Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(181,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("360.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.k (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 3x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.2 | ||
Root | \(-1.32288 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.181 |
Dual form | 360.2.k.d.181.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32288 | + | 0.500000i | −0.935414 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.50000 | − | 1.32288i | 0.750000 | − | 0.661438i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | −1.32288 | + | 2.50000i | −0.467707 | + | 0.883883i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.500000 | + | 1.32288i | 0.158114 | + | 0.418330i | ||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −2.64575 | + | 1.00000i | −0.707107 | + | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 3.96863i | 0.125000 | − | 0.992157i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.29150i | − | 1.21395i | −0.794719 | − | 0.606977i | \(-0.792382\pi\) | ||
0.794719 | − | 0.606977i | \(-0.207618\pi\) | |||||||
\(20\) | −1.32288 | − | 1.50000i | −0.295804 | − | 0.335410i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | + | 2.64575i | 0.213201 | + | 0.564076i | ||||
\(23\) | 5.29150 | 1.10335 | 0.551677 | − | 0.834058i | \(-0.313988\pi\) | ||||
0.551677 | + | 0.834058i | \(0.313988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.00000 | − | 2.64575i | 0.566947 | − | 0.500000i | ||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 1.32288 | + | 5.50000i | 0.233854 | + | 0.972272i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 2.00000i | − | 0.338062i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5830i | 1.73984i | 0.493197 | + | 0.869918i | \(0.335828\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 2.64575 | + | 7.00000i | 0.429198 | + | 1.13555i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.50000 | + | 1.32288i | 0.395285 | + | 0.209165i | ||||
\(41\) | 10.5830 | 1.65279 | 0.826394 | − | 0.563093i | \(-0.190389\pi\) | ||||
0.826394 | + | 0.563093i | \(0.190389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.5830i | − | 1.61389i | −0.590624 | − | 0.806947i | \(-0.701119\pi\) | ||
0.590624 | − | 0.806947i | \(-0.298881\pi\) | |||||||
\(44\) | −2.64575 | − | 3.00000i | −0.398862 | − | 0.452267i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.00000 | + | 2.64575i | −1.03209 | + | 0.390095i | ||||
\(47\) | 5.29150 | 0.771845 | 0.385922 | − | 0.922531i | \(-0.373883\pi\) | ||||
0.385922 | + | 0.922531i | \(0.373883\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 1.32288 | − | 0.500000i | 0.187083 | − | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000i | 0.274721i | 0.990521 | + | 0.137361i | \(0.0438619\pi\) | ||||
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | −2.64575 | + | 5.00000i | −0.353553 | + | 0.668153i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | + | 7.93725i | 0.393919 | + | 1.04221i | ||||
\(59\) | − | 10.0000i | − | 1.30189i | −0.759125 | − | 0.650945i | \(-0.774373\pi\) | ||
0.759125 | − | 0.650945i | \(-0.225627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5830i | 1.35501i | 0.735516 | + | 0.677507i | \(0.236940\pi\) | ||||
−0.735516 | + | 0.677507i | \(0.763060\pi\) | |||||||
\(62\) | −5.29150 | + | 2.00000i | −0.672022 | + | 0.254000i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.50000 | − | 6.61438i | −0.562500 | − | 0.826797i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | + | 2.64575i | 0.119523 | + | 0.316228i | ||||
\(71\) | −10.5830 | −1.25597 | −0.627986 | − | 0.778225i | \(-0.716120\pi\) | ||||
−0.627986 | + | 0.778225i | \(0.716120\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0000 | −1.63858 | −0.819288 | − | 0.573382i | \(-0.805631\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | −5.29150 | − | 14.0000i | −0.615125 | − | 1.62747i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.00000 | − | 7.93725i | −0.802955 | − | 0.910465i | ||||
\(77\) | − | 4.00000i | − | 0.455842i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | −3.96863 | − | 0.500000i | −0.443706 | − | 0.0559017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.0000 | + | 5.29150i | −1.54604 | + | 0.584349i | ||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.29150 | + | 14.0000i | 0.570597 | + | 1.50966i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.00000 | + | 2.64575i | 0.533002 | + | 0.282038i | ||||
\(89\) | −10.5830 | −1.12180 | −0.560898 | − | 0.827885i | \(-0.689544\pi\) | ||||
−0.560898 | + | 0.827885i | \(0.689544\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.93725 | − | 7.00000i | 0.827516 | − | 0.729800i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.00000 | + | 2.64575i | −0.721995 | + | 0.272888i | ||||
\(95\) | −5.29150 | −0.542897 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 3.96863 | − | 1.50000i | 0.400892 | − | 0.151523i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.50000 | + | 1.32288i | −0.150000 | + | 0.132288i | ||||
\(101\) | 14.0000i | 1.39305i | 0.717532 | + | 0.696526i | \(0.245272\pi\) | ||||
−0.717532 | + | 0.696526i | \(0.754728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | −1.37946 | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||||
−0.689730 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.00000 | − | 2.64575i | −0.0971286 | − | 0.256978i | ||||
\(107\) | 4.00000i | 0.386695i | 0.981130 | + | 0.193347i | \(0.0619344\pi\) | ||||
−0.981130 | + | 0.193347i | \(0.938066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.5830i | 1.01367i | 0.862044 | + | 0.506834i | \(0.169184\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(110\) | 2.64575 | − | 1.00000i | 0.252262 | − | 0.0953463i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | − | 7.93725i | 0.0944911 | − | 0.750000i | ||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.29150i | − | 0.493435i | ||||||
\(116\) | −7.93725 | − | 9.00000i | −0.736956 | − | 0.835629i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.00000 | + | 13.2288i | 0.460287 | + | 1.21781i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −5.29150 | − | 14.0000i | −0.479070 | − | 1.26750i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.00000 | − | 5.29150i | 0.538816 | − | 0.475191i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(128\) | 9.26013 | + | 6.50000i | 0.818488 | + | 0.574524i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000i | 0.524222i | 0.965038 | + | 0.262111i | \(0.0844187\pi\) | ||||
