Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 152 x^{17} - 274 x^{16} - 1061 x^{15} + 3125 x^{14} + 2977 x^{13} - 15474 x^{12} - 56 x^{11} + 39579 x^{10} - 17664 x^{9} - 52271 x^{8} + 35701 x^{7} + \cdots + 31 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.72132\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.72132 | −1.21716 | −0.608580 | − | 0.793492i | \(-0.708261\pi\) | ||||
−0.608580 | + | 0.793492i | \(0.708261\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.962958 | 0.481479 | ||||||||
\(5\) | −2.01516 | −0.901208 | −0.450604 | − | 0.892724i | \(-0.648791\pi\) | ||||
−0.450604 | + | 0.892724i | \(0.648791\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.78509 | 0.631123 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.46875 | 1.09691 | ||||||||
\(11\) | −3.24791 | −0.979283 | −0.489641 | − | 0.871924i | \(-0.662872\pi\) | ||||
−0.489641 | + | 0.871924i | \(0.662872\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.61833 | −0.726195 | −0.363097 | − | 0.931751i | \(-0.618281\pi\) | ||||
−0.363097 | + | 0.931751i | \(0.618281\pi\) | |||||||
\(14\) | −1.72132 | −0.460043 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.99863 | −1.24966 | ||||||||
\(17\) | 1.03520 | 0.251073 | 0.125537 | − | 0.992089i | \(-0.459935\pi\) | ||||
0.125537 | + | 0.992089i | \(0.459935\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.18405 | −1.64813 | −0.824067 | − | 0.566492i | \(-0.808300\pi\) | ||||
−0.824067 | + | 0.566492i | \(0.808300\pi\) | |||||||
\(20\) | −1.94052 | −0.433913 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.59071 | 1.19194 | ||||||||
\(23\) | 8.35185 | 1.74148 | 0.870741 | − | 0.491742i | \(-0.163640\pi\) | ||||
0.870741 | + | 0.491742i | \(0.163640\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.939119 | −0.187824 | ||||||||
\(26\) | 4.50700 | 0.883895 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.962958 | 0.181982 | ||||||||
\(29\) | 2.77158 | 0.514670 | 0.257335 | − | 0.966322i | \(-0.417156\pi\) | ||||
0.257335 | + | 0.966322i | \(0.417156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.77241 | 1.39597 | 0.697983 | − | 0.716114i | \(-0.254081\pi\) | ||||
0.697983 | + | 0.716114i | \(0.254081\pi\) | |||||||
\(32\) | 5.03409 | 0.889910 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.78192 | −0.305596 | ||||||||
\(35\) | −2.01516 | −0.340625 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.894661 | −0.147081 | −0.0735407 | − | 0.997292i | \(-0.523430\pi\) | ||||
−0.0735407 | + | 0.997292i | \(0.523430\pi\) | |||||||
\(38\) | 12.3661 | 2.00604 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.59724 | −0.568773 | ||||||||
\(41\) | −9.16796 | −1.43179 | −0.715897 | − | 0.698206i | \(-0.753982\pi\) | ||||
−0.715897 | + | 0.698206i | \(0.753982\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.1174 | 1.69538 | 0.847691 | − | 0.530490i | \(-0.177992\pi\) | ||||
0.847691 | + | 0.530490i | \(0.177992\pi\) | |||||||
\(44\) | −3.12760 | −0.471504 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.3762 | −2.11966 | ||||||||
\(47\) | −11.4796 | −1.67447 | −0.837236 | − | 0.546841i | \(-0.815830\pi\) | ||||
−0.837236 | + | 0.546841i | \(0.815830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.61653 | 0.228612 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.52134 | −0.349648 | ||||||||
\(53\) | 1.21297 | 0.166614 | 0.0833072 | − | 0.996524i | \(-0.473452\pi\) | ||||
0.0833072 | + | 0.996524i | \(0.473452\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.54507 | 0.882537 | ||||||||
\(56\) | 1.78509 | 0.238542 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.77079 | −0.626436 | ||||||||
\(59\) | 10.8406 | 1.41133 | 0.705664 | − | 0.708547i | \(-0.250649\pi\) | ||||
0.705664 | + | 0.708547i | \(0.250649\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.59471 | 0.204181 | 0.102091 | − | 0.994775i | \(-0.467447\pi\) | ||||
0.102091 | + | 0.994775i | \(0.467447\pi\) | |||||||
\(62\) | −13.3788 | −1.69911 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.33195 | 0.166494 | ||||||||
\(65\) | 5.27637 | 0.654453 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.57264 | −0.802976 | −0.401488 | − | 0.915864i | \(-0.631507\pi\) | ||||
−0.401488 | + | 0.915864i | \(0.631507\pi\) | |||||||
\(68\) | 0.996855 | 0.120886 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.46875 | 0.414595 | ||||||||
\(71\) | −5.66866 | −0.672746 | −0.336373 | − | 0.941729i | \(-0.609200\pi\) | ||||
−0.336373 | + | 0.941729i | \(0.609200\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.1440 | 1.88951 | 0.944754 | − | 0.327780i | \(-0.106300\pi\) | ||||
0.944754 | + | 0.327780i | \(0.106300\pi\) | |||||||
\(74\) | 1.54000 | 0.179022 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.91794 | −0.793542 | ||||||||
\(77\) | −3.24791 | −0.370134 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.54507 | 0.736378 | 0.368189 | − | 0.929751i | \(-0.379978\pi\) | ||||
0.368189 | + | 0.929751i | \(0.379978\pi\) | |||||||
\(80\) | 10.0730 | 1.12620 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15.7810 | 1.74272 | ||||||||
\(83\) | 15.6260 | 1.71517 | 0.857587 | − | 0.514339i | \(-0.171963\pi\) | ||||
0.857587 | + | 0.514339i | \(0.171963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.08610 | −0.226269 | ||||||||
\(86\) | −19.1366 | −2.06355 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.79780 | −0.618048 | ||||||||
\(89\) | 2.20445 | 0.233671 | 0.116835 | − | 0.993151i | \(-0.462725\pi\) | ||||
0.116835 | + | 0.993151i | \(0.462725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.61833 | −0.274476 | ||||||||
\(92\) | 8.04248 | 0.838487 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 19.7601 | 2.03810 | ||||||||
\(95\) | 14.4770 | 1.48531 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.3102 | −1.75758 | −0.878792 | − | 0.477205i | \(-0.841650\pi\) | ||||
−0.878792 | + | 0.477205i | \(0.841650\pi\) | |||||||
\(98\) | −1.72132 | −0.173880 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.904333 | −0.0904333 | ||||||||
\(101\) | 0.549704 | 0.0546976 | 0.0273488 | − | 0.999626i | \(-0.491294\pi\) | ||||
0.0273488 | + | 0.999626i | \(0.491294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.42799 | −0.337770 | −0.168885 | − | 0.985636i | \(-0.554017\pi\) | ||||
−0.168885 | + | 0.985636i | \(0.554017\pi\) | |||||||
\(104\) | −4.67395 | −0.458318 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.08792 | −0.202796 | ||||||||
\(107\) | −2.93235 | −0.283480 | −0.141740 | − | 0.989904i | \(-0.545270\pi\) | ||||
−0.141740 | + | 0.989904i | \(0.545270\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.63710 | 0.539936 | 0.269968 | − | 0.962869i | \(-0.412987\pi\) | ||||
