Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.576474 | −0.407629 | −0.203814 | − | 0.979010i | \(-0.565334\pi\) | ||||
−0.203814 | + | 0.979010i | \(0.565334\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.66768 | −0.833839 | ||||||||
\(5\) | 0.828352 | 0.370450 | 0.185225 | − | 0.982696i | \(-0.440699\pi\) | ||||
0.185225 | + | 0.982696i | \(0.440699\pi\) | |||||||
\(6\) | −0.576474 | −0.235345 | ||||||||
\(7\) | −0.479856 | −0.181369 | −0.0906843 | − | 0.995880i | \(-0.528905\pi\) | ||||
−0.0906843 | + | 0.995880i | \(0.528905\pi\) | |||||||
\(8\) | 2.11432 | 0.747525 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.477524 | −0.151006 | ||||||||
\(11\) | 5.91719 | 1.78410 | 0.892050 | − | 0.451937i | \(-0.149267\pi\) | ||||
0.892050 | + | 0.451937i | \(0.149267\pi\) | |||||||
\(12\) | −1.66768 | −0.481417 | ||||||||
\(13\) | −2.47116 | −0.685377 | −0.342688 | − | 0.939449i | \(-0.611337\pi\) | ||||
−0.342688 | + | 0.939449i | \(0.611337\pi\) | |||||||
\(14\) | 0.276625 | 0.0739310 | ||||||||
\(15\) | 0.828352 | 0.213880 | ||||||||
\(16\) | 2.11650 | 0.529126 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.576474 | −0.135876 | ||||||||
\(19\) | 2.75787 | 0.632699 | 0.316349 | − | 0.948643i | \(-0.397543\pi\) | ||||
0.316349 | + | 0.948643i | \(0.397543\pi\) | |||||||
\(20\) | −1.38142 | −0.308896 | ||||||||
\(21\) | −0.479856 | −0.104713 | ||||||||
\(22\) | −3.41111 | −0.727250 | ||||||||
\(23\) | 4.50266 | 0.938870 | 0.469435 | − | 0.882967i | \(-0.344458\pi\) | ||||
0.469435 | + | 0.882967i | \(0.344458\pi\) | |||||||
\(24\) | 2.11432 | 0.431584 | ||||||||
\(25\) | −4.31383 | −0.862767 | ||||||||
\(26\) | 1.42456 | 0.279379 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.800245 | 0.151232 | ||||||||
\(29\) | −6.59210 | −1.22412 | −0.612061 | − | 0.790810i | \(-0.709659\pi\) | ||||
−0.612061 | + | 0.790810i | \(0.709659\pi\) | |||||||
\(30\) | −0.477524 | −0.0871835 | ||||||||
\(31\) | −2.35371 | −0.422739 | −0.211370 | − | 0.977406i | \(-0.567792\pi\) | ||||
−0.211370 | + | 0.977406i | \(0.567792\pi\) | |||||||
\(32\) | −5.44875 | −0.963212 | ||||||||
\(33\) | 5.91719 | 1.03005 | ||||||||
\(34\) | 0.576474 | 0.0988645 | ||||||||
\(35\) | −0.397490 | −0.0671880 | ||||||||
\(36\) | −1.66768 | −0.277946 | ||||||||
\(37\) | −9.35003 | −1.53713 | −0.768567 | − | 0.639769i | \(-0.779030\pi\) | ||||
−0.768567 | + | 0.639769i | \(0.779030\pi\) | |||||||
\(38\) | −1.58984 | −0.257906 | ||||||||
\(39\) | −2.47116 | −0.395702 | ||||||||
\(40\) | 1.75140 | 0.276921 | ||||||||
\(41\) | −7.84656 | −1.22543 | −0.612713 | − | 0.790305i | \(-0.709922\pi\) | ||||
−0.612713 | + | 0.790305i | \(0.709922\pi\) | |||||||
\(42\) | 0.276625 | 0.0426841 | ||||||||
\(43\) | −10.6454 | −1.62341 | −0.811703 | − | 0.584071i | \(-0.801459\pi\) | ||||
−0.811703 | + | 0.584071i | \(0.801459\pi\) | |||||||
\(44\) | −9.86797 | −1.48765 | ||||||||
\(45\) | 0.828352 | 0.123483 | ||||||||
\(46\) | −2.59567 | −0.382711 | ||||||||
\(47\) | −10.0395 | −1.46441 | −0.732203 | − | 0.681087i | \(-0.761508\pi\) | ||||
−0.732203 | + | 0.681087i | \(0.761508\pi\) | |||||||
\(48\) | 2.11650 | 0.305491 | ||||||||
\(49\) | −6.76974 | −0.967105 | ||||||||
\(50\) | 2.48681 | 0.351688 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 4.12110 | 0.571494 | ||||||||
\(53\) | 10.7649 | 1.47867 | 0.739335 | − | 0.673338i | \(-0.235140\pi\) | ||||
0.739335 | + | 0.673338i | \(0.235140\pi\) | |||||||
\(54\) | −0.576474 | −0.0784482 | ||||||||
\(55\) | 4.90152 | 0.660920 | ||||||||
\(56\) | −1.01457 | −0.135578 | ||||||||
\(57\) | 2.75787 | 0.365289 | ||||||||
\(58\) | 3.80018 | 0.498988 | ||||||||
\(59\) | 0.266454 | 0.0346893 | 0.0173447 | − | 0.999850i | \(-0.494479\pi\) | ||||
0.0173447 | + | 0.999850i | \(0.494479\pi\) | |||||||
\(60\) | −1.38142 | −0.178341 | ||||||||
\(61\) | −7.69049 | −0.984666 | −0.492333 | − | 0.870407i | \(-0.663856\pi\) | ||||
−0.492333 | + | 0.870407i | \(0.663856\pi\) | |||||||
\(62\) | 1.35685 | 0.172321 | ||||||||
\(63\) | −0.479856 | −0.0604562 | ||||||||
\(64\) | −1.09194 | −0.136493 | ||||||||
\(65\) | −2.04699 | −0.253898 | ||||||||
\(66\) | −3.41111 | −0.419878 | ||||||||
\(67\) | −12.4138 | −1.51659 | −0.758293 | − | 0.651914i | \(-0.773966\pi\) | ||||
−0.758293 | + | 0.651914i | \(0.773966\pi\) | |||||||
\(68\) | 1.66768 | 0.202236 | ||||||||
\(69\) | 4.50266 | 0.542057 | ||||||||
\(70\) | 0.229143 | 0.0273878 | ||||||||
\(71\) | 7.86135 | 0.932970 | 0.466485 | − | 0.884529i | \(-0.345520\pi\) | ||||
0.466485 | + | 0.884529i | \(0.345520\pi\) | |||||||
\(72\) | 2.11432 | 0.249175 | ||||||||
\(73\) | 2.29870 | 0.269043 | 0.134521 | − | 0.990911i | \(-0.457050\pi\) | ||||
0.134521 | + | 0.990911i | \(0.457050\pi\) | |||||||
\(74\) | 5.39005 | 0.626580 | ||||||||
\(75\) | −4.31383 | −0.498118 | ||||||||
\(76\) | −4.59924 | −0.527569 | ||||||||
\(77\) | −2.83940 | −0.323580 | ||||||||
\(78\) | 1.42456 | 0.161300 | ||||||||
\(79\) | −6.28776 | −0.707428 | −0.353714 | − | 0.935354i | \(-0.615081\pi\) | ||||
−0.353714 | + | 0.935354i | \(0.615081\pi\) | |||||||
\(80\) | 1.75321 | 0.196015 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.52334 | 0.499519 | ||||||||
\(83\) | 11.7711 | 1.29204 | 0.646022 | − | 0.763319i | \(-0.276432\pi\) | ||||
0.646022 | + | 0.763319i | \(0.276432\pi\) | |||||||
\(84\) | 0.800245 | 0.0873139 | ||||||||
\(85\) | −0.828352 | −0.0898474 | ||||||||
\(86\) | 6.13679 | 0.661747 | ||||||||
\(87\) | −6.59210 | −0.706748 | ||||||||
\(88\) | 12.5108 | 1.33366 | ||||||||
\(89\) | 10.1686 | 1.07787 | 0.538934 | − | 0.842348i | \(-0.318827\pi\) | ||||
0.538934 | + | 0.842348i | \(0.318827\pi\) | |||||||
\(90\) | −0.477524 | −0.0503354 | ||||||||
\(91\) | 1.18580 | 0.124306 | ||||||||
\(92\) | −7.50899 | −0.782867 | ||||||||
\(93\) | −2.35371 | −0.244069 | ||||||||
\(94\) | 5.78749 | 0.596934 | ||||||||
\(95\) | 2.28449 | 0.234384 | ||||||||
\(96\) | −5.44875 | −0.556111 | ||||||||
\(97\) | 0.346481 | 0.0351798 | 0.0175899 | − | 0.999845i | \(-0.494401\pi\) | ||||
0.0175899 | + | 0.999845i | \(0.494401\pi\) | |||||||
\(98\) | 3.90258 | 0.394220 | ||||||||
\(99\) | 5.91719 | 0.594700 | ||||||||
\(100\) | 7.19408 | 0.719408 | ||||||||
\(101\) | 11.5452 | 1.14879 | 0.574397 | − | 0.818577i | \(-0.305237\pi\) | ||||
0.574397 | + | 0.818577i | \(0.305237\pi\) | |||||||
\(102\) | 0.576474 | 0.0570794 | ||||||||
\(103\) | 7.18519 | 0.707978 | 0.353989 | − | 0.935250i | \(-0.384825\pi\) | ||||
0.353989 | + | 0.935250i | \(0.384825\pi\) | |||||||
\(104\) | −5.22483 | −0.512336 | ||||||||
\(105\) | −0.397490 | −0.0387910 | ||||||||
\(106\) | −6.20568 | −0.602749 | ||||||||
\(107\) | −2.35202 | −0.227379 | −0.113689 | − | 0.993516i | \(-0.536267\pi\) | ||||
−0.113689 | + | 0.993516i | \(0.536267\pi\) | |||||||
\(108\) | −1.66768 | −0.160472 | ||||||||
\(109\) | 3.67918 | 0.352402 | 0.176201 | − | 0.984354i | \(-0.443619\pi\) | ||||
0.176201 | + | 0.984354i | \(0.443619\pi\) | |||||||
\(110\) | −2.82560 | −0.269410 | ||||||||
\(111\) | −9.35003 | −0.887465 | ||||||||
\(112\) | −1.01562 | −0.0959668 | ||||||||
\(113\) | 10.6804 | 1.00473 | 0.502366 | − | 0.864655i | \(-0.332463\pi\) | ||||