−0.965038 | + | 0.262111i | \(0.915581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 10.5830i | − | 0.917663i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.1660 | −1.80833 | −0.904167 | − | 0.427179i | \(-0.859507\pi\) | ||||
−0.904167 | + | 0.427179i | \(0.859507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.29150i | 0.448819i | 0.974495 | + | 0.224410i | \(0.0720454\pi\) | ||||
−0.974495 | + | 0.224410i | \(0.927955\pi\) | |||||||
\(140\) | −2.64575 | − | 3.00000i | −0.223607 | − | 0.253546i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.0000 | − | 5.29150i | 1.17485 | − | 0.444053i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 18.5203 | − | 7.00000i | 1.53275 | − | 0.579324i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.0000 | + | 15.8745i | 1.15079 | + | 1.30488i | ||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 13.2288 | + | 7.00000i | 1.07299 | + | 0.567775i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | + | 5.29150i | 0.161165 | + | 0.426401i | ||||
\(155\) | − | 4.00000i | − | 0.321288i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.5830i | − | 0.844616i | −0.906452 | − | 0.422308i | \(-0.861220\pi\) | ||
0.906452 | − | 0.422308i | \(-0.138780\pi\) | |||||||
\(158\) | −5.29150 | + | 2.00000i | −0.420969 | + | 0.159111i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.50000 | − | 1.32288i | 0.434813 | − | 0.104583i | ||||
\(161\) | 10.5830 | 0.834058 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.5830i | − | 0.828925i | −0.910066 | − | 0.414462i | \(-0.863970\pi\) | ||
0.910066 | − | 0.414462i | \(-0.136030\pi\) | |||||||
\(164\) | 15.8745 | − | 14.0000i | 1.23959 | − | 1.09322i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | − | 15.8745i | −0.465690 | − | 1.23210i | ||||
\(167\) | 15.8745 | 1.22841 | 0.614203 | − | 0.789148i | \(-0.289478\pi\) | ||||
0.614203 | + | 0.789148i | \(0.289478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.0000 | − | 15.8745i | −1.06749 | − | 1.21042i | ||||
\(173\) | 14.0000i | 1.06440i | 0.846619 | + | 0.532200i | \(0.178635\pi\) | ||||
−0.846619 | + | 0.532200i | \(0.821365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | −7.93725 | − | 1.00000i | −0.598293 | − | 0.0753778i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.0000 | − | 5.29150i | 1.04934 | − | 0.396615i | ||||
\(179\) | 18.0000i | 1.34538i | 0.739923 | + | 0.672692i | \(0.234862\pi\) | ||||
−0.739923 | + | 0.672692i | \(0.765138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5830i | 0.786629i | 0.919404 | + | 0.393314i | \(0.128672\pi\) | ||||
−0.919404 | + | 0.393314i | \(0.871328\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.00000 | + | 13.2288i | −0.516047 | + | 0.975237i | ||||
\(185\) | 10.5830 | 0.778078 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.93725 | − | 7.00000i | 0.578884 | − | 0.510527i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.00000 | − | 2.64575i | 0.507833 | − | 0.191943i | ||||
\(191\) | −21.1660 | −1.53152 | −0.765759 | − | 0.643127i | \(-0.777637\pi\) | ||||
−0.765759 | + | 0.643127i | \(0.777637\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | −2.64575 | + | 1.00000i | −0.189954 | + | 0.0717958i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.50000 | + | 3.96863i | −0.321429 | + | 0.283473i | ||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 1.32288 | − | 2.50000i | 0.0935414 | − | 0.176777i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.00000 | − | 18.5203i | −0.492518 | − | 1.30308i | ||||
\(203\) | − | 12.0000i | − | 0.842235i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 10.5830i | − | 0.739149i | ||||||
\(206\) | 18.5203 | − | 7.00000i | 1.29037 | − | 0.487713i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5830 | −0.732042 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8745i | 1.09285i | 0.837509 | + | 0.546423i | \(0.184011\pi\) | ||||
−0.837509 | + | 0.546423i | \(0.815989\pi\) | |||||||
\(212\) | 2.64575 | + | 3.00000i | 0.181711 | + | 0.206041i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.00000 | − | 5.29150i | −0.136717 | − | 0.361720i | ||||
\(215\) | −10.5830 | −0.721755 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | −5.29150 | − | 14.0000i | −0.358386 | − | 0.948200i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.00000 | + | 2.64575i | −0.202260 | + | 0.178377i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.00000 | −0.133930 | −0.0669650 | − | 0.997755i | \(-0.521332\pi\) | ||||
−0.0669650 | + | 0.997755i | \(0.521332\pi\) | |||||||
\(224\) | 2.64575 | + | 11.0000i | 0.176777 | + | 0.734968i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.0000i | 1.59294i | 0.604681 | + | 0.796468i | \(0.293301\pi\) | ||||
−0.604681 | + | 0.796468i | \(0.706699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.5830i | − | 0.699345i | −0.936872 | − | 0.349672i | \(-0.886293\pi\) | ||
0.936872 | − | 0.349672i | \(-0.113707\pi\) | |||||||
\(230\) | 2.64575 | + | 7.00000i | 0.174456 | + | 0.461566i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.0000 | + | 7.93725i | 0.984798 | + | 0.521106i | ||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5.29150i | − | 0.345180i | ||||||
\(236\) | −13.2288 | − | 15.0000i | −0.861119 | − | 0.976417i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.5830 | 0.684558 | 0.342279 | − | 0.939598i | \(-0.388801\pi\) | ||||
0.342279 | + | 0.939598i | \(0.388801\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | −9.26013 | + | 3.50000i | −0.595264 | + | 0.224989i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.0000 | + | 15.8745i | 0.896258 | + | 1.01626i | ||||
\(245\) | 3.00000i | 0.191663i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.29150 | + | 10.0000i | −0.336011 | + | 0.635001i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | − | 1.32288i | −0.0316228 | − | 0.0836660i | ||||
\(251\) | − | 30.0000i | − | 1.89358i | −0.321847 | − | 0.946792i | \(-0.604304\pi\) | ||
0.321847 | − | 0.946792i | \(-0.395696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 10.5830i | − | 0.665348i | ||||||
\(254\) | −7.93725 | + | 3.00000i | −0.498028 | + | 0.188237i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5000 | − | 3.96863i | −0.968750 | − | 0.248039i | ||||
