Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(109,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.d (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: | \(1.72476868366\) |
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 | 109.2 | ||
Root | \(-1.32288 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.109 |
Dual form | 216.2.d.b.109.1 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | −0.974679 | − | 0.223607i | \(-0.928217\pi\) | ||
0.974679 | − | 0.223607i | \(-0.0717831\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −1.32288 | + | 2.50000i | −0.467707 | + | 0.883883i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.500000 | + | 1.32288i | 0.158114 | + | 0.418330i | ||||
\(11\) | − | 3.00000i | − | 0.904534i | −0.891883 | − | 0.452267i | \(-0.850615\pi\) | ||
0.891883 | − | 0.452267i | \(-0.149385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.29150i | − | 1.46760i | −0.679366 | − | 0.733799i | \(-0.737745\pi\) | ||
0.679366 | − | 0.733799i | \(-0.262255\pi\) | |||||||
\(14\) | −1.32288 | + | 0.500000i | −0.353553 | + | 0.133631i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 3.96863i | 0.125000 | − | 0.992157i | ||||
\(17\) | 5.29150 | 1.28338 | 0.641689 | − | 0.766965i | \(-0.278234\pi\) | ||||
0.641689 | + | 0.766965i | \(0.278234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.29150i | 1.21395i | 0.794719 | + | 0.606977i | \(0.207618\pi\) | ||||
−0.794719 | + | 0.606977i | \(0.792382\pi\) | |||||||
\(20\) | −1.32288 | − | 1.50000i | −0.295804 | − | 0.335410i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.50000 | + | 3.96863i | 0.319801 | + | 0.846114i | ||||
\(23\) | 5.29150 | 1.10335 | 0.551677 | − | 0.834058i | \(-0.313988\pi\) | ||||
0.551677 | + | 0.834058i | \(0.313988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 2.64575 | + | 7.00000i | 0.518875 | + | 1.37281i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.50000 | − | 1.32288i | 0.283473 | − | 0.250000i | ||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00000 | −1.25724 | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 1.32288 | + | 5.50000i | 0.233854 | + | 0.972272i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.00000 | + | 2.64575i | −1.20049 | + | 0.453743i | ||||
\(35\) | − | 1.00000i | − | 0.169031i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.29150i | − | 0.869918i | −0.900450 | − | 0.434959i | \(-0.856763\pi\) | ||
0.900450 | − | 0.434959i | \(-0.143237\pi\) | |||||||
\(38\) | −2.64575 | − | 7.00000i | −0.429198 | − | 1.13555i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.50000 | + | 1.32288i | 0.395285 | + | 0.209165i | ||||
\(41\) | −5.29150 | −0.826394 | −0.413197 | − | 0.910642i | \(-0.635588\pi\) | ||||
−0.413197 | + | 0.910642i | \(0.635588\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5830i | 1.61389i | 0.590624 | + | 0.806947i | \(0.298881\pi\) | ||||
−0.590624 | + | 0.806947i | \(0.701119\pi\) | |||||||
\(44\) | −3.96863 | − | 4.50000i | −0.598293 | − | 0.678401i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.00000 | + | 2.64575i | −1.03209 | + | 0.390095i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −5.29150 | + | 2.00000i | −0.748331 | + | 0.282843i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.00000 | − | 7.93725i | −0.970725 | − | 1.10070i | ||||
\(53\) | 9.00000i | 1.23625i | 0.786082 | + | 0.618123i | \(0.212106\pi\) | ||||
−0.786082 | + | 0.618123i | \(0.787894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | −1.32288 | + | 2.50000i | −0.176777 | + | 0.334077i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | + | 7.93725i | 0.393919 | + | 1.04221i | ||||
\(59\) | 4.00000i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838471\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 9.26013 | − | 3.50000i | 1.17604 | − | 0.444500i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.50000 | − | 6.61438i | −0.562500 | − | 0.826797i | ||||
\(65\) | −5.29150 | −0.656330 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 7.93725 | − | 7.00000i | 0.962533 | − | 0.848875i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.500000 | + | 1.32288i | 0.0597614 | + | 0.158114i | ||||
\(71\) | −15.8745 | −1.88396 | −0.941979 | − | 0.335673i | \(-0.891036\pi\) | ||||
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | 0.351123 | 0.175562 | − | 0.984468i | \(-0.443826\pi\) | ||||
0.175562 | + | 0.984468i | \(0.443826\pi\) | |||||||
\(74\) | 2.64575 | + | 7.00000i | 0.307562 | + | 0.813733i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.00000 | + | 7.93725i | 0.802955 | + | 0.910465i | ||||
\(77\) | − | 3.00000i | − | 0.341882i | ||||||
\(78\) | 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 | ||||||||
\(82\) | 7.00000 | − | 2.64575i | 0.773021 | − | 0.292174i | ||||
\(83\) | 7.00000i | 0.768350i | 0.923260 | + | 0.384175i | \(0.125514\pi\) | ||||
−0.923260 | + | 0.384175i | \(0.874486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 5.29150i | − | 0.573944i | ||||||
\(86\) | −5.29150 | − | 14.0000i | −0.570597 | − | 1.50966i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.50000 | + | 3.96863i | 0.799503 | + | 0.423057i | ||||
\(89\) | 10.5830 | 1.12180 | 0.560898 | − | 0.827885i | \(-0.310456\pi\) | ||||
0.560898 | + | 0.827885i | \(0.310456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.29150i | − | 0.554700i | ||||||
\(92\) | 7.93725 | − | 7.00000i | 0.827516 | − | 0.729800i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.29150 | 0.542897 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 7.93725 | − | 3.00000i | 0.801784 | − | 0.303046i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.00000 | − | 5.29150i | 0.600000 | − | 0.529150i | ||||
\(101\) | 17.0000i | 1.69156i | 0.533529 | + | 0.845782i | \(0.320865\pi\) | ||||
−0.533529 | + | 0.845782i | \(0.679135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 13.2288 | + | 7.00000i | 1.29719 | + | 0.686406i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.50000 | − | 11.9059i | −0.437079 | − | 1.15640i | ||||
\(107\) | − | 3.00000i | − | 0.290021i | −0.989430 | − | 0.145010i | \(-0.953678\pi\) | ||
0.989430 | − | 0.145010i | \(-0.0463216\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.29150i | 0.506834i | 0.967357 | + | 0.253417i | \(0.0815545\pi\) | ||||
−0.967357 | + | 0.253417i | \(0.918446\pi\) | |||||||
\(110\) | 3.96863 | − | 1.50000i | 0.378394 | − | 0.143019i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 3.96863i | 0.0472456 | − | 0.375000i | ||||
\(113\) | −15.8745 | −1.49335 | −0.746674 | − | 0.665190i | \(-0.768350\pi\) | ||||
−0.746674 | + | 0.665190i | \(0.768350\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.29150i | − | 0.493435i | ||||||
\(116\) | −7.93725 | − | 9.00000i | −0.736956 | − | 0.835629i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.00000 | − | 5.29150i | −0.184115 | − | 0.487122i | ||||
\(119\) | 5.29150 | 0.485071 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | 0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.5000 | + | 9.26013i | −0.942928 | + | 0.831584i | ||||
