Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 15x^{7} + 45x^{6} + 64x^{5} - 201x^{4} - 63x^{3} + 282x^{2} + 3x - 116 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.763644\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 0.763644 | 0.440890 | 0.220445 | − | 0.975399i | \(-0.429249\pi\) | ||||
0.220445 | + | 0.975399i | \(0.429249\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.55421 | 0.695064 | 0.347532 | − | 0.937668i | \(-0.387020\pi\) | ||||
0.347532 | + | 0.937668i | \(0.387020\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.41685 | −0.805616 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.18686 | 0.306447 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.61102 | 0.875801 | 0.437900 | − | 0.899024i | \(-0.355722\pi\) | ||||
0.437900 | + | 0.899024i | \(0.355722\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.02809 | 0.235859 | 0.117930 | − | 0.993022i | \(-0.462374\pi\) | ||||
0.117930 | + | 0.993022i | \(0.462374\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.763644 | −0.166641 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.55145 | 0.949043 | 0.474522 | − | 0.880244i | \(-0.342621\pi\) | ||||
0.474522 | + | 0.880244i | \(0.342621\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.58443 | −0.516885 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.13654 | −0.796078 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.78553 | −0.888651 | −0.444325 | − | 0.895865i | \(-0.646557\pi\) | ||||
−0.444325 | + | 0.895865i | \(0.646557\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.84863 | 0.511630 | 0.255815 | − | 0.966726i | \(-0.417656\pi\) | ||||
0.255815 | + | 0.966726i | \(0.417656\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.763644 | 0.132933 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.55421 | −0.262710 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.27046 | 0.208862 | 0.104431 | − | 0.994532i | \(-0.466698\pi\) | ||||
0.104431 | + | 0.994532i | \(0.466698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.763644 | −0.122281 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.11068 | 0.485806 | 0.242903 | − | 0.970051i | \(-0.421900\pi\) | ||||
0.242903 | + | 0.970051i | \(0.421900\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.35432 | 1.27402 | 0.637011 | − | 0.770855i | \(-0.280171\pi\) | ||||
0.637011 | + | 0.770855i | \(0.280171\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.75629 | −0.559955 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.30529 | 1.35732 | 0.678658 | − | 0.734455i | \(-0.262562\pi\) | ||||
0.678658 | + | 0.734455i | \(0.262562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.75753 | 0.386132 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.24483 | 0.170990 | 0.0854950 | − | 0.996339i | \(-0.472753\pi\) | ||||
0.0854950 | + | 0.996339i | \(0.472753\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.55421 | 0.209570 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.785092 | 0.103988 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.95515 | −0.384728 | −0.192364 | − | 0.981324i | \(-0.561615\pi\) | ||||
−0.192364 | + | 0.981324i | \(0.561615\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.44819 | −0.825606 | −0.412803 | − | 0.910820i | \(-0.635450\pi\) | ||||
−0.412803 | + | 0.910820i | \(0.635450\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.41685 | 0.304494 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.55421 | −0.192776 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.51850 | −0.796362 | −0.398181 | − | 0.917307i | \(-0.630358\pi\) | ||||
−0.398181 | + | 0.917307i | \(0.630358\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.47569 | 0.418424 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4003 | −1.23429 | −0.617146 | − | 0.786849i | \(-0.711711\pi\) | ||||
−0.617146 | + | 0.786849i | \(0.711711\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.95921 | 0.814514 | 0.407257 | − | 0.913314i | \(-0.366485\pi\) | ||||
0.407257 | + | 0.913314i | \(0.366485\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.97358 | −0.227890 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.23287 | 0.251217 | 0.125609 | − | 0.992080i | \(-0.459912\pi\) | ||||
0.125609 | + | 0.992080i | \(0.459912\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.09170 | 0.454633 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.5278 | −1.15558 | −0.577788 | − | 0.816187i | \(-0.696084\pi\) | ||||
−0.577788 | + | 0.816187i | \(0.696084\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.61229 | 0.608738 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.65444 | −0.391797 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.4084 | 1.31529 | 0.657646 | − | 0.753327i | \(-0.271552\pi\) | ||||
0.657646 | + | 0.753327i | \(0.271552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.17534 | 0.225572 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.59786 | 0.163937 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.06194 | 0.107824 | 0.0539120 | − | 0.998546i | \(-0.482831\pi\) | ||||
0.0539120 | + | 0.998546i | \(0.482831\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.41685 | −0.242902 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.07986 | 0.903480 | 0.451740 | − | 0.892150i | \(-0.350804\pi\) | ||||
0.451740 | + | 0.892150i | \(0.350804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.1645 | 1.39567 | 0.697837 | − | 0.716257i | \(-0.254146\pi\) | ||||