0.502366 | + | 0.864655i | \(0.332463\pi\) | |||||||
\(114\) | −1.58984 | −0.148902 | ||||||||
\(115\) | 3.72979 | 0.347805 | ||||||||
\(116\) | 10.9935 | 1.02072 | ||||||||
\(117\) | −2.47116 | −0.228459 | ||||||||
\(118\) | −0.153604 | −0.0141404 | ||||||||
\(119\) | 0.479856 | 0.0439883 | ||||||||
\(120\) | 1.75140 | 0.159880 | ||||||||
\(121\) | 24.0131 | 2.18301 | ||||||||
\(122\) | 4.43337 | 0.401378 | ||||||||
\(123\) | −7.84656 | −0.707500 | ||||||||
\(124\) | 3.92523 | 0.352496 | ||||||||
\(125\) | −7.71513 | −0.690063 | ||||||||
\(126\) | 0.276625 | 0.0246437 | ||||||||
\(127\) | −7.23512 | −0.642013 | −0.321007 | − | 0.947077i | \(-0.604021\pi\) | ||||
−0.321007 | + | 0.947077i | \(0.604021\pi\) | |||||||
\(128\) | 11.5270 | 1.01885 | ||||||||
\(129\) | −10.6454 | −0.937274 | ||||||||
\(130\) | 1.18004 | 0.103496 | ||||||||
\(131\) | −16.6001 | −1.45036 | −0.725180 | − | 0.688560i | \(-0.758243\pi\) | ||||
−0.725180 | + | 0.688560i | \(0.758243\pi\) | |||||||
\(132\) | −9.86797 | −0.858896 | ||||||||
\(133\) | −1.32338 | −0.114752 | ||||||||
\(134\) | 7.15623 | 0.618204 | ||||||||
\(135\) | 0.828352 | 0.0712932 | ||||||||
\(136\) | −2.11432 | −0.181302 | ||||||||
\(137\) | −8.81614 | −0.753214 | −0.376607 | − | 0.926373i | \(-0.622909\pi\) | ||||
−0.376607 | + | 0.926373i | \(0.622909\pi\) | |||||||
\(138\) | −2.59567 | −0.220958 | ||||||||
\(139\) | −1.60980 | −0.136542 | −0.0682709 | − | 0.997667i | \(-0.521748\pi\) | ||||
−0.0682709 | + | 0.997667i | \(0.521748\pi\) | |||||||
\(140\) | 0.662885 | 0.0560240 | ||||||||
\(141\) | −10.0395 | −0.845475 | ||||||||
\(142\) | −4.53186 | −0.380306 | ||||||||
\(143\) | −14.6223 | −1.22278 | ||||||||
\(144\) | 2.11650 | 0.176375 | ||||||||
\(145\) | −5.46058 | −0.453477 | ||||||||
\(146\) | −1.32514 | −0.109670 | ||||||||
\(147\) | −6.76974 | −0.558359 | ||||||||
\(148\) | 15.5928 | 1.28172 | ||||||||
\(149\) | 1.20969 | 0.0991016 | 0.0495508 | − | 0.998772i | \(-0.484221\pi\) | ||||
0.0495508 | + | 0.998772i | \(0.484221\pi\) | |||||||
\(150\) | 2.48681 | 0.203047 | ||||||||
\(151\) | −19.6838 | −1.60184 | −0.800922 | − | 0.598769i | \(-0.795657\pi\) | ||||
−0.800922 | + | 0.598769i | \(0.795657\pi\) | |||||||
\(152\) | 5.83103 | 0.472959 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 1.63684 | 0.131900 | ||||||||
\(155\) | −1.94970 | −0.156604 | ||||||||
\(156\) | 4.12110 | 0.329952 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 3.62473 | 0.288368 | ||||||||
\(159\) | 10.7649 | 0.853711 | ||||||||
\(160\) | −4.51349 | −0.356822 | ||||||||
\(161\) | −2.16063 | −0.170282 | ||||||||
\(162\) | −0.576474 | −0.0452921 | ||||||||
\(163\) | −13.6542 | −1.06948 | −0.534742 | − | 0.845016i | \(-0.679591\pi\) | ||||
−0.534742 | + | 0.845016i | \(0.679591\pi\) | |||||||
\(164\) | 13.0855 | 1.02181 | ||||||||
\(165\) | 4.90152 | 0.381583 | ||||||||
\(166\) | −6.78572 | −0.526674 | ||||||||
\(167\) | 18.4779 | 1.42986 | 0.714930 | − | 0.699196i | \(-0.246459\pi\) | ||||
0.714930 | + | 0.699196i | \(0.246459\pi\) | |||||||
\(168\) | −1.01457 | −0.0782758 | ||||||||
\(169\) | −6.89337 | −0.530259 | ||||||||
\(170\) | 0.477524 | 0.0366244 | ||||||||
\(171\) | 2.75787 | 0.210900 | ||||||||
\(172\) | 17.7531 | 1.35366 | ||||||||
\(173\) | 12.7582 | 0.969989 | 0.484995 | − | 0.874517i | \(-0.338822\pi\) | ||||
0.484995 | + | 0.874517i | \(0.338822\pi\) | |||||||
\(174\) | 3.80018 | 0.288091 | ||||||||
\(175\) | 2.07002 | 0.156479 | ||||||||
\(176\) | 12.5238 | 0.944013 | ||||||||
\(177\) | 0.266454 | 0.0200279 | ||||||||
\(178\) | −5.86193 | −0.439370 | ||||||||
\(179\) | 9.56385 | 0.714836 | 0.357418 | − | 0.933945i | \(-0.383657\pi\) | ||||
0.357418 | + | 0.933945i | \(0.383657\pi\) | |||||||
\(180\) | −1.38142 | −0.102965 | ||||||||
\(181\) | −18.9044 | −1.40516 | −0.702578 | − | 0.711607i | \(-0.747968\pi\) | ||||
−0.702578 | + | 0.711607i | \(0.747968\pi\) | |||||||
\(182\) | −0.683584 | −0.0506706 | ||||||||
\(183\) | −7.69049 | −0.568497 | ||||||||
\(184\) | 9.52008 | 0.701830 | ||||||||
\(185\) | −7.74511 | −0.569432 | ||||||||
\(186\) | 1.35685 | 0.0994894 | ||||||||
\(187\) | −5.91719 | −0.432708 | ||||||||
\(188\) | 16.7426 | 1.22108 | ||||||||
\(189\) | −0.479856 | −0.0349044 | ||||||||
\(190\) | −1.31695 | −0.0955415 | ||||||||
\(191\) | −19.8281 | −1.43471 | −0.717355 | − | 0.696707i | \(-0.754648\pi\) | ||||
−0.717355 | + | 0.696707i | \(0.754648\pi\) | |||||||
\(192\) | −1.09194 | −0.0788041 | ||||||||
\(193\) | −23.4458 | −1.68766 | −0.843831 | − | 0.536608i | \(-0.819705\pi\) | ||||
−0.843831 | + | 0.536608i | \(0.819705\pi\) | |||||||
\(194\) | −0.199737 | −0.0143403 | ||||||||
\(195\) | −2.04699 | −0.146588 | ||||||||
\(196\) | 11.2897 | 0.806410 | ||||||||
\(197\) | 9.98421 | 0.711346 | 0.355673 | − | 0.934611i | \(-0.384252\pi\) | ||||
0.355673 | + | 0.934611i | \(0.384252\pi\) | |||||||
\(198\) | −3.41111 | −0.242417 | ||||||||
\(199\) | 4.12796 | 0.292623 | 0.146311 | − | 0.989239i | \(-0.453260\pi\) | ||||
0.146311 | + | 0.989239i | \(0.453260\pi\) | |||||||
\(200\) | −9.12083 | −0.644940 | ||||||||
\(201\) | −12.4138 | −0.875601 | ||||||||
\(202\) | −6.65553 | −0.468282 | ||||||||
\(203\) | 3.16326 | 0.222017 | ||||||||
\(204\) | 1.66768 | 0.116761 | ||||||||
\(205\) | −6.49971 | −0.453960 | ||||||||
\(206\) | −4.14208 | −0.288592 | ||||||||
\(207\) | 4.50266 | 0.312957 | ||||||||
\(208\) | −5.23022 | −0.362650 | ||||||||
\(209\) | 16.3188 | 1.12880 | ||||||||
\(210\) | 0.229143 | 0.0158123 | ||||||||
\(211\) | −8.50287 | −0.585362 | −0.292681 | − | 0.956210i | \(-0.594547\pi\) | ||||
−0.292681 | + | 0.956210i | \(0.594547\pi\) | |||||||
\(212\) | −17.9524 | −1.23297 | ||||||||
\(213\) | 7.86135 | 0.538651 | ||||||||
\(214\) | 1.35588 | 0.0926861 | ||||||||
\(215\) | −8.81813 | −0.601391 | ||||||||
\(216\) | 2.11432 | 0.143861 | ||||||||
\(217\) | 1.12944 | 0.0766716 | ||||||||
\(218\) | −2.12095 | −0.143649 | ||||||||
\(219\) | 2.29870 | 0.155332 | ||||||||
\(220\) | −8.17415 | −0.551101 | ||||||||
\(221\) | 2.47116 | 0.166228 | ||||||||
\(222\) | 5.39005 | 0.361756 | ||||||||
\(223\) | −15.1528 | −1.01471 | −0.507354 | − | 0.861738i | \(-0.669376\pi\) | ||||
−0.507354 | + | 0.861738i | \(0.669376\pi\) | |||||||
\(224\) | 2.61462 | 0.174696 | ||||||||
\(225\) | −4.31383 | −0.287589 | ||||||||
\(226\) | −6.15700 | −0.409557 | ||||||||
\(227\) | −22.2243 | −1.47508 | −0.737539 | − | 0.675305i | \(-0.764012\pi\) | ||||
−0.737539 | + | 0.675305i | \(0.764012\pi\) | |||||||
\(228\) | −4.59924 | −0.304592 | ||||||||
\(229\) | 11.3305 | 0.748742 | 0.374371 | − | 0.927279i | \(-0.377859\pi\) | ||||
0.374371 | + | 0.927279i | \(0.377859\pi\) | |||||||
\(230\) | −2.15013 | −0.141775 | ||||||||
\(231\) | −2.83940 | −0.186819 | ||||||||
\(232\) | −13.9378 | −0.915063 | ||||||||
\(233\) | 4.18406 | 0.274107 | 0.137053 | − | 0.990564i | \(-0.456237\pi\) | ||||
0.137053 | + | 0.990564i | \(0.456237\pi\) | |||||||
\(234\) | 1.42456 | 0.0931264 | ||||||||
\(235\) | −8.31621 | −0.542490 | ||||||||
\(236\) | −0.444359 | −0.0289253 | ||||||||
\(237\) | −6.28776 | −0.408434 | ||||||||
