Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,4,Mod(1,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.a (trivial) |
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: | yes |
Analytic conductor: | \(23.1287487223\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −5.65685 | −1.08866 | −0.544331 | − | 0.838870i | \(-0.683216\pi\) | ||||
−0.544331 | + | 0.838870i | \(0.683216\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.65685 | −0.505964 | −0.252982 | − | 0.967471i | \(-0.581411\pi\) | ||||
−0.252982 | + | 0.967471i | \(0.581411\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.00000 | 0.185185 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −0.109640 | −0.0548202 | − | 0.998496i | \(-0.517459\pi\) | ||||
−0.0548202 | + | 0.998496i | \(0.517459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.65685 | 0.120687 | 0.0603434 | − | 0.998178i | \(-0.480780\pi\) | ||||
0.0603434 | + | 0.998178i | \(0.480780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 32.0000 | 0.550824 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −124.451 | −1.77551 | −0.887757 | − | 0.460312i | \(-0.847738\pi\) | ||||
−0.887757 | + | 0.460312i | \(0.847738\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −130.108 | −1.57099 | −0.785493 | − | 0.618870i | \(-0.787591\pi\) | ||||
−0.785493 | + | 0.618870i | \(0.787591\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 120.000 | 1.08790 | 0.543951 | − | 0.839117i | \(-0.316928\pi\) | ||||
0.543951 | + | 0.839117i | \(0.316928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −93.0000 | −0.744000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 124.451 | 0.887058 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 218.000 | 1.39592 | 0.697958 | − | 0.716138i | \(-0.254092\pi\) | ||||
0.697958 | + | 0.716138i | \(0.254092\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 147.078 | 0.852130 | 0.426065 | − | 0.904693i | \(-0.359900\pi\) | ||||
0.426065 | + | 0.904693i | \(0.359900\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 22.6274 | 0.119361 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 130.000 | 0.577618 | 0.288809 | − | 0.957387i | \(-0.406741\pi\) | ||||
0.288809 | + | 0.957387i | \(0.406741\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −32.0000 | −0.131387 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −147.078 | −0.560238 | −0.280119 | − | 0.959965i | \(-0.590374\pi\) | ||||
−0.280119 | + | 0.959965i | \(0.590374\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 332.000 | 1.17743 | 0.588715 | − | 0.808340i | \(-0.299634\pi\) | ||||
0.588715 | + | 0.808340i | \(0.299634\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −28.2843 | −0.0936971 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 124.451 | 0.386234 | 0.193117 | − | 0.981176i | \(-0.438140\pi\) | ||||
0.193117 | + | 0.981176i | \(0.438140\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 704.000 | 1.93294 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −498.000 | −1.29067 | −0.645335 | − | 0.763899i | \(-0.723282\pi\) | ||||
−0.645335 | + | 0.763899i | \(0.723282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 22.6274 | 0.0554742 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 736.000 | 1.71027 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 548.715 | 1.21079 | 0.605395 | − | 0.795925i | \(-0.293015\pi\) | ||||
0.605395 | + | 0.795925i | \(0.293015\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 650.538 | 1.36546 | 0.682729 | − | 0.730672i | \(-0.260793\pi\) | ||||
0.682729 | + | 0.730672i | \(0.260793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −32.0000 | −0.0610633 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 156.000 | 0.284454 | 0.142227 | − | 0.989834i | \(-0.454574\pi\) | ||||
0.142227 | + | 0.989834i | \(0.454574\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −678.823 | −1.18436 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 240.000 | 0.401166 | 0.200583 | − | 0.979677i | \(-0.435716\pi\) | ||||
0.200583 | + | 0.979677i | \(0.435716\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 526.087 | 0.809965 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1112.00 | 1.58367 | 0.791834 | − | 0.610736i | \(-0.209126\pi\) | ||||
0.791834 | + | 0.610736i | \(0.209126\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −839.000 | −1.15089 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 28.2843 | 0.0374048 | 0.0187024 | − | 0.999825i | \(-0.494046\pi\) | ||||
0.0187024 | + | 0.999825i | \(0.494046\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 704.000 | 0.898347 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1233.19 | −1.51968 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1357.65 | −1.61697 | −0.808484 | − | 0.588519i | \(-0.799711\pi\) | ||||
−0.808484 | + | 0.588519i | \(0.799711\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −832.000 | −0.927682 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 736.000 | 0.794863 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1482.10 | 1.55138 | 0.775691 | − | 0.631113i | \(-0.217402\pi\) | ||||
0.775691 | + | 0.631113i | \(0.217402\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.0000 | −0.0203038 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1238.85 | 1.22050 | 0.610249 | − | 0.792210i | \(-0.291069\pi\) | ||||
0.610249 | + | 0.792210i | \(0.291069\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −644.881 | −0.616913 | −0.308457 | − | 0.951238i | \(-0.599812\pi\) | ||||
−0.308457 | + | 0.951238i | \(0.599812\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1044.00 | 0.943246 | 0.471623 | − | 0.881800i | \(-0.343668\pi\) | ||||
0.471623 | + | 0.881800i | \(0.343668\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −502.000 | −0.441127 | −0.220564 | − | 0.975373i | \(-0.570790\pi\) | ||||