0.697837 | + | 0.716257i | \(0.254146\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.18686 | −0.115826 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.191694 | 0.0185317 | 0.00926586 | − | 0.999957i | \(-0.497051\pi\) | ||||
0.00926586 | + | 0.999957i | \(0.497051\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3709 | 1.47226 | 0.736131 | − | 0.676839i | \(-0.236651\pi\) | ||||
0.736131 | + | 0.676839i | \(0.236651\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.970177 | 0.0920851 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.4325 | 1.54584 | 0.772921 | − | 0.634503i | \(-0.218795\pi\) | ||||
0.772921 | + | 0.634503i | \(0.218795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.07392 | 0.659646 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.41685 | 0.223438 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.61102 | −0.331022 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.37545 | 0.214187 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7878 | −1.05433 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.82092 | −0.427788 | −0.213894 | − | 0.976857i | \(-0.568615\pi\) | ||||
−0.213894 | + | 0.976857i | \(0.568615\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.37973 | 0.561704 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.95281 | 0.345358 | 0.172679 | − | 0.984978i | \(-0.444758\pi\) | ||||
0.172679 | + | 0.984978i | \(0.444758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.02809 | −0.0891464 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.42906 | −0.553326 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4629 | −1.15021 | −0.575105 | − | 0.818080i | \(-0.695039\pi\) | ||||
−0.575105 | + | 0.818080i | \(0.695039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.51502 | 0.722234 | 0.361117 | − | 0.932520i | \(-0.382395\pi\) | ||||
0.361117 | + | 0.932520i | \(0.382395\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.10593 | 0.598427 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.43773 | −0.617669 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.763644 | 0.0629843 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.1535 | 0.995653 | 0.497826 | − | 0.867277i | \(-0.334132\pi\) | ||||
0.497826 | + | 0.867277i | \(0.334132\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.43997 | −0.686835 | −0.343417 | − | 0.939183i | \(-0.611585\pi\) | ||||
−0.343417 | + | 0.939183i | \(0.611585\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.72728 | −0.705559 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.42738 | 0.355616 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.7574 | −0.938346 | −0.469173 | − | 0.883106i | \(-0.655448\pi\) | ||||
−0.469173 | + | 0.883106i | \(0.655448\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.950604 | 0.0753878 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.55145 | −0.358705 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4942 | −0.978620 | −0.489310 | − | 0.872110i | \(-0.662751\pi\) | ||||
−0.489310 | + | 0.872110i | \(0.662751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.18686 | 0.0923973 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.4830 | 1.89455 | 0.947277 | − | 0.320415i | \(-0.103822\pi\) | ||||
0.947277 | + | 0.320415i | \(0.103822\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.48473 | −0.190012 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.8952 | −1.51261 | −0.756303 | − | 0.654221i | \(-0.772997\pi\) | ||||
−0.756303 | + | 0.654221i | \(0.772997\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.58443 | 0.195364 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.25668 | −0.169623 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.89979 | −0.665202 | −0.332601 | − | 0.943068i | \(-0.607926\pi\) | ||||
−0.332601 | + | 0.943068i | \(0.607926\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7538 | 1.39396 | 0.696980 | − | 0.717090i | \(-0.254526\pi\) | ||||
0.696980 | + | 0.717090i | \(0.254526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.92412 | −0.364002 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.97456 | 0.145172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.61102 | 0.264064 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.13654 | 0.300889 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.1866 | −0.881794 | −0.440897 | − | 0.897558i | \(-0.645340\pi\) | ||||
−0.440897 | + | 0.897558i | \(0.645340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.7549 | 1.06208 | 0.531042 | − | 0.847346i | \(-0.321801\pi\) | ||||
0.531042 | + | 0.847346i | \(0.321801\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.18686 | −0.0849931 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1653 | 0.795496 | 0.397748 | − | 0.917495i | \(-0.369792\pi\) | ||||
0.397748 | + | 0.917495i | \(0.369792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.7758 | 1.89808 | 0.949042 | − | 0.315149i | \(-0.102055\pi\) | ||||
0.949042 | + | 0.315149i | \(0.102055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.97782 | −0.351108 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.78553 | 0.335878 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.83465 | 0.337666 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.0002 | −0.764565 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.02809 | 0.0711142 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.7307 | 1.42716 | 0.713582 | − | 0.700572i | \(-0.247072\pi\) | ||||
