Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(289,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 960) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.4 | ||
Root | \(-1.09445 + 0.895644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.289 |
Dual form | 2880.2.d.i.289.3 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.456850 | + | 2.18890i | −0.204310 | + | 0.978906i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.37780i | 1.65465i | 0.561721 | + | 0.827327i | \(0.310140\pi\) | ||||
−0.561721 | + | 0.827327i | \(0.689860\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.58258i | 1.68321i | 0.540094 | + | 0.841605i | \(0.318389\pi\) | ||||
−0.540094 | + | 0.841605i | \(0.681611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.37780 | 1.21418 | 0.607092 | − | 0.794632i | \(-0.292336\pi\) | ||||
0.607092 | + | 0.794632i | \(0.292336\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.58258i | 1.35397i | 0.735995 | + | 0.676987i | \(0.236715\pi\) | ||||
−0.735995 | + | 0.676987i | \(0.763285\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.58258 | − | 2.00000i | −0.916515 | − | 0.400000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.55040i | − | 0.473598i | −0.971559 | − | 0.236799i | \(-0.923902\pi\) | ||
0.971559 | − | 0.236799i | \(-0.0760982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.29150 | 0.950382 | 0.475191 | − | 0.879883i | \(-0.342379\pi\) | ||||
0.475191 | + | 0.879883i | \(0.342379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.58258 | − | 2.00000i | −1.61975 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.55040 | 0.419283 | 0.209642 | − | 0.977778i | \(-0.432770\pi\) | ||||
0.209642 | + | 0.977778i | \(0.432770\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.1652 | 1.70267 | 0.851335 | − | 0.524623i | \(-0.175794\pi\) | ||||
0.851335 | + | 0.524623i | \(0.175794\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.92820i | − | 1.01058i | −0.862949 | − | 0.505291i | \(-0.831385\pi\) | ||
0.862949 | − | 0.505291i | \(-0.168615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.1652 | −1.73788 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.84190 | 1.07717 | 0.538584 | − | 0.842572i | \(-0.318959\pi\) | ||||
0.538584 | + | 0.842572i | \(0.318959\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.2197 | − | 2.55040i | −1.64770 | − | 0.343896i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.58258i | 0.206034i | 0.994680 | + | 0.103017i | \(0.0328496\pi\) | ||||
−0.994680 | + | 0.103017i | \(0.967150\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.5830i | − | 1.35501i | −0.735516 | − | 0.677507i | \(-0.763060\pi\) | ||
0.735516 | − | 0.677507i | \(-0.236940\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | + | 9.58258i | −0.248069 | + | 1.18857i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.16515 | 0.386685 | 0.193342 | − | 0.981131i | \(-0.438067\pi\) | ||||
0.193342 | + | 0.981131i | \(0.438067\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92820 | 0.822226 | 0.411113 | − | 0.911584i | \(-0.365140\pi\) | ||||
0.411113 | + | 0.911584i | \(0.365140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.0000i | − | 1.40449i | −0.711934 | − | 0.702247i | \(-0.752180\pi\) | ||
0.711934 | − | 0.702247i | \(-0.247820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −24.4394 | −2.78513 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.29150 | −0.595341 | −0.297670 | − | 0.954669i | \(-0.596210\pi\) | ||||
−0.297670 | + | 0.954669i | \(0.596210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.16515 | 0.786478 | 0.393239 | − | 0.919436i | \(-0.371355\pi\) | ||||
0.393239 | + | 0.919436i | \(0.371355\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.2197 | − | 2.55040i | −1.32541 | − | 0.276630i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.1652i | 2.00905i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.75560 | − | 1.82740i | −0.898306 | − | 0.187487i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.1652i | 1.13365i | 0.823838 | + | 0.566825i | \(0.191828\pi\) | ||||
−0.823838 | + | 0.566825i | \(0.808172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.723000i | 0.0719412i | 0.999353 | + | 0.0359706i | \(0.0114523\pi\) | ||||
−0.999353 | + | 0.0359706i | \(0.988548\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.723000i | − | 0.0712393i | −0.999365 | − | 0.0356197i | \(-0.988660\pi\) | ||
0.999365 | − | 0.0356197i | \(-0.0113405\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.82740i | − | 0.175033i | −0.996163 | − | 0.0875166i | \(-0.972107\pi\) | ||
0.996163 | − | 0.0875166i | \(-0.0278931\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.5826i | − | 1.27774i | −0.769314 | − | 0.638871i | \(-0.779402\pi\) | ||