−0.220564 | + | 0.975373i | \(0.570790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −735.391 | −0.628831 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 130.000 | 0.108225 | 0.0541123 | − | 0.998535i | \(-0.482767\pi\) | ||||
0.0541123 | + | 0.998535i | \(0.482767\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −678.823 | −0.550439 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 28.2843 | 0.0223494 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1315.00 | −0.987979 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 832.000 | 0.609910 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1233.19 | 0.882402 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2416.00 | −1.68807 | −0.844037 | − | 0.536285i | \(-0.819827\pi\) | ||||
−0.844037 | + | 0.536285i | \(0.819827\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1878.08 | −1.28182 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1329.36 | −0.886617 | −0.443308 | − | 0.896369i | \(-0.646195\pi\) | ||||
−0.443308 | + | 0.896369i | \(0.646195\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −704.000 | −0.448820 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −730.000 | −0.455242 | −0.227621 | − | 0.973750i | \(-0.573095\pi\) | ||||
−0.227621 | + | 0.973750i | \(0.573095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −28.2843 | −0.0172593 | −0.00862964 | − | 0.999963i | \(-0.502747\pi\) | ||||
−0.00862964 | + | 0.999963i | \(0.502747\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −704.000 | −0.420479 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.6274 | −0.0132322 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1233.19 | −0.706284 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2770.00 | −1.52300 | −0.761501 | − | 0.648164i | \(-0.775537\pi\) | ||||
−0.761501 | + | 0.648164i | \(0.775537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2776.00 | 1.49608 | 0.748039 | − | 0.663655i | \(-0.230996\pi\) | ||||
0.748039 | + | 0.663655i | \(0.230996\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −622.254 | −0.328799 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −832.000 | −0.431147 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2743.57 | 1.39466 | 0.697328 | − | 0.716752i | \(-0.254372\pi\) | ||||
0.697328 | + | 0.716752i | \(0.254372\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2817.11 | 1.40510 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1460.00 | 0.701571 | 0.350785 | − | 0.936456i | \(-0.385915\pi\) | ||||
0.350785 | + | 0.936456i | \(0.385915\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −128.000 | −0.0603926 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1482.10 | −0.686755 | −0.343377 | − | 0.939198i | \(-0.611571\pi\) | ||||
−0.343377 | + | 0.939198i | \(0.611571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2165.00 | −0.985435 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −650.538 | −0.290923 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4078.59 | 1.79243 | 0.896213 | − | 0.443625i | \(-0.146308\pi\) | ||||
0.896213 | + | 0.443625i | \(0.146308\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3104.00 | −1.31814 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 220.000 | 0.0918635 | 0.0459318 | − | 0.998945i | \(-0.485374\pi\) | ||||
0.0459318 | + | 0.998945i | \(0.485374\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1917.67 | −0.787511 | −0.393756 | − | 0.919215i | \(-0.628824\pi\) | ||||
−0.393756 | + | 0.919215i | \(0.628824\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3680.00 | −1.48652 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −735.391 | −0.292254 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 497.803 | 0.194668 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3816.00 | −1.44563 | −0.722817 | − | 0.691040i | \(-0.757153\pi\) | ||||
−0.722817 | + | 0.691040i | \(0.757153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2290.00 | 0.854082 | 0.427041 | − | 0.904232i | \(-0.359556\pi\) | ||||
0.427041 | + | 0.904232i | \(0.359556\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 181.019 | 0.0664773 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1634.00 | −0.590953 | −0.295476 | − | 0.955350i | \(-0.595478\pi\) | ||||
−0.295476 | + | 0.955350i | \(0.595478\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4174.76 | 1.48714 | 0.743570 | − | 0.668658i | \(-0.233131\pi\) | ||||
0.743570 | + | 0.668658i | \(0.233131\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −882.469 | −0.309675 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 832.000 | 0.283460 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 600.000 | 0.201463 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 520.431 | 0.172244 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 236.000 | 0.0769996 | 0.0384998 | − | 0.999259i | \(-0.487742\pi\) | ||||
0.0384998 | + | 0.999259i | \(0.487742\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1357.65 | −0.436734 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1878.08 | −0.595738 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −704.000 | −0.214281 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5453.21 | 1.63755 | 0.818775 | − | 0.574114i | \(-0.194653\pi\) | ||||
0.818775 | + | 0.574114i | \(0.194653\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −465.000 | −0.137778 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3920.20 | 1.14622 | 0.573112 | − | 0.819477i | \(-0.305736\pi\) | ||||
0.573112 | + | 0.819477i | \(0.305736\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1544.32 | 0.445640 | 0.222820 | − | 0.974860i | \(-0.428474\pi\) | ||||
0.222820 | + | 0.974860i | \(0.428474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −250.000 | −0.0702920 | −0.0351460 | − | 0.999382i | \(-0.511190\pi\) | ||||