0.269968 | + | 0.962869i | \(0.412987\pi\) | |||||||
\(110\) | −11.2662 | −1.07419 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.99863 | −0.472326 | ||||||||
\(113\) | −17.1714 | −1.61535 | −0.807675 | − | 0.589627i | \(-0.799275\pi\) | ||||
−0.807675 | + | 0.589627i | \(0.799275\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.8303 | −1.56944 | ||||||||
\(116\) | 2.66892 | 0.247803 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −18.6602 | −1.71781 | ||||||||
\(119\) | 1.03520 | 0.0948967 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.451062 | −0.0410056 | ||||||||
\(122\) | −2.74501 | −0.248521 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.48451 | 0.672129 | ||||||||
\(125\) | 11.9683 | 1.07048 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −12.3609 | −1.09256 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.08234 | −0.796574 | ||||||||
\(131\) | 13.6960 | 1.19663 | 0.598315 | − | 0.801261i | \(-0.295837\pi\) | ||||
0.598315 | + | 0.801261i | \(0.295837\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.18405 | −0.622936 | ||||||||
\(134\) | 11.3136 | 0.977350 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.84792 | 0.158458 | ||||||||
\(137\) | −14.1852 | −1.21192 | −0.605961 | − | 0.795495i | \(-0.707211\pi\) | ||||
−0.605961 | + | 0.795495i | \(0.707211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.5176 | 1.48582 | 0.742912 | − | 0.669389i | \(-0.233444\pi\) | ||||
0.742912 | + | 0.669389i | \(0.233444\pi\) | |||||||
\(140\) | −1.94052 | −0.164004 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.75760 | 0.818839 | ||||||||
\(143\) | 8.50412 | 0.711150 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.58519 | −0.463825 | ||||||||
\(146\) | −27.7890 | −2.29983 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.861521 | −0.0708166 | ||||||||
\(149\) | 2.82930 | 0.231785 | 0.115893 | − | 0.993262i | \(-0.463027\pi\) | ||||
0.115893 | + | 0.993262i | \(0.463027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.01483 | −0.0825854 | −0.0412927 | − | 0.999147i | \(-0.513148\pi\) | ||||
−0.0412927 | + | 0.999147i | \(0.513148\pi\) | |||||||
\(152\) | −12.8241 | −1.04018 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.59071 | 0.450512 | ||||||||
\(155\) | −15.6627 | −1.25806 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.81914 | −0.703844 | −0.351922 | − | 0.936029i | \(-0.614472\pi\) | ||||
−0.351922 | + | 0.936029i | \(0.614472\pi\) | |||||||
\(158\) | −11.2662 | −0.896290 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.1445 | −0.801994 | ||||||||
\(161\) | 8.35185 | 0.658218 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.0894 | −1.41687 | −0.708435 | − | 0.705776i | \(-0.750599\pi\) | ||||
−0.708435 | + | 0.705776i | \(0.750599\pi\) | |||||||
\(164\) | −8.82836 | −0.689379 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −26.8974 | −2.08764 | ||||||||
\(167\) | −2.26326 | −0.175136 | −0.0875682 | − | 0.996159i | \(-0.527910\pi\) | ||||
−0.0875682 | + | 0.996159i | \(0.527910\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.14433 | −0.472641 | ||||||||
\(170\) | 3.59085 | 0.275406 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.7056 | 0.816291 | ||||||||
\(173\) | 22.7872 | 1.73248 | 0.866241 | − | 0.499626i | \(-0.166529\pi\) | ||||
0.866241 | + | 0.499626i | \(0.166529\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.939119 | −0.0709908 | ||||||||
\(176\) | 16.2351 | 1.22377 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.79457 | −0.284415 | ||||||||
\(179\) | −4.20646 | −0.314405 | −0.157203 | − | 0.987566i | \(-0.550248\pi\) | ||||
−0.157203 | + | 0.987566i | \(0.550248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.09021 | 0.527011 | 0.263505 | − | 0.964658i | \(-0.415121\pi\) | ||||
0.263505 | + | 0.964658i | \(0.415121\pi\) | |||||||
\(182\) | 4.50700 | 0.334081 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.9088 | 1.09909 | ||||||||
\(185\) | 1.80289 | 0.132551 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.36224 | −0.245872 | ||||||||
\(188\) | −11.0544 | −0.806223 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24.9197 | −1.80786 | ||||||||
\(191\) | −22.5450 | −1.63130 | −0.815650 | − | 0.578546i | \(-0.803620\pi\) | ||||
−0.815650 | + | 0.578546i | \(0.803620\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.98495 | −0.502788 | −0.251394 | − | 0.967885i | \(-0.580889\pi\) | ||||
−0.251394 | + | 0.967885i | \(0.580889\pi\) | |||||||
\(194\) | 29.7965 | 2.13926 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.962958 | 0.0687827 | ||||||||
\(197\) | −13.5537 | −0.965664 | −0.482832 | − | 0.875713i | \(-0.660392\pi\) | ||||
−0.482832 | + | 0.875713i | \(0.660392\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.1726 | 1.92621 | 0.963106 | − | 0.269123i | \(-0.0867340\pi\) | ||||
0.963106 | + | 0.269123i | \(0.0867340\pi\) | |||||||
\(200\) | −1.67641 | −0.118540 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.946219 | −0.0665757 | ||||||||
\(203\) | 2.77158 | 0.194527 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.4749 | 1.29034 | ||||||||
\(206\) | 5.90069 | 0.411120 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.0881 | 0.907494 | ||||||||
\(209\) | 23.3332 | 1.61399 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.72446 | 0.600616 | 0.300308 | − | 0.953842i | \(-0.402910\pi\) | ||||
0.300308 | + | 0.953842i | \(0.402910\pi\) | |||||||
\(212\) | 1.16804 | 0.0802213 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.04752 | 0.345041 | ||||||||
\(215\) | −22.4033 | −1.52789 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.77241 | 0.527626 | ||||||||
\(218\) | −9.70327 | −0.657189 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.30263 | 0.424923 | ||||||||
\(221\) | −2.71050 | −0.182328 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.258796 | −0.0173303 | −0.00866514 | − | 0.999962i | \(-0.502758\pi\) | ||||
−0.00866514 | + | 0.999962i | \(0.502758\pi\) | |||||||
\(224\) | 5.03409 | 0.336354 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 29.5576 | 1.96614 | ||||||||
\(227\) | 5.53304 | 0.367240 | 0.183620 | − | 0.982997i | \(-0.441218\pi\) | ||||
0.183620 | + | 0.982997i | \(0.441218\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.68175 | −0.111133 | −0.0555665 | − | 0.998455i | \(-0.517696\pi\) | ||||
−0.0555665 | + | 0.998455i | \(0.517696\pi\) | |||||||
\(230\) | 28.9705 | 1.91026 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.94751 | 0.324820 | ||||||||
\(233\) | −18.9196 | −1.23946 | −0.619732 | − | 0.784814i | \(-0.712759\pi\) | ||||