\(125\) | − | 9.00000i | − | 0.804984i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0000 | 1.15356 | 0.576782 | − | 0.816898i | \(-0.304308\pi\) | ||||
0.576782 | + | 0.816898i | \(0.304308\pi\) | |||||||
\(128\) | 9.26013 | + | 6.50000i | 0.818488 | + | 0.574524i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.00000 | − | 2.64575i | 0.613941 | − | 0.232048i | ||||
\(131\) | 7.00000i | 0.611593i | 0.952097 | + | 0.305796i | \(0.0989227\pi\) | ||||
−0.952097 | + | 0.305796i | \(0.901077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.29150i | 0.458831i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.00000 | + | 13.2288i | −0.600245 | + | 1.13436i | ||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.5830i | − | 0.897639i | −0.893622 | − | 0.448819i | \(-0.851845\pi\) | ||
0.893622 | − | 0.448819i | \(-0.148155\pi\) | |||||||
\(140\) | −1.32288 | − | 1.50000i | −0.111803 | − | 0.126773i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 21.0000 | − | 7.93725i | 1.76228 | − | 0.666080i | ||||
\(143\) | −15.8745 | −1.32749 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | −3.96863 | + | 1.50000i | −0.328446 | + | 0.124141i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.00000 | − | 7.93725i | −0.575396 | − | 0.652438i | ||||
\(149\) | 3.00000i | 0.245770i | 0.992421 | + | 0.122885i | \(0.0392146\pi\) | ||||
−0.992421 | + | 0.122885i | \(0.960785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.00000 | 0.244137 | 0.122068 | − | 0.992522i | \(-0.461047\pi\) | ||||
0.122068 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(152\) | −13.2288 | − | 7.00000i | −1.07299 | − | 0.567775i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.50000 | + | 3.96863i | 0.120873 | + | 0.319801i | ||||
\(155\) | 7.00000i | 0.562254i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5830i | 0.844616i | 0.906452 | + | 0.422308i | \(0.138780\pi\) | ||||
−0.906452 | + | 0.422308i | \(0.861220\pi\) | |||||||
\(158\) | −5.29150 | + | 2.00000i | −0.420969 | + | 0.159111i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.50000 | − | 1.32288i | 0.434813 | − | 0.104583i | ||||
\(161\) | 5.29150 | 0.417029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.29150i | − | 0.414462i | −0.978292 | − | 0.207231i | \(-0.933555\pi\) | ||
0.978292 | − | 0.207231i | \(-0.0664452\pi\) | |||||||
\(164\) | −7.93725 | + | 7.00000i | −0.619795 | + | 0.546608i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.50000 | − | 9.26013i | −0.271653 | − | 0.718725i | ||||
\(167\) | 10.5830 | 0.818938 | 0.409469 | − | 0.912324i | \(-0.365714\pi\) | ||||
0.409469 | + | 0.912324i | \(0.365714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.0000 | −1.15385 | ||||||||
\(170\) | 2.64575 | + | 7.00000i | 0.202920 | + | 0.536875i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.0000 | + | 15.8745i | 1.06749 | + | 1.21042i | ||||
\(173\) | − | 15.0000i | − | 1.14043i | −0.821496 | − | 0.570214i | \(-0.806860\pi\) | ||
0.821496 | − | 0.570214i | \(-0.193140\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | −11.9059 | − | 1.50000i | −0.897440 | − | 0.113067i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.0000 | + | 5.29150i | −1.04934 | + | 0.396615i | ||||
\(179\) | − | 23.0000i | − | 1.71910i | −0.511051 | − | 0.859550i | \(-0.670744\pi\) | ||
0.511051 | − | 0.859550i | \(-0.329256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.1660i | 1.57326i | 0.617426 | + | 0.786629i | \(0.288175\pi\) | ||||
−0.617426 | + | 0.786629i | \(0.711825\pi\) | |||||||
\(182\) | 2.64575 | + | 7.00000i | 0.196116 | + | 0.518875i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.00000 | + | 13.2288i | −0.516047 | + | 0.975237i | ||||
\(185\) | −5.29150 | −0.389039 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 15.8745i | − | 1.16086i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.00000 | + | 2.64575i | −0.507833 | + | 0.191943i | ||||
\(191\) | 5.29150 | 0.382880 | 0.191440 | − | 0.981504i | \(-0.438684\pi\) | ||||
0.191440 | + | 0.981504i | \(0.438684\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.00000 | −0.215945 | −0.107972 | − | 0.994154i | \(-0.534436\pi\) | ||||
−0.107972 | + | 0.994154i | \(0.534436\pi\) | |||||||
\(194\) | −9.26013 | + | 3.50000i | −0.664839 | + | 0.251285i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.00000 | + | 7.93725i | −0.642857 | + | 0.566947i | ||||
\(197\) | 13.0000i | 0.926212i | 0.886303 | + | 0.463106i | \(0.153265\pi\) | ||||
−0.886303 | + | 0.463106i | \(0.846735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.0000 | −1.20510 | −0.602549 | − | 0.798082i | \(-0.705848\pi\) | ||||
−0.602549 | + | 0.798082i | \(0.705848\pi\) | |||||||
\(200\) | −5.29150 | + | 10.0000i | −0.374166 | + | 0.707107i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.50000 | − | 22.4889i | −0.598058 | − | 1.58231i | ||||
\(203\) | − | 6.00000i | − | 0.421117i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.29150i | 0.369575i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −21.0000 | − | 2.64575i | −1.45609 | − | 0.183450i | ||||
\(209\) | 15.8745 | 1.09806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5.29150i | − | 0.364282i | −0.983272 | − | 0.182141i | \(-0.941697\pi\) | ||
0.983272 | − | 0.182141i | \(-0.0583027\pi\) | |||||||
\(212\) | 11.9059 | + | 13.5000i | 0.817699 | + | 0.927184i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.50000 | + | 3.96863i | 0.102538 | + | 0.271290i | ||||
\(215\) | 10.5830 | 0.721755 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.00000 | −0.475191 | ||||||||
\(218\) | −2.64575 | − | 7.00000i | −0.179193 | − | 0.474100i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.50000 | + | 3.96863i | −0.303390 | + | 0.267565i | ||||
\(221\) | − | 28.0000i | − | 1.88348i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 1.32288 | + | 5.50000i | 0.0883883 | + | 0.367484i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.0000 | − | 7.93725i | 1.39690 | − | 0.527978i | ||||
\(227\) | − | 4.00000i | − | 0.265489i | −0.991150 | − | 0.132745i | \(-0.957621\pi\) | ||
0.991150 | − | 0.132745i | \(-0.0423790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.1660i | 1.39869i | 0.714785 | + | 0.699345i | \(0.246525\pi\) | ||||
−0.714785 | + | 0.699345i | \(0.753475\pi\) | |||||||
\(230\) | 2.64575 | + | 7.00000i | 0.174456 | + | 0.461566i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.0000 | + | 7.93725i | 0.984798 | + | 0.521106i | ||||
\(233\) | 10.5830 | 0.693316 | 0.346658 | − | 0.937992i | \(-0.387316\pi\) | ||||
0.346658 | + | 0.937992i | \(0.387316\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.29150 | + | 6.00000i | 0.344447 | + | 0.390567i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.00000 | + | 2.64575i | −0.453743 | + | 0.171499i | ||||
\(239\) | 15.8745 | 1.02684 | 0.513418 | − | 0.858138i | \(-0.328379\pi\) | ||||
0.513418 | + | 0.858138i | \(0.328379\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | −2.64575 | + | 1.00000i | −0.170075 | + | 0.0642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.00000i | 0.383326i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.0000 | 1.78160 | ||||||||
