Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2800,2,Mod(2351,2800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("2800.2351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2800.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.3581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2351.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2800.2351 |
Dual form | 2800.2.k.c.2351.2 |
$q$-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 \(\left(\mathbb{Z}/2800\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(801\) | \(2101\) | \(2577\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −2.00000 | −1.15470 | −0.577350 | − | 0.816497i | \(-0.695913\pi\) | ||||
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.19615i | 1.56670i | 0.621582 | + | 0.783349i | \(0.286490\pi\) | ||||
−0.621582 | + | 0.783349i | \(0.713510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.00000 | 1.83533 | 0.917663 | − | 0.397360i | \(-0.130073\pi\) | ||||
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00000 | + | 3.46410i | −0.872872 | + | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.19615i | − | 1.08347i | −0.840548 | − | 0.541736i | \(-0.817767\pi\) | ||
0.840548 | − | 0.541736i | \(-0.182233\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 10.3923i | − | 1.80907i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.92820i | − | 1.10940i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3923i | 1.62301i | 0.584349 | + | 0.811503i | \(0.301350\pi\) | ||||
−0.584349 | + | 0.811503i | \(0.698650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.73205i | 0.264135i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) | ||||
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.0000 | −2.11925 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.46410i | 0.443533i | 0.975100 | + | 0.221766i | \(0.0711822\pi\) | ||||
−0.975100 | + | 0.221766i | \(0.928818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | − | 1.73205i | 0.251976 | − | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.1244i | − | 1.48123i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) | ||
0.671932 | − | 0.740613i | \(-0.265465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.3923i | 1.25109i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.19615i | 0.616670i | 0.951278 | + | 0.308335i | \(0.0997717\pi\) | ||||
−0.951278 | + | 0.308335i | \(0.900228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.3923i | − | 1.21633i | −0.793812 | − | 0.608164i | \(-0.791906\pi\) | ||
0.793812 | − | 0.608164i | \(-0.208094\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.00000 | + | 10.3923i | 1.02565 | + | 1.18431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.19615i | 0.584613i | 0.956325 | + | 0.292306i | \(0.0944227\pi\) | ||||
−0.956325 | + | 0.292306i | \(0.905577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.0000 | 1.92980 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3923i | 1.10158i | 0.834643 | + | 0.550791i | \(0.185674\pi\) | ||||
−0.834643 | + | 0.550791i | \(0.814326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 6.92820i | 0.628971 | + | 0.726273i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.46410i | − | 0.351726i | −0.984415 | − | 0.175863i | \(-0.943728\pi\) | ||
0.984415 | − | 0.175863i | \(-0.0562716\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.19615i | 0.522233i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3923i | 1.03407i | 0.855963 | + | 0.517036i | \(0.172965\pi\) | ||||
−0.855963 | + | 0.517036i | \(0.827035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3923i | 1.00466i | 0.864675 | + | 0.502331i | \(0.167524\pi\) | ||||
−0.864675 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0000 | 1.32882 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | −0.282216 | −0.141108 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141108 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.46410i | 0.320256i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0000 | −1.45455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 20.7846i | − | 1.87409i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.5885i | 1.38325i | 0.722256 | + | 0.691626i | \(0.243105\pi\) | ||||
−0.722256 | + | 0.691626i | \(0.756895\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 3.46410i | − | 0.304997i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.0000 | − | 13.8564i | 1.38738 | − | 1.20150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.0000 | 1.86602 | 0.933008 | − | 0.359856i | \(-0.117174\pi\) | ||||