−0.619732 | + | 0.784814i | \(0.712759\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.1333 | 1.50905 | ||||||||
\(236\) | 10.4391 | 0.679525 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.78192 | −0.115505 | ||||||||
\(239\) | 21.0437 | 1.36121 | 0.680603 | − | 0.732653i | \(-0.261718\pi\) | ||||
0.680603 | + | 0.732653i | \(0.261718\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.7612 | 1.01527 | 0.507634 | − | 0.861573i | \(-0.330520\pi\) | ||||
0.507634 | + | 0.861573i | \(0.330520\pi\) | |||||||
\(242\) | 0.776424 | 0.0499104 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.53564 | 0.0983090 | ||||||||
\(245\) | −2.01516 | −0.128744 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.8102 | 1.19687 | ||||||||
\(248\) | 13.8744 | 0.881027 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −20.6013 | −1.30294 | ||||||||
\(251\) | 7.62207 | 0.481101 | 0.240550 | − | 0.970637i | \(-0.422672\pi\) | ||||
0.240550 | + | 0.970637i | \(0.422672\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.1261 | −1.70540 | ||||||||
\(254\) | 1.72132 | 0.108006 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.6132 | 1.16333 | ||||||||
\(257\) | 10.8383 | 0.676076 | 0.338038 | − | 0.941132i | \(-0.390237\pi\) | ||||
0.338038 | + | 0.941132i | \(0.390237\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.894661 | −0.0555915 | ||||||||
\(260\) | 5.08092 | 0.315105 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −23.5753 | −1.45649 | ||||||||
\(263\) | −4.06704 | −0.250784 | −0.125392 | − | 0.992107i | \(-0.540019\pi\) | ||||
−0.125392 | + | 0.992107i | \(0.540019\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.44433 | −0.150154 | ||||||||
\(266\) | 12.3661 | 0.758213 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.32918 | −0.386616 | ||||||||
\(269\) | −16.5919 | −1.01163 | −0.505813 | − | 0.862643i | \(-0.668808\pi\) | ||||
−0.505813 | + | 0.862643i | \(0.668808\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.2383 | 0.986406 | 0.493203 | − | 0.869914i | \(-0.335826\pi\) | ||||
0.493203 | + | 0.869914i | \(0.335826\pi\) | |||||||
\(272\) | −5.17459 | −0.313755 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.4173 | 1.47510 | ||||||||
\(275\) | 3.05018 | 0.183933 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.6414 | 1.24022 | 0.620111 | − | 0.784514i | \(-0.287088\pi\) | ||||
0.620111 | + | 0.784514i | \(0.287088\pi\) | |||||||
\(278\) | −30.1535 | −1.80849 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.59724 | −0.214976 | ||||||||
\(281\) | −13.2288 | −0.789163 | −0.394581 | − | 0.918861i | \(-0.629110\pi\) | ||||
−0.394581 | + | 0.918861i | \(0.629110\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.53483 | −0.329011 | −0.164506 | − | 0.986376i | \(-0.552603\pi\) | ||||
−0.164506 | + | 0.986376i | \(0.552603\pi\) | |||||||
\(284\) | −5.45868 | −0.323913 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.6383 | −0.865583 | ||||||||
\(287\) | −9.16796 | −0.541167 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9284 | −0.936962 | ||||||||
\(290\) | 9.61392 | 0.564549 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.5460 | 0.909759 | ||||||||
\(293\) | 28.9827 | 1.69319 | 0.846593 | − | 0.532241i | \(-0.178650\pi\) | ||||
0.846593 | + | 0.532241i | \(0.178650\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.8456 | −1.27190 | ||||||||
\(296\) | −1.59705 | −0.0928264 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.87014 | −0.282120 | ||||||||
\(299\) | −21.8679 | −1.26466 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.1174 | 0.640794 | ||||||||
\(302\) | 1.74684 | 0.100520 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 35.9104 | 2.05960 | ||||||||
\(305\) | −3.21359 | −0.184010 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.1303 | −0.863530 | −0.431765 | − | 0.901986i | \(-0.642109\pi\) | ||||
−0.431765 | + | 0.901986i | \(0.642109\pi\) | |||||||
\(308\) | −3.12760 | −0.178212 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 26.9605 | 1.53126 | ||||||||
\(311\) | 7.21480 | 0.409114 | 0.204557 | − | 0.978855i | \(-0.434425\pi\) | ||||
0.204557 | + | 0.978855i | \(0.434425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.70534 | −0.322485 | −0.161242 | − | 0.986915i | \(-0.551550\pi\) | ||||
−0.161242 | + | 0.986915i | \(0.551550\pi\) | |||||||
\(314\) | 15.1806 | 0.856690 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.30263 | 0.354550 | ||||||||
\(317\) | 5.85063 | 0.328604 | 0.164302 | − | 0.986410i | \(-0.447463\pi\) | ||||
0.164302 | + | 0.986410i | \(0.447463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00186 | −0.504007 | ||||||||
\(320\) | −2.68410 | −0.150046 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.3762 | −0.801157 | ||||||||
\(323\) | −7.43694 | −0.413802 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.45893 | 0.136397 | ||||||||
\(326\) | 31.1377 | 1.72456 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16.3656 | −0.903638 | ||||||||
\(329\) | −11.4796 | −0.632891 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.3118 | −1.06147 | −0.530736 | − | 0.847537i | \(-0.678084\pi\) | ||||
−0.530736 | + | 0.847537i | \(0.678084\pi\) | |||||||
\(332\) | 15.0472 | 0.825821 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.89581 | 0.213169 | ||||||||
\(335\) | 13.2449 | 0.723648 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.41941 | 0.0773203 | 0.0386602 | − | 0.999252i | \(-0.487691\pi\) | ||||
0.0386602 | + | 0.999252i | \(0.487691\pi\) | |||||||
\(338\) | 10.5764 | 0.575280 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.00883 | −0.108944 | ||||||||
\(341\) | −25.2441 | −1.36705 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 19.8455 | 1.07000 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −39.2243 | −2.10871 | ||||||||
\(347\) | 14.9267 | 0.801307 | 0.400653 | − | 0.916230i | \(-0.368783\pi\) | ||||
0.400653 | + | 0.916230i | \(0.368783\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.7344 | −1.05636 | −0.528180 | − | 0.849132i | \(-0.677125\pi\) | ||||
−0.528180 | + | 0.849132i | \(0.677125\pi\) | |||||||
\(350\) | 1.61653 | 0.0864071 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.3503 | −0.871473 | ||||||||
\(353\) | −0.300628 | −0.0160008 | −0.00800040 | − | 0.999968i | \(-0.502547\pi\) | ||||
−0.00800040 | + | 0.999968i | \(0.502547\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.4233 | 0.606284 | ||||||||
\(356\) | 2.12279 | 0.112508 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.24068 | 0.382682 | ||||||||
\(359\) | −29.5700 | −1.56065 | −0.780324 | − | 0.625376i | \(-0.784946\pi\) | ||||