0.769314 | − | 0.638871i | \(-0.220598\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.4394 | −2.24036 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −20.1652 | −1.83320 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.47135 | − | 9.11710i | 0.578815 | − | 0.815459i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.47860i | 0.841090i | 0.907272 | + | 0.420545i | \(0.138161\pi\) | ||||
−0.907272 | + | 0.420545i | \(0.861839\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.41742i | 0.560693i | 0.959899 | + | 0.280346i | \(0.0904494\pi\) | ||||
−0.959899 | + | 0.280346i | \(0.909551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.5112 | −1.51841 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.4174i | − | 0.890021i | −0.895525 | − | 0.445010i | \(-0.853200\pi\) | ||
0.895525 | − | 0.445010i | \(-0.146800\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.16515i | 0.607740i | 0.952713 | + | 0.303870i | \(0.0982789\pi\) | ||||
−0.952713 | + | 0.303870i | \(0.901721\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.4394i | 2.04373i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.58258 | + | 1.16515i | 0.463608 | + | 0.0967606i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 14.9608i | − | 1.22564i | −0.790224 | − | 0.612819i | \(-0.790036\pi\) | ||
0.790224 | − | 0.612819i | \(-0.209964\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8745 | −1.29185 | −0.645925 | − | 0.763401i | \(-0.723528\pi\) | ||||
−0.645925 | + | 0.763401i | \(0.723528\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.41742 | + | 11.5826i | −0.194172 | + | 0.930335i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4068 | 1.30941 | 0.654703 | − | 0.755886i | \(-0.272794\pi\) | ||||
0.654703 | + | 0.755886i | \(0.272794\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.0290i | − | 0.930832i | −0.885092 | − | 0.465416i | \(-0.845905\pi\) | ||
0.885092 | − | 0.465416i | \(-0.154095\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.16515 | 0.474242 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.01450 | 0.457274 | 0.228637 | − | 0.973512i | \(-0.426573\pi\) | ||||
0.228637 | + | 0.973512i | \(0.426573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.75560 | − | 20.0616i | 0.661861 | − | 1.51652i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1.58258i | − | 0.118287i | −0.998249 | − | 0.0591436i | \(-0.981163\pi\) | ||
0.998249 | − | 0.0591436i | \(-0.0188370\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.82740i | 0.135830i | 0.997691 | + | 0.0679148i | \(0.0216346\pi\) | ||||
−0.997691 | + | 0.0679148i | \(0.978365\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.16515 | + | 5.58258i | −0.0856636 | + | 0.410439i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −31.1652 | −2.27902 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8564 | 1.00261 | 0.501307 | − | 0.865269i | \(-0.332853\pi\) | ||||
0.501307 | + | 0.865269i | \(0.332853\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.1652i | 1.09161i | 0.837912 | + | 0.545806i | \(0.183776\pi\) | ||||
−0.837912 | + | 0.545806i | \(0.816224\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.0797 | 1.57311 | 0.786557 | − | 0.617518i | \(-0.211862\pi\) | ||||
0.786557 | + | 0.617518i | \(0.211862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.2197 | −0.866232 | −0.433116 | − | 0.901338i | \(-0.642586\pi\) | ||||
−0.433116 | + | 0.901338i | \(0.642586\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.1652 | 0.783640 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.74110 | − | 13.1334i | 0.191447 | − | 0.917277i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.3303 | −1.54462 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.16515i | 0.493269i | 0.969109 | + | 0.246635i | \(0.0793248\pi\) | ||||
−0.969109 | + | 0.246635i | \(0.920675\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.10080 | + | 24.4394i | −0.347872 | + | 1.66675i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.1652i | 1.57255i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.4394i | 1.64397i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.37780i | 0.293159i | 0.989199 | + | 0.146580i | \(0.0468265\pi\) | ||||
−0.989199 | + | 0.146580i | \(0.953174\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.1652 | 1.00655 | 0.503273 | − | 0.864127i | \(-0.332129\pi\) | ||||
0.503273 | + | 0.864127i | \(0.332129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.0290i | − | 0.794899i | −0.917624 | − | 0.397450i | \(-0.869895\pi\) | ||
0.917624 | − | 0.397450i | \(-0.130105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.4174i | 0.682468i | 0.939978 | + | 0.341234i | \(0.110845\pi\) | ||||
−0.939978 | + | 0.341234i | \(0.889155\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.1652 | + | 3.16515i | 0.989265 | + | 0.206472i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.1660 | 1.36912 | 0.684558 | − | 0.728959i | \(-0.259995\pi\) | ||||