0.933008 | + | 0.359856i | \(0.117174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.0000 | −1.50524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.00000 | + | 13.8564i | −0.164957 | + | 1.14286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.00000 | −0.737309 | −0.368654 | − | 0.929567i | \(-0.620181\pi\) | ||||
−0.368654 | + | 0.929567i | \(0.620181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.1244i | 0.986666i | 0.869841 | + | 0.493333i | \(0.164222\pi\) | ||||
−0.869841 | + | 0.493333i | \(0.835778\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.2487i | 1.93526i | 0.252377 | + | 0.967629i | \(0.418788\pi\) | ||||
−0.252377 | + | 0.967629i | \(0.581212\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.0000 | −0.951662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.00000 | − | 10.3923i | −0.709299 | − | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.3205i | 1.35665i | 0.734763 | + | 0.678323i | \(0.237293\pi\) | ||||
−0.734763 | + | 0.678323i | \(0.762707\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.0000 | −1.39288 | −0.696441 | − | 0.717614i | \(-0.745234\pi\) | ||||
−0.696441 | + | 0.717614i | \(0.745234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000 | 0.611775 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.7846i | 1.58022i | 0.612962 | + | 0.790112i | \(0.289978\pi\) | ||||
−0.612962 | + | 0.790112i | \(0.710022\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923i | 0.776757i | 0.921500 | + | 0.388379i | \(0.126965\pi\) | ||||
−0.921500 | + | 0.388379i | \(0.873035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3205i | 1.28742i | 0.765268 | + | 0.643712i | \(0.222606\pi\) | ||||
−0.765268 | + | 0.643712i | \(0.777394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.92820i | − | 0.512148i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.00000 | − | 6.92820i | 0.581914 | − | 0.503953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.3923i | − | 0.751961i | −0.926628 | − | 0.375980i | \(-0.877306\pi\) | ||
0.926628 | − | 0.375980i | \(-0.122694\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | −0.503871 | −0.251936 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | −0.708881 | −0.354441 | − | 0.935079i | \(-0.615329\pi\) | ||||
−0.354441 | + | 0.935079i | \(0.615329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.2487i | 1.71037i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.0000 | + | 15.5885i | −1.26335 | + | 1.09410i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.19615i | − | 0.361158i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 41.5692i | 2.87540i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.46410i | − | 0.238479i | −0.992866 | − | 0.119239i | \(-0.961954\pi\) | ||
0.992866 | − | 0.119239i | \(-0.0380456\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 10.3923i | − | 0.712069i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | + | 3.46410i | −0.271538 | + | 0.235159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.7846i | 1.40449i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.0000 | −0.937509 | −0.468755 | − | 0.883328i | \(-0.655297\pi\) | ||||
−0.468755 | + | 0.883328i | \(0.655297\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.0000 | −1.59294 | −0.796468 | − | 0.604681i | \(-0.793301\pi\) | ||||
−0.796468 | + | 0.604681i | \(0.793301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.92820i | − | 0.457829i | −0.973447 | − | 0.228914i | \(-0.926482\pi\) | ||
0.973447 | − | 0.228914i | \(-0.0735176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.0000 | − | 20.7846i | −1.18431 | − | 1.36753i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.00000 | 0.589610 | 0.294805 | − | 0.955557i | \(-0.404745\pi\) | ||||
0.294805 | + | 0.955557i | \(0.404745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 10.3923i | − | 0.675053i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.92820i | − | 0.446285i | −0.974786 | − | 0.223142i | \(-0.928369\pi\) | ||
0.974786 | − | 0.223142i | \(-0.0716315\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0000 | 0.641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.7128i | 1.76332i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.0000 | 1.69748 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.3923i | 0.648254i | 0.946014 | + | 0.324127i | \(0.105071\pi\) | ||||
−0.946014 | + | 0.324127i | \(0.894929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.0000 | + | 12.1244i | −0.869918 | + | 0.753371i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.00000 | −0.557086 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.5885i | 0.961225i | 0.876933 | + | 0.480613i | \(0.159586\pi\) | ||||
−0.876933 | + | 0.480613i | \(0.840414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 20.7846i | − | 1.27200i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 31.1769i | − | 1.90089i | −0.310893 | − | 0.950445i | \(-0.600628\pi\) | ||