−0.780324 | + | 0.625376i | \(0.784946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.6106 | 1.71635 | ||||||||
\(362\) | −12.2045 | −0.641457 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.52134 | −0.132154 | ||||||||
\(365\) | −32.5327 | −1.70284 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.98916 | −0.260432 | −0.130216 | − | 0.991486i | \(-0.541567\pi\) | ||||
−0.130216 | + | 0.991486i | \(0.541567\pi\) | |||||||
\(368\) | −41.7478 | −2.17625 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.10335 | −0.161336 | ||||||||
\(371\) | 1.21297 | 0.0629743 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.4646 | 1.31851 | 0.659255 | − | 0.751920i | \(-0.270872\pi\) | ||||
0.659255 | + | 0.751920i | \(0.270872\pi\) | |||||||
\(374\) | 5.78751 | 0.299265 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.4921 | −1.05680 | ||||||||
\(377\) | −7.25692 | −0.373751 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6469 | −0.649630 | −0.324815 | − | 0.945778i | \(-0.605302\pi\) | ||||
−0.324815 | + | 0.945778i | \(0.605302\pi\) | |||||||
\(380\) | 13.9408 | 0.715147 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 38.8073 | 1.98555 | ||||||||
\(383\) | 12.4457 | 0.635946 | 0.317973 | − | 0.948100i | \(-0.396998\pi\) | ||||
0.317973 | + | 0.948100i | \(0.396998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.54507 | 0.333568 | ||||||||
\(386\) | 12.0234 | 0.611973 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.6690 | −0.846240 | ||||||||
\(389\) | 14.3780 | 0.728991 | 0.364496 | − | 0.931205i | \(-0.381241\pi\) | ||||
0.364496 | + | 0.931205i | \(0.381241\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.64585 | 0.437239 | ||||||||
\(392\) | 1.78509 | 0.0901604 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23.3304 | 1.17537 | ||||||||
\(395\) | −13.1894 | −0.663629 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.33916 | 0.217776 | 0.108888 | − | 0.994054i | \(-0.465271\pi\) | ||||
0.108888 | + | 0.994054i | \(0.465271\pi\) | |||||||
\(398\) | −46.7728 | −2.34451 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.69431 | 0.234715 | ||||||||
\(401\) | 5.64032 | 0.281664 | 0.140832 | − | 0.990033i | \(-0.455022\pi\) | ||||
0.140832 | + | 0.990033i | \(0.455022\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.3508 | −1.01374 | ||||||||
\(404\) | 0.529342 | 0.0263357 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.77079 | −0.236770 | ||||||||
\(407\) | 2.90578 | 0.144034 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.85710 | −0.0918276 | −0.0459138 | − | 0.998945i | \(-0.514620\pi\) | ||||
−0.0459138 | + | 0.998945i | \(0.514620\pi\) | |||||||
\(410\) | −31.8013 | −1.57056 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.30101 | −0.162629 | ||||||||
\(413\) | 10.8406 | 0.533432 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31.4889 | −1.54573 | ||||||||
\(416\) | −13.1809 | −0.646248 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −40.1640 | −1.96448 | ||||||||
\(419\) | 1.24203 | 0.0606774 | 0.0303387 | − | 0.999540i | \(-0.490341\pi\) | ||||
0.0303387 | + | 0.999540i | \(0.490341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4574 | −0.509661 | −0.254831 | − | 0.966986i | \(-0.582020\pi\) | ||||
−0.254831 | + | 0.966986i | \(0.582020\pi\) | |||||||
\(422\) | −15.0176 | −0.731046 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.16526 | 0.105154 | ||||||||
\(425\) | −0.972178 | −0.0471575 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.59471 | 0.0771733 | ||||||||
\(428\) | −2.82373 | −0.136490 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 38.5634 | 1.85969 | ||||||||
\(431\) | −17.3256 | −0.834543 | −0.417272 | − | 0.908782i | \(-0.637014\pi\) | ||||
−0.417272 | + | 0.908782i | \(0.637014\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.4038 | −1.89362 | −0.946812 | − | 0.321787i | \(-0.895716\pi\) | ||||
−0.946812 | + | 0.321787i | \(0.895716\pi\) | |||||||
\(434\) | −13.3788 | −0.642205 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.42829 | 0.259968 | ||||||||
\(437\) | −60.0001 | −2.87020 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.2773 | −1.44506 | −0.722529 | − | 0.691341i | \(-0.757020\pi\) | ||||
−0.722529 | + | 0.691341i | \(0.757020\pi\) | |||||||
\(440\) | 11.6835 | 0.556990 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.66565 | 0.221922 | ||||||||
\(443\) | −13.0145 | −0.618338 | −0.309169 | − | 0.951007i | \(-0.600051\pi\) | ||||
−0.309169 | + | 0.951007i | \(0.600051\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.44232 | −0.210586 | ||||||||
\(446\) | 0.445472 | 0.0210937 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.33195 | 0.0629289 | ||||||||
\(449\) | −12.3009 | −0.580514 | −0.290257 | − | 0.956949i | \(-0.593741\pi\) | ||||
−0.290257 | + | 0.956949i | \(0.593741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.7767 | 1.40213 | ||||||||
\(452\) | −16.5354 | −0.777758 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.52415 | −0.446990 | ||||||||
\(455\) | 5.27637 | 0.247360 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.9505 | −0.512244 | −0.256122 | − | 0.966644i | \(-0.582445\pi\) | ||||
−0.256122 | + | 0.966644i | \(0.582445\pi\) | |||||||
\(458\) | 2.89483 | 0.135267 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16.2069 | −0.755651 | ||||||||
\(461\) | −10.3995 | −0.484355 | −0.242177 | − | 0.970232i | \(-0.577862\pi\) | ||||
−0.242177 | + | 0.970232i | \(0.577862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.5446 | 0.629470 | 0.314735 | − | 0.949180i | \(-0.398084\pi\) | ||||
0.314735 | + | 0.949180i | \(0.398084\pi\) | |||||||
\(464\) | −13.8541 | −0.643161 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 32.5668 | 1.50863 | ||||||||
\(467\) | −32.5621 | −1.50679 | −0.753397 | − | 0.657566i | \(-0.771586\pi\) | ||||
−0.753397 | + | 0.657566i | \(0.771586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.57264 | −0.303496 | ||||||||
\(470\) | −39.8199 | −1.83675 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19.3514 | 0.890721 | ||||||||
\(473\) | −36.1082 | −1.66026 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.74668 | 0.309559 | ||||||||
\(476\) | 0.996855 | 0.0456908 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −36.2231 | −1.65681 | ||||||||
\(479\) | −16.0336 | −0.732593 | −0.366296 | − | 0.930498i | \(-0.619374\pi\) | ||||
−0.366296 | + | 0.930498i | \(0.619374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.34252 | 0.106810 | ||||||||
\(482\) | −27.1301 | −1.23574 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.434354 | −0.0197433 | ||||||||