−0.0351460 | + | 0.999382i | \(0.511190\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −704.000 | −0.195421 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6290.42 | −1.72408 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1712.00 | −0.463348 | −0.231674 | − | 0.972794i | \(-0.574420\pi\) | ||||
−0.231674 | + | 0.972794i | \(0.574420\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2093.04 | −0.559437 | −0.279718 | − | 0.960082i | \(-0.590241\pi\) | ||||
−0.279718 | + | 0.960082i | \(0.590241\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1385.93 | 0.365874 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −736.000 | −0.189597 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −160.000 | −0.0407212 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2008.18 | 0.505002 | 0.252501 | − | 0.967597i | \(-0.418747\pi\) | ||||
0.252501 | + | 0.967597i | \(0.418747\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −480.000 | −0.119278 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3982.43 | −0.977997 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4072.94 | −0.988571 | −0.494285 | − | 0.869300i | \(-0.664570\pi\) | ||||
−0.494285 | + | 0.869300i | \(0.664570\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1090.00 | 0.258503 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −352.000 | −0.0825295 | −0.0412647 | − | 0.999148i | \(-0.513139\pi\) | ||||
−0.0412647 | + | 0.999148i | \(0.513139\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2817.11 | 0.653034 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7680.00 | 1.76033 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2687.01 | −0.609032 | −0.304516 | − | 0.952507i | \(-0.598495\pi\) | ||||
−0.304516 | + | 0.952507i | \(0.598495\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6788.23 | −1.52161 | −0.760803 | − | 0.648983i | \(-0.775195\pi\) | ||||
−0.760803 | + | 0.648983i | \(0.775195\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 372.000 | 0.0815725 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5390.00 | 1.16915 | 0.584573 | − | 0.811341i | \(-0.301262\pi\) | ||||
0.584573 | + | 0.811341i | \(0.301262\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 735.391 | 0.157802 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2166.00 | 0.459832 | 0.229916 | − | 0.973211i | \(-0.426155\pi\) | ||||
0.229916 | + | 0.973211i | \(0.426155\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4746.10 | −0.996913 | −0.498457 | − | 0.866915i | \(-0.666100\pi\) | ||||
−0.498457 | + | 0.866915i | \(0.666100\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4163.44 | −0.865337 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10575.0 | 2.15245 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8384.00 | −1.68893 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7461.39 | 1.48771 | 0.743855 | − | 0.668341i | \(-0.232995\pi\) | ||||
0.743855 | + | 0.668341i | \(0.232995\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3104.00 | −0.612616 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −497.803 | −0.0972575 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 678.823 | 0.131295 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7008.00 | −1.32871 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3680.00 | −0.690873 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8977.43 | −1.66895 | −0.834477 | − | 0.551043i | \(-0.814230\pi\) | ||||
−0.834477 | + | 0.551043i | \(0.814230\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3648.00 | 0.671610 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1945.96 | 0.354808 | 0.177404 | − | 0.984138i | \(-0.443230\pi\) | ||||
0.177404 | + | 0.984138i | \(0.443230\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7500.99 | 1.35457 | 0.677286 | − | 0.735720i | \(-0.263156\pi\) | ||||
0.677286 | + | 0.735720i | \(0.263156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5766.00 | 1.02161 | 0.510806 | − | 0.859696i | \(-0.329347\pi\) | ||||
0.510806 | + | 0.859696i | \(0.329347\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −872.000 | −0.153049 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5905.76 | −1.02688 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16192.0 | 2.78931 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −526.087 | −0.0897910 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2839.74 | 0.480239 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10780.0 | 1.79010 | 0.895049 | − | 0.445968i | \(-0.147140\pi\) | ||||
0.895049 | + | 0.445968i | \(0.147140\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 650.000 | 0.106966 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −882.469 | −0.143924 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 350.000 | 0.0565748 | 0.0282874 | − | 0.999600i | \(-0.490995\pi\) | ||||
0.0282874 | + | 0.999600i | \(0.490995\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −735.391 | −0.117820 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −588.313 | −0.0934279 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3840.00 | 0.599242 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7940.00 | −1.22836 | −0.614181 | − | 0.789165i | \(-0.710513\pi\) | ||||
−0.614181 | + | 0.789165i | \(0.710513\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4259.61 | 0.653329 | 0.326664 | − | 0.945140i | \(-0.394075\pi\) | ||||
0.326664 | + | 0.945140i | \(0.394075\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 704.000 | 0.107056 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5407.95 | 0.815400 | 0.407700 | − | 0.913116i | \(-0.366331\pi\) | ||||
0.407700 | + | 0.913116i | \(0.366331\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1357.65 | −0.202976 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9480.00 | −1.39369 | −0.696846 | − | 0.717221i | \(-0.745414\pi\) | ||||