0.310893 | − | 0.950445i | \(-0.399372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.00000 | −0.121491 | −0.0607457 | − | 0.998153i | \(-0.519348\pi\) | ||||
−0.0607457 | + | 0.998153i | \(0.519348\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | − | 13.8564i | −0.726273 | − | 0.838628i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.0000 | −1.25275 | −0.626377 | − | 0.779520i | \(-0.715463\pi\) | ||||
−0.626377 | + | 0.779520i | \(0.715463\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0000 | 0.951101 | 0.475551 | − | 0.879688i | \(-0.342249\pi\) | ||||
0.475551 | + | 0.879688i | \(0.342249\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.0000 | + | 20.7846i | 1.06251 | + | 1.22688i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.92820i | 0.406138i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3923i | 0.607125i | 0.952812 | + | 0.303562i | \(0.0981761\pi\) | ||||
−0.952812 | + | 0.303562i | \(0.901824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.7846i | 1.20605i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.0000 | 1.04097 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.00000 | + | 3.46410i | 0.172917 | + | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 20.7846i | − | 1.19404i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.00000 | −0.456584 | −0.228292 | − | 0.973593i | \(-0.573314\pi\) | ||||
−0.228292 | + | 0.973593i | \(0.573314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.92820i | 0.391605i | 0.980643 | + | 0.195803i | \(0.0627312\pi\) | ||||
−0.980643 | + | 0.195803i | \(0.937269\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.0000 | 1.17948 | 0.589739 | − | 0.807594i | \(-0.299231\pi\) | ||||
0.589739 | + | 0.807594i | \(0.299231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 46.7654i | − | 2.61836i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 20.7846i | − | 1.16008i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | 0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.19615i | 0.285606i | 0.989751 | + | 0.142803i | \(0.0456116\pi\) | ||||
−0.989751 | + | 0.142803i | \(0.954388\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.00000 | −0.383598 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.0000 | 1.85210 | 0.926049 | − | 0.377403i | \(-0.123183\pi\) | ||||
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 10.3923i | − | 0.562775i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 25.9808i | − | 1.39472i | −0.716721 | − | 0.697360i | \(-0.754358\pi\) | ||
0.716721 | − | 0.697360i | \(-0.245642\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.7846i | 1.11257i | 0.830990 | + | 0.556287i | \(0.187775\pi\) | ||||
−0.830990 | + | 0.556287i | \(0.812225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.8564i | 0.739600i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.3923i | − | 0.553127i | −0.960996 | − | 0.276563i | \(-0.910804\pi\) | ||
0.960996 | − | 0.276563i | \(-0.0891955\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.19615i | 0.274242i | 0.990554 | + | 0.137121i | \(0.0437850\pi\) | ||||
−0.990554 | + | 0.137121i | \(0.956215\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.0000 | 2.36842 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.0000 | 1.67956 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.0000 | 1.14839 | 0.574195 | − | 0.818718i | \(-0.305315\pi\) | ||||
0.574195 | + | 0.818718i | \(0.305315\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.3923i | 0.541002i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | − | 10.3923i | 0.623009 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | −0.569558 | −0.284779 | − | 0.958593i | \(-0.591920\pi\) | ||||
−0.284779 | + | 0.958593i | \(0.591920\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 31.1769i | − | 1.60569i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.73205i | − | 0.0889695i | −0.999010 | − | 0.0444847i | \(-0.985835\pi\) | ||
0.999010 | − | 0.0444847i | \(-0.0141646\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 31.1769i | − | 1.59724i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.00000 | 0.306586 | 0.153293 | − | 0.988181i | \(-0.451012\pi\) | ||||
0.153293 | + | 0.988181i | \(0.451012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.73205i | 0.0880451i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.0000 | −1.67317 | −0.836583 | − | 0.547840i | \(-0.815450\pi\) | ||||
−0.836583 | + | 0.547840i | \(0.815450\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.0000 | −1.21064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 27.7128i | − | 1.39087i | −0.718591 | − | 0.695433i | \(-0.755213\pi\) | ||
