Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(2591,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.j (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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.162447943996702457856.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.16 | ||
Root | \(1.40721 - 0.140577i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.2591 |
Dual form | 4032.2.j.e.2591.13 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 3.09557 | 1.38438 | 0.692191 | − | 0.721714i | \(-0.256645\pi\) | ||||
0.692191 | + | 0.721714i | \(0.256645\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.646084i | − 0.194802i | −0.995245 | − | 0.0974008i | \(-0.968947\pi\) | ||||
0.995245 | − | 0.0974008i | \(-0.0310529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.37780i | 1.21418i | 0.794632 | + | 0.607092i | \(0.207664\pi\) | ||||
−0.794632 | + | 0.607092i | \(0.792336\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.295164i | 0.0715877i | 0.999359 | + | 0.0357938i | \(0.0113960\pi\) | ||||
−0.999359 | + | 0.0357938i | \(0.988604\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.29150 | −1.21395 | −0.606977 | − | 0.794719i | \(-0.707618\pi\) | ||||
−0.606977 | + | 0.794719i | \(0.707618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.94748 | −0.823106 | −0.411553 | − | 0.911386i | \(-0.635013\pi\) | ||||
−0.411553 | + | 0.911386i | \(0.635013\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.58258 | 0.916515 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.03383 | −0.934758 | −0.467379 | − | 0.884057i | \(-0.654802\pi\) | ||||
−0.467379 | + | 0.884057i | \(0.654802\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.16515i | 1.64611i | 0.567962 | + | 0.823055i | \(0.307732\pi\) | ||||
−0.567962 | + | 0.823055i | \(0.692268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.09557i | 0.523247i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.55040i | 0.419283i | 0.977778 | + | 0.209642i | \(0.0672297\pi\) | ||||
−0.977778 | + | 0.209642i | \(0.932770\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4282i | 1.62861i | 0.580434 | + | 0.814307i | \(0.302883\pi\) | ||||
−0.580434 | + | 0.814307i | \(0.697117\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.63670 | −0.249595 | −0.124797 | − | 0.992182i | \(-0.539828\pi\) | ||||
−0.124797 | + | 0.992182i | \(0.539828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65685 | −0.825137 | −0.412568 | − | 0.910927i | \(-0.635368\pi\) | ||||
−0.412568 | + | 0.910927i | \(0.635368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.64064 | 1.18688 | 0.593441 | − | 0.804877i | \(-0.297769\pi\) | ||||
0.593441 | + | 0.804877i | \(0.297769\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.00000i | − 0.269680i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.92820i | 0.887066i | 0.896258 | + | 0.443533i | \(0.146275\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.5518i | 1.68089i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.55040 | −0.311581 | −0.155791 | − | 0.987790i | \(-0.549792\pi\) | ||||
−0.155791 | + | 0.987790i | \(0.549792\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.11905 | 0.132807 | 0.0664034 | − | 0.997793i | \(-0.478848\pi\) | ||||
0.0664034 | + | 0.997793i | \(0.478848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.58258 | −1.12156 | −0.560778 | − | 0.827966i | \(-0.689498\pi\) | ||||
−0.560778 | + | 0.827966i | \(0.689498\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.646084 | 0.0736281 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 16.7477i | − 1.88427i | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
0.335239 | − | 0.942133i | \(-0.391183\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.50579i | 0.933632i | 0.884354 | + | 0.466816i | \(0.154599\pi\) | ||||
−0.884354 | + | 0.466816i | \(0.845401\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.913701i | 0.0991047i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 10.4282i | − 1.10539i | −0.833384 | − | 0.552694i | \(-0.813600\pi\) | ||||
0.833384 | − | 0.552694i | \(-0.186400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.37780 | −0.458918 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.3802 | −1.68058 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.41742 | −0.245452 | −0.122726 | − | 0.992441i | \(-0.539164\pi\) | ||||
−0.122726 | + | 0.992441i | \(0.539164\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.7925 | 1.77042 | 0.885211 | − | 0.465191i | \(-0.154014\pi\) | ||||
0.885211 | + | 0.465191i | \(0.154014\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000i | 0.197066i | 0.995134 | + | 0.0985329i | \(0.0314150\pi\) | ||||
−0.995134 | + | 0.0985329i | \(0.968585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.4440i | 1.00966i | 0.863218 | + | 0.504832i | \(0.168446\pi\) | ||||
−0.863218 | + | 0.504832i | \(0.831554\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.29150i | 0.506834i | 0.967357 | + | 0.253417i | \(0.0815545\pi\) | ||||