\(238\) | −0.276625 | −0.0179309 | ||||||||
\(239\) | 9.78127 | 0.632698 | 0.316349 | − | 0.948643i | \(-0.397543\pi\) | ||||
0.316349 | + | 0.948643i | \(0.397543\pi\) | |||||||
\(240\) | 1.75321 | 0.113169 | ||||||||
\(241\) | −21.7377 | −1.40025 | −0.700125 | − | 0.714020i | \(-0.746873\pi\) | ||||
−0.700125 | + | 0.714020i | \(0.746873\pi\) | |||||||
\(242\) | −13.8430 | −0.889859 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.8253 | 0.821053 | ||||||||
\(245\) | −5.60773 | −0.358265 | ||||||||
\(246\) | 4.52334 | 0.288397 | ||||||||
\(247\) | −6.81514 | −0.433637 | ||||||||
\(248\) | −4.97651 | −0.316008 | ||||||||
\(249\) | 11.7711 | 0.745962 | ||||||||
\(250\) | 4.44758 | 0.281289 | ||||||||
\(251\) | −23.3319 | −1.47270 | −0.736349 | − | 0.676602i | \(-0.763452\pi\) | ||||
−0.736349 | + | 0.676602i | \(0.763452\pi\) | |||||||
\(252\) | 0.800245 | 0.0504107 | ||||||||
\(253\) | 26.6431 | 1.67504 | ||||||||
\(254\) | 4.17086 | 0.261703 | ||||||||
\(255\) | −0.828352 | −0.0518734 | ||||||||
\(256\) | −4.46112 | −0.278820 | ||||||||
\(257\) | 13.3221 | 0.831011 | 0.415505 | − | 0.909591i | \(-0.363605\pi\) | ||||
0.415505 | + | 0.909591i | \(0.363605\pi\) | |||||||
\(258\) | 6.13679 | 0.382060 | ||||||||
\(259\) | 4.48667 | 0.278788 | ||||||||
\(260\) | 3.41372 | 0.211710 | ||||||||
\(261\) | −6.59210 | −0.408041 | ||||||||
\(262\) | 9.56954 | 0.591208 | ||||||||
\(263\) | −13.5052 | −0.832765 | −0.416382 | − | 0.909190i | \(-0.636702\pi\) | ||||
−0.416382 | + | 0.909190i | \(0.636702\pi\) | |||||||
\(264\) | 12.5108 | 0.769989 | ||||||||
\(265\) | 8.91711 | 0.547774 | ||||||||
\(266\) | 0.762895 | 0.0467761 | ||||||||
\(267\) | 10.1686 | 0.622308 | ||||||||
\(268\) | 20.7022 | 1.26459 | ||||||||
\(269\) | −11.2883 | −0.688259 | −0.344129 | − | 0.938922i | \(-0.611826\pi\) | ||||
−0.344129 | + | 0.938922i | \(0.611826\pi\) | |||||||
\(270\) | −0.477524 | −0.0290612 | ||||||||
\(271\) | 8.30026 | 0.504205 | 0.252103 | − | 0.967701i | \(-0.418878\pi\) | ||||
0.252103 | + | 0.967701i | \(0.418878\pi\) | |||||||
\(272\) | −2.11650 | −0.128332 | ||||||||
\(273\) | 1.18580 | 0.0717680 | ||||||||
\(274\) | 5.08228 | 0.307032 | ||||||||
\(275\) | −25.5258 | −1.53926 | ||||||||
\(276\) | −7.50899 | −0.451988 | ||||||||
\(277\) | 23.1419 | 1.39046 | 0.695232 | − | 0.718786i | \(-0.255302\pi\) | ||||
0.695232 | + | 0.718786i | \(0.255302\pi\) | |||||||
\(278\) | 0.928010 | 0.0556583 | ||||||||
\(279\) | −2.35371 | −0.140913 | ||||||||
\(280\) | −0.840421 | −0.0502248 | ||||||||
\(281\) | −10.0789 | −0.601255 | −0.300627 | − | 0.953742i | \(-0.597196\pi\) | ||||
−0.300627 | + | 0.953742i | \(0.597196\pi\) | |||||||
\(282\) | 5.78749 | 0.344640 | ||||||||
\(283\) | −13.2197 | −0.785828 | −0.392914 | − | 0.919575i | \(-0.628533\pi\) | ||||
−0.392914 | + | 0.919575i | \(0.628533\pi\) | |||||||
\(284\) | −13.1102 | −0.777947 | ||||||||
\(285\) | 2.28449 | 0.135321 | ||||||||
\(286\) | 8.42939 | 0.498440 | ||||||||
\(287\) | 3.76522 | 0.222254 | ||||||||
\(288\) | −5.44875 | −0.321071 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 3.14788 | 0.184850 | ||||||||
\(291\) | 0.346481 | 0.0203111 | ||||||||
\(292\) | −3.83349 | −0.224338 | ||||||||
\(293\) | 18.9435 | 1.10669 | 0.553346 | − | 0.832952i | \(-0.313351\pi\) | ||||
0.553346 | + | 0.832952i | \(0.313351\pi\) | |||||||
\(294\) | 3.90258 | 0.227603 | ||||||||
\(295\) | 0.220718 | 0.0128507 | ||||||||
\(296\) | −19.7690 | −1.14905 | ||||||||
\(297\) | 5.91719 | 0.343350 | ||||||||
\(298\) | −0.697354 | −0.0403966 | ||||||||
\(299\) | −11.1268 | −0.643480 | ||||||||
\(300\) | 7.19408 | 0.415351 | ||||||||
\(301\) | 5.10825 | 0.294435 | ||||||||
\(302\) | 11.3472 | 0.652958 | ||||||||
\(303\) | 11.5452 | 0.663257 | ||||||||
\(304\) | 5.83704 | 0.334777 | ||||||||
\(305\) | −6.37043 | −0.364770 | ||||||||
\(306\) | 0.576474 | 0.0329548 | ||||||||
\(307\) | 22.9698 | 1.31096 | 0.655479 | − | 0.755213i | \(-0.272467\pi\) | ||||
0.655479 | + | 0.755213i | \(0.272467\pi\) | |||||||
\(308\) | 4.73520 | 0.269813 | ||||||||
\(309\) | 7.18519 | 0.408751 | ||||||||
\(310\) | 1.12395 | 0.0638363 | ||||||||
\(311\) | 21.1653 | 1.20017 | 0.600086 | − | 0.799935i | \(-0.295133\pi\) | ||||
0.600086 | + | 0.799935i | \(0.295133\pi\) | |||||||
\(312\) | −5.22483 | −0.295798 | ||||||||
\(313\) | 13.2039 | 0.746329 | 0.373164 | − | 0.927765i | \(-0.378273\pi\) | ||||
0.373164 | + | 0.927765i | \(0.378273\pi\) | |||||||
\(314\) | −0.576474 | −0.0325323 | ||||||||
\(315\) | −0.397490 | −0.0223960 | ||||||||
\(316\) | 10.4860 | 0.589881 | ||||||||
\(317\) | −10.0021 | −0.561775 | −0.280887 | − | 0.959741i | \(-0.590629\pi\) | ||||
−0.280887 | + | 0.959741i | \(0.590629\pi\) | |||||||
\(318\) | −6.20568 | −0.347997 | ||||||||
\(319\) | −39.0067 | −2.18396 | ||||||||
\(320\) | −0.904513 | −0.0505638 | ||||||||
\(321\) | −2.35202 | −0.131277 | ||||||||
\(322\) | 1.24555 | 0.0694117 | ||||||||
\(323\) | −2.75787 | −0.153452 | ||||||||
\(324\) | −1.66768 | −0.0926488 | ||||||||
\(325\) | 10.6602 | 0.591320 | ||||||||
\(326\) | 7.87132 | 0.435952 | ||||||||
\(327\) | 3.67918 | 0.203459 | ||||||||
\(328\) | −16.5901 | −0.916037 | ||||||||
\(329\) | 4.81750 | 0.265597 | ||||||||
\(330\) | −2.82560 | −0.155544 | ||||||||
\(331\) | 12.4144 | 0.682360 | 0.341180 | − | 0.939998i | \(-0.389173\pi\) | ||||
0.341180 | + | 0.939998i | \(0.389173\pi\) | |||||||
\(332\) | −19.6304 | −1.07736 | ||||||||
\(333\) | −9.35003 | −0.512378 | ||||||||
\(334\) | −10.6520 | −0.582852 | ||||||||
\(335\) | −10.2830 | −0.561820 | ||||||||
\(336\) | −1.01562 | −0.0554065 | ||||||||
\(337\) | −5.55921 | −0.302829 | −0.151415 | − | 0.988470i | \(-0.548383\pi\) | ||||
−0.151415 | + | 0.988470i | \(0.548383\pi\) | |||||||
\(338\) | 3.97385 | 0.216149 | ||||||||
\(339\) | 10.6804 | 0.580082 | ||||||||
\(340\) | 1.38142 | 0.0749183 | ||||||||
\(341\) | −13.9274 | −0.754209 | ||||||||
\(342\) | −1.58984 | −0.0859688 | ||||||||
\(343\) | 6.60749 | 0.356771 | ||||||||
\(344\) | −22.5078 | −1.21354 | ||||||||
\(345\) | 3.72979 | 0.200805 | ||||||||
\(346\) | −7.35478 | −0.395396 | ||||||||
\(347\) | −12.7321 | −0.683494 | −0.341747 | − | 0.939792i | \(-0.611019\pi\) | ||||
−0.341747 | + | 0.939792i | \(0.611019\pi\) | |||||||
\(348\) | 10.9935 | 0.589313 | ||||||||
\(349\) | 19.5735 | 1.04775 | 0.523874 | − | 0.851796i | \(-0.324486\pi\) | ||||
0.523874 | + | 0.851796i | \(0.324486\pi\) | |||||||
\(350\) | −1.19331 | −0.0637852 | ||||||||
\(351\) | −2.47116 | −0.131901 | ||||||||
\(352\) | −32.2413 | −1.71847 | ||||||||
\(353\) | −16.4742 | −0.876834 | −0.438417 | − | 0.898772i | \(-0.644461\pi\) | ||||
−0.438417 | + | 0.898772i | \(0.644461\pi\) | |||||||
\(354\) | −0.153604 | −0.00816395 | ||||||||
\(355\) | 6.51197 | 0.345619 | ||||||||
\(356\) | −16.9579 | −0.898769 | ||||||||
\(357\) | 0.479856 | 0.0253967 | ||||||||
\(358\) | −5.51331 | −0.291388 | ||||||||
\(359\) | −10.4095 | −0.549391 | −0.274695 | − | 0.961531i | \(-0.588577\pi\) | ||||
−0.274695 | + | 0.961531i | \(0.588577\pi\) | |||||||
\(360\) | 1.75140 | 0.0923070 | ||||||||
\(361\) | −11.3941 | −0.599692 | ||||||||
\(362\) | 10.8979 | 0.572782 | ||||||||