0.684558 | + | 0.728959i | \(0.259995\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.55765 | − | 26.6283i | 0.355065 | − | 1.70122i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.5112i | 1.11421i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.41742i | 0.152586i | 0.997085 | + | 0.0762932i | \(0.0243085\pi\) | ||||
−0.997085 | + | 0.0762932i | \(0.975691\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 24.7477i | − | 1.54372i | −0.635792 | − | 0.771860i | \(-0.719326\pi\) | ||
0.635792 | − | 0.771860i | \(-0.280674\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.1652i | 0.693769i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.82740i | 0.112682i | 0.998412 | + | 0.0563412i | \(0.0179435\pi\) | ||||
−0.998412 | + | 0.0563412i | \(0.982057\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.58258 | + | 17.1652i | −0.220076 | + | 1.05445i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.20520i | 0.378338i | 0.981945 | + | 0.189169i | \(0.0605794\pi\) | ||||
−0.981945 | + | 0.189169i | \(0.939421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.4931 | 0.941139 | 0.470570 | − | 0.882363i | \(-0.344048\pi\) | ||||
0.470570 | + | 0.882363i | \(0.344048\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.1652 | − | 25.5826i | 0.673284 | − | 1.54269i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.47860 | 0.569514 | 0.284757 | − | 0.958600i | \(-0.408087\pi\) | ||||
0.284757 | + | 0.958600i | \(0.408087\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.3303 | −1.92866 | −0.964332 | − | 0.264695i | \(-0.914729\pi\) | ||||
−0.964332 | + | 0.264695i | \(0.914729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.1652 | −0.663699 | −0.331850 | − | 0.943332i | \(-0.607673\pi\) | ||||
−0.331850 | + | 0.943332i | \(0.607673\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 26.2668i | − | 1.55048i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.1652 | −0.833244 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.913701 | −0.0533790 | −0.0266895 | − | 0.999644i | \(-0.508497\pi\) | ||||
−0.0266895 | + | 0.999644i | \(0.508497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.46410 | − | 0.723000i | −0.201688 | − | 0.0420947i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 48.8788i | 2.81733i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.1652 | + | 4.83485i | 1.32643 | + | 0.276843i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.65480 | −0.207245 | −0.103622 | − | 0.994617i | \(-0.533043\pi\) | ||||
−0.103622 | + | 0.994617i | \(0.533043\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 0.834849i | − | 0.0471884i | −0.999722 | − | 0.0235942i | \(-0.992489\pi\) | ||
0.999722 | − | 0.0235942i | \(-0.00751097\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −34.1087 | −1.91574 | −0.957868 | − | 0.287208i | \(-0.907273\pi\) | ||||
−0.957868 | + | 0.287208i | \(0.907273\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.2378 | 0.797164 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.3303 | −1.24249 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.0616 | − | 8.75560i | −1.11282 | − | 0.485674i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.3303 | 1.67216 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10.3303i | − | 0.567805i | −0.958853 | − | 0.283902i | \(-0.908371\pi\) | ||
0.958853 | − | 0.283902i | \(-0.0916292\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.44600 | + | 6.92820i | −0.0790034 | + | 0.378528i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.3303i | − | 1.43430i | −0.696917 | − | 0.717151i | \(-0.745446\pi\) | ||
0.696917 | − | 0.717151i | \(-0.254554\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.5402i | 1.59969i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 22.6120i | − | 1.22093i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.834849 | 0.0448170 | 0.0224085 | − | 0.999749i | \(-0.492867\pi\) | ||||
0.0224085 | + | 0.999749i | \(0.492867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 24.4394i | − | 1.30821i | −0.756403 | − | 0.654106i | \(-0.773045\pi\) | ||
0.756403 | − | 0.654106i | \(-0.226955\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.9129i | 0.634059i | 0.948416 | + | 0.317029i | \(0.102685\pi\) | ||||
−0.948416 | + | 0.317029i | \(0.897315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.16515 | + | 15.1652i | −0.167989 | + | 0.804883i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.92820 | 0.365657 | 0.182828 | − | 0.983145i | \(-0.441475\pi\) | ||||
0.182828 | + | 0.983145i | \(0.441475\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.2668 | + | 5.48220i | 1.37487 | + | 0.286952i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11.6874i | − | 0.610078i | −0.952340 | − | 0.305039i | \(-0.901331\pi\) | ||