0.718591 | − | 0.695433i | \(-0.244787\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −32.0000 | + | 27.7128i | −1.60200 | + | 1.38738i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.0000 | 0.749064 | 0.374532 | − | 0.927214i | \(-0.377803\pi\) | ||||
0.374532 | + | 0.927214i | \(0.377803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.92820i | − | 0.345118i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 36.3731i | − | 1.80295i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 27.7128i | − | 1.37031i | −0.728397 | − | 0.685155i | \(-0.759734\pi\) | ||
0.728397 | − | 0.685155i | \(-0.240266\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | + | 10.3923i | −0.590481 | + | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −44.0000 | −2.15469 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0000 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | + | 6.92820i | 0.290360 | + | 0.335279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 36.0000 | 1.73810 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.1769i | 1.50174i | 0.660451 | + | 0.750870i | \(0.270365\pi\) | ||||
−0.660451 | + | 0.750870i | \(0.729635\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.6410i | 1.66474i | 0.554220 | + | 0.832370i | \(0.313017\pi\) | ||||
−0.554220 | + | 0.832370i | \(0.686983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 41.5692i | − | 1.98853i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0000 | −1.05000 | −0.525001 | − | 0.851101i | \(-0.675935\pi\) | ||||
−0.525001 | + | 0.851101i | \(0.675935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.1769i | 1.48126i | 0.671913 | + | 0.740630i | \(0.265473\pi\) | ||||
−0.671913 | + | 0.740630i | \(0.734527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.0000 | 0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.0000 | 0.707894 | 0.353947 | − | 0.935266i | \(-0.384839\pi\) | ||||
0.353947 | + | 0.935266i | \(0.384839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −54.0000 | −2.54276 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 24.2487i | − | 1.13930i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00000 | 0.0467780 | 0.0233890 | − | 0.999726i | \(-0.492554\pi\) | ||||
0.0233890 | + | 0.999726i | \(0.492554\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.1769i | 1.45205i | 0.687666 | + | 0.726027i | \(0.258635\pi\) | ||||
−0.687666 | + | 0.726027i | \(0.741365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.3923i | − | 0.482971i | −0.970404 | − | 0.241486i | \(-0.922365\pi\) | ||
0.970404 | − | 0.241486i | \(-0.0776347\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.0000 | − | 24.2487i | −0.969690 | − | 1.11970i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 48.4974i | − | 2.23464i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.00000 | −0.413820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00000 | 0.274147 | 0.137073 | − | 0.990561i | \(-0.456230\pi\) | ||||
0.137073 | + | 0.990561i | \(0.456230\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 24.2487i | − | 1.10565i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.0000 | + | 20.7846i | 0.819028 | + | 0.945732i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 32.9090i | − | 1.49125i | −0.666367 | − | 0.745624i | \(-0.732152\pi\) | ||
0.666367 | − | 0.745624i | \(-0.267848\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 34.6410i | − | 1.56652i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.9808i | 1.17250i | 0.810132 | + | 0.586248i | \(0.199395\pi\) | ||||
−0.810132 | + | 0.586248i | \(0.800605\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.00000 | + | 10.3923i | 0.403705 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 24.2487i | − | 1.08552i | −0.839887 | − | 0.542761i | \(-0.817379\pi\) | ||
0.839887 | − | 0.542761i | \(-0.182621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 36.0000 | 1.60836 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.00000 | −0.0888231 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.1769i | 1.38189i | 0.722906 | + | 0.690946i | \(0.242806\pi\) | ||||
−0.722906 | + | 0.690946i | \(0.757194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.0000 | − | 20.7846i | −0.796273 | − | 0.919457i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.0000 | 1.41283 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 41.5692i | − | 1.82469i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.0000 | −1.22435 | −0.612177 | − | 0.790721i | \(-0.709706\pi\) | ||||