\(257\) | −21.1660 | −1.32030 | −0.660150 | − | 0.751134i | \(-0.729507\pi\) | ||||
−0.660150 | + | 0.751134i | \(0.729507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.1660i | 1.31519i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.00000 | − | 7.93725i | −0.185341 | − | 0.490365i | ||||
\(263\) | −15.8745 | −0.978864 | −0.489432 | − | 0.872041i | \(-0.662796\pi\) | ||||
−0.489432 | + | 0.872041i | \(0.662796\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | 5.29150 | + | 14.0000i | 0.324443 | + | 0.858395i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000i | 0.609711i | 0.952399 | + | 0.304855i | \(0.0986081\pi\) | ||||
−0.952399 | + | 0.304855i | \(0.901392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 28.0000 | − | 10.5830i | 1.69154 | − | 0.639343i | ||||
\(275\) | 2.00000i | 0.120605i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 10.5830i | − | 0.635871i | −0.948112 | − | 0.317936i | \(-0.897010\pi\) | ||
0.948112 | − | 0.317936i | \(-0.102990\pi\) | |||||||
\(278\) | −2.64575 | − | 7.00000i | −0.158682 | − | 0.419832i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.00000 | + | 2.64575i | 0.298807 | + | 0.158114i | ||||
\(281\) | 21.1660 | 1.26266 | 0.631329 | − | 0.775515i | \(-0.282510\pi\) | ||||
0.631329 | + | 0.775515i | \(0.282510\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.1660i | 1.25819i | 0.777329 | + | 0.629094i | \(0.216574\pi\) | ||||
−0.777329 | + | 0.629094i | \(0.783426\pi\) | |||||||
\(284\) | −15.8745 | + | 14.0000i | −0.941979 | + | 0.830747i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.1660 | 1.24939 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 7.93725 | − | 3.00000i | 0.466092 | − | 0.176166i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −21.0000 | + | 18.5203i | −1.22893 | + | 1.08382i | ||||
\(293\) | − | 26.0000i | − | 1.51894i | −0.650545 | − | 0.759468i | \(-0.725459\pi\) | ||
0.650545 | − | 0.759468i | \(-0.274541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.0000 | −0.582223 | ||||||||
\(296\) | −26.4575 | − | 14.0000i | −1.53781 | − | 0.813733i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | + | 7.93725i | 0.173785 | + | 0.459793i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 21.1660i | − | 1.21999i | ||||||
\(302\) | −21.1660 | + | 8.00000i | −1.21797 | + | 0.460348i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −21.0000 | − | 2.64575i | −1.20443 | − | 0.151744i | ||||
\(305\) | 10.5830 | 0.605981 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.5830i | 0.604004i | 0.953307 | + | 0.302002i | \(0.0976549\pi\) | ||||
−0.953307 | + | 0.302002i | \(0.902345\pi\) | |||||||
\(308\) | −5.29150 | − | 6.00000i | −0.301511 | − | 0.341882i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.00000 | + | 5.29150i | 0.113592 | + | 0.300537i | ||||
\(311\) | −10.5830 | −0.600107 | −0.300054 | − | 0.953922i | \(-0.597005\pi\) | ||||
−0.300054 | + | 0.953922i | \(0.597005\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 5.29150 | + | 14.0000i | 0.298617 | + | 0.790066i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.00000 | − | 5.29150i | 0.337526 | − | 0.297670i | ||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | −6.61438 | + | 4.50000i | −0.369755 | + | 0.251558i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.0000 | + | 5.29150i | −0.780189 | + | 0.294884i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.29150 | + | 14.0000i | 0.293069 | + | 0.775388i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.0000 | + | 26.4575i | −0.773021 | + | 1.46087i | ||||
\(329\) | 10.5830 | 0.583460 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.4575i | 1.45424i | 0.686512 | + | 0.727118i | \(0.259141\pi\) | ||||
−0.686512 | + | 0.727118i | \(0.740859\pi\) | |||||||
\(332\) | 15.8745 | + | 18.0000i | 0.871227 | + | 0.987878i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −21.0000 | + | 7.93725i | −1.14907 | + | 0.434307i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00000 | 0.326841 | 0.163420 | − | 0.986557i | \(-0.447747\pi\) | ||||
0.163420 | + | 0.986557i | \(0.447747\pi\) | |||||||
\(338\) | −17.1974 | + | 6.50000i | −0.935414 | + | 0.353553i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8.00000i | − | 0.433224i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 26.4575 | + | 14.0000i | 1.42649 | + | 0.754829i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.00000 | − | 18.5203i | −0.376322 | − | 0.995655i | ||||
\(347\) | − | 32.0000i | − | 1.71785i | −0.512101 | − | 0.858925i | \(-0.671133\pi\) | ||
0.512101 | − | 0.858925i | \(-0.328867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.5830i | − | 0.566495i | −0.959047 | − | 0.283248i | \(-0.908588\pi\) | ||
0.959047 | − | 0.283248i | \(-0.0914118\pi\) | |||||||
\(350\) | 2.64575 | − | 1.00000i | 0.141421 | − | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.0000 | − | 2.64575i | 0.586302 | − | 0.141019i | ||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.5830i | 0.561688i | ||||||||
\(356\) | −15.8745 | + | 14.0000i | −0.841347 | + | 0.741999i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.00000 | − | 23.8118i | −0.475665 | − | 1.25849i | ||||
\(359\) | 31.7490 | 1.67565 | 0.837824 | − | 0.545940i | \(-0.183827\pi\) | ||||
0.837824 | + | 0.545940i | \(0.183827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | −5.29150 | − | 14.0000i | −0.278115 | − | 0.735824i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000i | 0.732793i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.0000 | −0.939592 | −0.469796 | − | 0.882775i | \(-0.655673\pi\) | ||||
−0.469796 | + | 0.882775i | \(0.655673\pi\) | |||||||
\(368\) | 2.64575 | − | 21.0000i | 0.137919 | − | 1.09470i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.0000 | + | 5.29150i | −0.727825 | + | 0.275092i | ||||
\(371\) | 4.00000i | 0.207670i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 10.5830i | − | 0.547967i | −0.961734 | − | 0.273984i | \(-0.911659\pi\) | ||
0.961734 | − | 0.273984i | \(-0.0883414\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.00000 | + | 13.2288i | −0.360997 | + | 0.682221i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.8745i | − | 0.815419i | −0.913112 | − | 0.407709i | \(-0.866328\pi\) | ||
0.913112 | − | 0.407709i | \(-0.133672\pi\) | |||||||