\(248\) | 9.26013 | − | 17.5000i | 0.588019 | − | 1.11125i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.50000 | + | 11.9059i | 0.284605 | + | 0.752994i | ||||
\(251\) | 12.0000i | 0.757433i | 0.925513 | + | 0.378717i | \(0.123635\pi\) | ||||
−0.925513 | + | 0.378717i | \(0.876365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 15.8745i | − | 0.998022i | ||||||
\(254\) | −17.1974 | + | 6.50000i | −1.07906 | + | 0.407846i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5000 | − | 3.96863i | −0.968750 | − | 0.248039i | ||||
\(257\) | 15.8745 | 0.990225 | 0.495112 | − | 0.868829i | \(-0.335127\pi\) | ||||
0.495112 | + | 0.868829i | \(0.335127\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5.29150i | − | 0.328798i | ||||||
\(260\) | −7.93725 | + | 7.00000i | −0.492248 | + | 0.434122i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.50000 | − | 9.26013i | −0.216231 | − | 0.572093i | ||||
\(263\) | −5.29150 | −0.326288 | −0.163144 | − | 0.986602i | \(-0.552164\pi\) | ||||
−0.163144 | + | 0.986602i | \(0.552164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | −2.64575 | − | 7.00000i | −0.162221 | − | 0.429198i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 18.0000i | − | 1.09748i | −0.835993 | − | 0.548740i | \(-0.815108\pi\) | ||
0.835993 | − | 0.548740i | \(-0.184892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.0000 | 0.911185 | 0.455593 | − | 0.890188i | \(-0.349427\pi\) | ||||
0.455593 | + | 0.890188i | \(0.349427\pi\) | |||||||
\(272\) | 2.64575 | − | 21.0000i | 0.160422 | − | 1.27331i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 12.0000i | − | 0.723627i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 10.5830i | − | 0.635871i | −0.948112 | − | 0.317936i | \(-0.897010\pi\) | ||
0.948112 | − | 0.317936i | \(-0.102990\pi\) | |||||||
\(278\) | 5.29150 | + | 14.0000i | 0.317363 | + | 0.839664i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.50000 | + | 1.32288i | 0.149404 | + | 0.0790569i | ||||
\(281\) | −15.8745 | −0.946994 | −0.473497 | − | 0.880795i | \(-0.657008\pi\) | ||||
−0.473497 | + | 0.880795i | \(0.657008\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.4575i | 1.57274i | 0.617758 | + | 0.786368i | \(0.288041\pi\) | ||||
−0.617758 | + | 0.786368i | \(0.711959\pi\) | |||||||
\(284\) | −23.8118 | + | 21.0000i | −1.41297 | + | 1.24612i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.0000 | − | 7.93725i | 1.24176 | − | 0.469340i | ||||
\(287\) | −5.29150 | −0.312348 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.0000 | 0.647059 | ||||||||
\(290\) | 7.93725 | − | 3.00000i | 0.466092 | − | 0.176166i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.50000 | − | 3.96863i | 0.263343 | − | 0.232246i | ||||
\(293\) | 30.0000i | 1.75262i | 0.481749 | + | 0.876309i | \(0.340002\pi\) | ||||
−0.481749 | + | 0.876309i | \(0.659998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 13.2288 | + | 7.00000i | 0.768906 | + | 0.406867i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.50000 | − | 3.96863i | −0.0868927 | − | 0.229896i | ||||
\(299\) | − | 28.0000i | − | 1.61928i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.5830i | 0.609994i | ||||||||
\(302\) | −3.96863 | + | 1.50000i | −0.228369 | + | 0.0863153i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 21.0000 | + | 2.64575i | 1.20443 | + | 0.151744i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.8745i | − | 0.906006i | −0.891509 | − | 0.453003i | \(-0.850353\pi\) | ||
0.891509 | − | 0.453003i | \(-0.149647\pi\) | |||||||
\(308\) | −3.96863 | − | 4.50000i | −0.226134 | − | 0.256411i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.50000 | − | 9.26013i | −0.198787 | − | 0.525940i | ||||
\(311\) | −26.4575 | −1.50027 | −0.750134 | − | 0.661286i | \(-0.770011\pi\) | ||||
−0.750134 | + | 0.661286i | \(0.770011\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00000 | −0.0565233 | −0.0282617 | − | 0.999601i | \(-0.508997\pi\) | ||||
−0.0282617 | + | 0.999601i | \(0.508997\pi\) | |||||||
\(314\) | −5.29150 | − | 14.0000i | −0.298617 | − | 0.790066i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.00000 | − | 5.29150i | 0.337526 | − | 0.297670i | ||||
\(317\) | − | 13.0000i | − | 0.730153i | −0.930978 | − | 0.365076i | \(-0.881043\pi\) | ||
0.930978 | − | 0.365076i | \(-0.118957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | −6.61438 | + | 4.50000i | −0.369755 | + | 0.251558i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.00000 | + | 2.64575i | −0.390095 | + | 0.147442i | ||||
\(323\) | 28.0000i | 1.55796i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 21.1660i | − | 1.17408i | ||||||
\(326\) | 2.64575 | + | 7.00000i | 0.146535 | + | 0.387694i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.00000 | − | 13.2288i | 0.386510 | − | 0.730436i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 21.1660i | − | 1.16339i | −0.813407 | − | 0.581695i | \(-0.802390\pi\) | ||
0.813407 | − | 0.581695i | \(-0.197610\pi\) | |||||||
\(332\) | 9.26013 | + | 10.5000i | 0.508216 | + | 0.576262i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.0000 | + | 5.29150i | −0.766046 | + | 0.289538i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.0000 | 1.85210 | 0.926049 | − | 0.377403i | \(-0.123183\pi\) | ||||
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | 19.8431 | − | 7.50000i | 1.07932 | − | 0.407946i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.00000 | − | 7.93725i | −0.379628 | − | 0.430458i | ||||
\(341\) | 21.0000i | 1.13721i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −26.4575 | − | 14.0000i | −1.42649 | − | 0.754829i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.50000 | + | 19.8431i | 0.403202 | + | 1.06677i | ||||
\(347\) | 23.0000i | 1.23470i | 0.786687 | + | 0.617352i | \(0.211795\pi\) | ||||
−0.786687 | + | 0.617352i | \(0.788205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.29150i | − | 0.283248i | −0.989921 | − | 0.141624i | \(-0.954768\pi\) | ||
0.989921 | − | 0.141624i | \(-0.0452323\pi\) | |||||||
\(350\) | −5.29150 | + | 2.00000i | −0.282843 | + | 0.106904i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.5000 | − | 3.96863i | 0.879453 | − | 0.211529i | ||||
\(353\) | −15.8745 | −0.844915 | −0.422457 | − | 0.906383i | \(-0.638832\pi\) | ||||
−0.422457 | + | 0.906383i | \(0.638832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.8745i | 0.842531i | ||||||||
\(356\) | 15.8745 | − | 14.0000i | 0.841347 | − | 0.741999i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.5000 | + | 30.4261i | 0.607794 | + | 1.60807i | ||||
\(359\) | 21.1660 | 1.11710 | 0.558550 | − | 0.829471i | \(-0.311358\pi\) | ||||
0.558550 | + | 0.829471i | \(0.311358\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | −10.5830 | − | 28.0000i | −0.556230 | − | 1.47165i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.00000 | − | 7.93725i | −0.366900 | − | 0.416025i | ||||
\(365\) | − | 3.00000i | − | 0.157027i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.00000 | −0.156599 | −0.0782994 | − | 0.996930i | \(-0.524949\pi\) | ||||
−0.0782994 | + | 0.996930i | \(0.524949\pi\) | |||||||