\(363\) | 24.0131 | 1.26036 | ||||||||
\(364\) | −1.97753 | −0.103651 | ||||||||
\(365\) | 1.90413 | 0.0996669 | ||||||||
\(366\) | 4.43337 | 0.231736 | ||||||||
\(367\) | −22.6560 | −1.18263 | −0.591316 | − | 0.806440i | \(-0.701391\pi\) | ||||
−0.591316 | + | 0.806440i | \(0.701391\pi\) | |||||||
\(368\) | 9.52991 | 0.496781 | ||||||||
\(369\) | −7.84656 | −0.408475 | ||||||||
\(370\) | 4.46486 | 0.232117 | ||||||||
\(371\) | −5.16559 | −0.268184 | ||||||||
\(372\) | 3.92523 | 0.203514 | ||||||||
\(373\) | 23.1860 | 1.20052 | 0.600262 | − | 0.799803i | \(-0.295063\pi\) | ||||
0.600262 | + | 0.799803i | \(0.295063\pi\) | |||||||
\(374\) | 3.41111 | 0.176384 | ||||||||
\(375\) | −7.71513 | −0.398408 | ||||||||
\(376\) | −21.2266 | −1.09468 | ||||||||
\(377\) | 16.2901 | 0.838985 | ||||||||
\(378\) | 0.276625 | 0.0142280 | ||||||||
\(379\) | 18.9940 | 0.975654 | 0.487827 | − | 0.872940i | \(-0.337790\pi\) | ||||
0.487827 | + | 0.872940i | \(0.337790\pi\) | |||||||
\(380\) | −3.80979 | −0.195438 | ||||||||
\(381\) | −7.23512 | −0.370667 | ||||||||
\(382\) | 11.4304 | 0.584829 | ||||||||
\(383\) | 1.12690 | 0.0575818 | 0.0287909 | − | 0.999585i | \(-0.490834\pi\) | ||||
0.0287909 | + | 0.999585i | \(0.490834\pi\) | |||||||
\(384\) | 11.5270 | 0.588234 | ||||||||
\(385\) | −2.35202 | −0.119870 | ||||||||
\(386\) | 13.5159 | 0.687940 | ||||||||
\(387\) | −10.6454 | −0.541135 | ||||||||
\(388\) | −0.577818 | −0.0293343 | ||||||||
\(389\) | −28.1550 | −1.42751 | −0.713757 | − | 0.700393i | \(-0.753008\pi\) | ||||
−0.713757 | + | 0.700393i | \(0.753008\pi\) | |||||||
\(390\) | 1.18004 | 0.0597535 | ||||||||
\(391\) | −4.50266 | −0.227710 | ||||||||
\(392\) | −14.3134 | −0.722936 | ||||||||
\(393\) | −16.6001 | −0.837365 | ||||||||
\(394\) | −5.75564 | −0.289965 | ||||||||
\(395\) | −5.20848 | −0.262067 | ||||||||
\(396\) | −9.86797 | −0.495884 | ||||||||
\(397\) | −28.7826 | −1.44456 | −0.722278 | − | 0.691603i | \(-0.756905\pi\) | ||||
−0.722278 | + | 0.691603i | \(0.756905\pi\) | |||||||
\(398\) | −2.37966 | −0.119282 | ||||||||
\(399\) | −1.32338 | −0.0662519 | ||||||||
\(400\) | −9.13024 | −0.456512 | ||||||||
\(401\) | 19.0968 | 0.953649 | 0.476825 | − | 0.878998i | \(-0.341788\pi\) | ||||
0.476825 | + | 0.878998i | \(0.341788\pi\) | |||||||
\(402\) | 7.15623 | 0.356920 | ||||||||
\(403\) | 5.81640 | 0.289736 | ||||||||
\(404\) | −19.2537 | −0.957909 | ||||||||
\(405\) | 0.828352 | 0.0411612 | ||||||||
\(406\) | −1.82354 | −0.0905007 | ||||||||
\(407\) | −55.3259 | −2.74240 | ||||||||
\(408\) | −2.11432 | −0.104675 | ||||||||
\(409\) | 30.9140 | 1.52860 | 0.764300 | − | 0.644861i | \(-0.223085\pi\) | ||||
0.764300 | + | 0.644861i | \(0.223085\pi\) | |||||||
\(410\) | 3.74692 | 0.185047 | ||||||||
\(411\) | −8.81614 | −0.434868 | ||||||||
\(412\) | −11.9826 | −0.590339 | ||||||||
\(413\) | −0.127860 | −0.00629156 | ||||||||
\(414\) | −2.59567 | −0.127570 | ||||||||
\(415\) | 9.75060 | 0.478638 | ||||||||
\(416\) | 13.4647 | 0.660163 | ||||||||
\(417\) | −1.60980 | −0.0788324 | ||||||||
\(418\) | −9.40739 | −0.460131 | ||||||||
\(419\) | 14.4095 | 0.703952 | 0.351976 | − | 0.936009i | \(-0.385510\pi\) | ||||
0.351976 | + | 0.936009i | \(0.385510\pi\) | |||||||
\(420\) | 0.662885 | 0.0323455 | ||||||||
\(421\) | 6.23018 | 0.303640 | 0.151820 | − | 0.988408i | \(-0.451487\pi\) | ||||
0.151820 | + | 0.988408i | \(0.451487\pi\) | |||||||
\(422\) | 4.90168 | 0.238610 | ||||||||
\(423\) | −10.0395 | −0.488135 | ||||||||
\(424\) | 22.7604 | 1.10534 | ||||||||
\(425\) | 4.31383 | 0.209252 | ||||||||
\(426\) | −4.53186 | −0.219570 | ||||||||
\(427\) | 3.69033 | 0.178587 | ||||||||
\(428\) | 3.92242 | 0.189597 | ||||||||
\(429\) | −14.6223 | −0.705973 | ||||||||
\(430\) | 5.08342 | 0.245144 | ||||||||
\(431\) | 8.93404 | 0.430337 | 0.215169 | − | 0.976577i | \(-0.430970\pi\) | ||||
0.215169 | + | 0.976577i | \(0.430970\pi\) | |||||||
\(432\) | 2.11650 | 0.101830 | ||||||||
\(433\) | −38.2328 | −1.83735 | −0.918677 | − | 0.395010i | \(-0.870741\pi\) | ||||
−0.918677 | + | 0.395010i | \(0.870741\pi\) | |||||||
\(434\) | −0.651095 | −0.0312536 | ||||||||
\(435\) | −5.46058 | −0.261815 | ||||||||
\(436\) | −6.13569 | −0.293846 | ||||||||
\(437\) | 12.4178 | 0.594022 | ||||||||
\(438\) | −1.32514 | −0.0633177 | ||||||||
\(439\) | −7.98160 | −0.380941 | −0.190471 | − | 0.981693i | \(-0.561001\pi\) | ||||
−0.190471 | + | 0.981693i | \(0.561001\pi\) | |||||||
\(440\) | 10.3634 | 0.494055 | ||||||||
\(441\) | −6.76974 | −0.322368 | ||||||||
\(442\) | −1.42456 | −0.0677594 | ||||||||
\(443\) | −6.80632 | −0.323378 | −0.161689 | − | 0.986842i | \(-0.551694\pi\) | ||||
−0.161689 | + | 0.986842i | \(0.551694\pi\) | |||||||
\(444\) | 15.5928 | 0.740003 | ||||||||
\(445\) | 8.42318 | 0.399297 | ||||||||
\(446\) | 8.73521 | 0.413624 | ||||||||
\(447\) | 1.20969 | 0.0572163 | ||||||||
\(448\) | 0.523975 | 0.0247555 | ||||||||
\(449\) | −2.60492 | −0.122934 | −0.0614669 | − | 0.998109i | \(-0.519578\pi\) | ||||
−0.0614669 | + | 0.998109i | \(0.519578\pi\) | |||||||
\(450\) | 2.48681 | 0.117229 | ||||||||
\(451\) | −46.4296 | −2.18628 | ||||||||
\(452\) | −17.8115 | −0.837784 | ||||||||
\(453\) | −19.6838 | −0.924825 | ||||||||
\(454\) | 12.8117 | 0.601284 | ||||||||
\(455\) | 0.982261 | 0.0460491 | ||||||||
\(456\) | 5.83103 | 0.273063 | ||||||||
\(457\) | 36.9769 | 1.72971 | 0.864853 | − | 0.502026i | \(-0.167412\pi\) | ||||
0.864853 | + | 0.502026i | \(0.167412\pi\) | |||||||
\(458\) | −6.53176 | −0.305209 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −6.22009 | −0.290013 | ||||||||
\(461\) | −11.9000 | −0.554239 | −0.277119 | − | 0.960835i | \(-0.589380\pi\) | ||||
−0.277119 | + | 0.960835i | \(0.589380\pi\) | |||||||
\(462\) | 1.63684 | 0.0761527 | ||||||||
\(463\) | −18.0312 | −0.837983 | −0.418991 | − | 0.907990i | \(-0.637616\pi\) | ||||
−0.418991 | + | 0.907990i | \(0.637616\pi\) | |||||||
\(464\) | −13.9522 | −0.647715 | ||||||||
\(465\) | −1.94970 | −0.0904153 | ||||||||
\(466\) | −2.41200 | −0.111734 | ||||||||
\(467\) | −36.7066 | −1.69858 | −0.849289 | − | 0.527929i | \(-0.822969\pi\) | ||||
−0.849289 | + | 0.527929i | \(0.822969\pi\) | |||||||
\(468\) | 4.12110 | 0.190498 | ||||||||
\(469\) | 5.95683 | 0.275061 | ||||||||
\(470\) | 4.79408 | 0.221134 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 0.563369 | 0.0259312 | ||||||||
\(473\) | −62.9908 | −2.89632 | ||||||||
\(474\) | 3.62473 | 0.166489 | ||||||||
\(475\) | −11.8970 | −0.545872 | ||||||||
\(476\) | −0.800245 | −0.0366792 | ||||||||
\(477\) | 10.7649 | 0.492890 | ||||||||
\(478\) | −5.63865 | −0.257906 | ||||||||
\(479\) | −39.4505 | −1.80254 | −0.901269 | − | 0.433260i | \(-0.857363\pi\) | ||||
−0.901269 | + | 0.433260i | \(0.857363\pi\) | |||||||
\(480\) | −4.51349 | −0.206011 | ||||||||
\(481\) | 23.1054 | 1.05352 | ||||||||
\(482\) | 12.5312 | 0.570782 | ||||||||
\(483\) | −2.16063 | −0.0983121 | ||||||||
\(484\) | −40.0462 | −1.82028 | ||||||||
\(485\) | 0.287008 | 0.0130324 | ||||||||
\(486\) | −0.576474 | −0.0261494 | ||||||||
\(487\) | 37.0843 | 1.68045 | 0.840225 | − | 0.542239i | \(-0.182423\pi\) | ||||