\(380\) | −7.93725 | + | 7.00000i | −0.407173 | + | 0.359092i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 28.0000 | − | 10.5830i | 1.43260 | − | 0.541474i | ||||
\(383\) | 15.8745 | 0.811149 | 0.405575 | − | 0.914062i | \(-0.367071\pi\) | ||||
0.405575 | + | 0.914062i | \(0.367071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | 2.64575 | − | 1.00000i | 0.134665 | − | 0.0508987i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.00000 | − | 2.64575i | 0.152302 | − | 0.134318i | ||||
\(389\) | 10.0000i | 0.507020i | 0.967333 | + | 0.253510i | \(0.0815851\pi\) | ||||
−0.967333 | + | 0.253510i | \(0.918415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.96863 | − | 7.50000i | 0.200446 | − | 0.378807i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.00000 | − | 2.64575i | −0.0503793 | − | 0.133291i | ||||
\(395\) | − | 4.00000i | − | 0.201262i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.1660i | 1.06229i | 0.847280 | + | 0.531146i | \(0.178238\pi\) | ||||
−0.847280 | + | 0.531146i | \(0.821762\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | + | 3.96863i | −0.0250000 | + | 0.198431i | ||||
\(401\) | 31.7490 | 1.58547 | 0.792735 | − | 0.609566i | \(-0.208656\pi\) | ||||
0.792735 | + | 0.609566i | \(0.208656\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 18.5203 | + | 21.0000i | 0.921417 | + | 1.04479i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 15.8745i | 0.297775 | + | 0.787839i | ||||
\(407\) | 21.1660 | 1.04916 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.0000 | 0.890043 | 0.445021 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445021 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(410\) | 5.29150 | + | 14.0000i | 0.261329 | + | 0.691411i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21.0000 | + | 18.5203i | −1.03460 | + | 0.912428i | ||||
\(413\) | − | 20.0000i | − | 0.984136i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.0000 | − | 5.29150i | 0.684762 | − | 0.258816i | ||||
\(419\) | 14.0000i | 0.683945i | 0.939710 | + | 0.341972i | \(0.111095\pi\) | ||||
−0.939710 | + | 0.341972i | \(0.888905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 10.5830i | − | 0.515784i | −0.966174 | − | 0.257892i | \(-0.916972\pi\) | ||
0.966174 | − | 0.257892i | \(-0.0830279\pi\) | |||||||
\(422\) | −7.93725 | − | 21.0000i | −0.386379 | − | 1.02226i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.00000 | − | 2.64575i | −0.242821 | − | 0.128489i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.1660i | 1.02430i | ||||||||
\(428\) | 5.29150 | + | 6.00000i | 0.255774 | + | 0.290021i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.0000 | − | 5.29150i | 0.675140 | − | 0.255179i | ||||
\(431\) | −31.7490 | −1.52930 | −0.764648 | − | 0.644448i | \(-0.777087\pi\) | ||||
−0.764648 | + | 0.644448i | \(0.777087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | −10.5830 | + | 4.00000i | −0.508001 | + | 0.192006i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.0000 | + | 15.8745i | 0.670478 | + | 0.760251i | ||||
\(437\) | − | 28.0000i | − | 1.33942i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 2.64575 | − | 5.00000i | 0.126131 | − | 0.238366i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 32.0000i | − | 1.52037i | −0.649709 | − | 0.760183i | \(-0.725109\pi\) | ||
0.649709 | − | 0.760183i | \(-0.274891\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.5830i | 0.501683i | ||||||||
\(446\) | 2.64575 | − | 1.00000i | 0.125280 | − | 0.0473514i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.00000 | − | 13.2288i | −0.425210 | − | 0.625000i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 21.1660i | − | 0.996669i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.0000 | − | 31.7490i | −0.563188 | − | 1.49006i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | 5.29150 | + | 14.0000i | 0.247256 | + | 0.654177i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.00000 | − | 7.93725i | −0.326377 | − | 0.370076i | ||||
\(461\) | 14.0000i | 0.652045i | 0.945362 | + | 0.326023i | \(0.105709\pi\) | ||||
−0.945362 | + | 0.326023i | \(0.894291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | −23.8118 | − | 3.00000i | −1.10543 | − | 0.139272i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.0000i | 1.29569i | 0.761774 | + | 0.647843i | \(0.224329\pi\) | ||||
−0.761774 | + | 0.647843i | \(0.775671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.64575 | + | 7.00000i | 0.122039 | + | 0.322886i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 25.0000 | + | 13.2288i | 1.15072 | + | 0.608903i | ||||
\(473\) | −21.1660 | −0.973214 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.29150i | 0.242791i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.0000 | + | 5.29150i | −0.640345 | + | 0.242028i | ||||
\(479\) | 10.5830 | 0.483550 | 0.241775 | − | 0.970332i | \(-0.422270\pi\) | ||||
0.241775 | + | 0.970332i | \(0.422270\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −23.8118 | + | 9.00000i | −1.08460 | + | 0.409939i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.5000 | − | 9.26013i | 0.477273 | − | 0.420915i | ||||
\(485\) | − | 2.00000i | − | 0.0908153i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.0000 | 1.35943 | 0.679715 | − | 0.733476i | \(-0.262104\pi\) | ||||
0.679715 | + | 0.733476i | \(0.262104\pi\) | |||||||
\(488\) | −26.4575 | − | 14.0000i | −1.19768 | − | 0.633750i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.50000 | − | 3.96863i | −0.0677631 | − | 0.179284i | ||||
\(491\) | − | 22.0000i | − | 0.992846i | −0.868081 | − | 0.496423i | \(-0.834646\pi\) | ||
0.868081 | − | 0.496423i | \(-0.165354\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | − | 15.8745i | 0.0898027 | − | 0.712786i | ||||
\(497\) | −21.1660 | −0.949425 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 5.29150i | − | 0.236880i | −0.992961 | − | 0.118440i | \(-0.962211\pi\) | ||
0.992961 | − | 0.118440i | \(-0.0377894\pi\) | |||||||
\(500\) | 1.32288 | + | 1.50000i | 0.0591608 | + | 0.0670820i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.0000 | + | 39.6863i | 0.669483 | + | 1.77128i | ||||
\(503\) | 15.8745 | 0.707809 | 0.353905 | − | 0.935282i | \(-0.384854\pi\) | ||||
0.353905 | + | 0.935282i | \(0.384854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | 5.29150 | + | 14.0000i | 0.235236 | + | 0.622376i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.00000 | − | 7.93725i | 0.399310 | − | 0.352159i | ||||