0.713582 | + | 0.700572i | \(0.247072\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.94214 | −0.544187 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.9844 | 0.885528 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.84863 | −0.193378 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.31436 | 0.359111 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.61102 | −0.242903 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.70228 | −0.381853 | −0.190926 | − | 0.981604i | \(-0.561149\pi\) | ||||
−0.190926 | + | 0.981604i | \(0.561149\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.24617 | 0.416411 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.36092 | −0.621306 | −0.310653 | − | 0.950523i | \(-0.600548\pi\) | ||||
−0.310653 | + | 0.950523i | \(0.600548\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.4426 | 1.41697 | 0.708483 | − | 0.705728i | \(-0.249380\pi\) | ||||
0.708483 | + | 0.705728i | \(0.249380\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.763644 | −0.0502441 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.6958 | 1.29031 | 0.645157 | − | 0.764050i | \(-0.276792\pi\) | ||||
0.645157 | + | 0.764050i | \(0.276792\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.4624 | 0.943422 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.70511 | 0.110759 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.59704 | −0.103304 | −0.0516520 | − | 0.998665i | \(-0.516449\pi\) | ||||
−0.0516520 | + | 0.998665i | \(0.516449\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0106 | 1.22458 | 0.612290 | − | 0.790634i | \(-0.290249\pi\) | ||||
0.612290 | + | 0.790634i | \(0.290249\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5342 | 0.996521 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.55421 | 0.0992949 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.02809 | −0.0654155 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.03949 | −0.509482 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.42958 | 0.342712 | 0.171356 | − | 0.985209i | \(-0.445185\pi\) | ||||
0.171356 | + | 0.985209i | \(0.445185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.55145 | 0.286147 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.28579 | 0.268387 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.7935 | 0.922791 | 0.461396 | − | 0.887194i | \(-0.347349\pi\) | ||||
0.461396 | + | 0.887194i | \(0.347349\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.27046 | −0.0789424 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.5659 | 0.715911 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.19227 | −0.443494 | −0.221747 | − | 0.975104i | \(-0.571176\pi\) | ||||
−0.221747 | + | 0.975104i | \(0.571176\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.93472 | 0.118849 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.47563 | 0.579899 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.6556 | 1.44231 | 0.721155 | − | 0.692774i | \(-0.243612\pi\) | ||||
0.721155 | + | 0.692774i | \(0.243612\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.2942 | −0.989805 | −0.494902 | − | 0.868949i | \(-0.664796\pi\) | ||||
−0.494902 | + | 0.868949i | \(0.664796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.763644 | 0.0462178 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.58443 | −0.155847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.65531 | 0.279710 | 0.139855 | − | 0.990172i | \(-0.455336\pi\) | ||||
0.139855 | + | 0.990172i | \(0.455336\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.88471 | −0.412177 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.1294 | 0.663922 | 0.331961 | − | 0.943293i | \(-0.392290\pi\) | ||||
0.331961 | + | 0.943293i | \(0.392290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.69259 | 0.219502 | 0.109751 | − | 0.993959i | \(-0.464995\pi\) | ||||
0.109751 | + | 0.993959i | \(0.464995\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.22020 | 0.0722783 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.11068 | −0.183617 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.96054 | −0.232973 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.810946 | 0.0475385 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.8153 | −0.807098 | −0.403549 | − | 0.914958i | \(-0.632223\pi\) | ||||
−0.403549 | + | 0.914958i | \(0.632223\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.59293 | −0.267411 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.13654 | −0.240027 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.55145 | −0.263217 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.35432 | −0.481535 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.93378 | 0.398335 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.0218 | −0.573849 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.6569 | −0.893589 | −0.446794 | − | 0.894637i | \(-0.647434\pi\) | ||||
−0.446794 | + | 0.894637i | \(0.647434\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8167 | 0.615339 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.1559 | −0.916119 | −0.458059 | − | 0.888922i | \(-0.651455\pi\) | ||||
−0.458059 | + | 0.888922i | \(0.651455\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.5609 | 0.936077 | 0.468038 | − | 0.883708i | \(-0.344961\pi\) | ||||
0.468038 | + | 0.883708i | \(0.344961\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.75629 | 0.211643 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.6460 | 1.55275 | 0.776376 | − | 0.630270i | \(-0.217056\pi\) | ||||