\(368\) | 2.64575 | − | 21.0000i | 0.137919 | − | 1.09470i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.00000 | − | 2.64575i | 0.363913 | − | 0.137546i | ||||
\(371\) | 9.00000i | 0.467257i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.4575i | − | 1.36992i | −0.728582 | − | 0.684959i | \(-0.759820\pi\) | ||
0.728582 | − | 0.684959i | \(-0.240180\pi\) | |||||||
\(374\) | 7.93725 | + | 21.0000i | 0.410426 | + | 1.08588i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.7490 | −1.63516 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.1660i | 1.08722i | 0.839336 | + | 0.543612i | \(0.182944\pi\) | ||||
−0.839336 | + | 0.543612i | \(0.817056\pi\) | |||||||
\(380\) | 7.93725 | − | 7.00000i | 0.407173 | − | 0.359092i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.00000 | + | 2.64575i | −0.358151 | + | 0.135368i | ||||
\(383\) | −15.8745 | −0.811149 | −0.405575 | − | 0.914062i | \(-0.632929\pi\) | ||||
−0.405575 | + | 0.914062i | \(0.632929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.00000 | −0.152894 | ||||||||
\(386\) | 3.96863 | − | 1.50000i | 0.201998 | − | 0.0763480i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.5000 | − | 9.26013i | 0.533057 | − | 0.470112i | ||||
\(389\) | − | 5.00000i | − | 0.253510i | −0.991934 | − | 0.126755i | \(-0.959544\pi\) | ||
0.991934 | − | 0.126755i | \(-0.0404562\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.0000 | 1.41602 | ||||||||
\(392\) | 7.93725 | − | 15.0000i | 0.400892 | − | 0.757614i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.50000 | − | 17.1974i | −0.327465 | − | 0.866392i | ||||
\(395\) | − | 4.00000i | − | 0.201262i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.29150i | 0.265573i | 0.991145 | + | 0.132786i | \(0.0423924\pi\) | ||||
−0.991145 | + | 0.132786i | \(0.957608\pi\) | |||||||
\(398\) | 22.4889 | − | 8.50000i | 1.12727 | − | 0.426067i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | − | 15.8745i | 0.100000 | − | 0.793725i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.0405i | 1.84512i | ||||||||
\(404\) | 22.4889 | + | 25.5000i | 1.11886 | + | 1.26867i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | + | 7.93725i | 0.148888 | + | 0.393919i | ||||
\(407\) | −15.8745 | −0.786870 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0000 | −0.543915 | −0.271957 | − | 0.962309i | \(-0.587671\pi\) | ||||
−0.271957 | + | 0.962309i | \(0.587671\pi\) | |||||||
\(410\) | −2.64575 | − | 7.00000i | −0.130664 | − | 0.345705i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000i | 0.196827i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.00000 | 0.343616 | ||||||||
\(416\) | 29.1033 | − | 7.00000i | 1.42690 | − | 0.343203i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.0000 | + | 7.93725i | −1.02714 | + | 0.388224i | ||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 10.5830i | − | 0.515784i | −0.966174 | − | 0.257892i | \(-0.916972\pi\) | ||
0.966174 | − | 0.257892i | \(-0.0830279\pi\) | |||||||
\(422\) | 2.64575 | + | 7.00000i | 0.128793 | + | 0.340755i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −22.5000 | − | 11.9059i | −1.09270 | − | 0.578201i | ||||
\(425\) | 21.1660 | 1.02670 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.96863 | − | 4.50000i | −0.191831 | − | 0.217516i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.0000 | + | 5.29150i | −0.675140 | + | 0.255179i | ||||
\(431\) | 31.7490 | 1.52930 | 0.764648 | − | 0.644448i | \(-0.222913\pi\) | ||||
0.764648 | + | 0.644448i | \(0.222913\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000 | 0.240285 | 0.120142 | − | 0.992757i | \(-0.461665\pi\) | ||||
0.120142 | + | 0.992757i | \(0.461665\pi\) | |||||||
\(434\) | 9.26013 | − | 3.50000i | 0.444500 | − | 0.168005i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.00000 | + | 7.93725i | 0.335239 | + | 0.380126i | ||||
\(437\) | 28.0000i | 1.33942i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.0000 | −1.00228 | −0.501138 | − | 0.865368i | \(-0.667085\pi\) | ||||
−0.501138 | + | 0.865368i | \(0.667085\pi\) | |||||||
\(440\) | 3.96863 | − | 7.50000i | 0.189197 | − | 0.357548i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.0000 | + | 37.0405i | 0.665912 | + | 1.76184i | ||||
\(443\) | 24.0000i | 1.14027i | 0.821549 | + | 0.570137i | \(0.193110\pi\) | ||||
−0.821549 | + | 0.570137i | \(0.806890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 10.5830i | − | 0.501683i | ||||||
\(446\) | 21.1660 | − | 8.00000i | 1.00224 | − | 0.378811i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.50000 | − | 6.61438i | −0.212605 | − | 0.312500i | ||||
\(449\) | −15.8745 | −0.749164 | −0.374582 | − | 0.927194i | \(-0.622214\pi\) | ||||
−0.374582 | + | 0.927194i | \(0.622214\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.8745i | 0.747501i | ||||||||
\(452\) | −23.8118 | + | 21.0000i | −1.12001 | + | 0.987757i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.00000 | + | 5.29150i | 0.0938647 | + | 0.248343i | ||||
\(455\) | −5.29150 | −0.248069 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.0000 | 0.795226 | 0.397613 | − | 0.917553i | \(-0.369839\pi\) | ||||
0.397613 | + | 0.917553i | \(0.369839\pi\) | |||||||
\(458\) | −10.5830 | − | 28.0000i | −0.494511 | − | 1.30835i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.00000 | − | 7.93725i | −0.326377 | − | 0.370076i | ||||
\(461\) | 9.00000i | 0.419172i | 0.977790 | + | 0.209586i | \(0.0672116\pi\) | ||||
−0.977790 | + | 0.209586i | \(0.932788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.0000 | −1.90543 | −0.952716 | − | 0.303863i | \(-0.901724\pi\) | ||||
−0.952716 | + | 0.303863i | \(0.901724\pi\) | |||||||
\(464\) | −23.8118 | − | 3.00000i | −1.10543 | − | 0.139272i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.0000 | + | 5.29150i | −0.648537 | + | 0.245124i | ||||
\(467\) | − | 1.00000i | − | 0.0462745i | −0.999732 | − | 0.0231372i | \(-0.992635\pi\) | ||
0.999732 | − | 0.0231372i | \(-0.00736547\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.0000 | − | 5.29150i | −0.460287 | − | 0.243561i | ||||
\(473\) | 31.7490 | 1.45982 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.1660i | 0.971163i | ||||||||
\(476\) | 7.93725 | − | 7.00000i | 0.363803 | − | 0.320844i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21.0000 | + | 7.93725i | −0.960518 | + | 0.363042i | ||||
\(479\) | −21.1660 | −0.967100 | −0.483550 | − | 0.875317i | \(-0.660653\pi\) | ||||
−0.483550 | + | 0.875317i | \(0.660653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.0000 | −1.27669 | ||||||||
\(482\) | 13.2288 | − | 5.00000i | 0.602553 | − | 0.227744i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.00000 | − | 2.64575i | 0.136364 | − | 0.120261i | ||||
\(485\) | − | 7.00000i | − | 0.317854i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.0000 | −1.81257 | −0.906287 | − | 0.422664i | \(-0.861095\pi\) | ||||
−0.906287 | + | 0.422664i | \(0.861095\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.00000 | − | 7.93725i | −0.135526 | − | 0.358569i | ||||
\(491\) | − | 29.0000i | − | 1.30875i | −0.756169 | − | 0.654376i | \(-0.772931\pi\) | ||