−0.967357 | + | 0.253417i | \(0.918446\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.89949i | 0.931266i | 0.884978 | + | 0.465633i | \(0.154173\pi\) | ||||
−0.884978 | + | 0.465633i | \(0.845827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.2197 | −1.13949 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.295164 | −0.0270576 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5826 | 0.962052 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.29217 | −0.115575 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 13.5826i | − 1.20526i | −0.798021 | − | 0.602629i | \(-0.794120\pi\) | ||||
0.798021 | − | 0.602629i | \(-0.205880\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.60681i | 0.315129i | 0.987509 | + | 0.157564i | \(0.0503642\pi\) | ||||
−0.987509 | + | 0.157564i | \(0.949636\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 5.29150i | − 0.458831i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 20.0325i | − 1.71150i | −0.517393 | − | 0.855748i | \(-0.673097\pi\) | ||||
0.517393 | − | 0.855748i | \(-0.326903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.75560 | −0.742641 | −0.371320 | − | 0.928505i | \(-0.621095\pi\) | ||||
−0.371320 | + | 0.928505i | \(0.621095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.82843 | 0.236525 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.5826 | −1.29406 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.76413 | 0.390293 | 0.195147 | − | 0.980774i | \(-0.437482\pi\) | ||||
0.195147 | + | 0.980774i | \(0.437482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 4.83485i | − 0.393454i | −0.980458 | − | 0.196727i | \(-0.936969\pi\) | ||||
0.980458 | − | 0.196727i | \(-0.0630313\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 28.3714i | 2.27885i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.10080i | 0.407088i | 0.979066 | + | 0.203544i | \(0.0652461\pi\) | ||||
−0.979066 | + | 0.203544i | \(0.934754\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 3.94748i | − 0.311105i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.7164 | 1.85761 | 0.928806 | − | 0.370565i | \(-0.120836\pi\) | ||||
0.928806 | + | 0.370565i | \(0.120836\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.06653 | 0.392060 | 0.196030 | − | 0.980598i | \(-0.437195\pi\) | ||||
0.196030 | + | 0.980598i | \(0.437195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.16515 | −0.474242 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.0847 | 1.45098 | 0.725491 | − | 0.688232i | \(-0.241613\pi\) | ||||
0.725491 | + | 0.688232i | \(0.241613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.58258i | 0.346410i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.3430i | 1.14679i | 0.819279 | + | 0.573396i | \(0.194374\pi\) | ||||
−0.819279 | + | 0.573396i | \(0.805626\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.20520i | − 0.461229i | −0.973045 | − | 0.230615i | \(-0.925926\pi\) | ||||
0.973045 | − | 0.230615i | \(-0.0740736\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.89495i | 0.580449i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.190700 | 0.0139454 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.8039 | 1.79475 | 0.897374 | − | 0.441271i | \(-0.145472\pi\) | ||||
0.897374 | + | 0.441271i | \(0.145472\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.7477 | −1.49345 | −0.746727 | − | 0.665131i | \(-0.768376\pi\) | ||||
−0.746727 | + | 0.665131i | \(0.768376\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.0005 | 1.42497 | 0.712487 | − | 0.701686i | \(-0.247569\pi\) | ||||
0.712487 | + | 0.701686i | \(0.247569\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.834849i | 0.0591808i | 0.999562 | + | 0.0295904i | \(0.00942030\pi\) | ||||
−0.999562 | + | 0.0295904i | \(0.990580\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 5.03383i | − 0.353305i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.2813i | 2.25462i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.41875i | 0.236480i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.9753 | −1.44400 | −0.722000 | − | 0.691893i | \(-0.756777\pi\) | ||||
−0.722000 | + | 0.691893i | \(0.756777\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.06653 | −0.345534 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.16515 | −0.622171 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.29217 | −0.0869206 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 20.0000i | − 1.33930i | −0.742677 | − | 0.669650i | \(-0.766444\pi\) | ||||
0.742677 | − | 0.669650i | \(-0.233556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3.60681i | − 0.239393i | −0.992811 | − | 0.119696i | \(-0.961808\pi\) | ||||
0.992811 | − | 0.119696i | \(-0.0381921\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 14.9608i | − 0.988638i | −0.869281 | − | 0.494319i | \(-0.835417\pi\) | ||||
0.869281 | − | 0.494319i | \(-0.164583\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.07107i | 0.463241i | 0.972806 | + | 0.231621i | \(0.0744028\pi\) | ||||