\(509\) | − | 6.00000i | − | 0.265945i | −0.991120 | − | 0.132973i | \(-0.957548\pi\) | ||
0.991120 | − | 0.132973i | \(-0.0424523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0000 | −1.23865 | ||||||||
\(512\) | 22.4889 | − | 2.50000i | 0.993878 | − | 0.110485i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.0000 | − | 10.5830i | 1.23503 | − | 0.466796i | ||||
\(515\) | 14.0000i | 0.616914i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10.5830i | − | 0.465440i | ||||||
\(518\) | −10.5830 | − | 28.0000i | −0.464991 | − | 1.23025i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 21.1660i | − | 0.925525i | −0.886482 | − | 0.462763i | \(-0.846858\pi\) | ||
0.886482 | − | 0.462763i | \(-0.153142\pi\) | |||||||
\(524\) | 7.93725 | + | 9.00000i | 0.346741 | + | 0.393167i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.0000 | − | 7.93725i | 0.915644 | − | 0.346081i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.00000 | 0.217391 | ||||||||
\(530\) | −2.64575 | + | 1.00000i | −0.114924 | + | 0.0434372i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.0000 | − | 15.8745i | −0.606977 | − | 0.688247i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00000 | 0.172935 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.00000 | − | 13.2288i | −0.215565 | − | 0.570332i | ||||
\(539\) | 6.00000i | 0.258438i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5830i | 0.454999i | 0.973778 | + | 0.227499i | \(0.0730550\pi\) | ||||
−0.973778 | + | 0.227499i | \(0.926945\pi\) | |||||||
\(542\) | 10.5830 | − | 4.00000i | 0.454579 | − | 0.171815i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.5830 | 0.453326 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 10.5830i | − | 0.452497i | −0.974070 | − | 0.226248i | \(-0.927354\pi\) | ||
0.974070 | − | 0.226248i | \(-0.0726461\pi\) | |||||||
\(548\) | −31.7490 | + | 28.0000i | −1.35625 | + | 1.19610i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.00000 | − | 2.64575i | −0.0426401 | − | 0.112815i | ||||
\(551\) | −31.7490 | −1.35255 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | 5.29150 | + | 14.0000i | 0.224814 | + | 0.594803i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.00000 | + | 7.93725i | 0.296866 | + | 0.336615i | ||||
\(557\) | 30.0000i | 1.27114i | 0.772043 | + | 0.635570i | \(0.219235\pi\) | ||||
−0.772043 | + | 0.635570i | \(0.780765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −7.93725 | − | 1.00000i | −0.335410 | − | 0.0422577i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.0000 | + | 10.5830i | −1.18111 | + | 0.446417i | ||||
\(563\) | 24.0000i | 1.01148i | 0.862686 | + | 0.505740i | \(0.168780\pi\) | ||||
−0.862686 | + | 0.505740i | \(0.831220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.5830 | − | 28.0000i | −0.444837 | − | 1.17693i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.0000 | − | 26.4575i | 0.587427 | − | 1.11013i | ||||
\(569\) | −10.5830 | −0.443663 | −0.221831 | − | 0.975085i | \(-0.571203\pi\) | ||||
−0.221831 | + | 0.975085i | \(0.571203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 37.0405i | − | 1.55010i | −0.631901 | − | 0.775049i | \(-0.717725\pi\) | ||
0.631901 | − | 0.775049i | \(-0.282275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −28.0000 | + | 10.5830i | −1.16870 | + | 0.441726i | ||||
\(575\) | −5.29150 | −0.220671 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.0000 | 0.416305 | 0.208153 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208153 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(578\) | 22.4889 | − | 8.50000i | 0.935414 | − | 0.353553i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.00000 | + | 7.93725i | −0.373705 | + | 0.329577i | ||||
\(581\) | 24.0000i | 0.995688i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | 0.165663 | ||||||||
\(584\) | 18.5203 | − | 35.0000i | 0.766374 | − | 1.44831i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.0000 | + | 34.3948i | 0.537025 | + | 1.42083i | ||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 21.1660i | − | 0.872130i | ||||||
\(590\) | 13.2288 | − | 5.00000i | 0.544619 | − | 0.205847i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 42.0000 | + | 5.29150i | 1.72619 | + | 0.217479i | ||||
\(593\) | −21.1660 | −0.869184 | −0.434592 | − | 0.900627i | \(-0.643107\pi\) | ||||
−0.434592 | + | 0.900627i | \(0.643107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.93725 | − | 9.00000i | −0.325123 | − | 0.368654i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.7490 | −1.29723 | −0.648615 | − | 0.761117i | \(-0.724651\pi\) | ||||
−0.648615 | + | 0.761117i | \(0.724651\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 10.5830 | + | 28.0000i | 0.431331 | + | 1.14119i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 24.0000 | − | 21.1660i | 0.976546 | − | 0.861233i | ||||
\(605\) | − | 7.00000i | − | 0.284590i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.0000 | −0.892952 | −0.446476 | − | 0.894795i | \(-0.647321\pi\) | ||||
−0.446476 | + | 0.894795i | \(0.647321\pi\) | |||||||
\(608\) | 29.1033 | − | 7.00000i | 1.18029 | − | 0.283887i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.0000 | + | 5.29150i | −0.566843 | + | 0.214247i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.3320i | 1.70977i | 0.518814 | + | 0.854887i | \(0.326374\pi\) | ||||
−0.518814 | + | 0.854887i | \(0.673626\pi\) | |||||||
\(614\) | −5.29150 | − | 14.0000i | −0.213548 | − | 0.564994i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.0000 | + | 5.29150i | 0.402911 | + | 0.213201i | ||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.29150i | 0.212683i | 0.994330 | + | 0.106342i | \(0.0339137\pi\) | ||||
−0.994330 | + | 0.106342i | \(0.966086\pi\) | |||||||
\(620\) | −5.29150 | − | 6.00000i | −0.212512 | − | 0.240966i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.0000 | − | 5.29150i | 0.561349 | − | 0.212170i | ||||
\(623\) | −21.1660 | −0.847998 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.93725 | − | 3.00000i | 0.317236 | − | 0.119904i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0000 | − | 15.8745i | −0.558661 | − | 0.633462i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.0000 | 1.43314 | 0.716569 | − | 0.697517i | \(-0.245712\pi\) | ||||
0.716569 | + | 0.697517i | \(0.245712\pi\) | |||||||