\(485\) | 34.8828 | 1.58395 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.6892 | 0.575003 | 0.287502 | − | 0.957780i | \(-0.407175\pi\) | ||||
0.287502 | + | 0.957780i | \(0.407175\pi\) | |||||||
\(488\) | 2.84669 | 0.128864 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.46875 | 0.156702 | ||||||||
\(491\) | −20.3662 | −0.919112 | −0.459556 | − | 0.888149i | \(-0.651991\pi\) | ||||
−0.459556 | + | 0.888149i | \(0.651991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.86914 | 0.129220 | ||||||||
\(494\) | −32.3785 | −1.45678 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −38.8514 | −1.74448 | ||||||||
\(497\) | −5.66866 | −0.254274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.99576 | −0.223641 | −0.111820 | − | 0.993728i | \(-0.535668\pi\) | ||||
−0.111820 | + | 0.993728i | \(0.535668\pi\) | |||||||
\(500\) | 11.5250 | 0.515412 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.1201 | −0.585577 | ||||||||
\(503\) | −10.9715 | −0.489195 | −0.244598 | − | 0.969625i | \(-0.578656\pi\) | ||||
−0.244598 | + | 0.969625i | \(0.578656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.10774 | −0.0492939 | ||||||||
\(506\) | 46.6928 | 2.07575 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.962958 | −0.0427244 | ||||||||
\(509\) | 38.3271 | 1.69882 | 0.849409 | − | 0.527734i | \(-0.176958\pi\) | ||||
0.849409 | + | 0.527734i | \(0.176958\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.1440 | 0.714167 | ||||||||
\(512\) | −7.31758 | −0.323394 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.6563 | −0.822893 | ||||||||
\(515\) | 6.90796 | 0.304401 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.2848 | 1.63978 | ||||||||
\(518\) | 1.54000 | 0.0676638 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.41877 | 0.413040 | ||||||||
\(521\) | 21.3843 | 0.936862 | 0.468431 | − | 0.883500i | \(-0.344819\pi\) | ||||
0.468431 | + | 0.883500i | \(0.344819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.0915 | 1.18463 | 0.592315 | − | 0.805707i | \(-0.298214\pi\) | ||||
0.592315 | + | 0.805707i | \(0.298214\pi\) | |||||||
\(524\) | 13.1887 | 0.576152 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.00069 | 0.305245 | ||||||||
\(527\) | 8.04601 | 0.350490 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.7535 | 2.03276 | ||||||||
\(530\) | 4.20749 | 0.182762 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.91794 | −0.299931 | ||||||||
\(533\) | 24.0048 | 1.03976 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.90915 | 0.255475 | ||||||||
\(536\) | −11.7327 | −0.506777 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 28.5601 | 1.23131 | ||||||||
\(539\) | −3.24791 | −0.139898 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.1632 | −1.85573 | −0.927865 | − | 0.372917i | \(-0.878358\pi\) | ||||
−0.927865 | + | 0.372917i | \(0.878358\pi\) | |||||||
\(542\) | −27.9514 | −1.20061 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.21130 | 0.223432 | ||||||||
\(545\) | −11.3597 | −0.486595 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.41592 | 0.231568 | 0.115784 | − | 0.993274i | \(-0.463062\pi\) | ||||
0.115784 | + | 0.993274i | \(0.463062\pi\) | |||||||
\(548\) | −13.6597 | −0.583515 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.25035 | −0.223876 | ||||||||
\(551\) | −19.9112 | −0.848245 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.54507 | 0.278325 | ||||||||
\(554\) | −35.5305 | −1.50955 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.8687 | 0.715393 | ||||||||
\(557\) | −14.4602 | −0.612699 | −0.306350 | − | 0.951919i | \(-0.599108\pi\) | ||||
−0.306350 | + | 0.951919i | \(0.599108\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.1090 | −1.23118 | ||||||||
\(560\) | 10.0730 | 0.425664 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.7710 | 0.960537 | ||||||||
\(563\) | 1.35164 | 0.0569648 | 0.0284824 | − | 0.999594i | \(-0.490933\pi\) | ||||
0.0284824 | + | 0.999594i | \(0.490933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.6032 | 1.45577 | ||||||||
\(566\) | 9.52724 | 0.400460 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.1190 | −0.424585 | ||||||||
\(569\) | −19.4893 | −0.817034 | −0.408517 | − | 0.912751i | \(-0.633954\pi\) | ||||
−0.408517 | + | 0.912751i | \(0.633954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.57923 | 0.0660885 | 0.0330443 | − | 0.999454i | \(-0.489480\pi\) | ||||
0.0330443 | + | 0.999454i | \(0.489480\pi\) | |||||||
\(572\) | 8.18911 | 0.342404 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.7810 | 0.658687 | ||||||||
\(575\) | −7.84339 | −0.327092 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.7980 | −1.61518 | −0.807591 | − | 0.589743i | \(-0.799229\pi\) | ||||
−0.807591 | + | 0.589743i | \(0.799229\pi\) | |||||||
\(578\) | 27.4179 | 1.14043 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.37830 | −0.223322 | ||||||||
\(581\) | 15.6260 | 0.648275 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.93962 | −0.163162 | ||||||||
\(584\) | 28.8184 | 1.19251 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −49.8886 | −2.06088 | ||||||||
\(587\) | −7.94491 | −0.327922 | −0.163961 | − | 0.986467i | \(-0.552427\pi\) | ||||
−0.163961 | + | 0.986467i | \(0.552427\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −55.8374 | −2.30074 | ||||||||
\(590\) | 37.6034 | 1.54811 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.47208 | 0.183801 | ||||||||
\(593\) | −35.2002 | −1.44550 | −0.722749 | − | 0.691111i | \(-0.757122\pi\) | ||||
−0.722749 | + | 0.691111i | \(0.757122\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.08610 | −0.0855217 | ||||||||
\(596\) | 2.72450 | 0.111600 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 37.6418 | 1.53929 | ||||||||
\(599\) | −30.3691 | −1.24085 | −0.620425 | − | 0.784266i | \(-0.713040\pi\) | ||||
−0.620425 | + | 0.784266i | \(0.713040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.4918 | −1.65170 | −0.825848 | − | 0.563893i | \(-0.809303\pi\) | ||||
−0.825848 | + | 0.563893i | \(0.809303\pi\) | |||||||
\(602\) | −19.1366 | −0.779950 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.977235 | −0.0397631 | ||||||||
\(605\) | 0.908963 | 0.0369546 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.4539 | 0.708432 | 0.354216 | − | 0.935164i | \(-0.384748\pi\) | ||||
0.354216 | + | 0.935164i | \(0.384748\pi\) | |||||||
\(608\) | −36.1652 | −1.46669 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.53164 | 0.223969 | ||||||||
\(611\) | 30.0574 | 1.21599 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.64856 | 0.349312 | 0.174656 | − | 0.984630i | \(-0.444119\pi\) | ||||
0.174656 | + | 0.984630i | \(0.444119\pi\) | |||||||