−0.972806 | + | 0.231621i | \(0.925597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.5112 | −1.14231 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.4328 | −0.804208 | −0.402104 | − | 0.915594i | \(-0.631721\pi\) | ||||
−0.402104 | + | 0.915594i | \(0.631721\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.5826 | −1.90558 | −0.952791 | − | 0.303628i | \(-0.901802\pi\) | ||||
−0.952791 | + | 0.303628i | \(0.901802\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.09557 | −0.197769 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 23.1652i | − 1.47396i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.4724i | 1.48157i | 0.671744 | + | 0.740783i | \(0.265545\pi\) | ||||
−0.671744 | + | 0.740783i | \(0.734455\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.55040i | 0.160342i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.6754i | 1.04018i | 0.854111 | + | 0.520091i | \(0.174102\pi\) | ||||
−0.854111 | + | 0.520091i | \(0.825898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.55040 | −0.158474 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.4993 | −1.07905 | −0.539526 | − | 0.841969i | \(-0.681397\pi\) | ||||
−0.539526 | + | 0.841969i | \(0.681397\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.7477 | 1.64310 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.3993 | 1.30474 | 0.652370 | − | 0.757901i | \(-0.273775\pi\) | ||||
0.652370 | + | 0.757901i | \(0.273775\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.1652i | 0.799726i | 0.916575 | + | 0.399863i | \(0.130942\pi\) | ||||
−0.916575 | + | 0.399863i | \(0.869058\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2.96073i | − 0.178539i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 11.4967i | − 0.690770i | −0.938461 | − | 0.345385i | \(-0.887748\pi\) | ||||
0.938461 | − | 0.345385i | \(-0.112252\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 7.66139i | − 0.457041i | −0.973539 | − | 0.228520i | \(-0.926611\pi\) | ||||
0.973539 | − | 0.228520i | \(-0.0733887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3205 | 1.02960 | 0.514799 | − | 0.857311i | \(-0.327867\pi\) | ||||
0.514799 | + | 0.857311i | \(0.327867\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.4282 | −0.615558 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9129 | 0.994875 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.8711 | −0.693514 | −0.346757 | − | 0.937955i | \(-0.612717\pi\) | ||||
−0.346757 | + | 0.937955i | \(0.612717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 17.2813i | − 0.999402i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.63670i | − 0.0943379i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.4468i | 1.22804i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.94630 | 0.510593 | 0.255296 | − | 0.966863i | \(-0.417827\pi\) | ||||
0.255296 | + | 0.966863i | \(0.417827\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.4468 | −1.21613 | −0.608067 | − | 0.793886i | \(-0.708055\pi\) | ||||
−0.608067 | + | 0.793886i | \(0.708055\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.16515 | −0.518045 | −0.259022 | − | 0.965871i | \(-0.583400\pi\) | ||||
−0.259022 | + | 0.965871i | \(0.583400\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.8318 | 0.833036 | 0.416518 | − | 0.909127i | \(-0.363250\pi\) | ||||
0.416518 | + | 0.909127i | \(0.363250\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.25227i | 0.182092i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.56186i | − 0.0869041i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.0616i | 1.11282i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 5.65685i | − 0.311872i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.8027 | −1.25335 | −0.626675 | − | 0.779281i | \(-0.715585\pi\) | ||||
−0.626675 | + | 0.779281i | \(0.715585\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.89495 | −0.431347 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.3303 | 0.780621 | 0.390311 | − | 0.920683i | \(-0.372368\pi\) | ||||
0.390311 | + | 0.920683i | \(0.372368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.92146 | 0.320665 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.27537i | 0.283197i | 0.989924 | + | 0.141598i | \(0.0452242\pi\) | ||||
−0.989924 | + | 0.141598i | \(0.954776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.1660i | 1.13299i | 0.824065 | + | 0.566495i | \(0.191701\pi\) | ||||
−0.824065 | + | 0.566495i | \(0.808299\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0276i | 0.799840i | 0.916550 | + | 0.399920i | \(0.130962\pi\) | ||||
−0.916550 | + | 0.399920i | \(0.869038\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.46410 | 0.183855 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.2227 | 1.48954 | 0.744768 | − | 0.667324i | \(-0.232560\pi\) | ||||