0.952340 | − | 0.305039i | \(-0.0986694\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.3303i | 1.78234i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.3060 | −0.585403 | −0.292701 | − | 0.956204i | \(-0.594554\pi\) | ||||
−0.292701 | + | 0.956204i | \(0.594554\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11.1652i | − | 0.575035i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.1652i | − | 1.18991i | −0.803758 | − | 0.594957i | \(-0.797169\pi\) | ||
0.803758 | − | 0.594957i | \(-0.202831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 29.9216i | − | 1.52892i | −0.644669 | − | 0.764462i | \(-0.723005\pi\) | ||
0.644669 | − | 0.764462i | \(-0.276995\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.1652 | − | 53.4955i | 0.569029 | − | 2.72638i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.03260i | 0.407269i | 0.979047 | + | 0.203635i | \(0.0652755\pi\) | ||||
−0.979047 | + | 0.203635i | \(0.934725\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.41742 | − | 11.5826i | 0.121634 | − | 0.582783i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.55040 | −0.128001 | −0.0640005 | − | 0.997950i | \(-0.520386\pi\) | ||||
−0.0640005 | + | 0.997950i | \(0.520386\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.0000 | −1.09863 | −0.549314 | − | 0.835616i | \(-0.685111\pi\) | ||||
−0.549314 | + | 0.835616i | \(0.685111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.1652 | 1.15394 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.2378i | 0.705742i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.1652 | 1.83770 | 0.918849 | − | 0.394609i | \(-0.129120\pi\) | ||||
0.918849 | + | 0.394609i | \(0.129120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.92820 | −0.340915 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.27340 | + | 15.6838i | −0.160685 | + | 0.769888i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.7477i | 0.818180i | 0.912494 | + | 0.409090i | \(0.134154\pi\) | ||||
−0.912494 | + | 0.409090i | \(0.865846\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.5402i | 1.43970i | 0.694129 | + | 0.719851i | \(0.255790\pi\) | ||||
−0.694129 | + | 0.719851i | \(0.744210\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.1652 | − | 25.5826i | 0.541589 | − | 1.24094i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 46.3303 | 2.24208 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.2958 | 1.84464 | 0.922322 | − | 0.386421i | \(-0.126289\pi\) | ||||
0.922322 | + | 0.386421i | \(0.126289\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.66970i | 0.0802405i | 0.999195 | + | 0.0401203i | \(0.0127741\pi\) | ||||
−0.999195 | + | 0.0401203i | \(0.987226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.7309 | −1.41898 | −0.709490 | − | 0.704716i | \(-0.751074\pi\) | ||||
−0.709490 | + | 0.704716i | \(0.751074\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.1652 | −1.48070 | −0.740351 | − | 0.672221i | \(-0.765340\pi\) | ||||
−0.740351 | + | 0.672221i | \(0.765340\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.913701 | + | 4.37780i | −0.0433136 | + | 0.207528i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.3303 | 1.33699 | 0.668495 | − | 0.743717i | \(-0.266939\pi\) | ||||
0.668495 | + | 0.743717i | \(0.266939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 33.4955i | − | 1.57724i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −41.9506 | − | 8.75560i | −1.96668 | − | 0.410469i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.83485i | 0.226165i | 0.993586 | + | 0.113082i | \(0.0360724\pi\) | ||||
−0.993586 | + | 0.113082i | \(0.963928\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.10440i | − | 0.0514371i | −0.999669 | − | 0.0257185i | \(-0.991813\pi\) | ||
0.999669 | − | 0.0257185i | \(-0.00818737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.1986i | − | 1.35697i | −0.734612 | − | 0.678487i | \(-0.762636\pi\) | ||
0.734612 | − | 0.678487i | \(-0.237364\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.834849 | 0.0386322 | 0.0193161 | − | 0.999813i | \(-0.493851\pi\) | ||||
0.0193161 | + | 0.999813i | \(0.493851\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.8564i | 0.639829i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 62.3303i | 2.86595i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | − | 18.3303i | 0.367065 | − | 0.841052i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.7490 | −1.45065 | −0.725325 | − | 0.688407i | \(-0.758310\pi\) | ||||
−0.725325 | + | 0.688407i | \(0.758310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1652 | 0.509087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.4394 | − | 5.10080i | −1.10974 | − | 0.231615i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.7882i | 0.760746i | 0.924833 | + | 0.380373i | \(0.124204\pi\) | ||||
−0.924833 | + | 0.380373i | \(0.875796\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.7477i | − | 0.575297i | −0.957736 | − | 0.287648i | \(-0.907127\pi\) | ||