\(614\) | 26.0441 | 1.05105 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.79780 | −0.233600 | ||||||||
\(617\) | 15.7048 | 0.632251 | 0.316125 | − | 0.948717i | \(-0.397618\pi\) | ||||
0.316125 | + | 0.948717i | \(0.397618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.6788 | −0.429217 | −0.214609 | − | 0.976700i | \(-0.568848\pi\) | ||||
−0.214609 | + | 0.976700i | \(0.568848\pi\) | |||||||
\(620\) | −15.0825 | −0.605728 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.4190 | −0.497957 | ||||||||
\(623\) | 2.20445 | 0.0883193 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.4225 | −0.776898 | ||||||||
\(626\) | 9.82074 | 0.392516 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.49246 | −0.338886 | ||||||||
\(629\) | −0.926154 | −0.0369282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.18368 | −0.285978 | −0.142989 | − | 0.989724i | \(-0.545671\pi\) | ||||
−0.142989 | + | 0.989724i | \(0.545671\pi\) | |||||||
\(632\) | 11.6835 | 0.464745 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.0708 | −0.399964 | ||||||||
\(635\) | 2.01516 | 0.0799693 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.61833 | −0.103742 | ||||||||
\(638\) | 15.4951 | 0.613457 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.9092 | 0.984624 | ||||||||
\(641\) | −0.0204183 | −0.000806474 0 | −0.000403237 | − | 1.00000i | \(-0.500128\pi\) | ||||
−0.000403237 | 1.00000i | \(0.500128\pi\) | ||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.9366 | −1.57495 | −0.787473 | − | 0.616349i | \(-0.788611\pi\) | ||||
−0.787473 | + | 0.616349i | \(0.788611\pi\) | |||||||
\(644\) | 8.04248 | 0.316918 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.8014 | 0.503664 | ||||||||
\(647\) | 16.2781 | 0.639957 | 0.319979 | − | 0.947425i | \(-0.396324\pi\) | ||||
0.319979 | + | 0.947425i | \(0.396324\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.2094 | −1.38209 | ||||||||
\(650\) | −4.23261 | −0.166017 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.4193 | −0.682194 | ||||||||
\(653\) | −42.9659 | −1.68138 | −0.840692 | − | 0.541514i | \(-0.817851\pi\) | ||||
−0.840692 | + | 0.541514i | \(0.817851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.5998 | −1.07841 | ||||||||
\(656\) | 45.8272 | 1.78925 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 19.7601 | 0.770330 | ||||||||
\(659\) | −28.4514 | −1.10831 | −0.554156 | − | 0.832413i | \(-0.686959\pi\) | ||||
−0.554156 | + | 0.832413i | \(0.686959\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.86659 | 0.228184 | 0.114092 | − | 0.993470i | \(-0.463604\pi\) | ||||
0.114092 | + | 0.993470i | \(0.463604\pi\) | |||||||
\(662\) | 33.2418 | 1.29198 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27.8937 | 1.08249 | ||||||||
\(665\) | 14.4770 | 0.561395 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.1478 | 0.896288 | ||||||||
\(668\) | −2.17942 | −0.0843245 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −22.7988 | −0.880796 | ||||||||
\(671\) | −5.17947 | −0.199951 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.2506 | −0.857697 | −0.428849 | − | 0.903376i | \(-0.641081\pi\) | ||||
−0.428849 | + | 0.903376i | \(0.641081\pi\) | |||||||
\(674\) | −2.44327 | −0.0941112 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.91674 | −0.227567 | ||||||||
\(677\) | 6.29073 | 0.241772 | 0.120886 | − | 0.992666i | \(-0.461426\pi\) | ||||
0.120886 | + | 0.992666i | \(0.461426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.3102 | −0.664304 | ||||||||
\(680\) | −3.72387 | −0.142804 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 43.4533 | 1.66391 | ||||||||
\(683\) | −1.06197 | −0.0406352 | −0.0203176 | − | 0.999794i | \(-0.506468\pi\) | ||||
−0.0203176 | + | 0.999794i | \(0.506468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.5854 | 1.09219 | ||||||||
\(686\) | −1.72132 | −0.0657205 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −55.5716 | −2.11865 | ||||||||
\(689\) | −3.17596 | −0.120994 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.3544 | −0.850402 | −0.425201 | − | 0.905099i | \(-0.639797\pi\) | ||||
−0.425201 | + | 0.905099i | \(0.639797\pi\) | |||||||
\(692\) | 21.9432 | 0.834154 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.6937 | −0.975319 | ||||||||
\(695\) | −35.3008 | −1.33904 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.49068 | −0.359485 | ||||||||
\(698\) | 33.9694 | 1.28576 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.904333 | −0.0341806 | ||||||||
\(701\) | −10.9852 | −0.414907 | −0.207454 | − | 0.978245i | \(-0.566518\pi\) | ||||
−0.207454 | + | 0.978245i | \(0.566518\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.42729 | 0.242410 | ||||||||
\(704\) | −4.32607 | −0.163045 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.517478 | 0.0194755 | ||||||||
\(707\) | 0.549704 | 0.0206737 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.1642 | −0.757283 | −0.378641 | − | 0.925543i | \(-0.623609\pi\) | ||||
−0.378641 | + | 0.925543i | \(0.623609\pi\) | |||||||
\(710\) | −19.6631 | −0.737945 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.93512 | 0.147475 | ||||||||
\(713\) | 64.9140 | 2.43105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.1372 | −0.640894 | ||||||||
\(716\) | −4.05064 | −0.151380 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 50.8996 | 1.89956 | ||||||||
\(719\) | −6.75963 | −0.252092 | −0.126046 | − | 0.992024i | \(-0.540229\pi\) | ||||
−0.126046 | + | 0.992024i | \(0.540229\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.42799 | −0.127665 | ||||||||
\(722\) | −56.1334 | −2.08907 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.82757 | 0.253745 | ||||||||
\(725\) | −2.60285 | −0.0966673 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.42574 | −0.0899657 | −0.0449829 | − | 0.998988i | \(-0.514323\pi\) | ||||
−0.0449829 | + | 0.998988i | \(0.514323\pi\) | |||||||
\(728\) | −4.67395 | −0.173228 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 55.9994 | 2.07263 | ||||||||
\(731\) | 11.5087 | 0.425665 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.0765 | 1.51720 | 0.758598 | − | 0.651559i | \(-0.225885\pi\) | ||||
0.758598 | + | 0.651559i | \(0.225885\pi\) | |||||||
\(734\) | 8.58796 | 0.316988 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 42.0440 | 1.54976 | ||||||||
\(737\) | 21.3474 | 0.786340 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.4278 | 1.19287 | 0.596437 | − | 0.802660i | \(-0.296582\pi\) | ||||
0.596437 | + | 0.802660i | \(0.296582\pi\) | |||||||
\(740\) | 1.73610 | 0.0638205 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.08792 | −0.0766498 | ||||||||