0.744768 | + | 0.667324i | \(0.232560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | 0.473684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −29.6636 | −1.55266 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.1652i | 1.00041i | 0.865906 | + | 0.500206i | \(0.166743\pi\) | ||||
−0.865906 | + | 0.500206i | \(0.833257\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.64064i | 0.448600i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.1660i | 1.09593i | 0.836500 | + | 0.547967i | \(0.184598\pi\) | ||||
−0.836500 | + | 0.547967i | \(0.815402\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 22.0371i | − 1.13497i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7309 | 1.52717 | 0.763587 | − | 0.645705i | \(-0.223436\pi\) | ||||
0.763587 | + | 0.645705i | \(0.223436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.0371 | −1.12604 | −0.563021 | − | 0.826442i | \(-0.690361\pi\) | ||||
−0.563021 | + | 0.826442i | \(0.690361\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.8543 | −0.803843 | −0.401921 | − | 0.915674i | \(-0.631658\pi\) | ||||
−0.401921 | + | 0.915674i | \(0.631658\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 1.16515i | − 0.0589242i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 51.8438i | − 2.60855i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.82740i | 0.0917146i | 0.998948 | + | 0.0458573i | \(0.0146020\pi\) | ||||
−0.998948 | + | 0.0458573i | \(0.985398\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.5269i | 1.62432i | 0.583437 | + | 0.812158i | \(0.301707\pi\) | ||||
−0.583437 | + | 0.812158i | \(0.698293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40.1232 | −1.99868 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.64777 | 0.0816771 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.58258 | −0.0782533 | −0.0391267 | − | 0.999234i | \(-0.512458\pi\) | ||||
−0.0391267 | + | 0.999234i | \(0.512458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.3303i | 1.29250i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0677i | 0.491837i | 0.969291 | + | 0.245918i | \(0.0790895\pi\) | ||||
−0.969291 | + | 0.245918i | \(0.920910\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.01450i | 0.293129i | 0.989201 | + | 0.146564i | \(0.0468216\pi\) | ||||
−0.989201 | + | 0.146564i | \(0.953178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.35261i | 0.0656112i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.92820 | −0.335279 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.6323 | 1.33100 | 0.665501 | − | 0.746397i | \(-0.268218\pi\) | ||||
0.665501 | + | 0.746397i | \(0.268218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.83485 | 0.136234 | 0.0681171 | − | 0.997677i | \(-0.478301\pi\) | ||||
0.0681171 | + | 0.997677i | \(0.478301\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.8881 | 0.999213 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.3303i | 0.874858i | 0.899253 | + | 0.437429i | \(0.144111\pi\) | ||||
−0.899253 | + | 0.437429i | \(0.855889\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.7137i | 0.509025i | 0.967070 | + | 0.254512i | \(0.0819150\pi\) | ||||
−0.967070 | + | 0.254512i | \(0.918085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 32.2813i | − 1.53028i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 9.89949i | − 0.467186i | −0.972334 | − | 0.233593i | \(-0.924952\pi\) | ||||
0.972334 | − | 0.233593i | \(-0.0750483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.73750 | 0.317257 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.5518 | −0.635319 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1652 | 0.709396 | 0.354698 | − | 0.934981i | \(-0.384584\pi\) | ||||
0.354698 | + | 0.934981i | \(0.384584\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.55641 | 0.445086 | 0.222543 | − | 0.974923i | \(-0.428564\pi\) | ||||
0.222543 | + | 0.974923i | \(0.428564\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.41742i | − 0.112347i | −0.998421 | − | 0.0561736i | \(-0.982110\pi\) | ||||
0.998421 | − | 0.0561736i | \(-0.0178900\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.8431i | 0.871956i | 0.899957 | + | 0.435978i | \(0.143597\pi\) | ||||
−0.899957 | + | 0.435978i | \(0.856403\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2.55040i | − 0.117767i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.05745i | 0.0486214i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.2487 | −1.11261 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.66594 | 0.441648 | 0.220824 | − | 0.975314i | \(-0.429125\pi\) | ||||
0.220824 | + | 0.975314i | \(0.429125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1652 | −0.509087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.48331 | −0.339800 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.3303i | 0.649368i | 0.945823 | + | 0.324684i | \(0.105258\pi\) | ||||
−0.945823 | + | 0.324684i | \(0.894742\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2420i | 0.913509i | 0.889593 | + | 0.456754i | \(0.150988\pi\) | ||||