\(632\) | −5.29150 | + | 10.0000i | −0.210485 | + | 0.397779i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | + | 23.8118i | 0.357436 | + | 0.945686i | ||||
\(635\) | − | 6.00000i | − | 0.238103i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 15.8745 | − | 6.00000i | 0.628478 | − | 0.237542i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.50000 | − | 9.26013i | 0.256935 | − | 0.366039i | ||||
\(641\) | 21.1660 | 0.836007 | 0.418004 | − | 0.908445i | \(-0.362730\pi\) | ||||
0.418004 | + | 0.908445i | \(0.362730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.7490i | 1.25206i | 0.779799 | + | 0.626029i | \(0.215321\pi\) | ||||
−0.779799 | + | 0.626029i | \(0.784679\pi\) | |||||||
\(644\) | 15.8745 | − | 14.0000i | 0.625543 | − | 0.551677i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.8745 | −0.624091 | −0.312046 | − | 0.950067i | \(-0.601014\pi\) | ||||
−0.312046 | + | 0.950067i | \(0.601014\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0000 | −0.785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.0000 | − | 15.8745i | −0.548282 | − | 0.621694i | ||||
\(653\) | 18.0000i | 0.704394i | 0.935926 | + | 0.352197i | \(0.114565\pi\) | ||||
−0.935926 | + | 0.352197i | \(0.885435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | 0.234439 | ||||||||
\(656\) | 5.29150 | − | 42.0000i | 0.206598 | − | 1.63982i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.0000 | + | 5.29150i | −0.545777 | + | 0.206284i | ||||
\(659\) | 30.0000i | 1.16863i | 0.811525 | + | 0.584317i | \(0.198638\pi\) | ||||
−0.811525 | + | 0.584317i | \(0.801362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.5830i | − | 0.411631i | −0.978591 | − | 0.205816i | \(-0.934015\pi\) | ||
0.978591 | − | 0.205816i | \(-0.0659847\pi\) | |||||||
\(662\) | −13.2288 | − | 35.0000i | −0.514150 | − | 1.36031i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −30.0000 | − | 15.8745i | −1.16423 | − | 0.616050i | ||||
\(665\) | −10.5830 | −0.410391 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 31.7490i | − | 1.22933i | ||||||
\(668\) | 23.8118 | − | 21.0000i | 0.921305 | − | 0.812514i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.1660 | 0.817105 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0000 | 0.848038 | 0.424019 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424019 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(674\) | −7.93725 | + | 3.00000i | −0.305732 | + | 0.115556i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.5000 | − | 17.1974i | 0.750000 | − | 0.661438i | ||||
\(677\) | 22.0000i | 0.845529i | 0.906240 | + | 0.422764i | \(0.138940\pi\) | ||||
−0.906240 | + | 0.422764i | \(0.861060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00000 | 0.153506 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.00000 | + | 10.5830i | 0.153168 | + | 0.405244i | ||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.1660i | 0.808712i | ||||||||
\(686\) | 26.4575 | − | 10.0000i | 1.01015 | − | 0.381802i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −42.0000 | − | 5.29150i | −1.60123 | − | 0.201737i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 15.8745i | − | 0.603895i | −0.953325 | − | 0.301947i | \(-0.902363\pi\) | ||
0.953325 | − | 0.301947i | \(-0.0976367\pi\) | |||||||
\(692\) | 18.5203 | + | 21.0000i | 0.704035 | + | 0.798300i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0000 | + | 42.3320i | 0.607352 | + | 1.60690i | ||||
\(695\) | 5.29150 | 0.200718 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 5.29150 | + | 14.0000i | 0.200286 | + | 0.529908i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.00000 | + | 2.64575i | −0.113389 | + | 0.100000i | ||||
\(701\) | − | 22.0000i | − | 0.830929i | −0.909610 | − | 0.415464i | \(-0.863619\pi\) | ||
0.909610 | − | 0.415464i | \(-0.136381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 56.0000 | 2.11208 | ||||||||
\(704\) | −13.2288 | + | 9.00000i | −0.498578 | + | 0.339200i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.0000i | 1.05305i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.9150i | 1.98727i | 0.112667 | + | 0.993633i | \(0.464061\pi\) | ||||
−0.112667 | + | 0.993633i | \(0.535939\pi\) | |||||||
\(710\) | −5.29150 | − | 14.0000i | −0.198587 | − | 0.525411i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.0000 | − | 26.4575i | 0.524672 | − | 0.991537i | ||||
\(713\) | 21.1660 | 0.792673 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23.8118 | + | 27.0000i | 0.889887 | + | 1.00904i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −42.0000 | + | 15.8745i | −1.56743 | + | 0.592431i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.0000 | −1.04277 | ||||||||
\(722\) | 11.9059 | − | 4.50000i | 0.443091 | − | 0.167473i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.0000 | + | 15.8745i | 0.520306 | + | 0.589971i | ||||
\(725\) | 6.00000i | 0.222834i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.0000 | −0.964287 | −0.482143 | − | 0.876092i | \(-0.660142\pi\) | ||||
−0.482143 | + | 0.876092i | \(0.660142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.00000 | − | 18.5203i | −0.259082 | − | 0.685466i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.7490i | 1.17268i | 0.810066 | + | 0.586338i | \(0.199431\pi\) | ||||
−0.810066 | + | 0.586338i | \(0.800569\pi\) | |||||||
\(734\) | 23.8118 | − | 9.00000i | 0.878908 | − | 0.332196i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.00000 | + | 29.1033i | 0.258023 | + | 1.07276i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 47.6235i | − | 1.75186i | −0.482439 | − | 0.875930i | \(-0.660249\pi\) | ||
0.482439 | − | 0.875930i | \(-0.339751\pi\) | |||||||
\(740\) | 15.8745 | − | 14.0000i | 0.583559 | − | 0.514650i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.00000 | − | 5.29150i | −0.0734223 | − | 0.194257i | ||||
\(743\) | 15.8745 | 0.582379 | 0.291190 | − | 0.956665i | \(-0.405949\pi\) | ||||
0.291190 | + | 0.956665i | \(0.405949\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | −0.219823 | ||||||||
\(746\) | 5.29150 | + | 14.0000i | 0.193736 | + | 0.512576i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.00000i | 0.292314i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.0000 | −1.89751 | −0.948753 | − | 0.316017i | \(-0.897654\pi\) | ||||
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 2.64575 | − | 21.0000i | 0.0964806 | − | 0.765791i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 16.0000i | − | 0.582300i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.5830i | 0.384646i | 0.981332 | + | 0.192323i | \(0.0616021\pi\) | ||||