\(743\) | 49.6144 | 1.82017 | 0.910087 | − | 0.414417i | \(-0.136014\pi\) | ||||
0.910087 | + | 0.414417i | \(0.136014\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.70150 | −0.208887 | ||||||||
\(746\) | −43.8329 | −1.60484 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.23770 | −0.118382 | ||||||||
\(749\) | −2.93235 | −0.107146 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.6044 | −0.386959 | −0.193480 | − | 0.981104i | \(-0.561977\pi\) | ||||
−0.193480 | + | 0.981104i | \(0.561977\pi\) | |||||||
\(752\) | 57.3823 | 2.09252 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.4915 | 0.454914 | ||||||||
\(755\) | 2.04504 | 0.0744266 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.5334 | −0.855336 | −0.427668 | − | 0.903936i | \(-0.640665\pi\) | ||||
−0.427668 | + | 0.903936i | \(0.640665\pi\) | |||||||
\(758\) | 21.7695 | 0.790703 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 25.8427 | 0.937415 | ||||||||
\(761\) | −4.46951 | −0.162020 | −0.0810098 | − | 0.996713i | \(-0.525815\pi\) | ||||
−0.0810098 | + | 0.996713i | \(0.525815\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.63710 | 0.204077 | ||||||||
\(764\) | −21.7099 | −0.785436 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.4231 | −0.774049 | ||||||||
\(767\) | −28.3843 | −1.02490 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.0331 | −0.974838 | −0.487419 | − | 0.873168i | \(-0.662062\pi\) | ||||
−0.487419 | + | 0.873168i | \(0.662062\pi\) | |||||||
\(770\) | −11.2662 | −0.406005 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.72622 | −0.242082 | ||||||||
\(773\) | −45.1300 | −1.62321 | −0.811607 | − | 0.584204i | \(-0.801407\pi\) | ||||
−0.811607 | + | 0.584204i | \(0.801407\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.29922 | −0.262196 | ||||||||
\(776\) | −30.9002 | −1.10925 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.7491 | −0.887299 | ||||||||
\(779\) | 65.8631 | 2.35979 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.4113 | 0.658808 | ||||||||
\(782\) | −14.8823 | −0.532190 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.99863 | −0.178522 | ||||||||
\(785\) | 17.7720 | 0.634310 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.14036 | −0.111942 | −0.0559709 | − | 0.998432i | \(-0.517825\pi\) | ||||
−0.0559709 | + | 0.998432i | \(0.517825\pi\) | |||||||
\(788\) | −13.0517 | −0.464947 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22.7032 | 0.807743 | ||||||||
\(791\) | −17.1714 | −0.610545 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.17547 | −0.148275 | ||||||||
\(794\) | −7.46911 | −0.265069 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.1660 | 0.927430 | ||||||||
\(797\) | 24.8520 | 0.880304 | 0.440152 | − | 0.897923i | \(-0.354925\pi\) | ||||
0.440152 | + | 0.897923i | \(0.354925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.8837 | −0.420415 | ||||||||
\(800\) | −4.72761 | −0.167146 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.70883 | −0.342831 | ||||||||
\(803\) | −52.4342 | −1.85036 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.8303 | −0.593192 | ||||||||
\(806\) | 35.0303 | 1.23389 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.981268 | 0.0345209 | ||||||||
\(809\) | 18.8062 | 0.661191 | 0.330595 | − | 0.943773i | \(-0.392750\pi\) | ||||
0.330595 | + | 0.943773i | \(0.392750\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.4579 | 0.858833 | 0.429416 | − | 0.903107i | \(-0.358719\pi\) | ||||
0.429416 | + | 0.903107i | \(0.358719\pi\) | |||||||
\(812\) | 2.66892 | 0.0936606 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.00179 | −0.175313 | ||||||||
\(815\) | 36.4531 | 1.27690 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −79.8677 | −2.79422 | ||||||||
\(818\) | 3.19667 | 0.111769 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.7906 | 0.621274 | ||||||||
\(821\) | −22.0065 | −0.768031 | −0.384015 | − | 0.923327i | \(-0.625459\pi\) | ||||
−0.384015 | + | 0.923327i | \(0.625459\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.3836 | 0.780243 | 0.390122 | − | 0.920763i | \(-0.372433\pi\) | ||||
0.390122 | + | 0.920763i | \(0.372433\pi\) | |||||||
\(824\) | −6.11926 | −0.213174 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.6602 | −0.649272 | ||||||||
\(827\) | −42.9231 | −1.49258 | −0.746292 | − | 0.665619i | \(-0.768167\pi\) | ||||
−0.746292 | + | 0.665619i | \(0.768167\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.3720 | −1.22852 | −0.614261 | − | 0.789103i | \(-0.710546\pi\) | ||||
−0.614261 | + | 0.789103i | \(0.710546\pi\) | |||||||
\(830\) | 54.2026 | 1.88140 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.48750 | −0.120907 | ||||||||
\(833\) | 1.03520 | 0.0358676 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.56084 | 0.157834 | ||||||||
\(836\) | 22.4689 | 0.777102 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.13795 | −0.0738541 | ||||||||
\(839\) | −33.4309 | −1.15416 | −0.577082 | − | 0.816686i | \(-0.695809\pi\) | ||||
−0.577082 | + | 0.816686i | \(0.695809\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.3183 | −0.735115 | ||||||||
\(842\) | 18.0005 | 0.620340 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.40129 | 0.289184 | ||||||||
\(845\) | 12.3818 | 0.425948 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.451062 | −0.0154987 | ||||||||
\(848\) | −6.06319 | −0.208211 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.67343 | 0.0573983 | ||||||||
\(851\) | −7.47207 | −0.256139 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.3404 | −0.936119 | −0.468060 | − | 0.883697i | \(-0.655047\pi\) | ||||
−0.468060 | + | 0.883697i | \(0.655047\pi\) | |||||||
\(854\) | −2.74501 | −0.0939322 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.23449 | −0.178911 | ||||||||
\(857\) | 28.1895 | 0.962936 | 0.481468 | − | 0.876464i | \(-0.340104\pi\) | ||||
0.481468 | + | 0.876464i | \(0.340104\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.0793 | −0.889813 | −0.444907 | − | 0.895577i | \(-0.646763\pi\) | ||||
−0.444907 | + | 0.895577i | \(0.646763\pi\) | |||||||
\(860\) | −21.5734 | −0.735648 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.8229 | 1.01577 | ||||||||
\(863\) | −19.7358 | −0.671813 | −0.335907 | − | 0.941895i | \(-0.609043\pi\) | ||||
−0.335907 | + | 0.941895i | \(0.609043\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −45.9200 | −1.56133 | ||||||||
\(866\) | 67.8267 | 2.30484 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.48451 | 0.254041 | ||||||||
\(869\) | −21.2578 | −0.721122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.2094 | 0.583117 | ||||||||
\(872\) | 10.0627 | 0.340766 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 103.280 | 3.49349 | ||||||||