0.756169 | − | 0.654376i | \(-0.227069\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 31.7490i | − | 1.42990i | ||||||
\(494\) | −37.0405 | + | 14.0000i | −1.66653 | + | 0.629890i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.50000 | + | 27.7804i | −0.157155 | + | 1.24738i | ||||
\(497\) | −15.8745 | −0.712069 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | −11.9059 | − | 13.5000i | −0.532447 | − | 0.603738i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.00000 | − | 15.8745i | −0.267793 | − | 0.708514i | ||||
\(503\) | −15.8745 | −0.707809 | −0.353905 | − | 0.935282i | \(-0.615146\pi\) | ||||
−0.353905 | + | 0.935282i | \(0.615146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.0000 | 0.756490 | ||||||||
\(506\) | 7.93725 | + | 21.0000i | 0.352854 | + | 0.933564i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.5000 | − | 17.1974i | 0.865173 | − | 0.763011i | ||||
\(509\) | − | 21.0000i | − | 0.930809i | −0.885098 | − | 0.465404i | \(-0.845909\pi\) | ||
0.885098 | − | 0.465404i | \(-0.154091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | 0.132712 | ||||||||
\(512\) | 22.4889 | − | 2.50000i | 0.993878 | − | 0.110485i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.0000 | + | 7.93725i | −0.926270 | + | 0.350097i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.64575 | + | 7.00000i | 0.116248 | + | 0.307562i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.00000 | − | 13.2288i | 0.306970 | − | 0.580119i | ||||
\(521\) | −15.8745 | −0.695475 | −0.347737 | − | 0.937592i | \(-0.613050\pi\) | ||||
−0.347737 | + | 0.937592i | \(0.613050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.8745i | 0.694144i | 0.937839 | + | 0.347072i | \(0.112824\pi\) | ||||
−0.937839 | + | 0.347072i | \(0.887176\pi\) | |||||||
\(524\) | 9.26013 | + | 10.5000i | 0.404531 | + | 0.458695i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.00000 | − | 2.64575i | 0.305215 | − | 0.115360i | ||||
\(527\) | −37.0405 | −1.61351 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.00000 | 0.217391 | ||||||||
\(530\) | −11.9059 | + | 4.50000i | −0.517158 | + | 0.195468i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.00000 | + | 7.93725i | 0.303488 | + | 0.344124i | ||||
\(533\) | 28.0000i | 1.21281i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.00000 | −0.129701 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.00000 | + | 23.8118i | 0.388018 | + | 1.02660i | ||||
\(539\) | 18.0000i | 0.775315i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5830i | 0.454999i | 0.973778 | + | 0.227499i | \(0.0730550\pi\) | ||||
−0.973778 | + | 0.227499i | \(0.926945\pi\) | |||||||
\(542\) | −19.8431 | + | 7.50000i | −0.852336 | + | 0.322153i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.00000 | + | 29.1033i | 0.300123 | + | 1.24779i | ||||
\(545\) | 5.29150 | 0.226663 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.29150i | 0.226248i | 0.993581 | + | 0.113124i | \(0.0360858\pi\) | ||||
−0.993581 | + | 0.113124i | \(0.963914\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.00000 | + | 15.8745i | 0.255841 | + | 0.676891i | ||||
\(551\) | 31.7490 | 1.35255 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | 5.29150 | + | 14.0000i | 0.224814 | + | 0.594803i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.0000 | − | 15.8745i | −0.593732 | − | 0.673229i | ||||
\(557\) | − | 39.0000i | − | 1.65248i | −0.563316 | − | 0.826242i | \(-0.690475\pi\) | ||
0.563316 | − | 0.826242i | \(-0.309525\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 56.0000 | 2.36855 | ||||||||
\(560\) | −3.96863 | − | 0.500000i | −0.167705 | − | 0.0211289i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.0000 | − | 7.93725i | 0.885832 | − | 0.334813i | ||||
\(563\) | − | 3.00000i | − | 0.126435i | −0.998000 | − | 0.0632175i | \(-0.979864\pi\) | ||
0.998000 | − | 0.0632175i | \(-0.0201362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.8745i | 0.667846i | ||||||||
\(566\) | −13.2288 | − | 35.0000i | −0.556046 | − | 1.47116i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.0000 | − | 39.6863i | 0.881140 | − | 1.66520i | ||||
\(569\) | 31.7490 | 1.33099 | 0.665494 | − | 0.746403i | \(-0.268221\pi\) | ||||
0.665494 | + | 0.746403i | \(0.268221\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 26.4575i | − | 1.10721i | −0.832779 | − | 0.553606i | \(-0.813251\pi\) | ||
0.832779 | − | 0.553606i | \(-0.186749\pi\) | |||||||
\(572\) | −23.8118 | + | 21.0000i | −0.995620 | + | 0.878054i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.00000 | − | 2.64575i | 0.292174 | − | 0.110432i | ||||
\(575\) | 21.1660 | 0.882684 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | −14.5516 | + | 5.50000i | −0.605268 | + | 0.228770i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.00000 | + | 7.93725i | −0.373705 | + | 0.329577i | ||||
\(581\) | 7.00000i | 0.290409i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.0000 | 1.11823 | ||||||||
\(584\) | −3.96863 | + | 7.50000i | −0.164223 | + | 0.310352i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.0000 | − | 39.6863i | −0.619644 | − | 1.63942i | ||||
\(587\) | − | 23.0000i | − | 0.949312i | −0.880172 | − | 0.474656i | \(-0.842573\pi\) | ||
0.880172 | − | 0.474656i | \(-0.157427\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 37.0405i | − | 1.52623i | ||||||
\(590\) | −5.29150 | + | 2.00000i | −0.217848 | + | 0.0823387i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −21.0000 | − | 2.64575i | −0.863095 | − | 0.108740i | ||||
\(593\) | −31.7490 | −1.30378 | −0.651888 | − | 0.758315i | \(-0.726023\pi\) | ||||
−0.651888 | + | 0.758315i | \(0.726023\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 5.29150i | − | 0.216930i | ||||||
\(596\) | 3.96863 | + | 4.50000i | 0.162561 | + | 0.184327i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.0000 | + | 37.0405i | 0.572503 | + | 1.51470i | ||||
\(599\) | 21.1660 | 0.864820 | 0.432410 | − | 0.901677i | \(-0.357663\pi\) | ||||
0.432410 | + | 0.901677i | \(0.357663\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.00000 | 0.203954 | 0.101977 | − | 0.994787i | \(-0.467483\pi\) | ||||
0.101977 | + | 0.994787i | \(0.467483\pi\) | |||||||
\(602\) | −5.29150 | − | 14.0000i | −0.215666 | − | 0.570597i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.50000 | − | 3.96863i | 0.183102 | − | 0.161481i | ||||
\(605\) | − | 2.00000i | − | 0.0813116i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.00000 | −0.324710 | −0.162355 | − | 0.986732i | \(-0.551909\pi\) | ||||
−0.162355 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(608\) | −29.1033 | + | 7.00000i | −1.18029 | + | 0.283887i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 10.5830i | − | 0.427444i | −0.976895 | − | 0.213722i | \(-0.931441\pi\) | ||
0.976895 | − | 0.213722i | \(-0.0685586\pi\) | |||||||
\(614\) | 7.93725 | + | 21.0000i | 0.320321 | + | 0.847491i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.50000 | + | 3.96863i | 0.302184 | + | 0.159901i | ||||
\(617\) | 5.29150 | 0.213028 | 0.106514 | − | 0.994311i | \(-0.466031\pi\) | ||||