0.840225 | + | 0.542239i | \(0.182423\pi\) | |||||||
\(488\) | −16.2602 | −0.736063 | ||||||||
\(489\) | −13.6542 | −0.617466 | ||||||||
\(490\) | 3.23271 | 0.146039 | ||||||||
\(491\) | 35.3651 | 1.59601 | 0.798003 | − | 0.602653i | \(-0.205890\pi\) | ||||
0.798003 | + | 0.602653i | \(0.205890\pi\) | |||||||
\(492\) | 13.0855 | 0.589941 | ||||||||
\(493\) | 6.59210 | 0.296893 | ||||||||
\(494\) | 3.92875 | 0.176763 | ||||||||
\(495\) | 4.90152 | 0.220307 | ||||||||
\(496\) | −4.98164 | −0.223682 | ||||||||
\(497\) | −3.77232 | −0.169211 | ||||||||
\(498\) | −6.78572 | −0.304075 | ||||||||
\(499\) | −23.6503 | −1.05873 | −0.529366 | − | 0.848394i | \(-0.677570\pi\) | ||||
−0.529366 | + | 0.848394i | \(0.677570\pi\) | |||||||
\(500\) | 12.8664 | 0.575401 | ||||||||
\(501\) | 18.4779 | 0.825530 | ||||||||
\(502\) | 13.4503 | 0.600314 | ||||||||
\(503\) | 5.15704 | 0.229941 | 0.114971 | − | 0.993369i | \(-0.463323\pi\) | ||||
0.114971 | + | 0.993369i | \(0.463323\pi\) | |||||||
\(504\) | −1.01457 | −0.0451925 | ||||||||
\(505\) | 9.56353 | 0.425571 | ||||||||
\(506\) | −15.3591 | −0.682794 | ||||||||
\(507\) | −6.89337 | −0.306145 | ||||||||
\(508\) | 12.0659 | 0.535336 | ||||||||
\(509\) | 14.8015 | 0.656066 | 0.328033 | − | 0.944666i | \(-0.393614\pi\) | ||||
0.328033 | + | 0.944666i | \(0.393614\pi\) | |||||||
\(510\) | 0.477524 | 0.0211451 | ||||||||
\(511\) | −1.10305 | −0.0487959 | ||||||||
\(512\) | −20.4822 | −0.905196 | ||||||||
\(513\) | 2.75787 | 0.121763 | ||||||||
\(514\) | −7.67986 | −0.338744 | ||||||||
\(515\) | 5.95187 | 0.262271 | ||||||||
\(516\) | 17.7531 | 0.781535 | ||||||||
\(517\) | −59.4054 | −2.61265 | ||||||||
\(518\) | −2.58645 | −0.113642 | ||||||||
\(519\) | 12.7582 | 0.560024 | ||||||||
\(520\) | −4.32800 | −0.189795 | ||||||||
\(521\) | −6.86900 | −0.300936 | −0.150468 | − | 0.988615i | \(-0.548078\pi\) | ||||
−0.150468 | + | 0.988615i | \(0.548078\pi\) | |||||||
\(522\) | 3.80018 | 0.166329 | ||||||||
\(523\) | −43.1892 | −1.88853 | −0.944267 | − | 0.329181i | \(-0.893227\pi\) | ||||
−0.944267 | + | 0.329181i | \(0.893227\pi\) | |||||||
\(524\) | 27.6837 | 1.20937 | ||||||||
\(525\) | 2.07002 | 0.0903430 | ||||||||
\(526\) | 7.78538 | 0.339459 | ||||||||
\(527\) | 2.35371 | 0.102529 | ||||||||
\(528\) | 12.5238 | 0.545026 | ||||||||
\(529\) | −2.72601 | −0.118522 | ||||||||
\(530\) | −5.14049 | −0.223288 | ||||||||
\(531\) | 0.266454 | 0.0115631 | ||||||||
\(532\) | 2.20697 | 0.0956844 | ||||||||
\(533\) | 19.3901 | 0.839878 | ||||||||
\(534\) | −5.86193 | −0.253671 | ||||||||
\(535\) | −1.94830 | −0.0842325 | ||||||||
\(536\) | −26.2467 | −1.13369 | ||||||||
\(537\) | 9.56385 | 0.412711 | ||||||||
\(538\) | 6.50740 | 0.280554 | ||||||||
\(539\) | −40.0578 | −1.72541 | ||||||||
\(540\) | −1.38142 | −0.0594470 | ||||||||
\(541\) | 44.4463 | 1.91089 | 0.955447 | − | 0.295162i | \(-0.0953737\pi\) | ||||
0.955447 | + | 0.295162i | \(0.0953737\pi\) | |||||||
\(542\) | −4.78489 | −0.205528 | ||||||||
\(543\) | −18.9044 | −0.811267 | ||||||||
\(544\) | 5.44875 | 0.233613 | ||||||||
\(545\) | 3.04766 | 0.130547 | ||||||||
\(546\) | −0.683584 | −0.0292547 | ||||||||
\(547\) | 12.2060 | 0.521890 | 0.260945 | − | 0.965354i | \(-0.415966\pi\) | ||||
0.260945 | + | 0.965354i | \(0.415966\pi\) | |||||||
\(548\) | 14.7025 | 0.628059 | ||||||||
\(549\) | −7.69049 | −0.328222 | ||||||||
\(550\) | 14.7149 | 0.627447 | ||||||||
\(551\) | −18.1802 | −0.774501 | ||||||||
\(552\) | 9.52008 | 0.405202 | ||||||||
\(553\) | 3.01722 | 0.128305 | ||||||||
\(554\) | −13.3407 | −0.566793 | ||||||||
\(555\) | −7.74511 | −0.328762 | ||||||||
\(556\) | 2.68463 | 0.113854 | ||||||||
\(557\) | 42.0547 | 1.78191 | 0.890956 | − | 0.454089i | \(-0.150035\pi\) | ||||
0.890956 | + | 0.454089i | \(0.150035\pi\) | |||||||
\(558\) | 1.35685 | 0.0574402 | ||||||||
\(559\) | 26.3064 | 1.11264 | ||||||||
\(560\) | −0.841289 | −0.0355509 | ||||||||
\(561\) | −5.91719 | −0.249824 | ||||||||
\(562\) | 5.81021 | 0.245089 | ||||||||
\(563\) | −9.38469 | −0.395518 | −0.197759 | − | 0.980251i | \(-0.563366\pi\) | ||||
−0.197759 | + | 0.980251i | \(0.563366\pi\) | |||||||
\(564\) | 16.7426 | 0.704990 | ||||||||
\(565\) | 8.84717 | 0.372203 | ||||||||
\(566\) | 7.62080 | 0.320326 | ||||||||
\(567\) | −0.479856 | −0.0201521 | ||||||||
\(568\) | 16.6214 | 0.697419 | ||||||||
\(569\) | 26.4031 | 1.10688 | 0.553438 | − | 0.832890i | \(-0.313316\pi\) | ||||
0.553438 | + | 0.832890i | \(0.313316\pi\) | |||||||
\(570\) | −1.31695 | −0.0551609 | ||||||||
\(571\) | 45.7159 | 1.91315 | 0.956575 | − | 0.291487i | \(-0.0941500\pi\) | ||||
0.956575 | + | 0.291487i | \(0.0941500\pi\) | |||||||
\(572\) | 24.3853 | 1.01960 | ||||||||
\(573\) | −19.8281 | −0.828331 | ||||||||
\(574\) | −2.17055 | −0.0905970 | ||||||||
\(575\) | −19.4237 | −0.810026 | ||||||||
\(576\) | −1.09194 | −0.0454976 | ||||||||
\(577\) | −39.1130 | −1.62830 | −0.814148 | − | 0.580658i | \(-0.802795\pi\) | ||||
−0.814148 | + | 0.580658i | \(0.802795\pi\) | |||||||
\(578\) | −0.576474 | −0.0239782 | ||||||||
\(579\) | −23.4458 | −0.974372 | ||||||||
\(580\) | 9.10649 | 0.378126 | ||||||||
\(581\) | −5.64842 | −0.234336 | ||||||||
\(582\) | −0.199737 | −0.00827937 | ||||||||
\(583\) | 63.6979 | 2.63810 | ||||||||
\(584\) | 4.86019 | 0.201116 | ||||||||
\(585\) | −2.04699 | −0.0846327 | ||||||||
\(586\) | −10.9204 | −0.451119 | ||||||||
\(587\) | −15.3040 | −0.631662 | −0.315831 | − | 0.948815i | \(-0.602283\pi\) | ||||
−0.315831 | + | 0.948815i | \(0.602283\pi\) | |||||||
\(588\) | 11.2897 | 0.465581 | ||||||||
\(589\) | −6.49124 | −0.267467 | ||||||||
\(590\) | −0.127238 | −0.00523831 | ||||||||
\(591\) | 9.98421 | 0.410696 | ||||||||
\(592\) | −19.7894 | −0.813338 | ||||||||
\(593\) | 17.9368 | 0.736574 | 0.368287 | − | 0.929712i | \(-0.379944\pi\) | ||||
0.368287 | + | 0.929712i | \(0.379944\pi\) | |||||||
\(594\) | −3.41111 | −0.139959 | ||||||||
\(595\) | 0.397490 | 0.0162955 | ||||||||
\(596\) | −2.01737 | −0.0826347 | ||||||||
\(597\) | 4.12796 | 0.168946 | ||||||||
\(598\) | 6.41432 | 0.262301 | ||||||||
\(599\) | 34.6784 | 1.41692 | 0.708460 | − | 0.705751i | \(-0.249390\pi\) | ||||
0.708460 | + | 0.705751i | \(0.249390\pi\) | |||||||
\(600\) | −9.12083 | −0.372356 | ||||||||
\(601\) | −8.64543 | −0.352655 | −0.176327 | − | 0.984332i | \(-0.556422\pi\) | ||||
−0.176327 | + | 0.984332i | \(0.556422\pi\) | |||||||
\(602\) | −2.94477 | −0.120020 | ||||||||
\(603\) | −12.4138 | −0.505529 | ||||||||
\(604\) | 32.8262 | 1.33568 | ||||||||
\(605\) | 19.8913 | 0.808698 | ||||||||
\(606\) | −6.65553 | −0.270363 | ||||||||
\(607\) | 9.90149 | 0.401889 | 0.200945 | − | 0.979603i | \(-0.435599\pi\) | ||||
0.200945 | + | 0.979603i | \(0.435599\pi\) | |||||||
\(608\) | −15.0270 | −0.609424 | ||||||||
\(609\) | 3.16326 | 0.128182 | ||||||||
\(610\) | 3.67239 | 0.148691 | ||||||||
\(611\) | 24.8091 | 1.00367 | ||||||||
\(612\) | 1.66768 | 0.0674119 | ||||||||
\(613\) | −24.5725 | −0.992473 | −0.496236 | − | 0.868188i | \(-0.665285\pi\) | ||||
−0.496236 | + | 0.868188i | \(0.665285\pi\) | |||||||
\(614\) | −13.2415 | −0.534384 | ||||||||
\(615\) | −6.49971 | −0.262094 | ||||||||