−0.612177 | + | 0.790721i | \(0.709706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.00000 | −0.173913 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.0000 | −1.55933 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 20.7846i | − | 0.896922i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.0000 | + | 5.19615i | 1.55063 | + | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0000 | −0.730887 | −0.365444 | − | 0.930834i | \(-0.619083\pi\) | ||||
−0.365444 | + | 0.930834i | \(0.619083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 34.6410i | − | 1.48659i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.9808i | − | 1.11086i | −0.831564 | − | 0.555429i | \(-0.812554\pi\) | ||
0.831564 | − | 0.555429i | \(-0.187446\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.46410i | 0.147844i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −72.0000 | −3.06730 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.00000 | + | 10.3923i | 0.382719 | + | 0.441926i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.00000 | −0.127114 | −0.0635570 | − | 0.997978i | \(-0.520244\pi\) | ||||
−0.0635570 | + | 0.997978i | \(0.520244\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.00000 | −0.253773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0000 | 0.505740 | 0.252870 | − | 0.967500i | \(-0.418626\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.0000 | + | 19.0526i | −0.923913 | + | 0.800132i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.0000 | −1.38343 | −0.691716 | − | 0.722170i | \(-0.743145\pi\) | ||||
−0.691716 | + | 0.722170i | \(0.743145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.73205i | − | 0.0724841i | −0.999343 | − | 0.0362420i | \(-0.988461\pi\) | ||
0.999343 | − | 0.0362420i | \(-0.0115387\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.7846i | 0.868290i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.92820i | 0.288425i | 0.989547 | + | 0.144212i | \(0.0460649\pi\) | ||||
−0.989547 | + | 0.144212i | \(0.953935\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.0000 | 0.581820 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | − | 10.3923i | 0.497844 | − | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.1769i | 1.29122i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −42.0000 | −1.73353 | −0.866763 | − | 0.498721i | \(-0.833803\pi\) | ||||
−0.866763 | + | 0.498721i | \(0.833803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | 0.246807 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.7846i | 0.853522i | 0.904365 | + | 0.426761i | \(0.140345\pi\) | ||||
−0.904365 | + | 0.426761i | \(0.859655\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.0000 | 0.818546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 36.3731i | − | 1.48616i | −0.669201 | − | 0.743082i | \(-0.733363\pi\) | ||
0.669201 | − | 0.743082i | \(-0.266637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.8564i | − | 0.565215i | −0.959236 | − | 0.282607i | \(-0.908801\pi\) | ||
0.959236 | − | 0.282607i | \(-0.0911993\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.1244i | − | 0.493742i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0000 | −0.568242 | −0.284121 | − | 0.958788i | \(-0.591702\pi\) | ||||
−0.284121 | + | 0.958788i | \(0.591702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 36.0000 | − | 31.1769i | 1.45879 | − | 1.26335i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.0000 | −1.89831 | −0.949156 | − | 0.314806i | \(-0.898061\pi\) | ||||
−0.949156 | + | 0.314806i | \(0.898061\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | −0.120775 | −0.0603877 | − | 0.998175i | \(-0.519234\pi\) | ||||
−0.0603877 | + | 0.998175i | \(0.519234\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0000 | −0.562708 | −0.281354 | − | 0.959604i | \(-0.590783\pi\) | ||||
−0.281354 | + | 0.959604i | \(0.590783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 20.7846i | − | 0.834058i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.0000 | + | 20.7846i | 0.721155 | + | 0.832718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 83.1384i | − | 3.32023i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 29.4449i | − | 1.17218i | −0.810245 | − | 0.586091i | \(-0.800666\pi\) | ||
0.810245 | − | 0.586091i | \(-0.199334\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.92820i | 0.275371i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.0000 | + | 3.46410i | 0.950915 | + | 0.137253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.19615i | 0.205557i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0000 | 0.592464 | 0.296232 | − | 0.955116i | \(-0.404270\pi\) | ||||
0.296232 | + | 0.955116i | \(0.404270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.00000 | 0.157745 | 0.0788723 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788723 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 31.1769i | − | 1.22380i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.00000 | − | 6.92820i | 0.313545 | − | 0.271538i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 10.3923i | − | 0.405442i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.1769i | 1.21448i | 0.794518 | + | 0.607240i | \(0.207723\pi\) | ||||