0.106514 | + | 0.994311i | \(0.466031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.8745i | 0.638050i | 0.947746 | + | 0.319025i | \(0.103355\pi\) | ||||
−0.947746 | + | 0.319025i | \(0.896645\pi\) | |||||||
\(620\) | 9.26013 | + | 10.5000i | 0.371896 | + | 0.421690i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 35.0000 | − | 13.2288i | 1.40337 | − | 0.530425i | ||||
\(623\) | 10.5830 | 0.423999 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 1.32288 | − | 0.500000i | 0.0528727 | − | 0.0199840i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000 | + | 15.8745i | 0.558661 | + | 0.633462i | ||||
\(629\) | − | 28.0000i | − | 1.11643i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0000 | −0.915616 | −0.457808 | − | 0.889051i | \(-0.651365\pi\) | ||||
−0.457808 | + | 0.889051i | \(0.651365\pi\) | |||||||
\(632\) | −5.29150 | + | 10.0000i | −0.210485 | + | 0.397779i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.50000 | + | 17.1974i | 0.258148 | + | 0.682995i | ||||
\(635\) | − | 13.0000i | − | 0.515889i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.7490i | 1.25794i | ||||||||
\(638\) | 23.8118 | − | 9.00000i | 0.942717 | − | 0.356313i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.50000 | − | 9.26013i | 0.256935 | − | 0.366039i | ||||
\(641\) | 37.0405 | 1.46301 | 0.731506 | − | 0.681835i | \(-0.238818\pi\) | ||||
0.731506 | + | 0.681835i | \(0.238818\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 21.1660i | − | 0.834706i | −0.908744 | − | 0.417353i | \(-0.862958\pi\) | ||
0.908744 | − | 0.417353i | \(-0.137042\pi\) | |||||||
\(644\) | 7.93725 | − | 7.00000i | 0.312772 | − | 0.275839i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.0000 | − | 37.0405i | −0.550823 | − | 1.45734i | ||||
\(647\) | 31.7490 | 1.24818 | 0.624091 | − | 0.781351i | \(-0.285469\pi\) | ||||
0.624091 | + | 0.781351i | \(0.285469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | 10.5830 | + | 28.0000i | 0.415100 | + | 1.09825i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.00000 | − | 7.93725i | −0.274141 | − | 0.310847i | ||||
\(653\) | − | 3.00000i | − | 0.117399i | −0.998276 | − | 0.0586995i | \(-0.981305\pi\) | ||
0.998276 | − | 0.0586995i | \(-0.0186954\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.00000 | 0.273513 | ||||||||
\(656\) | −2.64575 | + | 21.0000i | −0.103299 | + | 0.819912i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 15.0000i | − | 0.584317i | −0.956370 | − | 0.292159i | \(-0.905627\pi\) | ||
0.956370 | − | 0.292159i | \(-0.0943735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.4575i | 1.02908i | 0.857467 | + | 0.514539i | \(0.172037\pi\) | ||||
−0.857467 | + | 0.514539i | \(0.827963\pi\) | |||||||
\(662\) | 10.5830 | + | 28.0000i | 0.411320 | + | 1.08825i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.5000 | − | 9.26013i | −0.679132 | − | 0.359363i | ||||
\(665\) | 5.29150 | 0.205196 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 31.7490i | − | 1.22933i | ||||||
\(668\) | 15.8745 | − | 14.0000i | 0.614203 | − | 0.541676i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.0000 | 1.11787 | 0.558934 | − | 0.829212i | \(-0.311211\pi\) | ||||
0.558934 | + | 0.829212i | \(0.311211\pi\) | |||||||
\(674\) | −44.9778 | + | 17.0000i | −1.73248 | + | 0.654816i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.5000 | + | 19.8431i | −0.865385 | + | 0.763197i | ||||
\(677\) | − | 6.00000i | − | 0.230599i | −0.993331 | − | 0.115299i | \(-0.963217\pi\) | ||
0.993331 | − | 0.115299i | \(-0.0367827\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.00000 | 0.268635 | ||||||||
\(680\) | 13.2288 | + | 7.00000i | 0.507300 | + | 0.268438i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.5000 | − | 27.7804i | −0.402066 | − | 1.06377i | ||||
\(683\) | − | 44.0000i | − | 1.68361i | −0.539779 | − | 0.841807i | \(-0.681492\pi\) | ||
0.539779 | − | 0.841807i | \(-0.318508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.1974 | − | 6.50000i | 0.656599 | − | 0.248171i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 42.0000 | + | 5.29150i | 1.60123 | + | 0.201737i | ||||
\(689\) | 47.6235 | 1.81431 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 42.3320i | − | 1.61039i | −0.593013 | − | 0.805193i | \(-0.702062\pi\) | ||
0.593013 | − | 0.805193i | \(-0.297938\pi\) | |||||||
\(692\) | −19.8431 | − | 22.5000i | −0.754323 | − | 0.855322i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.5000 | − | 30.4261i | −0.436534 | − | 1.15496i | ||||
\(695\) | −10.5830 | −0.401436 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0000 | −1.06058 | ||||||||
\(698\) | 2.64575 | + | 7.00000i | 0.100143 | + | 0.264954i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.00000 | − | 5.29150i | 0.226779 | − | 0.200000i | ||||
\(701\) | − | 1.00000i | − | 0.0377695i | −0.999822 | − | 0.0188847i | \(-0.993988\pi\) | ||
0.999822 | − | 0.0188847i | \(-0.00601156\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.0000 | 1.05604 | ||||||||
\(704\) | −19.8431 | + | 13.5000i | −0.747866 | + | 0.508800i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.0000 | − | 7.93725i | 0.790345 | − | 0.298722i | ||||
\(707\) | 17.0000i | 0.639351i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1660i | 0.794906i | 0.917622 | + | 0.397453i | \(0.130106\pi\) | ||||
−0.917622 | + | 0.397453i | \(0.869894\pi\) | |||||||
\(710\) | −7.93725 | − | 21.0000i | −0.297880 | − | 0.788116i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.0000 | + | 26.4575i | −0.524672 | + | 0.991537i | ||||
\(713\) | −37.0405 | −1.38718 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.8745i | 0.593673i | ||||||||
\(716\) | −30.4261 | − | 34.5000i | −1.13708 | − | 1.28933i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.0000 | + | 10.5830i | −1.04495 | + | 0.394954i | ||||
\(719\) | 21.1660 | 0.789359 | 0.394679 | − | 0.918819i | \(-0.370856\pi\) | ||||
0.394679 | + | 0.918819i | \(0.370856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11.9059 | − | 4.50000i | 0.443091 | − | 0.167473i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 28.0000 | + | 31.7490i | 1.04061 | + | 1.17994i | ||||
\(725\) | − | 24.0000i | − | 0.891338i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.0000 | 1.22390 | 0.611951 | − | 0.790896i | \(-0.290385\pi\) | ||||
0.611951 | + | 0.790896i | \(0.290385\pi\) | |||||||
\(728\) | 13.2288 | + | 7.00000i | 0.490290 | + | 0.259437i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.50000 | + | 3.96863i | 0.0555175 | + | 0.146885i | ||||
\(731\) | 56.0000i | 2.07123i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 5.29150i | − | 0.195446i | −0.995214 | − | 0.0977231i | \(-0.968844\pi\) | ||
0.995214 | − | 0.0977231i | \(-0.0311559\pi\) | |||||||
\(734\) | 3.96863 | − | 1.50000i | 0.146485 | − | 0.0553660i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.00000 | + | 29.1033i | 0.258023 | + | 1.07276i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.29150i | − | 0.194651i | −0.995253 | − | 0.0973255i | \(-0.968971\pi\) | ||
0.995253 | − | 0.0973255i | \(-0.0310288\pi\) | |||||||