0.957736 | − | 0.287648i | \(-0.0928735\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.2378 | 0.641239 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.3303i | 1.36050i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.3303i | − | 0.820577i | −0.911956 | − | 0.410289i | \(-0.865428\pi\) | ||
0.911956 | − | 0.410289i | \(-0.134572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 28.0942i | − | 1.25266i | −0.779558 | − | 0.626330i | \(-0.784556\pi\) | ||
0.779558 | − | 0.626330i | \(-0.215444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.58258 | − | 0.330303i | −0.0704237 | − | 0.0146983i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 39.4002i | − | 1.74638i | −0.487376 | − | 0.873192i | \(-0.662046\pi\) | ||
0.487376 | − | 0.873192i | \(-0.337954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 52.5336 | 2.32395 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.58258 | + | 0.330303i | 0.0697366 | + | 0.0145549i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.6772 | 1.70102 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.6606 | 1.51851 | 0.759254 | − | 0.650794i | \(-0.225564\pi\) | ||||
0.759254 | + | 0.650794i | \(0.225564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.3303 | −0.801528 | −0.400764 | − | 0.916181i | \(-0.631255\pi\) | ||||
−0.400764 | + | 0.916181i | \(0.631255\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.5402i | 1.28679i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.2668 | −1.13774 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.82740 | + | 8.75560i | −0.0790054 | + | 0.378538i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 67.9129i | − | 2.92521i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 36.8498i | − | 1.58430i | −0.610328 | − | 0.792149i | \(-0.708962\pi\) | ||
0.610328 | − | 0.792149i | \(-0.291038\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.00000 | + | 0.834849i | 0.171341 | + | 0.0357610i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.4955 | −1.09011 | −0.545053 | − | 0.838401i | \(-0.683491\pi\) | ||||
−0.545053 | + | 0.838401i | \(0.683491\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.2016 | 0.434603 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 23.1652i | − | 0.985082i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.18710 | −0.177413 | −0.0887066 | − | 0.996058i | \(-0.528273\pi\) | ||||
−0.0887066 | + | 0.996058i | \(0.528273\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.8788 | 2.06735 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.4955 | −1.24309 | −0.621543 | − | 0.783380i | \(-0.713494\pi\) | ||||
−0.621543 | + | 0.783380i | \(0.713494\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.7309 | + | 6.20520i | 1.25079 | + | 0.261055i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.3303 | −1.52305 | −0.761523 | − | 0.648138i | \(-0.775548\pi\) | ||||
−0.761523 | + | 0.648138i | \(0.775548\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000i | 0.836974i | 0.908223 | + | 0.418487i | \(0.137439\pi\) | ||||
−0.908223 | + | 0.418487i | \(0.862561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 15.1652i | − | 0.631334i | −0.948870 | − | 0.315667i | \(-0.897772\pi\) | ||
0.948870 | − | 0.315667i | \(-0.102228\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.3676i | 1.30135i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.7780i | 1.81310i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.66970 | −0.234013 | −0.117007 | − | 0.993131i | \(-0.537330\pi\) | ||||
−0.117007 | + | 0.993131i | \(0.537330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.1660i | 0.872130i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 35.9129i | − | 1.47477i | −0.675475 | − | 0.737383i | \(-0.736062\pi\) | ||
0.675475 | − | 0.737383i | \(-0.263938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.1652 | − | 53.4955i | 0.457727 | − | 2.19310i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.2378 | 0.581741 | 0.290871 | − | 0.956762i | \(-0.406055\pi\) | ||||
0.290871 | + | 0.956762i | \(0.406055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.1652 | 0.537018 | 0.268509 | − | 0.963277i | \(-0.413469\pi\) | ||||
0.268509 | + | 0.963277i | \(0.413469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.21245 | − | 44.1395i | 0.374540 | − | 1.79453i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.7454i | 1.45086i | 0.688295 | + | 0.725431i | \(0.258359\pi\) | ||||
−0.688295 | + | 0.725431i | \(0.741641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 30.3303i | − | 1.22703i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.4720 | 1.31153 | 0.655766 | − | 0.754964i | \(-0.272346\pi\) | ||||
0.655766 | + | 0.754964i | \(0.272346\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5826i | 0.546814i | 0.961898 | + | 0.273407i | \(0.0881506\pi\) | ||||