\(616\) | −6.00340 | −0.241884 | ||||||||
\(617\) | −44.2221 | −1.78031 | −0.890157 | − | 0.455654i | \(-0.849406\pi\) | ||||
−0.890157 | + | 0.455654i | \(0.849406\pi\) | |||||||
\(618\) | −4.14208 | −0.166619 | ||||||||
\(619\) | −0.932339 | −0.0374739 | −0.0187369 | − | 0.999824i | \(-0.505965\pi\) | ||||
−0.0187369 | + | 0.999824i | \(0.505965\pi\) | |||||||
\(620\) | 3.25148 | 0.130582 | ||||||||
\(621\) | 4.50266 | 0.180686 | ||||||||
\(622\) | −12.2012 | −0.489225 | ||||||||
\(623\) | −4.87946 | −0.195491 | ||||||||
\(624\) | −5.23022 | −0.209376 | ||||||||
\(625\) | 15.1783 | 0.607133 | ||||||||
\(626\) | −7.61171 | −0.304225 | ||||||||
\(627\) | 16.3188 | 0.651712 | ||||||||
\(628\) | −1.66768 | −0.0665476 | ||||||||
\(629\) | 9.35003 | 0.372810 | ||||||||
\(630\) | 0.229143 | 0.00912926 | ||||||||
\(631\) | 41.6049 | 1.65627 | 0.828133 | − | 0.560532i | \(-0.189403\pi\) | ||||
0.828133 | + | 0.560532i | \(0.189403\pi\) | |||||||
\(632\) | −13.2943 | −0.528821 | ||||||||
\(633\) | −8.50287 | −0.337959 | ||||||||
\(634\) | 5.76596 | 0.228995 | ||||||||
\(635\) | −5.99323 | −0.237834 | ||||||||
\(636\) | −17.9524 | −0.711857 | ||||||||
\(637\) | 16.7291 | 0.662831 | ||||||||
\(638\) | 22.4864 | 0.890244 | ||||||||
\(639\) | 7.86135 | 0.310990 | ||||||||
\(640\) | 9.54840 | 0.377434 | ||||||||
\(641\) | 34.7701 | 1.37334 | 0.686669 | − | 0.726970i | \(-0.259072\pi\) | ||||
0.686669 | + | 0.726970i | \(0.259072\pi\) | |||||||
\(642\) | 1.35588 | 0.0535124 | ||||||||
\(643\) | −0.624812 | −0.0246402 | −0.0123201 | − | 0.999924i | \(-0.503922\pi\) | ||||
−0.0123201 | + | 0.999924i | \(0.503922\pi\) | |||||||
\(644\) | 3.60324 | 0.141987 | ||||||||
\(645\) | −8.81813 | −0.347213 | ||||||||
\(646\) | 1.58984 | 0.0625515 | ||||||||
\(647\) | −13.1851 | −0.518360 | −0.259180 | − | 0.965829i | \(-0.583452\pi\) | ||||
−0.259180 | + | 0.965829i | \(0.583452\pi\) | |||||||
\(648\) | 2.11432 | 0.0830584 | ||||||||
\(649\) | 1.57666 | 0.0618893 | ||||||||
\(650\) | −6.14531 | −0.241039 | ||||||||
\(651\) | 1.12944 | 0.0442664 | ||||||||
\(652\) | 22.7709 | 0.891777 | ||||||||
\(653\) | −12.6116 | −0.493529 | −0.246765 | − | 0.969075i | \(-0.579367\pi\) | ||||
−0.246765 | + | 0.969075i | \(0.579367\pi\) | |||||||
\(654\) | −2.12095 | −0.0829358 | ||||||||
\(655\) | −13.7507 | −0.537286 | ||||||||
\(656\) | −16.6073 | −0.648405 | ||||||||
\(657\) | 2.29870 | 0.0896809 | ||||||||
\(658\) | −2.77716 | −0.108265 | ||||||||
\(659\) | 29.2162 | 1.13810 | 0.569051 | − | 0.822302i | \(-0.307311\pi\) | ||||
0.569051 | + | 0.822302i | \(0.307311\pi\) | |||||||
\(660\) | −8.17415 | −0.318178 | ||||||||
\(661\) | −18.3845 | −0.715073 | −0.357536 | − | 0.933899i | \(-0.616383\pi\) | ||||
−0.357536 | + | 0.933899i | \(0.616383\pi\) | |||||||
\(662\) | −7.15661 | −0.278149 | ||||||||
\(663\) | 2.47116 | 0.0959719 | ||||||||
\(664\) | 24.8878 | 0.965835 | ||||||||
\(665\) | −1.09623 | −0.0425098 | ||||||||
\(666\) | 5.39005 | 0.208860 | ||||||||
\(667\) | −29.6820 | −1.14929 | ||||||||
\(668\) | −30.8151 | −1.19227 | ||||||||
\(669\) | −15.1528 | −0.585842 | ||||||||
\(670\) | 5.92788 | 0.229014 | ||||||||
\(671\) | −45.5061 | −1.75674 | ||||||||
\(672\) | 2.61462 | 0.100861 | ||||||||
\(673\) | −21.1181 | −0.814043 | −0.407021 | − | 0.913419i | \(-0.633433\pi\) | ||||
−0.407021 | + | 0.913419i | \(0.633433\pi\) | |||||||
\(674\) | 3.20474 | 0.123442 | ||||||||
\(675\) | −4.31383 | −0.166039 | ||||||||
\(676\) | 11.4959 | 0.442150 | ||||||||
\(677\) | 3.95528 | 0.152014 | 0.0760068 | − | 0.997107i | \(-0.475783\pi\) | ||||
0.0760068 | + | 0.997107i | \(0.475783\pi\) | |||||||
\(678\) | −6.15700 | −0.236458 | ||||||||
\(679\) | −0.166261 | −0.00638051 | ||||||||
\(680\) | −1.75140 | −0.0671632 | ||||||||
\(681\) | −22.2243 | −0.851636 | ||||||||
\(682\) | 8.02877 | 0.307437 | ||||||||
\(683\) | −10.9882 | −0.420453 | −0.210227 | − | 0.977653i | \(-0.567420\pi\) | ||||
−0.210227 | + | 0.977653i | \(0.567420\pi\) | |||||||
\(684\) | −4.59924 | −0.175856 | ||||||||
\(685\) | −7.30287 | −0.279028 | ||||||||
\(686\) | −3.80905 | −0.145430 | ||||||||
\(687\) | 11.3305 | 0.432287 | ||||||||
\(688\) | −22.5310 | −0.858986 | ||||||||
\(689\) | −26.6018 | −1.01345 | ||||||||
\(690\) | −2.15013 | −0.0818540 | ||||||||
\(691\) | 44.1142 | 1.67818 | 0.839092 | − | 0.543989i | \(-0.183087\pi\) | ||||
0.839092 | + | 0.543989i | \(0.183087\pi\) | |||||||
\(692\) | −21.2766 | −0.808815 | ||||||||
\(693\) | −2.83940 | −0.107860 | ||||||||
\(694\) | 7.33971 | 0.278612 | ||||||||
\(695\) | −1.33348 | −0.0505819 | ||||||||
\(696\) | −13.9378 | −0.528312 | ||||||||
\(697\) | 7.84656 | 0.297210 | ||||||||
\(698\) | −11.2836 | −0.427092 | ||||||||
\(699\) | 4.18406 | 0.158256 | ||||||||
\(700\) | −3.45212 | −0.130478 | ||||||||
\(701\) | −26.1733 | −0.988553 | −0.494277 | − | 0.869305i | \(-0.664567\pi\) | ||||
−0.494277 | + | 0.869305i | \(0.664567\pi\) | |||||||
\(702\) | 1.42456 | 0.0537666 | ||||||||
\(703\) | −25.7862 | −0.972544 | ||||||||
\(704\) | −6.46123 | −0.243517 | ||||||||
\(705\) | −8.31621 | −0.313207 | ||||||||
\(706\) | 9.49696 | 0.357423 | ||||||||
\(707\) | −5.54005 | −0.208355 | ||||||||
\(708\) | −0.444359 | −0.0167000 | ||||||||
\(709\) | −1.69026 | −0.0634792 | −0.0317396 | − | 0.999496i | \(-0.510105\pi\) | ||||
−0.0317396 | + | 0.999496i | \(0.510105\pi\) | |||||||
\(710\) | −3.75398 | −0.140884 | ||||||||
\(711\) | −6.28776 | −0.235809 | ||||||||
\(712\) | 21.4997 | 0.805734 | ||||||||
\(713\) | −10.5980 | −0.396897 | ||||||||
\(714\) | −0.276625 | −0.0103524 | ||||||||
\(715\) | −12.1124 | −0.452979 | ||||||||
\(716\) | −15.9494 | −0.596058 | ||||||||
\(717\) | 9.78127 | 0.365288 | ||||||||
\(718\) | 6.00079 | 0.223948 | ||||||||
\(719\) | 3.93316 | 0.146682 | 0.0733411 | − | 0.997307i | \(-0.476634\pi\) | ||||
0.0733411 | + | 0.997307i | \(0.476634\pi\) | |||||||
\(720\) | 1.75321 | 0.0653383 | ||||||||
\(721\) | −3.44786 | −0.128405 | ||||||||
\(722\) | 6.56843 | 0.244452 | ||||||||
\(723\) | −21.7377 | −0.808435 | ||||||||
\(724\) | 31.5265 | 1.17167 | ||||||||
\(725\) | 28.4372 | 1.05613 | ||||||||
\(726\) | −13.8430 | −0.513760 | ||||||||
\(727\) | −29.0999 | −1.07926 | −0.539628 | − | 0.841903i | \(-0.681435\pi\) | ||||
−0.539628 | + | 0.841903i | \(0.681435\pi\) | |||||||
\(728\) | 2.50716 | 0.0929217 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.09768 | −0.0406271 | ||||||||
\(731\) | 10.6454 | 0.393734 | ||||||||
\(732\) | 12.8253 | 0.474035 | ||||||||
\(733\) | −52.2535 | −1.93003 | −0.965013 | − | 0.262203i | \(-0.915551\pi\) | ||||
−0.965013 | + | 0.262203i | \(0.915551\pi\) | |||||||
\(734\) | 13.0606 | 0.482075 | ||||||||
\(735\) | −5.60773 | −0.206844 | ||||||||
\(736\) | −24.5339 | −0.904332 | ||||||||
\(737\) | −73.4548 | −2.70574 | ||||||||
\(738\) | 4.52334 | 0.166506 | ||||||||
\(739\) | −4.32924 | −0.159254 | −0.0796268 | − | 0.996825i | \(-0.525373\pi\) | ||||
−0.0796268 | + | 0.996825i | \(0.525373\pi\) | |||||||
\(740\) | 12.9164 | 0.474815 | ||||||||
\(741\) | −6.81514 | −0.250360 | ||||||||
\(742\) | 2.97783 | 0.109320 | ||||||||