0.776376 | + | 0.630270i | \(0.217056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.78553 | −0.267938 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.146386 | 0.00817046 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.71244 | 0.206566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.58443 | 0.143358 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.7379 | 0.649106 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.30529 | −0.513017 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7209 | 0.589274 | 0.294637 | − | 0.955609i | \(-0.404801\pi\) | ||||
0.294637 | + | 0.955609i | \(0.404801\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.07050 | −0.168262 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.1311 | −0.553523 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.30889 | −0.507088 | −0.253544 | − | 0.967324i | \(-0.581596\pi\) | ||||
−0.253544 | + | 0.967324i | \(0.581596\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.5486 | 0.681546 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.84863 | 0.154262 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.40196 | 0.290832 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.1924 | −1.51345 | −0.756724 | − | 0.653734i | \(-0.773201\pi\) | ||||
−0.756724 | + | 0.653734i | \(0.773201\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.8050 | 1.06014 | 0.530068 | − | 0.847955i | \(-0.322166\pi\) | ||||
0.530068 | + | 0.847955i | \(0.322166\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.13654 | 0.220792 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.9753 | −1.16963 | −0.584813 | − | 0.811168i | \(-0.698832\pi\) | ||||
−0.584813 | + | 0.811168i | \(0.698832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.1643 | −0.857912 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.75753 | −0.145944 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.8772 | 1.10186 | 0.550928 | − | 0.834553i | \(-0.314274\pi\) | ||||
0.550928 | + | 0.834553i | \(0.314274\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9430 | −0.944370 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.763644 | 0.0400809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.8161 | 0.566140 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.25726 | 0.378826 | 0.189413 | − | 0.981898i | \(-0.439342\pi\) | ||||
0.189413 | + | 0.981898i | \(0.439342\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.51803 | −0.391373 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.24483 | −0.0646281 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.05017 | −0.468600 | −0.234300 | − | 0.972164i | \(-0.575280\pi\) | ||||
−0.234300 | + | 0.972164i | \(0.575280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.00169 | −0.464845 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.78553 | 0.246467 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.92065 | −0.406856 | −0.203428 | − | 0.979090i | \(-0.565208\pi\) | ||||
−0.203428 | + | 0.979090i | \(0.565208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.68147 | −0.188607 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.8448 | −1.72939 | −0.864695 | − | 0.502298i | \(-0.832488\pi\) | ||||
−0.864695 | + | 0.502298i | \(0.832488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.55421 | −0.0792099 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.1911 | −1.02637 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.1083 | −1.17164 | −0.585818 | − | 0.810443i | \(-0.699227\pi\) | ||||
−0.585818 | + | 0.810443i | \(0.699227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.4354 | 0.831173 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.01854 | 0.152265 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.47035 | 0.174612 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.7326 | 0.689217 | 0.344609 | − | 0.938746i | \(-0.388012\pi\) | ||||
0.344609 | + | 0.938746i | \(0.388012\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.785092 | −0.0393038 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.2794 | −1.91158 | −0.955790 | − | 0.294051i | \(-0.904997\pi\) | ||||
−0.955790 | + | 0.294051i | \(0.904997\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.84863 | −0.141901 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.35936 | 0.315999 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.27046 | 0.0629742 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.5213 | 1.85531 | 0.927655 | − | 0.373439i | \(-0.121821\pi\) | ||||
0.927655 | + | 0.373439i | \(0.121821\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.2808 | −0.507116 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.95515 | 0.145414 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.3624 | −0.803200 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.50244 | 0.318426 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.8698 | 1.31267 | 0.656337 | − | 0.754468i | \(-0.272105\pi\) | ||||
0.656337 | + | 0.754468i | \(0.272105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.8231 | −0.771170 | −0.385585 | − | 0.922672i | \(-0.626000\pi\) | ||||
−0.385585 | + | 0.922672i | \(0.626000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.4895 | −1.09347 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.33242 | −0.452689 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.44819 | 0.312050 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.763644 | −0.0368691 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.3780 | 1.46325 | 0.731627 | − | 0.681705i | \(-0.238761\pi\) | ||||
0.731627 | + | 0.681705i | \(0.238761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.2984 | −0.494911 | −0.247456 | − | 0.968899i | \(-0.579594\pi\) | ||||