−0.696846 | + | 0.717221i | \(0.745414\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10069.0 | 1.46800 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7438.76 | 1.07558 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3461.99 | 0.492411 | 0.246205 | − | 0.969218i | \(-0.420816\pi\) | ||||
0.246205 | + | 0.969218i | \(0.420816\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −735.391 | −0.103748 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11630.0 | 1.61442 | 0.807210 | − | 0.590265i | \(-0.200977\pi\) | ||||
0.807210 | + | 0.590265i | \(0.200977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6976.00 | −0.960638 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1233.19 | 0.168469 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6284.00 | 0.851682 | 0.425841 | − | 0.904798i | \(-0.359978\pi\) | ||||
0.425841 | + | 0.904798i | \(0.359978\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13667.0 | 1.83774 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12841.1 | 1.71318 | 0.856589 | − | 0.515999i | \(-0.172579\pi\) | ||||
0.856589 | + | 0.515999i | \(0.172579\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1660.00 | 0.218043 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6238.00 | −0.813057 | −0.406528 | − | 0.913638i | \(-0.633261\pi\) | ||||
−0.406528 | + | 0.913638i | \(0.633261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14934.1 | −1.93158 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7520.00 | 0.965226 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6290.42 | −0.801280 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2868.03 | −0.362574 | −0.181287 | − | 0.983430i | \(-0.558026\pi\) | ||||
−0.181287 | + | 0.983430i | \(0.558026\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2526.00 | 0.314570 | 0.157285 | − | 0.987553i | \(-0.449726\pi\) | ||||
0.157285 | + | 0.987553i | \(0.449726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 832.000 | 0.102841 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4746.10 | 0.582310 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −520.000 | −0.0633303 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9401.69 | 1.13664 | 0.568318 | − | 0.822809i | \(-0.307595\pi\) | ||||
0.568318 | + | 0.822809i | \(0.307595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4129.50 | 0.495604 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −160.000 | −0.0189255 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 160.000 | 0.0187895 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8694.58 | −1.01374 | −0.506871 | − | 0.862022i | \(-0.669198\pi\) | ||||
−0.506871 | + | 0.862022i | \(0.669198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −354.000 | −0.0409808 | −0.0204904 | − | 0.999790i | \(-0.506523\pi\) | ||||
−0.0204904 | + | 0.999790i | \(0.506523\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 622.254 | 0.0715249 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11573.9 | 1.32098 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 128.000 | 0.0144054 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5184.00 | 0.579361 | 0.289680 | − | 0.957123i | \(-0.406451\pi\) | ||||
0.289680 | + | 0.957123i | \(0.406451\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2025.15 | 0.224764 | 0.112382 | − | 0.993665i | \(-0.464152\pi\) | ||||
0.112382 | + | 0.993665i | \(0.464152\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6976.00 | 0.768905 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15612.9 | −1.70908 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5430.58 | −0.590404 | −0.295202 | − | 0.955435i | \(-0.595387\pi\) | ||||
−0.295202 | + | 0.955435i | \(0.595387\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5612.00 | −0.601883 | −0.300941 | − | 0.953643i | \(-0.597301\pi\) | ||||
−0.300941 | + | 0.953643i | \(0.597301\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7680.00 | 0.818128 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15669.5 | 1.65803 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11902.0 | −1.25098 | −0.625490 | − | 0.780232i | \(-0.715101\pi\) | ||||
−0.625490 | + | 0.780232i | \(0.715101\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 588.313 | 0.0614248 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15703.4 | −1.62872 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5034.00 | 0.515275 | 0.257637 | − | 0.966242i | \(-0.417056\pi\) | ||||
0.257637 | + | 0.966242i | \(0.417056\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15488.0 | −1.57498 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10154.1 | −1.02586 | −0.512930 | − | 0.858430i | \(-0.671440\pi\) | ||||
−0.512930 | + | 0.858430i | \(0.671440\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16760.0 | −1.68230 | −0.841148 | − | 0.540805i | \(-0.818120\pi\) | ||||
−0.841148 | + | 0.540805i | \(0.818120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4706.50 | 0.469374 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12371.5 | −1.22588 | −0.612941 | − | 0.790129i | \(-0.710014\pi\) | ||||
−0.612941 | + | 0.790129i | \(0.710014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15520.0 | −1.51831 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1328.00 | −0.129094 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12100.0 | 1.16881 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2490.00 | −0.239013 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11483.4 | −1.09539 | −0.547694 | − | 0.836679i | \(-0.684494\pi\) | ||||
−0.547694 | + | 0.836679i | \(0.684494\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 735.391 | 0.0697109 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8384.00 | −0.784944 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13080.0 | 1.21707 | 0.608533 | − | 0.793528i | \(-0.291758\pi\) | ||||