−0.794518 | + | 0.607240i | \(0.792277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 20.7846i | − | 0.808428i | −0.914665 | − | 0.404214i | \(-0.867545\pi\) | ||
0.914665 | − | 0.404214i | \(-0.132455\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46.7654i | 1.81076i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.0000 | 1.08254 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.0000 | −0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0000 | 1.00223 | 0.501113 | − | 0.865382i | \(-0.332924\pi\) | ||||
0.501113 | + | 0.865382i | \(0.332924\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 20.7846i | − | 0.798817i | −0.916773 | − | 0.399409i | \(-0.869215\pi\) | ||
0.916773 | − | 0.399409i | \(-0.130785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.00000 | − | 6.92820i | −0.230259 | − | 0.265880i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.0000 | 1.83936 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 5.19615i | − | 0.198825i | −0.995046 | − | 0.0994126i | \(-0.968304\pi\) | ||
0.995046 | − | 0.0994126i | \(-0.0316964\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8564i | 0.528655i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.7846i | 0.791831i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | 0.380418 | 0.190209 | − | 0.981744i | \(-0.439083\pi\) | ||||
0.190209 | + | 0.981744i | \(0.439083\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.00000 | + | 10.3923i | 0.341882 | + | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −56.0000 | −2.11208 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.0000 | + | 20.7846i | 0.676960 | + | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 50.0000 | 1.87779 | 0.938895 | − | 0.344204i | \(-0.111851\pi\) | ||||
0.938895 | + | 0.344204i | \(0.111851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.19615i | 0.194871i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.3923i | 0.389195i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.7846i | 0.776215i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.0000 | 0.671287 | 0.335643 | − | 0.941989i | \(-0.391046\pi\) | ||||
0.335643 | + | 0.941989i | \(0.391046\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | + | 6.92820i | −0.297936 | + | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.8564i | 0.515325i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 63.0000 | 2.32063 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 15.5885i | − | 0.573431i | −0.958016 | − | 0.286715i | \(-0.907437\pi\) | ||
0.958016 | − | 0.286715i | \(-0.0925634\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 55.4256i | − | 2.03611i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.3923i | 0.381257i | 0.981662 | + | 0.190628i | \(0.0610525\pi\) | ||||
−0.981662 | + | 0.190628i | \(0.938947\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | 0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000 | + | 20.7846i | 0.657706 | + | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.3923i | 0.379221i | 0.981859 | + | 0.189610i | \(0.0607225\pi\) | ||||
−0.981859 | + | 0.189610i | \(0.939278\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.0000 | −1.27210 | −0.636048 | − | 0.771649i | \(-0.719432\pi\) | ||||
−0.636048 | + | 0.771649i | \(0.719432\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −54.0000 | −1.96008 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 20.7846i | − | 0.753442i | −0.926327 | − | 0.376721i | \(-0.877052\pi\) | ||
0.926327 | − | 0.376721i | \(-0.122948\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | + | 1.73205i | −0.0724049 | + | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 20.7846i | − | 0.750489i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.46410i | − | 0.124919i | −0.998048 | − | 0.0624593i | \(-0.980106\pi\) | ||
0.998048 | − | 0.0624593i | \(-0.0198944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 20.7846i | − | 0.748539i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.1769i | 1.12136i | 0.828034 | + | 0.560678i | \(0.189459\pi\) | ||||
−0.828034 | + | 0.560678i | \(0.810541\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28.0000 | − | 24.2487i | 1.00449 | − | 0.869918i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 83.1384i | 2.97874i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | −0.966136 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.0000 | −1.28654 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.0000 | −1.21197 | −0.605985 | − | 0.795476i | \(-0.707221\pi\) | ||||