−0.961898 | + | 0.273407i | \(0.911849\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 45.4955i | − | 1.82862i | −0.405019 | − | 0.914308i | \(-0.632735\pi\) | ||
0.405019 | − | 0.914308i | \(-0.367265\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.75560i | 0.350786i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.0000 | + | 18.3303i | 0.680000 | + | 0.733212i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.2378i | 0.567699i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.2197 | 0.486459 | 0.243229 | − | 0.969969i | \(-0.421793\pi\) | ||||
0.243229 | + | 0.969969i | \(0.421793\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.7477 | − | 4.33030i | −0.823348 | − | 0.171843i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −53.2566 | −2.11010 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.33030 | 0.171037 | 0.0855183 | − | 0.996337i | \(-0.472745\pi\) | ||||
0.0855183 | + | 0.996337i | \(0.472745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.3303 | −0.722877 | −0.361438 | − | 0.932396i | \(-0.617714\pi\) | ||||
−0.361438 | + | 0.932396i | \(0.617714\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 17.8926i | − | 0.703431i | −0.936107 | − | 0.351716i | \(-0.885598\pi\) | ||
0.936107 | − | 0.351716i | \(-0.114402\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.83485 | −0.346798 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.0797 | 0.864046 | 0.432023 | − | 0.901863i | \(-0.357800\pi\) | ||||
0.432023 | + | 0.901863i | \(0.357800\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.0471 | − | 2.93180i | −0.548866 | − | 0.114555i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.5826i | 0.996556i | 0.867017 | + | 0.498278i | \(0.166034\pi\) | ||||
−0.867017 | + | 0.498278i | \(0.833966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 17.8926i | − | 0.695942i | −0.937505 | − | 0.347971i | \(-0.886871\pi\) | ||
0.937505 | − | 0.347971i | \(-0.113129\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | − | 38.3303i | 0.310227 | − | 1.48639i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 59.0804 | 2.28077 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.0000i | 1.54189i | 0.636904 | + | 0.770943i | \(0.280215\pi\) | ||||
−0.636904 | + | 0.770943i | \(0.719785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.6265 | 1.10021 | 0.550103 | − | 0.835097i | \(-0.314588\pi\) | ||||
0.550103 | + | 0.835097i | \(0.314588\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −48.8788 | −1.87580 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.49545 | −0.210278 | −0.105139 | − | 0.994458i | \(-0.533529\pi\) | ||||
−0.105139 | + | 0.994458i | \(0.533529\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.8027 | + | 4.75920i | 0.871247 | + | 0.181840i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.3303 | 1.30788 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.6606i | 1.54680i | 0.633917 | + | 0.773401i | \(0.281446\pi\) | ||||
−0.633917 | + | 0.773401i | \(0.718554\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.6838 | − | 3.27340i | −0.594921 | − | 0.124167i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 33.4955i | − | 1.26873i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.9470i | 1.73540i | 0.497093 | + | 0.867698i | \(0.334401\pi\) | ||||
−0.497093 | + | 0.867698i | \(0.665599\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.2016i | 0.384761i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.16515 | −0.119038 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.6838i | 0.589018i | 0.955649 | + | 0.294509i | \(0.0951561\pi\) | ||||
−0.955649 | + | 0.294509i | \(0.904844\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −53.4955 | − | 11.1652i | −2.00062 | − | 0.417553i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9862 | −1.15559 | −0.577795 | − | 0.816182i | \(-0.696087\pi\) | ||||
−0.577795 | + | 0.816182i | \(0.696087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.16515 | 0.117876 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.10080 | + | 11.6874i | −0.189439 | + | 0.434059i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 49.6018i | − | 1.83963i | −0.392353 | − | 0.919815i | \(-0.628339\pi\) | ||
0.392353 | − | 0.919815i | \(-0.371661\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 62.3303i | 2.30537i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.1986 | −1.07848 | −0.539238 | − | 0.842154i | \(-0.681288\pi\) | ||||
−0.539238 | + | 0.842154i | \(0.681288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.6697i | 0.650872i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000i | 0.735712i | 0.929883 | + | 0.367856i | \(0.119908\pi\) | ||||
−0.929883 | + | 0.367856i | \(0.880092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.4328i | 1.74014i | 0.492927 | + | 0.870071i | \(0.335927\pi\) | ||||