0.608533 | + | 0.793528i | \(0.291758\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8259.01 | −0.763773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11284.0 | 1.03715 | 0.518574 | − | 0.855033i | \(-0.326463\pi\) | ||||
0.518574 | + | 0.855033i | \(0.326463\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27130.3 | −2.47847 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 113.137 | 0.0102730 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18172.0 | 1.63024 | 0.815121 | − | 0.579291i | \(-0.196671\pi\) | ||||
0.815121 | + | 0.579291i | \(0.196671\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8384.00 | 0.747644 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1380.27 | −0.122352 | −0.0611762 | − | 0.998127i | \(-0.519485\pi\) | ||||
−0.0611762 | + | 0.998127i | \(0.519485\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7008.00 | −0.617529 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12247.1 | 1.07281 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3365.83 | −0.293100 | −0.146550 | − | 0.989203i | \(-0.546817\pi\) | ||||
−0.146550 | + | 0.989203i | \(0.546817\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16192.0 | −1.39356 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3648.00 | 0.312136 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −497.803 | −0.0423469 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23072.0 | −1.95135 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2862.37 | 0.240696 | 0.120348 | − | 0.992732i | \(-0.461599\pi\) | ||||
0.120348 | + | 0.992732i | \(0.461599\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13536.9 | 1.13179 | 0.565894 | − | 0.824478i | \(-0.308531\pi\) | ||||
0.565894 | + | 0.824478i | \(0.308531\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18304.0 | −1.51297 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2743.57 | 0.224220 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −832.000 | −0.0676134 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5905.76 | −0.477249 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1244.51 | −0.100008 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4474.00 | −0.355550 | −0.177775 | − | 0.984071i | \(-0.556890\pi\) | ||||
−0.177775 | + | 0.984071i | \(0.556890\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10848.0 | 0.857334 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2839.74 | 0.223195 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9100.00 | −0.711312 | −0.355656 | − | 0.934617i | \(-0.615743\pi\) | ||||
−0.355656 | + | 0.934617i | \(0.615743\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3252.69 | 0.252862 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28363.5 | −2.19297 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4160.00 | 0.318166 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17610.0 | −1.33960 | −0.669802 | − | 0.742540i | \(-0.733621\pi\) | ||||
−0.669802 | + | 0.742540i | \(0.733621\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1878.08 | 0.142100 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2816.00 | −0.211928 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14340.1 | 1.07347 | 0.536736 | − | 0.843751i | \(-0.319657\pi\) | ||||
0.536736 | + | 0.843751i | \(0.319657\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −735.391 | −0.0547578 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13050.0 | −0.961484 | −0.480742 | − | 0.876862i | \(-0.659633\pi\) | ||||
−0.480742 | + | 0.876862i | \(0.659633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9340.00 | 0.684530 | 0.342265 | − | 0.939603i | \(-0.388806\pi\) | ||||
0.342265 | + | 0.939603i | \(0.388806\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21586.6 | 1.57381 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11160.0 | −0.809399 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8756.81 | −0.631804 | −0.315902 | − | 0.948792i | \(-0.602307\pi\) | ||||
−0.315902 | + | 0.948792i | \(0.602307\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12954.2 | −0.929807 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1992.00 | 0.141510 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −160.000 | −0.0113080 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1272.79 | −0.0894953 | −0.0447477 | − | 0.998998i | \(-0.514248\pi\) | ||||
−0.0447477 | + | 0.998998i | \(0.514248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19136.0 | −1.33868 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9243.30 | 0.643348 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21744.9 | 1.50583 | 0.752916 | − | 0.658117i | \(-0.228647\pi\) | ||||
0.752916 | + | 0.658117i | \(0.228647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23616.0 | −1.61899 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8288.00 | 0.565340 | 0.282670 | − | 0.959217i | \(-0.408780\pi\) | ||||
0.282670 | + | 0.959217i | \(0.408780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19776.4 | −1.34225 | −0.671127 | − | 0.741342i | \(-0.734189\pi\) | ||||
−0.671127 | + | 0.741342i | \(0.734189\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 780.000 | 0.0526767 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7438.76 | 0.499882 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26293.1 | 1.75816 | 0.879079 | − | 0.476675i | \(-0.158158\pi\) | ||||
0.879079 | + | 0.476675i | \(0.158158\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 704.000 | 0.0466134 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24738.0 | 1.62995 | 0.814974 | − | 0.579497i | \(-0.196751\pi\) | ||||
0.814974 | + | 0.579497i | \(0.196751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4706.50 | −0.308593 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1590.00 | 0.103746 | 0.0518728 | − | 0.998654i | \(-0.483481\pi\) | ||||