−0.247456 | + | 0.968899i | \(0.579594\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.67978 | −0.272324 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.67928 | 0.223841 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.227077 | −0.0108378 | −0.00541889 | − | 0.999985i | \(-0.501725\pi\) | ||||
−0.00541889 | + | 0.999985i | \(0.501725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.41685 | −0.115088 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.57932 | 0.122547 | 0.0612737 | − | 0.998121i | \(-0.480484\pi\) | ||||
0.0612737 | + | 0.998121i | \(0.480484\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.2853 | 0.914212 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.28094 | 0.438973 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.8040 | 1.02899 | 0.514497 | − | 0.857492i | \(-0.327979\pi\) | ||||
0.514497 | + | 0.857492i | \(0.327979\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.11068 | 0.146476 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.44513 | −0.302819 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.55421 | 0.0728625 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.0371 | −1.35830 | −0.679149 | − | 0.734000i | \(-0.737651\pi\) | ||||
−0.679149 | + | 0.734000i | \(0.737651\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.9371 | −0.697206 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.2576 | −1.59553 | −0.797767 | − | 0.602966i | \(-0.793985\pi\) | ||||
−0.797767 | + | 0.602966i | \(0.793985\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.4791 | −1.18412 | −0.592058 | − | 0.805895i | \(-0.701684\pi\) | ||||
−0.592058 | + | 0.805895i | \(0.701684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.38094 | 0.156787 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.5467 | −1.22843 | −0.614216 | − | 0.789138i | \(-0.710528\pi\) | ||||
−0.614216 | + | 0.789138i | \(0.710528\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.51850 | 0.300997 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.97850 | −0.413707 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.35432 | 0.384132 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.65701 | −0.121912 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.00855 | −0.137752 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.3747 | 1.02233 | 0.511164 | − | 0.859483i | \(-0.329215\pi\) | ||||
0.511164 | + | 0.859483i | \(0.329215\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.27046 | −0.0579279 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.47569 | −0.158149 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.65048 | 0.0749446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.34573 | −0.151610 | −0.0758048 | − | 0.997123i | \(-0.524153\pi\) | ||||
−0.0758048 | + | 0.997123i | \(0.524153\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.54111 | −0.431464 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.58951 | 0.432768 | 0.216384 | − | 0.976308i | \(-0.430574\pi\) | ||||
0.216384 | + | 0.976308i | \(0.430574\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.2806 | −0.778281 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.75629 | −0.168833 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.4003 | 0.466518 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.05910 | 0.181710 | 0.0908552 | − | 0.995864i | \(-0.471040\pi\) | ||||
0.0908552 | + | 0.995864i | \(0.471040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.6963 | 0.835290 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.3910 | 1.13213 | 0.566065 | − | 0.824361i | \(-0.308465\pi\) | ||||
0.566065 | + | 0.824361i | \(0.308465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.1120 | 0.627977 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.763644 | 0.0339146 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.4880 | −0.464873 | −0.232436 | − | 0.972612i | \(-0.574670\pi\) | ||||
−0.232436 | + | 0.972612i | \(0.574670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.95921 | −0.307858 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.25272 | −0.187762 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.0147 | 0.970083 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.30529 | 0.409246 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.1929 | −0.666893 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.86958 | −0.169529 | −0.0847646 | − | 0.996401i | \(-0.527014\pi\) | ||||
−0.0847646 | + | 0.996401i | \(0.527014\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.4579 | −0.588472 | −0.294236 | − | 0.955733i | \(-0.595065\pi\) | ||||
−0.294236 | + | 0.955733i | \(0.595065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.97358 | 0.0861342 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.2865 | 0.448086 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.28428 | −0.0993165 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.14215 | 0.309943 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.11068 | −0.134738 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.297933 | 0.0128807 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.79627 | −0.293281 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.4446 | −0.535037 | −0.267518 | − | 0.963553i | \(-0.586204\pi\) | ||||
−0.267518 | + | 0.963553i | \(0.586204\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.3212 | 0.614583 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.8896 | 1.02332 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.0611 | 0.900507 | 0.450254 | − | 0.892901i | \(-0.351334\pi\) | ||||