−0.492927 | + | 0.870071i | \(0.664073\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.7477 | + | 6.83485i | 1.19978 | + | 0.250409i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.5112i | 0.639846i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.0043 | 1.20434 | 0.602172 | − | 0.798366i | \(-0.294302\pi\) | ||||
0.602172 | + | 0.798366i | \(0.294302\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.25227 | − | 34.7477i | 0.263937 | − | 1.26460i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.2342 | −0.662734 | −0.331367 | − | 0.943502i | \(-0.607510\pi\) | ||||
−0.331367 | + | 0.943502i | \(0.607510\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.0000 | 0.797499 | 0.398750 | − | 0.917060i | \(-0.369444\pi\) | ||||
0.398750 | + | 0.917060i | \(0.369444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | 0.289619 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.92820i | 0.250163i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.4955 | 0.847268 | 0.423634 | − | 0.905834i | \(-0.360754\pi\) | ||||
0.423634 | + | 0.905834i | \(0.360754\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.4539 | −1.09535 | −0.547676 | − | 0.836691i | \(-0.684487\pi\) | ||||
−0.547676 | + | 0.836691i | \(0.684487\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.2487 | − | 10.5830i | −0.871039 | − | 0.380153i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 24.0000i | − | 0.859889i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.6772i | 1.38398i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.49545 | + | 35.9129i | −0.267524 | + | 1.28179i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.0000 | 1.28326 | 0.641631 | − | 0.767014i | \(-0.278258\pi\) | ||||
0.641631 | + | 0.767014i | \(0.278258\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 59.4618 | 2.11422 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 46.3303i | − | 1.64524i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 53.0659 | 1.87969 | 0.939846 | − | 0.341599i | \(-0.110969\pi\) | ||||
0.939846 | + | 0.341599i | \(0.110969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.6772 | 1.36830 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 66.9909 | 2.36406 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.0000 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323177\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 0.834849i | − | 0.0293155i | −0.999893 | − | 0.0146577i | \(-0.995334\pi\) | ||
0.999893 | − | 0.0146577i | \(-0.00466587\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.82740 | − | 8.75560i | 0.0640111 | − | 0.306695i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.6606i | 1.56248i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.20520i | − | 0.216563i | −0.994120 | − | 0.108282i | \(-0.965465\pi\) | ||
0.994120 | − | 0.108282i | \(-0.0345348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.47860i | − | 0.330403i | −0.986260 | − | 0.165202i | \(-0.947172\pi\) | ||
0.986260 | − | 0.165202i | \(-0.0528275\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0000 | 0.973655 | 0.486828 | − | 0.873498i | \(-0.338154\pi\) | ||||
0.486828 | + | 0.873498i | \(0.338154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.8498i | 1.27985i | 0.768439 | + | 0.639924i | \(0.221034\pi\) | ||||
−0.768439 | + | 0.639924i | \(0.778966\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 67.9129i | − | 2.35304i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.3303 | + | 5.49545i | 0.911198 | + | 0.190178i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −55.8070 | −1.92667 | −0.963336 | − | 0.268297i | \(-0.913539\pi\) | ||||
−0.963336 | + | 0.268297i | \(0.913539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.4955 | 0.775705 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.81655 | + | 13.4949i | −0.0968923 | + | 0.464239i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 88.2790i | − | 3.03330i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.65120 | 0.261972 | 0.130986 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130986 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 29.5826i | − | 1.01052i | −0.862967 | − | 0.505261i | \(-0.831396\pi\) | ||
0.862967 | − | 0.505261i | \(-0.168604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 24.8348i | − | 0.847354i | −0.905813 | − | 0.423677i | \(-0.860739\pi\) | ||
0.905813 | − | 0.423677i | \(-0.139261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 50.7062i | − | 1.72606i | −0.505153 | − | 0.863030i | \(-0.668564\pi\) | ||
0.505153 | − | 0.863030i | \(-0.331436\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.74773 | + | 13.1652i | −0.0934255 | + | 0.447629i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 29.5402i | − | 1.00208i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.8564 | 0.469506 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 39.9129 | + | 28.3303i | 1.34930 | + | 0.957739i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.8528 | −0.602846 | −0.301423 | − | 0.953490i | \(-0.597462\pi\) | ||||