0.0518728 | + | 0.998654i | \(0.483481\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8852.98 | 0.574848 | 0.287424 | − | 0.957803i | \(-0.407201\pi\) | ||||
0.287424 | + | 0.957803i | \(0.407201\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14934.1 | 0.965032 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4649.00 | 0.297536 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2944.00 | −0.187515 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16178.6 | −1.02557 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18256.0 | −1.15176 | −0.575879 | − | 0.817535i | \(-0.695340\pi\) | ||||
−0.575879 | + | 0.817535i | \(0.695340\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1335.02 | −0.0838265 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13667.0 | 0.854105 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1200.00 | 0.0742899 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24370.0 | −1.50165 | −0.750825 | − | 0.660502i | \(-0.770344\pi\) | ||||
−0.750825 | + | 0.660502i | \(0.770344\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 627.911 | 0.0385107 | 0.0192554 | − | 0.999815i | \(-0.493870\pi\) | ||||
0.0192554 | + | 0.999815i | \(0.493870\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10624.0 | 0.648558 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13949.8 | 0.847640 | 0.423820 | − | 0.905746i | \(-0.360689\pi\) | ||||
0.423820 | + | 0.905746i | \(0.360689\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2194.86 | −0.132752 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5078.00 | −0.304315 | −0.152157 | − | 0.988356i | \(-0.548622\pi\) | ||||
−0.152157 | + | 0.988356i | \(0.548622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7520.00 | 0.448597 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5172.00 | 0.305725 | 0.152862 | − | 0.988247i | \(-0.451151\pi\) | ||||
0.152862 | + | 0.988247i | \(0.451151\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11511.7 | 0.677388 | 0.338694 | − | 0.940897i | \(-0.390015\pi\) | ||||
0.338694 | + | 0.940897i | \(0.390015\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3982.43 | 0.233280 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26160.0 | 1.51862 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30848.0 | −1.78274 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2602.15 | −0.149709 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16350.0 | 0.936473 | 0.468236 | − | 0.883603i | \(-0.344890\pi\) | ||||
0.468236 | + | 0.883603i | \(0.344890\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11573.9 | −0.659971 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11692.7 | −0.663793 | −0.331896 | − | 0.943316i | \(-0.607688\pi\) | ||||
−0.331896 | + | 0.943316i | \(0.607688\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22176.0 | −1.24785 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26420.0 | 1.48014 | 0.740068 | − | 0.672532i | \(-0.234793\pi\) | ||||
0.740068 | + | 0.672532i | \(0.234793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4129.50 | 0.230336 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8736.00 | −0.485152 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2817.11 | −0.155767 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16263.5 | −0.895356 | −0.447678 | − | 0.894195i | \(-0.647749\pi\) | ||||
−0.447678 | + | 0.894195i | \(0.647749\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 160.000 | 0.00873258 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18304.0 | 0.994711 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1414.21 | 0.0765243 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3686.00 | −0.198600 | −0.0992998 | − | 0.995058i | \(-0.531660\pi\) | ||||
−0.0992998 | + | 0.995058i | \(0.531660\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16914.0 | −0.907430 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3982.43 | 0.212747 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2882.00 | 0.152660 | 0.0763299 | − | 0.997083i | \(-0.475680\pi\) | ||||
0.0763299 | + | 0.997083i | \(0.475680\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5560.00 | 0.293272 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17649.4 | 0.927033 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 128.000 | 0.00669501 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9684.53 | 0.504429 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22457.7 | 1.16486 | 0.582428 | − | 0.812882i | \(-0.302103\pi\) | ||||
0.582428 | + | 0.812882i | \(0.302103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11840.0 | 0.609038 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20274.0 | −1.03856 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30603.6 | −1.56124 | −0.780622 | − | 0.625004i | \(-0.785097\pi\) | ||||
−0.780622 | + | 0.625004i | \(0.785097\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14813.0 | 0.752578 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41317.7 | −2.09055 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −729.734 | −0.0367713 | −0.0183856 | − | 0.999831i | \(-0.505853\pi\) | ||||
−0.0183856 | + | 0.999831i | \(0.505853\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −624.000 | −0.0311877 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20268.0 | −1.00889 | −0.504445 | − | 0.863444i | \(-0.668303\pi\) | ||||
−0.504445 | + | 0.863444i | \(0.668303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4163.44 | 0.206408 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19688.0 | 0.972117 | 0.486058 | − | 0.873926i | \(-0.338434\pi\) | ||||
0.486058 | + | 0.873926i | \(0.338434\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15669.5 | 0.770585 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 141.421 | 0.00692682 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31056.0 | 1.50899 | 0.754494 | − | 0.656307i | \(-0.227883\pi\) | ||||