−0.981332 | + | 0.192323i | \(0.938398\pi\) | |||||||
\(758\) | 7.93725 | + | 21.0000i | 0.288294 | + | 0.762754i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.00000 | − | 13.2288i | 0.253917 | − | 0.479857i | ||||
\(761\) | −21.1660 | −0.767267 | −0.383634 | − | 0.923485i | \(-0.625327\pi\) | ||||
−0.383634 | + | 0.923485i | \(0.625327\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.1660i | 0.766261i | ||||||||
\(764\) | −31.7490 | + | 28.0000i | −1.14864 | + | 1.01300i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.0000 | + | 7.93725i | −0.758761 | + | 0.286785i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.0000 | −1.08183 | −0.540914 | − | 0.841078i | \(-0.681921\pi\) | ||||
−0.540914 | + | 0.841078i | \(0.681921\pi\) | |||||||
\(770\) | 5.29150 | − | 2.00000i | 0.190693 | − | 0.0720750i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.00000 | + | 2.64575i | −0.107972 | + | 0.0952227i | ||||
\(773\) | 42.0000i | 1.51064i | 0.655359 | + | 0.755318i | \(0.272517\pi\) | ||||
−0.655359 | + | 0.755318i | \(0.727483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | −2.64575 | + | 5.00000i | −0.0949769 | + | 0.179490i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.00000 | − | 13.2288i | −0.179259 | − | 0.474274i | ||||
\(779\) | − | 56.0000i | − | 2.00641i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.1660i | 0.757379i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.50000 | + | 11.9059i | −0.0535714 | + | 0.425210i | ||||
\(785\) | −10.5830 | −0.377724 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 21.1660i | − | 0.754487i | −0.926114 | − | 0.377243i | \(-0.876872\pi\) | ||
0.926114 | − | 0.377243i | \(-0.123128\pi\) | |||||||
\(788\) | 2.64575 | + | 3.00000i | 0.0942510 | + | 0.106871i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.00000 | + | 5.29150i | 0.0711568 | + | 0.188263i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −10.5830 | − | 28.0000i | −0.375577 | − | 0.993683i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 30.0000i | − | 1.06265i | −0.847167 | − | 0.531327i | \(-0.821693\pi\) | ||
0.847167 | − | 0.531327i | \(-0.178307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.32288 | − | 5.50000i | −0.0467707 | − | 0.194454i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −42.0000 | + | 15.8745i | −1.48307 | + | 0.560548i | ||||
\(803\) | 28.0000i | 0.988099i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 10.5830i | − | 0.373002i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −35.0000 | − | 18.5203i | −1.23130 | − | 0.651540i | ||||
\(809\) | −21.1660 | −0.744157 | −0.372079 | − | 0.928201i | \(-0.621355\pi\) | ||||
−0.372079 | + | 0.928201i | \(0.621355\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 26.4575i | − | 0.929049i | −0.885560 | − | 0.464524i | \(-0.846225\pi\) | ||
0.885560 | − | 0.464524i | \(-0.153775\pi\) | |||||||
\(812\) | −15.8745 | − | 18.0000i | −0.557086 | − | 0.631676i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −28.0000 | + | 10.5830i | −0.981399 | + | 0.370934i | ||||
\(815\) | −10.5830 | −0.370707 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −56.0000 | −1.95919 | ||||||||
\(818\) | −23.8118 | + | 9.00000i | −0.832559 | + | 0.314678i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.0000 | − | 15.8745i | −0.488901 | − | 0.554362i | ||||
\(821\) | − | 10.0000i | − | 0.349002i | −0.984657 | − | 0.174501i | \(-0.944169\pi\) | ||
0.984657 | − | 0.174501i | \(-0.0558313\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.0000 | −0.627441 | −0.313720 | − | 0.949515i | \(-0.601575\pi\) | ||||
−0.313720 | + | 0.949515i | \(0.601575\pi\) | |||||||
\(824\) | 18.5203 | − | 35.0000i | 0.645184 | − | 1.21928i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.0000 | + | 26.4575i | 0.347945 | + | 0.920575i | ||||
\(827\) | 8.00000i | 0.278187i | 0.990279 | + | 0.139094i | \(0.0444189\pi\) | ||||
−0.990279 | + | 0.139094i | \(0.955581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.5830i | 0.367563i | 0.982967 | + | 0.183781i | \(0.0588339\pi\) | ||||
−0.982967 | + | 0.183781i | \(0.941166\pi\) | |||||||
\(830\) | −15.8745 | + | 6.00000i | −0.551012 | + | 0.208263i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 15.8745i | − | 0.549360i | ||||||
\(836\) | −15.8745 | + | 14.0000i | −0.549031 | + | 0.484200i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.00000 | − | 18.5203i | −0.241811 | − | 0.639772i | ||||
\(839\) | 10.5830 | 0.365366 | 0.182683 | − | 0.983172i | \(-0.441522\pi\) | ||||
0.182683 | + | 0.983172i | \(0.441522\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 5.29150 | + | 14.0000i | 0.182357 | + | 0.482472i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 21.0000 | + | 23.8118i | 0.722850 | + | 0.819635i | ||||
\(845\) | − | 13.0000i | − | 0.447214i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.0000 | 0.481046 | ||||||||
\(848\) | 7.93725 | + | 1.00000i | 0.272566 | + | 0.0343401i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56.0000i | 1.91966i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.3320i | 1.44942i | 0.689054 | + | 0.724710i | \(0.258026\pi\) | ||||
−0.689054 | + | 0.724710i | \(0.741974\pi\) | |||||||
\(854\) | −10.5830 | − | 28.0000i | −0.362143 | − | 0.958140i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.0000 | − | 5.29150i | −0.341793 | − | 0.180860i | ||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.4575i | 0.902719i | 0.892342 | + | 0.451359i | \(0.149061\pi\) | ||||
−0.892342 | + | 0.451359i | \(0.850939\pi\) | |||||||
\(860\) | −15.8745 | + | 14.0000i | −0.541316 | + | 0.477396i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.0000 | − | 15.8745i | 1.43053 | − | 0.540688i | ||||
\(863\) | −15.8745 | −0.540375 | −0.270187 | − | 0.962808i | \(-0.587086\pi\) | ||||
−0.270187 | + | 0.962808i | \(0.587086\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | 0.476014 | ||||||||
\(866\) | −18.5203 | + | 7.00000i | −0.629344 | + | 0.237870i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.0000 | − | 10.5830i | 0.407307 | − | 0.359211i | ||||
\(869\) | − | 8.00000i | − | 0.271381i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −26.4575 | − | 14.0000i | −0.895964 | − | 0.474100i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.0000 | + | 37.0405i | 0.473557 | + | 1.25291i | ||||