\(743\) | 36.1019 | 1.32445 | 0.662226 | − | 0.749304i | \(-0.269612\pi\) | ||||
0.662226 | + | 0.749304i | \(0.269612\pi\) | |||||||
\(744\) | −4.97651 | −0.182448 | ||||||||
\(745\) | 1.00205 | 0.0367122 | ||||||||
\(746\) | −13.3661 | −0.489369 | ||||||||
\(747\) | 11.7711 | 0.430681 | ||||||||
\(748\) | 9.86797 | 0.360809 | ||||||||
\(749\) | 1.12863 | 0.0412394 | ||||||||
\(750\) | 4.44758 | 0.162402 | ||||||||
\(751\) | −2.95922 | −0.107983 | −0.0539917 | − | 0.998541i | \(-0.517194\pi\) | ||||
−0.0539917 | + | 0.998541i | \(0.517194\pi\) | |||||||
\(752\) | −21.2486 | −0.774855 | ||||||||
\(753\) | −23.3319 | −0.850263 | ||||||||
\(754\) | −9.39085 | −0.341994 | ||||||||
\(755\) | −16.3051 | −0.593404 | ||||||||
\(756\) | 0.800245 | 0.0291046 | ||||||||
\(757\) | 49.0765 | 1.78372 | 0.891859 | − | 0.452314i | \(-0.149401\pi\) | ||||
0.891859 | + | 0.452314i | \(0.149401\pi\) | |||||||
\(758\) | −10.9495 | −0.397705 | ||||||||
\(759\) | 26.6431 | 0.967084 | ||||||||
\(760\) | 4.83014 | 0.175208 | ||||||||
\(761\) | 51.0121 | 1.84919 | 0.924593 | − | 0.380955i | \(-0.124405\pi\) | ||||
0.924593 | + | 0.380955i | \(0.124405\pi\) | |||||||
\(762\) | 4.17086 | 0.151094 | ||||||||
\(763\) | −1.76548 | −0.0639146 | ||||||||
\(764\) | 33.0669 | 1.19632 | ||||||||
\(765\) | −0.828352 | −0.0299491 | ||||||||
\(766\) | −0.649628 | −0.0234720 | ||||||||
\(767\) | −0.658450 | −0.0237753 | ||||||||
\(768\) | −4.46112 | −0.160977 | ||||||||
\(769\) | −7.49780 | −0.270378 | −0.135189 | − | 0.990820i | \(-0.543164\pi\) | ||||
−0.135189 | + | 0.990820i | \(0.543164\pi\) | |||||||
\(770\) | 1.35588 | 0.0488625 | ||||||||
\(771\) | 13.3221 | 0.479784 | ||||||||
\(772\) | 39.1000 | 1.40724 | ||||||||
\(773\) | 53.9391 | 1.94005 | 0.970027 | − | 0.242996i | \(-0.0781303\pi\) | ||||
0.970027 | + | 0.242996i | \(0.0781303\pi\) | |||||||
\(774\) | 6.13679 | 0.220582 | ||||||||
\(775\) | 10.1535 | 0.364725 | ||||||||
\(776\) | 0.732572 | 0.0262978 | ||||||||
\(777\) | 4.48667 | 0.160958 | ||||||||
\(778\) | 16.2306 | 0.581896 | ||||||||
\(779\) | −21.6398 | −0.775326 | ||||||||
\(780\) | 3.41372 | 0.122231 | ||||||||
\(781\) | 46.5171 | 1.66451 | ||||||||
\(782\) | 2.59567 | 0.0928210 | ||||||||
\(783\) | −6.59210 | −0.235583 | ||||||||
\(784\) | −14.3282 | −0.511721 | ||||||||
\(785\) | 0.828352 | 0.0295652 | ||||||||
\(786\) | 9.56954 | 0.341334 | ||||||||
\(787\) | 29.7518 | 1.06054 | 0.530268 | − | 0.847830i | \(-0.322091\pi\) | ||||
0.530268 | + | 0.847830i | \(0.322091\pi\) | |||||||
\(788\) | −16.6504 | −0.593148 | ||||||||
\(789\) | −13.5052 | −0.480797 | ||||||||
\(790\) | 3.00255 | 0.106826 | ||||||||
\(791\) | −5.12507 | −0.182227 | ||||||||
\(792\) | 12.5108 | 0.444553 | ||||||||
\(793\) | 19.0044 | 0.674867 | ||||||||
\(794\) | 16.5924 | 0.588842 | ||||||||
\(795\) | 8.91711 | 0.316257 | ||||||||
\(796\) | −6.88410 | −0.244000 | ||||||||
\(797\) | −41.0298 | −1.45335 | −0.726675 | − | 0.686981i | \(-0.758936\pi\) | ||||
−0.726675 | + | 0.686981i | \(0.758936\pi\) | |||||||
\(798\) | 0.762895 | 0.0270062 | ||||||||
\(799\) | 10.0395 | 0.355171 | ||||||||
\(800\) | 23.5050 | 0.831027 | ||||||||
\(801\) | 10.1686 | 0.359290 | ||||||||
\(802\) | −11.0088 | −0.388735 | ||||||||
\(803\) | 13.6019 | 0.479999 | ||||||||
\(804\) | 20.7022 | 0.730110 | ||||||||
\(805\) | −1.78976 | −0.0630809 | ||||||||
\(806\) | −3.35301 | −0.118105 | ||||||||
\(807\) | −11.2883 | −0.397366 | ||||||||
\(808\) | 24.4103 | 0.858753 | ||||||||
\(809\) | 14.8953 | 0.523692 | 0.261846 | − | 0.965110i | \(-0.415669\pi\) | ||||
0.261846 | + | 0.965110i | \(0.415669\pi\) | |||||||
\(810\) | −0.477524 | −0.0167785 | ||||||||
\(811\) | −20.0677 | −0.704673 | −0.352336 | − | 0.935873i | \(-0.614613\pi\) | ||||
−0.352336 | + | 0.935873i | \(0.614613\pi\) | |||||||
\(812\) | −5.27530 | −0.185127 | ||||||||
\(813\) | 8.30026 | 0.291103 | ||||||||
\(814\) | 31.8939 | 1.11788 | ||||||||
\(815\) | −11.3105 | −0.396190 | ||||||||
\(816\) | −2.11650 | −0.0740924 | ||||||||
\(817\) | −29.3586 | −1.02713 | ||||||||
\(818\) | −17.8211 | −0.623101 | ||||||||
\(819\) | 1.18580 | 0.0414352 | ||||||||
\(820\) | 10.8394 | 0.378529 | ||||||||
\(821\) | −37.3729 | −1.30432 | −0.652161 | − | 0.758080i | \(-0.726137\pi\) | ||||
−0.652161 | + | 0.758080i | \(0.726137\pi\) | |||||||
\(822\) | 5.08228 | 0.177265 | ||||||||
\(823\) | −25.4583 | −0.887419 | −0.443709 | − | 0.896171i | \(-0.646338\pi\) | ||||
−0.443709 | + | 0.896171i | \(0.646338\pi\) | |||||||
\(824\) | 15.1918 | 0.529231 | ||||||||
\(825\) | −25.5258 | −0.888693 | ||||||||
\(826\) | 0.0737077 | 0.00256462 | ||||||||
\(827\) | −12.9303 | −0.449631 | −0.224815 | − | 0.974401i | \(-0.572178\pi\) | ||||
−0.224815 | + | 0.974401i | \(0.572178\pi\) | |||||||
\(828\) | −7.50899 | −0.260956 | ||||||||
\(829\) | −14.7331 | −0.511700 | −0.255850 | − | 0.966716i | \(-0.582355\pi\) | ||||
−0.255850 | + | 0.966716i | \(0.582355\pi\) | |||||||
\(830\) | −5.62097 | −0.195107 | ||||||||
\(831\) | 23.1419 | 0.802785 | ||||||||
\(832\) | 2.69836 | 0.0935490 | ||||||||
\(833\) | 6.76974 | 0.234558 | ||||||||
\(834\) | 0.928010 | 0.0321344 | ||||||||
\(835\) | 15.3062 | 0.529692 | ||||||||
\(836\) | −27.2146 | −0.941236 | ||||||||
\(837\) | −2.35371 | −0.0813562 | ||||||||
\(838\) | −8.30672 | −0.286951 | ||||||||
\(839\) | 17.6593 | 0.609667 | 0.304834 | − | 0.952406i | \(-0.401399\pi\) | ||||
0.304834 | + | 0.952406i | \(0.401399\pi\) | |||||||
\(840\) | −0.840421 | −0.0289973 | ||||||||
\(841\) | 14.4558 | 0.498476 | ||||||||
\(842\) | −3.59154 | −0.123773 | ||||||||
\(843\) | −10.0789 | −0.347135 | ||||||||
\(844\) | 14.1800 | 0.488097 | ||||||||
\(845\) | −5.71014 | −0.196435 | ||||||||
\(846\) | 5.78749 | 0.198978 | ||||||||
\(847\) | −11.5228 | −0.395930 | ||||||||
\(848\) | 22.7839 | 0.782403 | ||||||||
\(849\) | −13.2197 | −0.453698 | ||||||||
\(850\) | −2.48681 | −0.0852970 | ||||||||
\(851\) | −42.1000 | −1.44317 | ||||||||
\(852\) | −13.1102 | −0.449148 | ||||||||
\(853\) | −30.9734 | −1.06051 | −0.530255 | − | 0.847838i | \(-0.677904\pi\) | ||||
−0.530255 | + | 0.847838i | \(0.677904\pi\) | |||||||
\(854\) | −2.12738 | −0.0727974 | ||||||||
\(855\) | 2.28449 | 0.0781279 | ||||||||
\(856\) | −4.97293 | −0.169971 | ||||||||
\(857\) | −39.7544 | −1.35799 | −0.678993 | − | 0.734145i | \(-0.737583\pi\) | ||||
−0.678993 | + | 0.734145i | \(0.737583\pi\) | |||||||
\(858\) | 8.42939 | 0.287775 | ||||||||
\(859\) | 24.0479 | 0.820504 | 0.410252 | − | 0.911972i | \(-0.365441\pi\) | ||||
0.410252 | + | 0.911972i | \(0.365441\pi\) | |||||||
\(860\) | 14.7058 | 0.501463 | ||||||||
\(861\) | 3.76522 | 0.128318 | ||||||||
\(862\) | −5.15024 | −0.175418 | ||||||||
\(863\) | 20.2167 | 0.688184 | 0.344092 | − | 0.938936i | \(-0.388187\pi\) | ||||
0.344092 | + | 0.938936i | \(0.388187\pi\) | |||||||
\(864\) | −5.44875 | −0.185370 | ||||||||
\(865\) | 10.5683 | 0.359333 | ||||||||
\(866\) | 22.0402 | 0.748958 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −1.88355 | −0.0639318 | ||||||||
\(869\) | −37.2059 | −1.26212 | ||||||||
\(870\) | 3.14788 | 0.106723 | ||||||||
\(871\) | 30.6765 | 1.03943 | ||||||||
\(872\) | 7.77897 | 0.263429 | ||||||||