0.754494 | + | 0.656307i | \(0.227883\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11360.0 | −0.549776 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15703.4 | −0.756962 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27250.0 | 1.30835 | 0.654173 | − | 0.756345i | \(-0.273017\pi\) | ||||
0.654173 | + | 0.756345i | \(0.273017\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2715.29 | 0.129853 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35921.0 | −1.71109 | −0.855543 | − | 0.517732i | \(-0.826776\pi\) | ||||
−0.855543 | + | 0.517732i | \(0.826776\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3520.00 | 0.166361 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3104.00 | 0.146126 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25897.1 | 1.21440 | 0.607199 | − | 0.794550i | \(-0.292293\pi\) | ||||
0.607199 | + | 0.794550i | \(0.292293\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23040.0 | 1.07622 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1465.13 | 0.0681719 | 0.0340860 | − | 0.999419i | \(-0.489148\pi\) | ||||
0.0340860 | + | 0.999419i | \(0.489148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13678.3 | −0.633985 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19136.0 | 0.880126 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −960.000 | −0.0439840 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27130.3 | 1.23826 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15520.0 | −0.705647 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5277.85 | 0.239053 | 0.119527 | − | 0.992831i | \(-0.461862\pi\) | ||||
0.119527 | + | 0.992831i | \(0.461862\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1991.21 | 0.0898467 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3680.00 | 0.164793 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15936.0 | −0.710933 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10335.1 | −0.459331 | −0.229666 | − | 0.973270i | \(-0.573763\pi\) | ||||
−0.229666 | + | 0.973270i | \(0.573763\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15488.0 | −0.685765 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6788.23 | −0.299438 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15200.0 | 0.663030 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25398.0 | −1.10377 | −0.551883 | − | 0.833922i | \(-0.686090\pi\) | ||||
−0.551883 | + | 0.833922i | \(0.686090\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37363.5 | 1.61777 | 0.808885 | − | 0.587968i | \(-0.200072\pi\) | ||||
0.808885 | + | 0.587968i | \(0.200072\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 38400.0 | 1.65652 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8259.01 | −0.354970 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43195.7 | −1.84973 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6894.00 | 0.293060 | 0.146530 | − | 0.989206i | \(-0.453190\pi\) | ||||
0.146530 | + | 0.989206i | \(0.453190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15008.0 | 0.635657 | 0.317829 | − | 0.948148i | \(-0.397046\pi\) | ||||
0.317829 | + | 0.948148i | \(0.397046\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2104.35 | −0.0888049 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30740.0 | 1.29254 | 0.646272 | − | 0.763107i | \(-0.276327\pi\) | ||||
0.646272 | + | 0.763107i | \(0.276327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8219.41 | −0.344357 | −0.172178 | − | 0.985066i | \(-0.555081\pi\) | ||||
−0.172178 | + | 0.985066i | \(0.555081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30490.4 | −1.27281 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8384.00 | 0.347473 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18304.0 | 0.755889 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22344.6 | 0.919452 | 0.459726 | − | 0.888061i | \(-0.347948\pi\) | ||||
0.459726 | + | 0.888061i | \(0.347948\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23135.0 | 0.948583 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12252.7 | −0.500601 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12247.1 | 0.498595 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26848.0 | 1.08530 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15600.0 | 0.628391 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11624.8 | −0.466620 | −0.233310 | − | 0.972402i | \(-0.574956\pi\) | ||||
−0.233310 | + | 0.972402i | \(0.574956\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3680.00 | 0.147197 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8881.26 | −0.354000 | −0.177000 | − | 0.984211i | \(-0.556639\pi\) | ||||
−0.177000 | + | 0.984211i | \(0.556639\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17055.4 | 0.677443 | 0.338721 | − | 0.940887i | \(-0.390006\pi\) | ||||
0.338721 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24552.0 | −0.968435 | −0.484218 | − | 0.874948i | \(-0.660896\pi\) | ||||
−0.484218 | + | 0.874948i | \(0.660896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23072.0 | −0.906904 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −59821.2 | −2.34329 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4448.00 | −0.173634 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 882.469 | 0.0343299 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7410.48 | 0.287293 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11306.0 | 0.435321 | 0.217660 | − | 0.976025i | \(-0.430157\pi\) | ||||
0.217660 | + | 0.976025i | \(0.430157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −42208.0 | −1.61961 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1357.65 | 0.0519185 | 0.0259593 | − | 0.999663i | \(-0.491736\pi\) | ||||
0.0259593 | + | 0.999663i | \(0.491736\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −980.000 | −0.0373495 | −0.0186748 | − | 0.999826i | \(-0.505945\pi\) | ||||