−0.605985 | + | 0.795476i | \(0.707221\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 31.1769i | − | 1.10993i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.00000 | + | 5.19615i | −0.213335 | + | 0.184754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0000 | −0.426132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.3923i | 0.367194i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 54.0000 | 1.90562 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 62.3538i | 2.19496i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.0000 | −1.58212 | −0.791058 | − | 0.611741i | \(-0.790469\pi\) | ||||
−0.791058 | + | 0.611741i | \(0.790469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.00000 | 0.140286 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.8564i | 0.484774i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.00000 | + | 6.92820i | 0.209657 | + | 0.242091i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 12.1244i | − | 0.422628i | −0.977418 | − | 0.211314i | \(-0.932226\pi\) | ||
0.977418 | − | 0.211314i | \(-0.0677743\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.5885i | 0.542064i | 0.962570 | + | 0.271032i | \(0.0873649\pi\) | ||||
−0.962570 | + | 0.271032i | \(0.912635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7846i | 0.721879i | 0.932589 | + | 0.360940i | \(0.117544\pi\) | ||||
−0.932589 | + | 0.360940i | \(0.882456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 44.0000 | 1.52634 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.00000 | −0.276520 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.0000 | −0.621429 | −0.310715 | − | 0.950503i | \(-0.600568\pi\) | ||||
−0.310715 | + | 0.950503i | \(0.600568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.0000 | 1.44656 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.0000 | + | 27.7128i | −1.09953 | + | 0.952224i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −32.0000 | −1.09824 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.3731i | 1.24685i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 55.4256i | − | 1.89774i | −0.315671 | − | 0.948869i | \(-0.602230\pi\) | ||
0.315671 | − | 0.948869i | \(-0.397770\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 51.9615i | − | 1.77497i | −0.460835 | − | 0.887486i | \(-0.652450\pi\) | ||
0.460835 | − | 0.887486i | \(-0.347550\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −36.0000 | − | 41.5692i | −1.22688 | − | 1.41668i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 5.19615i | − | 0.176879i | −0.996082 | − | 0.0884395i | \(-0.971812\pi\) | ||
0.996082 | − | 0.0884395i | \(-0.0281880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34.0000 | −1.15470 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.0000 | −0.915912 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.0000 | 1.42312 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.46410i | − | 0.117242i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.00000 | −0.0675352 | −0.0337676 | − | 0.999430i | \(-0.510751\pi\) | ||||
−0.0337676 | + | 0.999430i | \(0.510751\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 20.7846i | − | 0.701047i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.1769i | 1.05038i | 0.850986 | + | 0.525188i | \(0.176005\pi\) | ||||
−0.850986 | + | 0.525188i | \(0.823995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.5167i | 0.757746i | 0.925449 | + | 0.378873i | \(0.123688\pi\) | ||||
−0.925449 | + | 0.378873i | \(0.876312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.0000 | −1.41022 | −0.705111 | − | 0.709097i | \(-0.749103\pi\) | ||||
−0.705111 | + | 0.709097i | \(0.749103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.0000 | + | 31.1769i | 0.905551 | + | 1.04564i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 57.1577i | − | 1.91485i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.0000 | −1.20201 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.0000 | 0.600334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.00000 | − | 6.92820i | −0.199667 | − | 0.230556i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 10.3923i | − | 0.345071i | −0.985003 | − | 0.172535i | \(-0.944804\pi\) | ||
0.985003 | − | 0.172535i | \(-0.0551959\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.3923i | 0.344691i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 36.3731i | − | 1.20509i | −0.798084 | − | 0.602547i | \(-0.794153\pi\) | ||
0.798084 | − | 0.602547i | \(-0.205847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.1769i | 1.03181i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.0000 | − | 20.7846i | 0.792550 | − | 0.686368i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.1244i | 0.399946i | 0.979801 | + | 0.199973i | \(0.0640854\pi\) | ||||