\(873\) | 0.346481 | 0.0117266 | ||||||||
\(874\) | −7.15852 | −0.242141 | ||||||||
\(875\) | 3.70215 | 0.125156 | ||||||||
\(876\) | −3.83349 | −0.129522 | ||||||||
\(877\) | 20.0885 | 0.678341 | 0.339171 | − | 0.940725i | \(-0.389854\pi\) | ||||
0.339171 | + | 0.940725i | \(0.389854\pi\) | |||||||
\(878\) | 4.60119 | 0.155283 | ||||||||
\(879\) | 18.9435 | 0.638949 | ||||||||
\(880\) | 10.3741 | 0.349710 | ||||||||
\(881\) | −9.64903 | −0.325084 | −0.162542 | − | 0.986702i | \(-0.551969\pi\) | ||||
−0.162542 | + | 0.986702i | \(0.551969\pi\) | |||||||
\(882\) | 3.90258 | 0.131407 | ||||||||
\(883\) | −6.79260 | −0.228589 | −0.114295 | − | 0.993447i | \(-0.536461\pi\) | ||||
−0.114295 | + | 0.993447i | \(0.536461\pi\) | |||||||
\(884\) | −4.12110 | −0.138608 | ||||||||
\(885\) | 0.220718 | 0.00741934 | ||||||||
\(886\) | 3.92367 | 0.131818 | ||||||||
\(887\) | 54.1860 | 1.81939 | 0.909693 | − | 0.415280i | \(-0.136317\pi\) | ||||
0.909693 | + | 0.415280i | \(0.136317\pi\) | |||||||
\(888\) | −19.7690 | −0.663403 | ||||||||
\(889\) | 3.47182 | 0.116441 | ||||||||
\(890\) | −4.85574 | −0.162765 | ||||||||
\(891\) | 5.91719 | 0.198233 | ||||||||
\(892\) | 25.2700 | 0.846103 | ||||||||
\(893\) | −27.6875 | −0.926528 | ||||||||
\(894\) | −0.697354 | −0.0233230 | ||||||||
\(895\) | 7.92224 | 0.264811 | ||||||||
\(896\) | −5.53129 | −0.184787 | ||||||||
\(897\) | −11.1268 | −0.371513 | ||||||||
\(898\) | 1.50167 | 0.0501114 | ||||||||
\(899\) | 15.5159 | 0.517485 | ||||||||
\(900\) | 7.19408 | 0.239803 | ||||||||
\(901\) | −10.7649 | −0.358630 | ||||||||
\(902\) | 26.7654 | 0.891192 | ||||||||
\(903\) | 5.10825 | 0.169992 | ||||||||
\(904\) | 22.5819 | 0.751062 | ||||||||
\(905\) | −15.6595 | −0.520540 | ||||||||
\(906\) | 11.3472 | 0.376985 | ||||||||
\(907\) | −20.9908 | −0.696987 | −0.348493 | − | 0.937311i | \(-0.613307\pi\) | ||||
−0.348493 | + | 0.937311i | \(0.613307\pi\) | |||||||
\(908\) | 37.0629 | 1.22998 | ||||||||
\(909\) | 11.5452 | 0.382931 | ||||||||
\(910\) | −0.566248 | −0.0187709 | ||||||||
\(911\) | 33.3813 | 1.10597 | 0.552985 | − | 0.833191i | \(-0.313489\pi\) | ||||
0.552985 | + | 0.833191i | \(0.313489\pi\) | |||||||
\(912\) | 5.83704 | 0.193284 | ||||||||
\(913\) | 69.6517 | 2.30513 | ||||||||
\(914\) | −21.3162 | −0.705078 | ||||||||
\(915\) | −6.37043 | −0.210600 | ||||||||
\(916\) | −18.8957 | −0.624330 | ||||||||
\(917\) | 7.96567 | 0.263050 | ||||||||
\(918\) | 0.576474 | 0.0190265 | ||||||||
\(919\) | 37.4810 | 1.23639 | 0.618193 | − | 0.786027i | \(-0.287865\pi\) | ||||
0.618193 | + | 0.786027i | \(0.287865\pi\) | |||||||
\(920\) | 7.88598 | 0.259993 | ||||||||
\(921\) | 22.9698 | 0.756882 | ||||||||
\(922\) | 6.86005 | 0.225924 | ||||||||
\(923\) | −19.4267 | −0.639436 | ||||||||
\(924\) | 4.73520 | 0.155777 | ||||||||
\(925\) | 40.3344 | 1.32619 | ||||||||
\(926\) | 10.3945 | 0.341586 | ||||||||
\(927\) | 7.18519 | 0.235993 | ||||||||
\(928\) | 35.9187 | 1.17909 | ||||||||
\(929\) | 21.0780 | 0.691548 | 0.345774 | − | 0.938318i | \(-0.387616\pi\) | ||||
0.345774 | + | 0.938318i | \(0.387616\pi\) | |||||||
\(930\) | 1.12395 | 0.0368559 | ||||||||
\(931\) | −18.6701 | −0.611887 | ||||||||
\(932\) | −6.97767 | −0.228561 | ||||||||
\(933\) | 21.1653 | 0.692920 | ||||||||
\(934\) | 21.1604 | 0.692389 | ||||||||
\(935\) | −4.90152 | −0.160297 | ||||||||
\(936\) | −5.22483 | −0.170779 | ||||||||
\(937\) | −11.3980 | −0.372356 | −0.186178 | − | 0.982516i | \(-0.559610\pi\) | ||||
−0.186178 | + | 0.982516i | \(0.559610\pi\) | |||||||
\(938\) | −3.43396 | −0.112123 | ||||||||
\(939\) | 13.2039 | 0.430893 | ||||||||
\(940\) | 13.8688 | 0.452349 | ||||||||
\(941\) | −12.5444 | −0.408935 | −0.204468 | − | 0.978873i | \(-0.565546\pi\) | ||||
−0.204468 | + | 0.978873i | \(0.565546\pi\) | |||||||
\(942\) | −0.576474 | −0.0187825 | ||||||||
\(943\) | −35.3304 | −1.15052 | ||||||||
\(944\) | 0.563951 | 0.0183550 | ||||||||
\(945\) | −0.397490 | −0.0129303 | ||||||||
\(946\) | 36.3125 | 1.18062 | ||||||||
\(947\) | −0.0831248 | −0.00270119 | −0.00135060 | − | 0.999999i | \(-0.500430\pi\) | ||||
−0.00135060 | + | 0.999999i | \(0.500430\pi\) | |||||||
\(948\) | 10.4860 | 0.340568 | ||||||||
\(949\) | −5.68046 | −0.184395 | ||||||||
\(950\) | 6.85831 | 0.222513 | ||||||||
\(951\) | −10.0021 | −0.324341 | ||||||||
\(952\) | 1.01457 | 0.0328824 | ||||||||
\(953\) | −56.8291 | −1.84088 | −0.920438 | − | 0.390888i | \(-0.872168\pi\) | ||||
−0.920438 | + | 0.390888i | \(0.872168\pi\) | |||||||
\(954\) | −6.20568 | −0.200916 | ||||||||
\(955\) | −16.4246 | −0.531489 | ||||||||
\(956\) | −16.3120 | −0.527568 | ||||||||
\(957\) | −39.0067 | −1.26091 | ||||||||
\(958\) | 22.7422 | 0.734766 | ||||||||
\(959\) | 4.23048 | 0.136609 | ||||||||
\(960\) | −0.904513 | −0.0291930 | ||||||||
\(961\) | −25.4600 | −0.821291 | ||||||||
\(962\) | −13.3197 | −0.429444 | ||||||||
\(963\) | −2.35202 | −0.0757929 | ||||||||
\(964\) | 36.2515 | 1.16758 | ||||||||
\(965\) | −19.4213 | −0.625195 | ||||||||
\(966\) | 1.24555 | 0.0400748 | ||||||||
\(967\) | −48.6775 | −1.56536 | −0.782682 | − | 0.622422i | \(-0.786149\pi\) | ||||
−0.782682 | + | 0.622422i | \(0.786149\pi\) | |||||||
\(968\) | 50.7715 | 1.63186 | ||||||||
\(969\) | −2.75787 | −0.0885956 | ||||||||
\(970\) | −0.165453 | −0.00531237 | ||||||||
\(971\) | −32.6531 | −1.04789 | −0.523943 | − | 0.851753i | \(-0.675540\pi\) | ||||
−0.523943 | + | 0.851753i | \(0.675540\pi\) | |||||||
\(972\) | −1.66768 | −0.0534908 | ||||||||
\(973\) | 0.772474 | 0.0247644 | ||||||||
\(974\) | −21.3781 | −0.684999 | ||||||||
\(975\) | 10.6602 | 0.341399 | ||||||||
\(976\) | −16.2769 | −0.521012 | ||||||||
\(977\) | 1.95573 | 0.0625694 | 0.0312847 | − | 0.999511i | \(-0.490040\pi\) | ||||
0.0312847 | + | 0.999511i | \(0.490040\pi\) | |||||||
\(978\) | 7.87132 | 0.251697 | ||||||||
\(979\) | 60.1695 | 1.92303 | ||||||||
\(980\) | 9.35188 | 0.298735 | ||||||||
\(981\) | 3.67918 | 0.117467 | ||||||||
\(982\) | −20.3871 | −0.650578 | ||||||||
\(983\) | −15.5246 | −0.495157 | −0.247578 | − | 0.968868i | \(-0.579635\pi\) | ||||
−0.247578 | + | 0.968868i | \(0.579635\pi\) | |||||||
\(984\) | −16.5901 | −0.528874 | ||||||||
\(985\) | 8.27044 | 0.263518 | ||||||||
\(986\) | −3.80018 | −0.121022 | ||||||||
\(987\) | 4.81750 | 0.153343 | ||||||||
\(988\) | 11.3655 | 0.361583 | ||||||||
\(989\) | −47.9326 | −1.52417 | ||||||||
\(990\) | −2.82560 | −0.0898034 | ||||||||
\(991\) | −27.8062 | −0.883293 | −0.441646 | − | 0.897189i | \(-0.645605\pi\) | ||||
−0.441646 | + | 0.897189i | \(0.645605\pi\) | |||||||
\(992\) | 12.8248 | 0.407188 | ||||||||
\(993\) | 12.4144 | 0.393961 | ||||||||
\(994\) | 2.17464 | 0.0689755 | ||||||||
\(995\) | 3.41940 | 0.108402 | ||||||||
\(996\) | −19.6304 | −0.622012 | ||||||||
\(997\) | 58.8387 | 1.86344 | 0.931721 | − | 0.363175i | \(-0.118307\pi\) | ||||
0.931721 | + | 0.363175i | \(0.118307\pi\) | |||||||
\(998\) | 13.6338 | 0.431569 | ||||||||
\(999\) | −9.35003 | −0.295822 |
(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 | 8007.2.a.e.1.20 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.20 | ✓ | 46 | 1.1 | even | 1 | trivial |