−0.0186748 | + | 0.999826i | \(0.505945\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17558.9 | 0.666932 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7410.48 | 0.280518 | 0.140259 | − | 0.990115i | \(-0.455206\pi\) | ||||
0.140259 | + | 0.990115i | \(0.455206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3356.00 | 0.126184 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16192.0 | −0.606769 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1244.51 | −0.0464797 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3840.00 | −0.142936 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32063.0 | 1.18950 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61976.5 | 2.29161 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10848.0 | 0.398453 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3580.00 | −0.131061 | −0.0655303 | − | 0.997851i | \(-0.520874\pi\) | ||||
−0.0655303 | + | 0.997851i | \(0.520874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6194.26 | 0.226018 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51920.0 | 1.88824 | 0.944120 | − | 0.329602i | \(-0.106915\pi\) | ||||
0.944120 | + | 0.329602i | \(0.106915\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −113.137 | −0.00410109 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20817.2 | 0.752127 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26032.0 | 0.934403 | 0.467202 | − | 0.884151i | \(-0.345262\pi\) | ||||
0.467202 | + | 0.884151i | \(0.345262\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 50784.0 | 1.81693 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1357.65 | 0.0484154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12090.0 | −0.429748 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3224.41 | −0.114243 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7003.19 | −0.247327 | −0.123664 | − | 0.992324i | \(-0.539464\pi\) | ||||
−0.123664 | + | 0.992324i | \(0.539464\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11008.0 | −0.386266 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2816.00 | −0.0984952 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22582.2 | 0.787329 | 0.393664 | − | 0.919254i | \(-0.371207\pi\) | ||||
0.393664 | + | 0.919254i | \(0.371207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −42432.0 | −1.47467 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32555.2 | 1.12781 | 0.563905 | − | 0.825840i | \(-0.309298\pi\) | ||||
0.563905 | + | 0.825840i | \(0.309298\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17649.4 | −0.609484 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9996.00 | −0.343006 | −0.171503 | − | 0.985184i | \(-0.554862\pi\) | ||||
−0.171503 | + | 0.985184i | \(0.554862\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32617.4 | −1.11219 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27498.0 | 0.934677 | 0.467339 | − | 0.884078i | \(-0.345213\pi\) | ||||
0.467339 | + | 0.884078i | \(0.345213\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21586.6 | 0.731439 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4932.78 | 0.166619 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8159.00 | −0.273875 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5220.00 | 0.174675 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12954.2 | −0.432135 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16104.0 | 0.535543 | 0.267771 | − | 0.963482i | \(-0.413713\pi\) | ||||
0.267771 | + | 0.963482i | \(0.413713\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −91595.8 | −3.03662 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2211.83 | −0.0731009 | −0.0365505 | − | 0.999332i | \(-0.511637\pi\) | ||||
−0.0365505 | + | 0.999332i | \(0.511637\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2976.00 | 0.0977521 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19314.0 | −0.632456 | −0.316228 | − | 0.948683i | \(-0.602416\pi\) | ||||
−0.316228 | + | 0.948683i | \(0.602416\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5430.58 | 0.177285 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2510.00 | −0.0816902 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36056.8 | 1.16992 | 0.584961 | − | 0.811062i | \(-0.301110\pi\) | ||||
0.584961 | + | 0.811062i | \(0.301110\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9243.30 | 0.299001 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39840.0 | 1.28093 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11272.0 | −0.361319 | −0.180659 | − | 0.983546i | \(-0.557823\pi\) | ||||
−0.180659 | + | 0.983546i | \(0.557823\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −60980.9 | −1.94881 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23616.0 | −0.752440 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9973.03 | 0.316800 | 0.158400 | − | 0.987375i | \(-0.449367\pi\) | ||||
0.158400 | + | 0.987375i | \(0.449367\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16178.6 | 0.512381 |
(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 | 392.4.a.g.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 784.4.a.x.1.2 | 2 | |||
7.2 | even | 3 | 392.4.i.j.361.2 | 4 | |||
7.3 | odd | 6 | 392.4.i.j.177.1 | 4 | |||
7.4 | even | 3 | 392.4.i.j.177.2 | 4 | |||
7.5 | odd | 6 | 392.4.i.j.361.1 | 4 | |||
7.6 | odd | 2 | inner | 392.4.a.g.1.2 | yes | 2 | |
28.27 | even | 2 | 784.4.a.x.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
392.4.a.g.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
392.4.a.g.1.2 | yes | 2 | 7.6 | odd | 2 | inner | |
392.4.i.j.177.1 | 4 | 7.3 | odd | 6 | |||
392.4.i.j.177.2 | 4 | 7.4 | even | 3 | |||
392.4.i.j.361.1 | 4 | 7.5 | odd | 6 | |||
392.4.i.j.361.2 | 4 | 7.2 | even | 3 | |||
784.4.a.x.1.1 | 2 | 28.27 | even | 2 | |||
784.4.a.x.1.2 | 2 | 4.3 | odd | 2 |