−0.889593 | + | 0.456754i | \(0.849012\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.48580i | − 0.0669171i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.11905i | 0.0501963i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.0043 | 1.47748 | 0.738738 | − | 0.673993i | \(-0.235422\pi\) | ||||
0.738738 | + | 0.673993i | \(0.235422\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.7325 | −0.656888 | −0.328444 | − | 0.944523i | \(-0.606524\pi\) | ||||
−0.328444 | + | 0.944523i | \(0.606524\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 55.0780 | 2.45094 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.07310 | 0.0918884 | 0.0459442 | − | 0.998944i | \(-0.485370\pi\) | ||||
0.0459442 | + | 0.998944i | \(0.485370\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 9.58258i | − 0.423908i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.19115i | 0.272815i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.65480i | 0.160738i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 31.8750i | − 1.39647i | −0.715869 | − | 0.698234i | \(-0.753969\pi\) | ||||
0.715869 | − | 0.698234i | \(-0.246031\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.5764 | −1.46819 | −0.734097 | − | 0.679045i | \(-0.762394\pi\) | ||||
−0.734097 | + | 0.679045i | \(0.762394\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.70522 | −0.117841 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.41742 | −0.322497 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −45.6527 | −1.97744 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.3303i | 1.39776i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.646084i | 0.0278288i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 20.2523i | − 0.870715i | −0.900258 | − | 0.435357i | \(-0.856622\pi\) | ||||
0.900258 | − | 0.435357i | \(-0.143378\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.3802i | 0.701652i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.5010 | −1.90273 | −0.951363 | − | 0.308072i | \(-0.900316\pi\) | ||||
−0.951363 | + | 0.308072i | \(0.900316\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.6365 | 1.13475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.7477 | 0.712186 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.9110 | −1.77583 | −0.887913 | − | 0.460011i | \(-0.847846\pi\) | ||||
−0.887913 | + | 0.460011i | \(0.847846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 7.16515i | − 0.303054i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 44.3605i | − 1.86957i | −0.355211 | − | 0.934786i | \(-0.615591\pi\) | ||||
0.355211 | − | 0.934786i | \(-0.384409\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.6446i | 1.28923i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 8.25172i | − 0.345930i | −0.984928 | − | 0.172965i | \(-0.944665\pi\) | ||||
0.984928 | − | 0.172965i | \(-0.0553348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.8824 | 1.87827 | 0.939135 | − | 0.343547i | \(-0.111628\pi\) | ||||
0.939135 | + | 0.343547i | \(0.111628\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.0896 | −0.754389 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.1652 | −0.548072 | −0.274036 | − | 0.961719i | \(-0.588359\pi\) | ||||
−0.274036 | + | 0.961719i | \(0.588359\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.50579 | −0.352880 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 5.58258i | − 0.231207i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 23.7421i | − 0.979942i | −0.871739 | − | 0.489971i | \(-0.837007\pi\) | ||||
0.871739 | − | 0.489971i | \(-0.162993\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 48.4974i | − 1.99830i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.1992i | 0.500961i | 0.968122 | + | 0.250481i | \(0.0805886\pi\) | ||||
−0.968122 | + | 0.250481i | \(0.919411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.913701 | −0.0374581 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.95656 | −0.325096 | −0.162548 | − | 0.986701i | \(-0.551971\pi\) | ||||
−0.162548 | + | 0.986701i | \(0.551971\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.83485 | 0.278799 | 0.139400 | − | 0.990236i | \(-0.455483\pi\) | ||||
0.139400 | + | 0.990236i | \(0.455483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.7591 | 1.33185 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 22.3303i | − 0.906359i | −0.891419 | − | 0.453180i | \(-0.850290\pi\) | ||||
0.891419 | − | 0.453180i | \(-0.149710\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 24.7646i | − 1.00187i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.381401i | 0.0154046i | 0.999970 | + | 0.00770232i | \(0.00245175\pi\) | ||||
−0.999970 | + | 0.00770232i | \(0.997548\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 37.0031i | − 1.48969i | −0.667238 | − | 0.744845i | \(-0.732524\pi\) | ||||
0.667238 | − | 0.744845i | \(-0.267476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.9506 | 1.68614 | 0.843069 | − | 0.537806i | \(-0.180747\pi\) | ||||