−0.979801 | + | 0.199973i | \(0.935915\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.0000 | 0.527218 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.0000 | −0.592477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | −0.131377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 10.3923i | − | 0.340960i | −0.985361 | − | 0.170480i | \(-0.945468\pi\) | ||
0.985361 | − | 0.170480i | \(-0.0545319\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00000 | − | 55.4256i | 0.262189 | − | 1.81650i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.1051i | 1.24484i | 0.782683 | + | 0.622420i | \(0.213850\pi\) | ||||
−0.782683 | + | 0.622420i | \(0.786150\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 13.8564i | − | 0.452187i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.3923i | 0.338779i | 0.985549 | + | 0.169390i | \(0.0541797\pi\) | ||||
−0.985549 | + | 0.169390i | \(0.945820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 54.0000 | 1.75848 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 10.3923i | − | 0.337705i | −0.985641 | − | 0.168852i | \(-0.945994\pi\) | ||
0.985641 | − | 0.168852i | \(-0.0540061\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.0000 | 1.16861 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −42.0000 | −1.36194 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.0000 | −1.65205 | −0.826026 | − | 0.563632i | \(-0.809404\pi\) | ||||
−0.826026 | + | 0.563632i | \(0.809404\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 93.5307i | 3.02342i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.0000 | + | 10.3923i | −0.387500 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.3923i | 0.334887i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3923i | 0.334194i | 0.985940 | + | 0.167097i | \(0.0534393\pi\) | ||||
−0.985940 | + | 0.167097i | \(0.946561\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.0000 | 1.54039 | 0.770197 | − | 0.637806i | \(-0.220158\pi\) | ||||
0.770197 | + | 0.637806i | \(0.220158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44.0000 | − | 38.1051i | 1.41058 | − | 1.22159i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.0000 | 1.43968 | 0.719839 | − | 0.694141i | \(-0.244216\pi\) | ||||
0.719839 | + | 0.694141i | \(0.244216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −54.0000 | −1.72585 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.00000 | −0.0319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.00000 | 0.191370 | 0.0956851 | − | 0.995412i | \(-0.469496\pi\) | ||||
0.0956851 | + | 0.995412i | \(0.469496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.00000 | 0.286183 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.8372i | 1.26547i | 0.774369 | + | 0.632735i | \(0.218068\pi\) | ||||
−0.774369 | + | 0.632735i | \(0.781932\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 10.3923i | − | 0.329790i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.0000 | −0.885881 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2800.2.k.c.2351.1 | yes | 2 | |
4.3 | odd | 2 | 2800.2.k.d.2351.2 | yes | 2 | ||
5.2 | odd | 4 | 2800.2.e.a.2799.4 | 4 | |||
5.3 | odd | 4 | 2800.2.e.a.2799.1 | 4 | |||
5.4 | even | 2 | 2800.2.k.f.2351.2 | yes | 2 | ||
7.6 | odd | 2 | 2800.2.k.d.2351.1 | yes | 2 | ||
20.3 | even | 4 | 2800.2.e.d.2799.4 | 4 | |||
20.7 | even | 4 | 2800.2.e.d.2799.1 | 4 | |||
20.19 | odd | 2 | 2800.2.k.a.2351.1 | ✓ | 2 | ||
28.27 | even | 2 | inner | 2800.2.k.c.2351.2 | yes | 2 | |
35.13 | even | 4 | 2800.2.e.d.2799.3 | 4 | |||
35.27 | even | 4 | 2800.2.e.d.2799.2 | 4 | |||
35.34 | odd | 2 | 2800.2.k.a.2351.2 | yes | 2 | ||
140.27 | odd | 4 | 2800.2.e.a.2799.3 | 4 | |||
140.83 | odd | 4 | 2800.2.e.a.2799.2 | 4 | |||
140.139 | even | 2 | 2800.2.k.f.2351.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2800.2.e.a.2799.1 | 4 | 5.3 | odd | 4 | |||
2800.2.e.a.2799.2 | 4 | 140.83 | odd | 4 | |||
2800.2.e.a.2799.3 | 4 | 140.27 | odd | 4 | |||
2800.2.e.a.2799.4 | 4 | 5.2 | odd | 4 | |||
2800.2.e.d.2799.1 | 4 | 20.7 | even | 4 | |||
2800.2.e.d.2799.2 | 4 | 35.27 | even | 4 | |||
2800.2.e.d.2799.3 | 4 | 35.13 | even | 4 | |||
2800.2.e.d.2799.4 | 4 | 20.3 | even | 4 | |||
2800.2.k.a.2351.1 | ✓ | 2 | 20.19 | odd | 2 | ||
2800.2.k.a.2351.2 | yes | 2 | 35.34 | odd | 2 | ||
2800.2.k.c.2351.1 | yes | 2 | 1.1 | even | 1 | trivial | |
2800.2.k.c.2351.2 | yes | 2 | 28.27 | even | 2 | inner | |
2800.2.k.d.2351.1 | yes | 2 | 7.6 | odd | 2 | ||
2800.2.k.d.2351.2 | yes | 2 | 4.3 | odd | 2 | ||
2800.2.k.f.2351.1 | yes | 2 | 140.139 | even | 2 | ||
2800.2.k.f.2351.2 | yes | 2 | 5.4 | even | 2 |