930\) | −10.8170 | −0.354703 | ||||||||
\(931\) | −40.4363 | −1.32525 | ||||||||
\(932\) | −13.5300 | −0.443190 | ||||||||
\(933\) | 13.6751 | 0.447703 | ||||||||
\(934\) | 25.4854 | 0.833907 | ||||||||
\(935\) | 2.93996 | 0.0961469 | ||||||||
\(936\) | −1.45455 | −0.0475433 | ||||||||
\(937\) | 14.8066 | 0.483709 | 0.241855 | − | 0.970313i | \(-0.422244\pi\) | ||||
0.241855 | + | 0.970313i | \(0.422244\pi\) | |||||||
\(938\) | −13.4689 | −0.439775 | ||||||||
\(939\) | −20.8799 | −0.681390 | ||||||||
\(940\) | −9.38455 | −0.306090 | ||||||||
\(941\) | 42.8294 | 1.39620 | 0.698100 | − | 0.716000i | \(-0.254029\pi\) | ||||
0.698100 | + | 0.716000i | \(0.254029\pi\) | |||||||
\(942\) | 9.73803 | 0.317282 | ||||||||
\(943\) | −0.0594630 | −0.00193638 | ||||||||
\(944\) | 12.2524 | 0.398781 | ||||||||
\(945\) | 25.1235 | 0.817269 | ||||||||
\(946\) | −7.64379 | −0.248521 | ||||||||
\(947\) | −16.3276 | −0.530577 | −0.265288 | − | 0.964169i | \(-0.585467\pi\) | ||||
−0.265288 | + | 0.964169i | \(0.585467\pi\) | |||||||
\(948\) | 0.215277 | 0.00699188 | ||||||||
\(949\) | 0.124137 | 0.00402967 | ||||||||
\(950\) | 9.24039 | 0.299798 | ||||||||
\(951\) | −22.6383 | −0.734097 | ||||||||
\(952\) | 16.8618 | 0.546495 | ||||||||
\(953\) | −59.9891 | −1.94324 | −0.971619 | − | 0.236550i | \(-0.923983\pi\) | ||||
−0.971619 | + | 0.236550i | \(0.923983\pi\) | |||||||
\(954\) | 8.05195 | 0.260691 | ||||||||
\(955\) | −15.1492 | −0.490218 | ||||||||
\(956\) | −3.32174 | −0.107433 | ||||||||
\(957\) | −9.83915 | −0.318055 | ||||||||
\(958\) | 22.4360 | 0.724874 | ||||||||
\(959\) | 24.3292 | 0.785631 | ||||||||
\(960\) | 1.27102 | 0.0410219 | ||||||||
\(961\) | 41.4286 | 1.33641 | ||||||||
\(962\) | −18.3524 | −0.591704 | ||||||||
\(963\) | −13.6021 | −0.438320 | ||||||||
\(964\) | −1.44506 | −0.0465423 | ||||||||
\(965\) | 6.08454 | 0.195868 | ||||||||
\(966\) | 4.33575 | 0.139500 | ||||||||
\(967\) | 25.8926 | 0.832650 | 0.416325 | − | 0.909216i | \(-0.363318\pi\) | ||||
0.416325 | + | 0.909216i | \(0.363318\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −10.5466 | −0.338805 | ||||||||
\(970\) | −6.49654 | −0.208591 | ||||||||
\(971\) | 50.5802 | 1.62320 | 0.811598 | − | 0.584216i | \(-0.198598\pi\) | ||||
0.811598 | + | 0.584216i | \(0.198598\pi\) | |||||||
\(972\) | −9.13775 | −0.293093 | ||||||||
\(973\) | 84.4360 | 2.70689 | ||||||||
\(974\) | 21.2895 | 0.682161 | ||||||||
\(975\) | 9.69619 | 0.310527 | ||||||||
\(976\) | −6.41861 | −0.205455 | ||||||||
\(977\) | −1.71948 | −0.0550112 | −0.0275056 | − | 0.999622i | \(-0.508756\pi\) | ||||
−0.0275056 | + | 0.999622i | \(0.508756\pi\) | |||||||
\(978\) | 11.3548 | 0.363085 | ||||||||
\(979\) | −13.1212 | −0.419355 | ||||||||
\(980\) | −16.2756 | −0.519905 | ||||||||
\(981\) | −8.71498 | −0.278248 | ||||||||
\(982\) | −22.0437 | −0.703444 | ||||||||
\(983\) | −25.5480 | −0.814856 | −0.407428 | − | 0.913237i | \(-0.633574\pi\) | ||||
−0.407428 | + | 0.913237i | \(0.633574\pi\) | |||||||
\(984\) | 0.144355 | 0.00460188 | ||||||||
\(985\) | −0.880270 | −0.0280477 | ||||||||
\(986\) | −22.7587 | −0.724785 | ||||||||
\(987\) | 77.7163 | 2.47374 | ||||||||
\(988\) | −3.47598 | −0.110586 | ||||||||
\(989\) | −4.54630 | −0.144564 | ||||||||
\(990\) | 0.805595 | 0.0256035 | ||||||||
\(991\) | −8.90881 | −0.282998 | −0.141499 | − | 0.989938i | \(-0.545192\pi\) | ||||
−0.141499 | + | 0.989938i | \(0.545192\pi\) | |||||||
\(992\) | −8.51050 | −0.270209 | ||||||||
\(993\) | 24.0514 | 0.763247 | ||||||||
\(994\) | −44.3568 | −1.40691 | ||||||||
\(995\) | 4.73450 | 0.150094 | ||||||||
\(996\) | −9.73012 | −0.308311 | ||||||||
\(997\) | −47.9767 | −1.51944 | −0.759718 | − | 0.650253i | \(-0.774663\pi\) | ||||
−0.759718 | + | 0.650253i | \(0.774663\pi\) | |||||||
\(998\) | −34.1956 | −1.08244 | ||||||||
\(999\) | −65.2758 | −2.06523 |
(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 | 4334.2.a.g.1.7 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.g.1.7 | ✓ | 26 | 1.1 | even | 1 | trivial |