\(875\) | 2.00000i | 0.0676123i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 10.5830i | − | 0.357363i | −0.983907 | − | 0.178681i | \(-0.942817\pi\) | ||
0.983907 | − | 0.178681i | \(-0.0571831\pi\) | |||||||
\(878\) | −10.5830 | + | 4.00000i | −0.357159 | + | 0.134993i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | + | 7.93725i | −0.0337100 | + | 0.267565i | ||||
\(881\) | −31.7490 | −1.06965 | −0.534826 | − | 0.844962i | \(-0.679623\pi\) | ||||
−0.534826 | + | 0.844962i | \(0.679623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.5830i | − | 0.356146i | −0.984017 | − | 0.178073i | \(-0.943014\pi\) | ||
0.984017 | − | 0.178073i | \(-0.0569864\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.0000 | + | 42.3320i | 0.537531 | + | 1.42217i | ||||
\(887\) | −5.29150 | −0.177671 | −0.0888356 | − | 0.996046i | \(-0.528315\pi\) | ||||
−0.0888356 | + | 0.996046i | \(0.528315\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.0000 | 0.402467 | ||||||||
\(890\) | −5.29150 | − | 14.0000i | −0.177372 | − | 0.469281i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.00000 | + | 2.64575i | −0.100447 | + | 0.0885863i | ||||
\(893\) | − | 28.0000i | − | 0.936984i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | 0.601674 | ||||||||
\(896\) | 18.5203 | + | 13.0000i | 0.618718 | + | 0.434300i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 24.0000i | − | 0.800445i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 10.5830 | + | 28.0000i | 0.352376 | + | 0.932298i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.5830 | 0.351791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 42.3320i | − | 1.40561i | −0.711382 | − | 0.702806i | \(-0.751930\pi\) | ||
0.711382 | − | 0.702806i | \(-0.248070\pi\) | |||||||
\(908\) | 31.7490 | + | 36.0000i | 1.05363 | + | 1.19470i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.7490 | 1.05189 | 0.525946 | − | 0.850518i | \(-0.323711\pi\) | ||||
0.525946 | + | 0.850518i | \(0.323711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0000 | 0.794284 | ||||||||
\(914\) | 23.8118 | − | 9.00000i | 0.787623 | − | 0.297694i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.0000 | − | 15.8745i | −0.462573 | − | 0.524509i | ||||
\(917\) | 12.0000i | 0.396275i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.0000 | −0.659739 | −0.329870 | − | 0.944027i | \(-0.607005\pi\) | ||||
−0.329870 | + | 0.944027i | \(0.607005\pi\) | |||||||
\(920\) | 13.2288 | + | 7.00000i | 0.436139 | + | 0.230783i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.00000 | − | 18.5203i | −0.230533 | − | 0.609932i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 10.5830i | − | 0.347967i | ||||||
\(926\) | −34.3948 | + | 13.0000i | −1.13028 | + | 0.427207i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 33.0000 | − | 7.93725i | 1.08328 | − | 0.260553i | ||||
\(929\) | −21.1660 | −0.694434 | −0.347217 | − | 0.937785i | \(-0.612873\pi\) | ||||
−0.347217 | + | 0.937785i | \(0.612873\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.8745i | 0.520266i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.0000 | − | 37.0405i | −0.458094 | − | 1.21200i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.00000 | − | 7.93725i | −0.228315 | − | 0.258885i | ||||
\(941\) | 46.0000i | 1.49956i | 0.661689 | + | 0.749779i | \(0.269840\pi\) | ||||
−0.661689 | + | 0.749779i | \(0.730160\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.0000 | 1.82361 | ||||||||
\(944\) | −39.6863 | − | 5.00000i | −1.29168 | − | 0.162736i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.0000 | − | 10.5830i | 0.910359 | − | 0.344083i | ||||
\(947\) | − | 48.0000i | − | 1.55979i | −0.625910 | − | 0.779895i | \(-0.715272\pi\) | ||
0.625910 | − | 0.779895i | \(-0.284728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.64575 | − | 7.00000i | −0.0858395 | − | 0.227110i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.3320 | 1.37127 | 0.685634 | − | 0.727946i | \(-0.259525\pi\) | ||||
0.685634 | + | 0.727946i | \(0.259525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.1660i | 0.684916i | ||||||||
\(956\) | 15.8745 | − | 14.0000i | 0.513418 | − | 0.452792i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.0000 | + | 5.29150i | −0.452319 | + | 0.170961i | ||||
\(959\) | −42.3320 | −1.36697 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 27.0000 | − | 23.8118i | 0.869611 | − | 0.766925i | ||||
\(965\) | 2.00000i | 0.0643823i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.0000 | 1.09337 | 0.546683 | − | 0.837340i | \(-0.315890\pi\) | ||||
0.546683 | + | 0.837340i | \(0.315890\pi\) | |||||||
\(968\) | −9.26013 | + | 17.5000i | −0.297632 | + | 0.562471i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.00000 | + | 2.64575i | 0.0321081 | + | 0.0849500i | ||||
\(971\) | − | 6.00000i | − | 0.192549i | −0.995355 | − | 0.0962746i | \(-0.969307\pi\) | ||
0.995355 | − | 0.0962746i | \(-0.0306927\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.5830i | 0.339276i | ||||||||
\(974\) | −39.6863 | + | 15.0000i | −1.27163 | + | 0.480631i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 42.0000 | + | 5.29150i | 1.34439 | + | 0.169377i | ||||
\(977\) | 21.1660 | 0.677161 | 0.338580 | − | 0.940937i | \(-0.390053\pi\) | ||||
0.338580 | + | 0.940937i | \(0.390053\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.1660i | 0.676469i | ||||||||
\(980\) | 3.96863 | + | 4.50000i | 0.126773 | + | 0.143747i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.0000 | + | 29.1033i | 0.351024 | + | 0.928722i | ||||
\(983\) | −5.29150 | −0.168773 | −0.0843864 | − | 0.996433i | \(-0.526893\pi\) | ||||
−0.0843864 | + | 0.996433i | \(0.526893\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.00000 | 0.0637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 56.0000i | − | 1.78070i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 5.29150 | + | 22.0000i | 0.168005 | + | 0.698501i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 28.0000 | − | 10.5830i | 0.888106 | − | 0.335673i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 42.3320i | − | 1.34067i | −0.742059 | − | 0.670334i | \(-0.766151\pi\) | ||
0.742059 | − | 0.670334i | \(-0.233849\pi\) | |||||||
\(998\) | 2.64575 | + | 7.00000i | 0.0837498 | + | 0.221581i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))