\(740\) | −7.93725 | + | 7.00000i | −0.291779 | + | 0.257325i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.50000 | − | 11.9059i | −0.165200 | − | 0.437079i | ||||
\(743\) | −37.0405 | −1.35888 | −0.679442 | − | 0.733729i | \(-0.737778\pi\) | ||||
−0.679442 | + | 0.733729i | \(0.737778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.00000 | 0.109911 | ||||||||
\(746\) | 13.2288 | + | 35.0000i | 0.484339 | + | 1.28144i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −21.0000 | − | 23.8118i | −0.767836 | − | 0.870644i | ||||
\(749\) | − | 3.00000i | − | 0.109618i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.0000 | −1.13121 | −0.565603 | − | 0.824678i | \(-0.691357\pi\) | ||||
−0.565603 | + | 0.824678i | \(0.691357\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 42.0000 | − | 15.8745i | 1.52955 | − | 0.578115i | ||||
\(755\) | − | 3.00000i | − | 0.109181i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | −10.5830 | − | 28.0000i | −0.384392 | − | 1.01701i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.00000 | + | 13.2288i | −0.253917 | + | 0.479857i | ||||
\(761\) | −10.5830 | −0.383634 | −0.191817 | − | 0.981431i | \(-0.561438\pi\) | ||||
−0.191817 | + | 0.981431i | \(0.561438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.29150i | 0.191565i | ||||||||
\(764\) | 7.93725 | − | 7.00000i | 0.287160 | − | 0.253251i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.0000 | − | 7.93725i | 0.758761 | − | 0.286785i | ||||
\(767\) | 21.1660 | 0.764260 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.0000 | −1.26213 | −0.631066 | − | 0.775729i | \(-0.717382\pi\) | ||||
−0.631066 | + | 0.775729i | \(0.717382\pi\) | |||||||
\(770\) | 3.96863 | − | 1.50000i | 0.143019 | − | 0.0540562i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.50000 | + | 3.96863i | −0.161959 | + | 0.142834i | ||||
\(773\) | 14.0000i | 0.503545i | 0.967786 | + | 0.251773i | \(0.0810135\pi\) | ||||
−0.967786 | + | 0.251773i | \(0.918987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.0000 | −1.00579 | ||||||||
\(776\) | −9.26013 | + | 17.5000i | −0.332419 | + | 0.628213i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.50000 | + | 6.61438i | 0.0896293 | + | 0.237137i | ||||
\(779\) | − | 28.0000i | − | 1.00320i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.6235i | 1.70410i | ||||||||
\(782\) | −37.0405 | + | 14.0000i | −1.32457 | + | 0.500639i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00000 | + | 23.8118i | −0.107143 | + | 0.850420i | ||||
\(785\) | 10.5830 | 0.377724 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(788\) | 17.1974 | + | 19.5000i | 0.612631 | + | 0.694659i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.00000 | + | 5.29150i | 0.0711568 | + | 0.188263i | ||||
\(791\) | −15.8745 | −0.564433 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −2.64575 | − | 7.00000i | −0.0938942 | − | 0.248421i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25.5000 | + | 22.4889i | −0.903824 | + | 0.797097i | ||||
\(797\) | 49.0000i | 1.73567i | 0.496853 | + | 0.867835i | \(0.334489\pi\) | ||||
−0.496853 | + | 0.867835i | \(0.665511\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 5.29150 | + | 22.0000i | 0.187083 | + | 0.777817i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 9.00000i | − | 0.317603i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 5.29150i | − | 0.186501i | ||||||
\(806\) | −18.5203 | − | 49.0000i | −0.652348 | − | 1.72595i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −42.5000 | − | 22.4889i | −1.49514 | − | 0.791156i | ||||
\(809\) | −31.7490 | −1.11624 | −0.558118 | − | 0.829762i | \(-0.688476\pi\) | ||||
−0.558118 | + | 0.829762i | \(0.688476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37.0405i | − | 1.30067i | −0.759648 | − | 0.650334i | \(-0.774629\pi\) | ||
0.759648 | − | 0.650334i | \(-0.225371\pi\) | |||||||
\(812\) | −7.93725 | − | 9.00000i | −0.278543 | − | 0.315838i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.0000 | − | 7.93725i | 0.736050 | − | 0.278201i | ||||
\(815\) | −5.29150 | −0.185353 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −56.0000 | −1.95919 | ||||||||
\(818\) | 14.5516 | − | 5.50000i | 0.508786 | − | 0.192303i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.00000 | + | 7.93725i | 0.244451 | + | 0.277181i | ||||
\(821\) | − | 10.0000i | − | 0.349002i | −0.984657 | − | 0.174501i | \(-0.944169\pi\) | ||
0.984657 | − | 0.174501i | \(-0.0558313\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.0000 | 0.801730 | 0.400865 | − | 0.916137i | \(-0.368710\pi\) | ||||
0.400865 | + | 0.916137i | \(0.368710\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.00000 | − | 5.29150i | −0.0695889 | − | 0.184115i | ||||
\(827\) | 36.0000i | 1.25184i | 0.779886 | + | 0.625921i | \(0.215277\pi\) | ||||
−0.779886 | + | 0.625921i | \(0.784723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.1660i | 0.735126i | 0.929999 | + | 0.367563i | \(0.119808\pi\) | ||||
−0.929999 | + | 0.367563i | \(0.880192\pi\) | |||||||
\(830\) | −9.26013 | + | 3.50000i | −0.321424 | + | 0.121487i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −35.0000 | + | 23.8118i | −1.21341 | + | 0.825524i | ||||
\(833\) | −31.7490 | −1.10004 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 10.5830i | − | 0.366240i | ||||||
\(836\) | 23.8118 | − | 21.0000i | 0.823547 | − | 0.726300i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.0405 | −1.27878 | −0.639390 | − | 0.768882i | \(-0.720813\pi\) | ||||
−0.639390 | + | 0.768882i | \(0.720813\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 5.29150 | + | 14.0000i | 0.182357 | + | 0.482472i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.00000 | − | 7.93725i | −0.240950 | − | 0.273212i | ||||
\(845\) | 15.0000i | 0.516016i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | 35.7176 | + | 4.50000i | 1.22655 | + | 0.154531i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −28.0000 | + | 10.5830i | −0.960392 | + | 0.362994i | ||||
\(851\) | − | 28.0000i | − | 0.959828i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.50000 | + | 3.96863i | 0.256345 | + | 0.135645i | ||||
\(857\) | −15.8745 | −0.542263 | −0.271131 | − | 0.962542i | \(-0.587398\pi\) | ||||
−0.271131 | + | 0.962542i | \(0.587398\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 52.9150i | − | 1.80544i | −0.430231 | − | 0.902719i | \(-0.641568\pi\) | ||
0.430231 | − | 0.902719i | \(-0.358432\pi\) | |||||||
\(860\) | 15.8745 | − | 14.0000i | 0.541316 | − | 0.477396i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −42.0000 | + | 15.8745i | −1.43053 | + | 0.540688i | ||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0000 | −0.510015 | ||||||||
\(866\) | −6.61438 | + | 2.50000i | −0.224766 | + | 0.0849535i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.5000 | + | 9.26013i | −0.356393 | + | 0.314309i | ||||
\(869\) | − | 12.0000i | − | 0.407072i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −13.2288 | − | 7.00000i | −0.447982 | − | 0.237050i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.0000 | − | 37.0405i | −0.473557 | − | 1.25291i | ||||