−0.301423 | + | 0.953490i | \(0.597462\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.3303 | −1.22400 | −0.612000 | − | 0.790858i | \(-0.709635\pi\) | ||||
−0.612000 | + | 0.790858i | \(0.709635\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.3303 | −1.15531 | −0.577653 | − | 0.816282i | \(-0.696031\pi\) | ||||
−0.577653 | + | 0.816282i | \(0.696031\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.0514i | 1.57983i | 0.613215 | + | 0.789916i | \(0.289876\pi\) | ||||
−0.613215 | + | 0.789916i | \(0.710124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.4955 | −1.39171 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.7128 | 0.927374 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.46410 | + | 0.723000i | 0.115792 | + | 0.0241672i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 13.4955i | − | 0.450099i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.7780i | 1.45846i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.00000 | − | 0.834849i | −0.132964 | − | 0.0277513i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.4955 | −0.580927 | −0.290464 | − | 0.956886i | \(-0.593809\pi\) | ||||
−0.290464 | + | 0.956886i | \(0.593809\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.30960 | 0.242178 | 0.121089 | − | 0.992642i | \(-0.461361\pi\) | ||||
0.121089 | + | 0.992642i | \(0.461361\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.0000i | 1.32381i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.0942 | −0.927753 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.8383 | 0.390510 | 0.195255 | − | 0.980753i | \(-0.437447\pi\) | ||||
0.195255 | + | 0.980753i | \(0.437447\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.3303 | 0.998334 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.6874 | − | 5.10080i | −0.384280 | − | 0.167713i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.6606 | −1.00594 | −0.502971 | − | 0.864303i | \(-0.667760\pi\) | ||||
−0.502971 | + | 0.864303i | \(0.667760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 48.6606i | − | 1.59479i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.2378 | − | 68.2174i | 0.465626 | − | 2.23095i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.3303i | 0.468151i | 0.972218 | + | 0.234075i | \(0.0752062\pi\) | ||||
−0.972218 | + | 0.234075i | \(0.924794\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.4358i | 0.926981i | 0.886102 | + | 0.463491i | \(0.153403\pi\) | ||||
−0.886102 | + | 0.463491i | \(0.846597\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −52.0000 | −1.68977 | −0.844886 | − | 0.534946i | \(-0.820332\pi\) | ||||
−0.844886 | + | 0.534946i | \(0.820332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 52.5336i | − | 1.70531i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 26.2432i | − | 0.850100i | −0.905170 | − | 0.425050i | \(-0.860257\pi\) | ||
0.905170 | − | 0.425050i | \(-0.139743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.33030 | + | 30.3303i | −0.204844 | + | 0.981466i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.6054 | 1.47268 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.00000 | −0.0967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.1950 | − | 6.92820i | −1.06859 | − | 0.223027i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 26.9898i | − | 0.867934i | −0.900929 | − | 0.433967i | \(-0.857113\pi\) | ||
0.900929 | − | 0.433967i | \(-0.142887\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.08712i | 0.131162i | 0.997847 | + | 0.0655810i | \(0.0208901\pi\) | ||||
−0.997847 | + | 0.0655810i | \(0.979110\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.3676 | −1.00560 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.25227i | 0.232021i | 0.993248 | + | 0.116010i | \(0.0370106\pi\) | ||||
−0.993248 | + | 0.116010i | \(0.962989\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.1652i | 0.356840i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.20880i | 0.0704498i | 0.999379 | + | 0.0352249i | \(0.0112148\pi\) | ||||
−0.999379 | + | 0.0352249i | \(0.988785\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0871 | + | 48.3303i | −0.321402 | + | 1.53993i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.8383 | −0.376056 | −0.188028 | − | 0.982164i | \(-0.560210\pi\) | ||||
−0.188028 | + | 0.982164i | \(0.560210\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.58258 | − | 26.7477i | 0.176980 | − | 0.847960i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.7520 | −0.403860 | −0.201930 | − | 0.979400i | \(-0.564721\pi\) | ||||
−0.201930 | + | 0.979400i | \(0.564721\pi\) | |||||||
\(998\) | 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 \(a_p\))