0.843069 | + | 0.537806i | \(0.180747\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.4282 | 0.417798 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.9129 | −1.07652 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.752785 | −0.0300155 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 31.9129i | − 1.27043i | −0.772335 | − | 0.635216i | \(-0.780911\pi\) | ||||
0.772335 | − | 0.635216i | \(-0.219089\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 42.0459i | − 1.66854i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.37780i | − 0.173455i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 26.7468i | − 1.05644i | −0.849108 | − | 0.528219i | \(-0.822860\pi\) | ||||
0.849108 | − | 0.528219i | \(-0.177140\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.7599 | 1.64685 | 0.823425 | − | 0.567425i | \(-0.192060\pi\) | ||||
0.823425 | + | 0.567425i | \(0.192060\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.3508 | 1.31116 | 0.655578 | − | 0.755128i | \(-0.272425\pi\) | ||||
0.655578 | + | 0.755128i | \(0.272425\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.07878 | 0.277014 | 0.138507 | − | 0.990361i | \(-0.455770\pi\) | ||||
0.138507 | + | 0.990361i | \(0.455770\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.1652i | 0.436259i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 24.1185i | − 0.939524i | −0.882793 | − | 0.469762i | \(-0.844340\pi\) | ||||
0.882793 | − | 0.469762i | \(-0.155660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.3386i | 0.752185i | 0.926582 | + | 0.376092i | \(0.122732\pi\) | ||||
−0.926582 | + | 0.376092i | \(0.877268\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 16.3802i | − 0.635198i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.8709 | 0.769405 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.47620 | 0.172802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.9129 | −1.53853 | −0.769264 | − | 0.638931i | \(-0.779377\pi\) | ||||
−0.769264 | + | 0.638931i | \(0.779377\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.2534 | −0.932132 | −0.466066 | − | 0.884750i | \(-0.654329\pi\) | ||||
−0.466066 | + | 0.884750i | \(0.654329\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 2.41742i | − 0.0927722i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.1528i | 1.88078i | 0.340099 | + | 0.940390i | \(0.389539\pi\) | ||||
−0.340099 | + | 0.940390i | \(0.610461\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 62.0122i | − 2.36937i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37.8270i | 1.44109i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.8498 | 1.40183 | 0.700917 | − | 0.713243i | \(-0.252775\pi\) | ||||
0.700917 | + | 0.713243i | \(0.252775\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.1036 | −1.02810 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.07803 | −0.116589 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.37095 | −0.316166 | −0.158083 | − | 0.987426i | \(-0.550531\pi\) | ||||
−0.158083 | + | 0.987426i | \(0.550531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 13.4955i | − 0.508991i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.7925i | 0.669156i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 2.01810i | − 0.0757914i | −0.999282 | − | 0.0378957i | \(-0.987935\pi\) | ||||
0.999282 | − | 0.0378957i | \(-0.0120655\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 36.1792i | − 1.35492i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.75560 | 0.327441 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.3032 | 1.57764 | 0.788822 | − | 0.614622i | \(-0.210692\pi\) | ||||
0.788822 | + | 0.614622i | \(0.210692\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.00000 | −0.0744839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.0679 | −0.856720 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 35.4955i | − 1.31645i | −0.752820 | − | 0.658227i | \(-0.771307\pi\) | ||||
0.752820 | − | 0.658227i | \(-0.228693\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 0.483094i | − 0.0178679i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 28.8172i | − 1.06439i | −0.846622 | − | 0.532194i | \(-0.821368\pi\) | ||||
0.846622 | − | 0.532194i | \(-0.178632\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.64777i | 0.0606965i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.55040 | 0.0938180 | 0.0469090 | − | 0.998899i | \(-0.485063\pi\) | ||||
0.0469090 | + | 0.998899i | \(0.485063\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.17650 | −0.0798479 | −0.0399239 | − | 0.999203i | \(-0.512712\pi\) | ||||
−0.0399239 | + | 0.999203i | \(0.512712\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.7477 | 0.540315 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.4440 | −0.381617 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.8348i | 0.614312i | 0.951659 | + | 0.307156i | \(0.0993774\pi\) | ||||
−0.951659 | + | 0.307156i | \(0.900623\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 14.9666i | − 0.544691i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 20.5939i | − 0.748498i | −0.927328 | − | 0.374249i | \(-0.877900\pi\) | ||||