\(875\) | − | 9.00000i | − | 0.304256i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.9150i | 1.78681i | 0.449249 | + | 0.893407i | \(0.351692\pi\) | ||||
−0.449249 | + | 0.893407i | \(0.648308\pi\) | |||||||
\(878\) | 27.7804 | − | 10.5000i | 0.937543 | − | 0.354358i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.50000 | + | 11.9059i | −0.0505650 | + | 0.401347i | ||||
\(881\) | 26.4575 | 0.891376 | 0.445688 | − | 0.895188i | \(-0.352959\pi\) | ||||
0.445688 | + | 0.895188i | \(0.352959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.2065i | 1.95881i | 0.201916 | + | 0.979403i | \(0.435283\pi\) | ||||
−0.201916 | + | 0.979403i | \(0.564717\pi\) | |||||||
\(884\) | −37.0405 | − | 42.0000i | −1.24581 | − | 1.41261i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | − | 31.7490i | −0.403148 | − | 1.06663i | ||||
\(887\) | 15.8745 | 0.533014 | 0.266507 | − | 0.963833i | \(-0.414130\pi\) | ||||
0.266507 | + | 0.963833i | \(0.414130\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.0000 | 0.436006 | ||||||||
\(890\) | 5.29150 | + | 14.0000i | 0.177372 | + | 0.469281i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.0000 | + | 21.1660i | −0.803579 | + | 0.708690i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.0000 | −0.768805 | ||||||||
\(896\) | 9.26013 | + | 6.50000i | 0.309359 | + | 0.217150i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.0000 | − | 7.93725i | 0.700779 | − | 0.264870i | ||||
\(899\) | 42.0000i | 1.40078i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.6235i | 1.58657i | ||||||||
\(902\) | −7.93725 | − | 21.0000i | −0.264282 | − | 0.699224i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.0000 | − | 39.6863i | 0.698450 | − | 1.31995i | ||||
\(905\) | 21.1660 | 0.703582 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.29150i | 0.175701i | 0.996134 | + | 0.0878507i | \(0.0279999\pi\) | ||||
−0.996134 | + | 0.0878507i | \(0.972000\pi\) | |||||||
\(908\) | −5.29150 | − | 6.00000i | −0.175605 | − | 0.199117i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.00000 | − | 2.64575i | 0.232048 | − | 0.0877058i | ||||
\(911\) | −31.7490 | −1.05189 | −0.525946 | − | 0.850518i | \(-0.676289\pi\) | ||||
−0.525946 | + | 0.850518i | \(0.676289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.0000 | 0.694999 | ||||||||
\(914\) | −22.4889 | + | 8.50000i | −0.743866 | + | 0.281155i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.0000 | + | 31.7490i | 0.925146 | + | 1.04902i | ||||
\(917\) | 7.00000i | 0.231160i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.00000 | 0.0989609 | 0.0494804 | − | 0.998775i | \(-0.484243\pi\) | ||||
0.0494804 | + | 0.998775i | \(0.484243\pi\) | |||||||
\(920\) | 13.2288 | + | 7.00000i | 0.436139 | + | 0.230783i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.50000 | − | 11.9059i | −0.148200 | − | 0.392099i | ||||
\(923\) | 84.0000i | 2.76489i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 21.1660i | − | 0.695934i | ||||||
\(926\) | 54.2379 | − | 20.5000i | 1.78237 | − | 0.673672i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 33.0000 | − | 7.93725i | 1.08328 | − | 0.260553i | ||||
\(929\) | −10.5830 | −0.347217 | −0.173609 | − | 0.984815i | \(-0.555543\pi\) | ||||
−0.173609 | + | 0.984815i | \(0.555543\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 31.7490i | − | 1.04053i | ||||||
\(932\) | 15.8745 | − | 14.0000i | 0.519987 | − | 0.458585i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.500000 | + | 1.32288i | 0.0163605 | + | 0.0432858i | ||||
\(935\) | −15.8745 | −0.519152 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.0000 | −0.620703 | −0.310351 | − | 0.950622i | \(-0.600447\pi\) | ||||
−0.310351 | + | 0.950622i | \(0.600447\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.0000i | 0.684580i | 0.939594 | + | 0.342290i | \(0.111203\pi\) | ||||
−0.939594 | + | 0.342290i | \(0.888797\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.0000 | −0.911805 | ||||||||
\(944\) | 15.8745 | + | 2.00000i | 0.516671 | + | 0.0650945i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.0000 | + | 15.8745i | −1.36554 | + | 0.516125i | ||||
\(947\) | − | 39.0000i | − | 1.26733i | −0.773608 | − | 0.633665i | \(-0.781550\pi\) | ||
0.773608 | − | 0.633665i | \(-0.218450\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 15.8745i | − | 0.515308i | ||||||
\(950\) | −10.5830 | − | 28.0000i | −0.343358 | − | 0.908440i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.00000 | + | 13.2288i | −0.226871 | + | 0.428746i | ||||
\(953\) | 31.7490 | 1.02845 | 0.514226 | − | 0.857655i | \(-0.328079\pi\) | ||||
0.514226 | + | 0.857655i | \(0.328079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.29150i | − | 0.171229i | ||||||
\(956\) | 23.8118 | − | 21.0000i | 0.770127 | − | 0.679189i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.0000 | − | 10.5830i | 0.904639 | − | 0.341921i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 37.0405 | − | 14.0000i | 1.19423 | − | 0.451378i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.0000 | + | 13.2288i | −0.483117 | + | 0.426070i | ||||
\(965\) | 3.00000i | 0.0965734i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.0000 | 1.31847 | 0.659236 | − | 0.751936i | \(-0.270880\pi\) | ||||
0.659236 | + | 0.751936i | \(0.270880\pi\) | |||||||
\(968\) | −2.64575 | + | 5.00000i | −0.0850377 | + | 0.160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.50000 | + | 9.26013i | 0.112378 | + | 0.297325i | ||||
\(971\) | − | 15.0000i | − | 0.481373i | −0.970603 | − | 0.240686i | \(-0.922627\pi\) | ||
0.970603 | − | 0.240686i | \(-0.0773725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 10.5830i | − | 0.339276i | ||||||
\(974\) | 52.9150 | − | 20.0000i | 1.69551 | − | 0.640841i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.5830 | −0.338580 | −0.169290 | − | 0.985566i | \(-0.554148\pi\) | ||||
−0.169290 | + | 0.985566i | \(0.554148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31.7490i | − | 1.01470i | ||||||
\(980\) | 7.93725 | + | 9.00000i | 0.253546 | + | 0.287494i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.5000 | + | 38.3634i | 0.462714 | + | 1.22423i | ||||
\(983\) | 42.3320 | 1.35018 | 0.675091 | − | 0.737735i | \(-0.264104\pi\) | ||||
0.675091 | + | 0.737735i | \(0.264104\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0000 | 0.414214 | ||||||||
\(986\) | 15.8745 | + | 42.0000i | 0.505547 | + | 1.33755i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 42.0000 | − | 37.0405i | 1.33620 | − | 1.17842i | ||||
\(989\) | 56.0000i | 1.78070i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.0000 | 1.49300 | 0.746502 | − | 0.665383i | \(-0.231732\pi\) | ||||
0.746502 | + | 0.665383i | \(0.231732\pi\) | |||||||
\(992\) | −9.26013 | − | 38.5000i | −0.294009 | − | 1.22238i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 21.0000 | − | 7.93725i | 0.666080 | − | 0.251754i | ||||
\(995\) | 17.0000i | 0.538936i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 15.8745i | − | 0.502751i | −0.967890 | − | 0.251375i | \(-0.919117\pi\) | ||
0.967890 | − | 0.251375i | \(-0.0808829\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))