0.450254 | + | 0.892901i | \(0.351334\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.5843 | 0.665121 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.91994 | −0.209596 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.23287 | −0.0949511 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.50786 | 0.0640051 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.47725 | 0.147336 | 0.0736679 | − | 0.997283i | \(-0.476530\pi\) | ||||
0.0736679 | + | 0.997283i | \(0.476530\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.35432 | −0.353350 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.75753 | 0.116423 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5980 | 0.446652 | 0.223326 | − | 0.974744i | \(-0.428309\pi\) | ||||
0.223326 | + | 0.974744i | \(0.428309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.5396 | 1.07446 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.09170 | −0.171835 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.94541 | −0.123478 | −0.0617390 | − | 0.998092i | \(-0.519665\pi\) | ||||
−0.0617390 | + | 0.998092i | \(0.519665\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.7824 | 0.451230 | 0.225615 | − | 0.974217i | \(-0.427561\pi\) | ||||
0.225615 | + | 0.974217i | \(0.427561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.30626 | −0.388774 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.7629 | −0.490547 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0827 | 0.586271 | 0.293135 | − | 0.956071i | \(-0.405301\pi\) | ||||
0.293135 | + | 0.956071i | \(0.405301\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.2675 | 0.468262 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.5278 | 0.436767 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.24483 | 0.0515554 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.75629 | 0.155304 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.60754 | 0.107625 | 0.0538123 | − | 0.998551i | \(-0.482863\pi\) | ||||
0.0538123 | + | 0.998551i | \(0.482863\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.92864 | 0.120673 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.52633 | 0.350726 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.05565 | −0.371871 | −0.185936 | − | 0.982562i | \(-0.559532\pi\) | ||||
−0.185936 | + | 0.982562i | \(0.559532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.61229 | −0.230081 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.4472 | 0.836847 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.1995 | −1.80594 | −0.902971 | − | 0.429702i | \(-0.858619\pi\) | ||||
−0.902971 | + | 0.429702i | \(0.858619\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.4066 | −1.48506 | −0.742528 | − | 0.669815i | \(-0.766373\pi\) | ||||
−0.742528 | + | 0.669815i | \(0.766373\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.7542 | 0.641562 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.55421 | 0.0631877 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.3187 | −1.10883 | −0.554417 | − | 0.832239i | \(-0.687059\pi\) | ||||
−0.554417 | + | 0.832239i | \(0.687059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.65444 | 0.148085 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.30529 | −0.376452 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.6930 | 1.15890 | 0.579449 | − | 0.815008i | \(-0.303268\pi\) | ||||
0.579449 | + | 0.815008i | \(0.303268\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.69195 | 0.148874 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.4942 | 1.87178 | 0.935892 | − | 0.352286i | \(-0.114596\pi\) | ||||
0.935892 | + | 0.352286i | \(0.114596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.6265 | −0.909434 | −0.454717 | − | 0.890636i | \(-0.650260\pi\) | ||||
−0.454717 | + | 0.890636i | \(0.650260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.8273 | −0.755513 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.4084 | −0.497133 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.39860 | −0.215944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.785092 | 0.0313535 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.58765 | 0.182921 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.70304 | −0.0677970 | −0.0338985 | − | 0.999425i | \(-0.510792\pi\) | ||||
−0.0338985 | + | 0.999425i | \(0.510792\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.8309 | 0.629222 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.49273 | −0.297340 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.1360 | 0.994365 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.3537 | −0.724928 | −0.362464 | − | 0.931998i | \(-0.618064\pi\) | ||||
−0.362464 | + | 0.931998i | \(0.618064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.0360 | 0.435219 | 0.217609 | − | 0.976036i | \(-0.430174\pi\) | ||||
0.217609 | + | 0.976036i | \(0.430174\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.91545 | 0.390420 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.3081 | 0.719767 | 0.359884 | − | 0.932997i | \(-0.382816\pi\) | ||||
0.359884 | + | 0.932997i | \(0.382816\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.95515 | −0.116000 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.17534 | −0.0852584 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.10285 | −0.0431577 | −0.0215789 | − | 0.999767i | \(-0.506869\pi\) | ||||