0.927328 | − | 0.374249i | \(-0.122100\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 40.3603i | − 1.46306i | −0.681810 | − | 0.731529i | \(-0.738807\pi\) | ||||
0.681810 | − | 0.731529i | \(-0.261193\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.29150 | −0.191565 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.6129 | 1.02914 | 0.514568 | − | 0.857450i | \(-0.327952\pi\) | ||||
0.514568 | + | 0.857450i | \(0.327952\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 42.0000i | 1.50868i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 55.1809i | − 1.97706i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 0.723000i | − 0.0258710i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.7899i | 0.563566i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.2306 | 0.792436 | 0.396218 | − | 0.918157i | \(-0.370323\pi\) | ||||
0.396218 | + | 0.918157i | \(0.370323\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.89949 | −0.351986 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.3303 | −1.07706 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.0404 | −1.77252 | −0.886261 | − | 0.463186i | \(-0.846706\pi\) | ||||
−0.886261 | + | 0.463186i | \(0.846706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1.66970i | − 0.0590696i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.19115i | 0.218481i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 12.2197i | − 0.430688i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 8.84205i | − 0.310870i | −0.987846 | − | 0.155435i | \(-0.950322\pi\) | ||||
0.987846 | − | 0.155435i | \(-0.0496779\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.2668 | −0.922353 | −0.461176 | − | 0.887309i | \(-0.652572\pi\) | ||||
−0.461176 | + | 0.887309i | \(0.652572\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 73.4159 | 2.57165 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.66061 | 0.302996 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.74166 | 0.130585 | 0.0652924 | − | 0.997866i | \(-0.479202\pi\) | ||||
0.0652924 | + | 0.997866i | \(0.479202\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 43.9129i | − 1.53071i | −0.643610 | − | 0.765353i | \(-0.722564\pi\) | ||||
0.643610 | − | 0.765353i | \(-0.277436\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.8606i | 1.66428i | 0.554568 | + | 0.832138i | \(0.312883\pi\) | ||||
−0.554568 | + | 0.832138i | \(0.687117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.3712i | 0.950642i | 0.879813 | + | 0.475321i | \(0.157668\pi\) | ||||
−0.879813 | + | 0.475321i | \(0.842332\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.295164i | − 0.0102268i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.6838 | 0.542761 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.0462 | 0.899214 | 0.449607 | − | 0.893227i | \(-0.351564\pi\) | ||||
0.449607 | + | 0.893227i | \(0.351564\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.66061 | −0.126228 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.0847 | −0.656533 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.5826i | 0.363622i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 10.0677i | − 0.345115i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7.30960i | − 0.250276i | −0.992139 | − | 0.125138i | \(-0.960063\pi\) | ||||
0.992139 | − | 0.125138i | \(-0.0399374\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.5038i | 0.666238i | 0.942885 | + | 0.333119i | \(0.108101\pi\) | ||||
−0.942885 | + | 0.333119i | \(0.891899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.5221 | 0.939042 | 0.469521 | − | 0.882921i | \(-0.344427\pi\) | ||||
0.469521 | + | 0.882921i | \(0.344427\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.1947 | 0.347030 | 0.173515 | − | 0.984831i | \(-0.444487\pi\) | ||||
0.173515 | + | 0.984831i | \(0.444487\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 59.0780 | 2.00871 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.8204 | −0.367058 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 11.1652i | − 0.378317i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.29217i | − 0.0436832i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 35.0224i | − 1.18262i | −0.806443 | − | 0.591311i | \(-0.798610\pi\) | ||||
0.806443 | − | 0.591311i | \(-0.201390\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 11.6089i | − 0.391113i | −0.980692 | − | 0.195556i | \(-0.937349\pi\) | ||||
0.980692 | − | 0.195556i | \(-0.0626513\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2487 | −0.816034 | −0.408017 | − | 0.912974i | \(-0.633780\pi\) | ||||
−0.408017 | + | 0.912974i | \(0.633780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.3032 | 1.42040 | 0.710201 | − | 0.703999i | \(-0.248604\pi\) | ||||