\(875\) | 11.9683 | 0.404602 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.40535 | 0.216293 | 0.108147 | − | 0.994135i | \(-0.465508\pi\) | ||||
0.108147 | + | 0.994135i | \(0.465508\pi\) | |||||||
\(878\) | 52.1171 | 1.75887 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −32.7164 | −1.10287 | ||||||||
\(881\) | 52.8133 | 1.77933 | 0.889663 | − | 0.456618i | \(-0.150939\pi\) | ||||
0.889663 | + | 0.456618i | \(0.150939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.1835 | 1.48689 | 0.743446 | − | 0.668796i | \(-0.233190\pi\) | ||||
0.743446 | + | 0.668796i | \(0.233190\pi\) | |||||||
\(884\) | −2.61010 | −0.0877871 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.4022 | 0.752616 | ||||||||
\(887\) | −39.5788 | −1.32893 | −0.664463 | − | 0.747322i | \(-0.731340\pi\) | ||||
−0.664463 | + | 0.747322i | \(0.731340\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 7.64667 | 0.256317 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.249210 | −0.00834417 | ||||||||
\(893\) | 82.4701 | 2.75976 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.47669 | 0.283345 | ||||||||
\(896\) | −12.3609 | −0.412949 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.1738 | 0.706578 | ||||||||
\(899\) | 21.5419 | 0.718462 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.25567 | 0.0418324 | ||||||||
\(902\) | −51.2554 | −1.70662 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30.6524 | −1.01949 | ||||||||
\(905\) | −14.2879 | −0.474946 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.5378 | −1.01399 | −0.506995 | − | 0.861949i | \(-0.669244\pi\) | ||||
−0.506995 | + | 0.861949i | \(0.669244\pi\) | |||||||
\(908\) | 5.32808 | 0.176819 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.08234 | −0.301077 | ||||||||
\(911\) | 27.6405 | 0.915770 | 0.457885 | − | 0.889012i | \(-0.348607\pi\) | ||||
0.457885 | + | 0.889012i | \(0.348607\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.7518 | −1.67964 | ||||||||
\(914\) | 18.8494 | 0.623483 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.61945 | −0.0535082 | ||||||||
\(917\) | 13.6960 | 0.452283 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.2756 | −1.82337 | −0.911687 | − | 0.410885i | \(-0.865220\pi\) | ||||
−0.911687 | + | 0.410885i | \(0.865220\pi\) | |||||||
\(920\) | −30.0436 | −0.990508 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.9010 | 0.589537 | ||||||||
\(923\) | 14.8424 | 0.488545 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.840193 | 0.0276254 | ||||||||
\(926\) | −23.3146 | −0.766166 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.9524 | 0.458010 | ||||||||
\(929\) | −35.8329 | −1.17564 | −0.587820 | − | 0.808991i | \(-0.700014\pi\) | ||||
−0.587820 | + | 0.808991i | \(0.700014\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.18405 | −0.235448 | ||||||||
\(932\) | −18.2188 | −0.596776 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 56.0499 | 1.83401 | ||||||||
\(935\) | 6.77547 | 0.221581 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.3521 | −0.534199 | −0.267100 | − | 0.963669i | \(-0.586065\pi\) | ||||
−0.267100 | + | 0.963669i | \(0.586065\pi\) | |||||||
\(938\) | 11.3136 | 0.369404 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 22.2764 | 0.726575 | ||||||||
\(941\) | 41.0319 | 1.33760 | 0.668801 | − | 0.743441i | \(-0.266808\pi\) | ||||
0.668801 | + | 0.743441i | \(0.266808\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −76.5694 | −2.49344 | ||||||||
\(944\) | −54.1882 | −1.76368 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 62.1540 | 2.02080 | ||||||||
\(947\) | −18.8533 | −0.612650 | −0.306325 | − | 0.951927i | \(-0.599099\pi\) | ||||
−0.306325 | + | 0.951927i | \(0.599099\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.2703 | −1.37215 | ||||||||
\(950\) | −11.6132 | −0.376783 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.84792 | 0.0598915 | ||||||||
\(953\) | 30.0702 | 0.974069 | 0.487034 | − | 0.873383i | \(-0.338079\pi\) | ||||
0.487034 | + | 0.873383i | \(0.338079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.4319 | 1.47014 | ||||||||
\(956\) | 20.2642 | 0.655392 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.5990 | 0.891683 | ||||||||
\(959\) | −14.1852 | −0.458063 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.4104 | 0.948722 | ||||||||
\(962\) | −4.03224 | −0.130005 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.1774 | 0.488830 | ||||||||
\(965\) | 14.0758 | 0.453117 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.0543 | −0.580587 | −0.290294 | − | 0.956938i | \(-0.593753\pi\) | ||||
−0.290294 | + | 0.956938i | \(0.593753\pi\) | |||||||
\(968\) | −0.805184 | −0.0258796 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −60.0447 | −1.92792 | ||||||||
\(971\) | −11.1615 | −0.358189 | −0.179094 | − | 0.983832i | \(-0.557317\pi\) | ||||
−0.179094 | + | 0.983832i | \(0.557317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.5176 | 0.561588 | ||||||||
\(974\) | −21.8423 | −0.699871 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.97135 | −0.255157 | ||||||||
\(977\) | −0.715429 | −0.0228886 | −0.0114443 | − | 0.999935i | \(-0.503643\pi\) | ||||
−0.0114443 | + | 0.999935i | \(0.503643\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.15985 | −0.228830 | ||||||||
\(980\) | −1.94052 | −0.0619875 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 35.0568 | 1.11871 | ||||||||
\(983\) | −11.1984 | −0.357175 | −0.178587 | − | 0.983924i | \(-0.557153\pi\) | ||||
−0.178587 | + | 0.983924i | \(0.557153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.3130 | 0.870264 | ||||||||
\(986\) | −4.93873 | −0.157281 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.1135 | 0.576266 | ||||||||
\(989\) | 92.8506 | 2.95248 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.0280 | 0.477381 | 0.238690 | − | 0.971096i | \(-0.423282\pi\) | ||||
0.238690 | + | 0.971096i | \(0.423282\pi\) | |||||||
\(992\) | 39.1270 | 1.24228 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.75760 | 0.309492 | ||||||||
\(995\) | −54.7571 | −1.73592 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.8352 | −0.406496 | −0.203248 | − | 0.979127i | \(-0.565150\pi\) | ||||
−0.203248 | + | 0.979127i | \(0.565150\pi\) | |||||||
\(998\) | 8.59932 | 0.272207 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.w.1.8 | 20 | ||
3.2 | odd | 2 | 889.2.a.d.1.13 | ✓ | 20 | ||
21.20 | even | 2 | 6223.2.a.l.1.13 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.d.1.13 | ✓ | 20 | 3.2 | odd | 2 | ||
6223.2.a.l.1.13 | 20 | 21.20 | even | 2 | |||
8001.2.a.w.1.8 | 20 | 1.1 | even | 1 | trivial |