0.710201 | + | 0.703999i | \(0.248604\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.5826 | 0.455545 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.9333 | 1.00168 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47.4955i | 1.58760i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 46.1358i | − 1.53871i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.55040i | 0.0849662i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 19.2087i | − 0.638518i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.8317 | −1.15657 | −0.578284 | − | 0.815835i | \(-0.696277\pi\) | ||||
−0.578284 | + | 0.815835i | \(0.696277\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.18558 | −0.204937 | −0.102469 | − | 0.994736i | \(-0.532674\pi\) | ||||
−0.102469 | + | 0.994736i | \(0.532674\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.49545 | 0.181873 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.60681 | −0.119107 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.1652i | 1.02804i | 0.857777 | + | 0.514022i | \(0.171845\pi\) | ||||
−0.857777 | + | 0.514022i | \(0.828155\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.89898i | 0.161252i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.6874i | 0.384280i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 5.36169i | − 0.175911i | −0.996124 | − | 0.0879557i | \(-0.971967\pi\) | ||||
0.996124 | − | 0.0879557i | \(-0.0280334\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.29150 | 0.173422 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.590327 | 0.0193058 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.4955 | −0.506214 | −0.253107 | − | 0.967438i | \(-0.581453\pi\) | ||||
−0.253107 | + | 0.967438i | \(0.581453\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.9837 | 0.781845 | 0.390922 | − | 0.920424i | \(-0.372156\pi\) | ||||
0.390922 | + | 0.920424i | \(0.372156\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 41.1652i | − 1.34052i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 53.7821i | − 1.74768i | −0.486211 | − | 0.873841i | \(-0.661621\pi\) | ||||
0.486211 | − | 0.873841i | \(-0.338379\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 41.9506i | − 1.36177i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 40.4219i | − 1.30939i | −0.755892 | − | 0.654696i | \(-0.772797\pi\) | ||||
0.755892 | − | 0.654696i | \(-0.227203\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 76.7823 | 2.48462 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.0325 | 0.646885 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −53.0000 | −1.70968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −64.2261 | −2.06751 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.0780i | 1.64256i | 0.570526 | + | 0.821279i | \(0.306739\pi\) | ||||
−0.570526 | + | 0.821279i | \(0.693261\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 39.4615i | − 1.26638i | −0.773996 | − | 0.633190i | \(-0.781745\pi\) | ||||
0.773996 | − | 0.633190i | \(-0.218255\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 8.75560i | − 0.280692i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 44.8981i | − 1.43642i | −0.695828 | − | 0.718208i | \(-0.744963\pi\) | ||||
0.695828 | − | 0.718208i | \(-0.255037\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.73750 | −0.215332 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.1982 | 1.60107 | 0.800536 | − | 0.599284i | \(-0.204548\pi\) | ||||
0.800536 | + | 0.599284i | \(0.204548\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 61.9129 | 1.97271 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.46084 | 0.205443 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 20.0000i | − 0.635321i | −0.948205 | − | 0.317660i | \(-0.897103\pi\) | ||||
0.948205 | − | 0.317660i | \(-0.102897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.58434i | 0.0819289i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.8788i | 1.54801i | 0.633181 | + | 0.774004i | \(0.281749\pi\) | ||||
−0.633181 | + | 0.774004i | \(0.718251\pi\) | |||||||
\(998\) | 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 \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.j.e.2591.16 | yes | 16 | |
3.2 | odd | 2 | inner | 4032.2.j.e.2591.4 | yes | 16 | |
4.3 | odd | 2 | inner | 4032.2.j.e.2591.14 | yes | 16 | |
8.3 | odd | 2 | inner | 4032.2.j.e.2591.1 | ✓ | 16 | |
8.5 | even | 2 | inner | 4032.2.j.e.2591.3 | yes | 16 | |
12.11 | even | 2 | inner | 4032.2.j.e.2591.2 | yes | 16 | |
24.5 | odd | 2 | inner | 4032.2.j.e.2591.15 | yes | 16 | |
24.11 | even | 2 | inner | 4032.2.j.e.2591.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4032.2.j.e.2591.1 | ✓ | 16 | 8.3 | odd | 2 | inner | |
4032.2.j.e.2591.2 | yes | 16 | 12.11 | even | 2 | inner | |
4032.2.j.e.2591.3 | yes | 16 | 8.5 | even | 2 | inner | |
4032.2.j.e.2591.4 | yes | 16 | 3.2 | odd | 2 | inner | |
4032.2.j.e.2591.13 | yes | 16 | 24.11 | even | 2 | inner | |
4032.2.j.e.2591.14 | yes | 16 | 4.3 | odd | 2 | inner | |
4032.2.j.e.2591.15 | yes | 16 | 24.5 | odd | 2 | inner | |
4032.2.j.e.2591.16 | yes | 16 | 1.1 | even | 1 | trivial |