−0.0215789 | + | 0.999767i | \(0.506869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.14349 | 0.240046 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.8194 | −0.656186 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.9239 | −1.32149 | −0.660743 | − | 0.750612i | \(-0.729759\pi\) | ||||
−0.660743 | + | 0.750612i | \(0.729759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.5526 | 0.954986 | 0.477493 | − | 0.878636i | \(-0.341546\pi\) | ||||
0.477493 | + | 0.878636i | \(0.341546\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.75753 | −0.107094 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.59786 | −0.0619625 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.7811 | −0.843368 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.35451 | −0.168355 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.44819 | −0.248930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.1038 | −0.543660 | −0.271830 | − | 0.962345i | \(-0.587629\pi\) | ||||
−0.271830 | + | 0.962345i | \(0.587629\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.6906 | 0.411481 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.2490 | 1.20100 | 0.600498 | − | 0.799626i | \(-0.294969\pi\) | ||||
0.600498 | + | 0.799626i | \(0.294969\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.06194 | −0.0407536 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.14841 | −0.273928 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −50.8580 | −1.94603 | −0.973013 | − | 0.230749i | \(-0.925882\pi\) | ||||
−0.973013 | + | 0.230749i | \(0.925882\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.9241 | −0.799469 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.3745 | 0.624726 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.24483 | −0.0474241 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.29206 | 0.315445 | 0.157722 | − | 0.987484i | \(-0.449585\pi\) | ||||
0.157722 | + | 0.987484i | \(0.449585\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.41685 | 0.0918085 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.2341 | 0.501999 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.2327 | 0.425469 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.0406 | 0.568886 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.1036 | 0.834840 | 0.417420 | − | 0.908714i | \(-0.362934\pi\) | ||||
0.417420 | + | 0.908714i | \(0.362934\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.30614 | 0.0492620 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.0441 | 0.415945 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.07986 | −0.341483 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.389720 | −0.0146362 | −0.00731811 | − | 0.999973i | \(-0.502329\pi\) | ||||
−0.00731811 | + | 0.999973i | \(0.502329\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.39650 | −0.202384 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.9654 | 0.485559 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.55421 | −0.0581242 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.21957 | −0.0455457 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.7073 | −0.473904 | −0.236952 | − | 0.971521i | \(-0.576148\pi\) | ||||
−0.236952 | + | 0.971521i | \(0.576148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.1645 | −0.527515 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.5173 | 0.539905 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.3679 | 0.459331 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.87754 | −0.180898 | −0.0904489 | − | 0.995901i | \(-0.528830\pi\) | ||||
−0.0904489 | + | 0.995901i | \(0.528830\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.412464 | −0.0152765 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.1676 | 1.11579 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.9663 | 0.811345 | 0.405672 | − | 0.914019i | \(-0.367037\pi\) | ||||
0.405672 | + | 0.914019i | \(0.367037\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.18686 | 0.0437781 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.51850 | −0.240112 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.9920 | 0.919346 | 0.459673 | − | 0.888088i | \(-0.347967\pi\) | ||||
0.459673 | + | 0.888088i | \(0.347967\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.785092 | −0.0288411 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.97156 | −0.329135 | −0.164567 | − | 0.986366i | \(-0.552623\pi\) | ||||
−0.164567 | + | 0.986366i | \(0.552623\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.8891 | 0.692043 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.4441 | 0.930951 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.191694 | −0.00700434 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.35304 | 0.341297 | 0.170649 | − | 0.985332i | \(-0.445414\pi\) | ||||
0.170649 | + | 0.985332i | \(0.445414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.14626 | 0.151098 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.1175 | −0.477394 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.1416 | 1.53166 | 0.765832 | − | 0.643041i | \(-0.222328\pi\) | ||||
0.765832 | + | 0.643041i | \(0.222328\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.47569 | 0.126160 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.7772 | −1.44192 | −0.720962 | − | 0.692975i | \(-0.756300\pi\) | ||||
−0.720962 | + | 0.692975i | \(0.756300\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3709 | −0.556463 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.5640 | −0.490409 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.95515 | 0.106704 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.61322 | −0.202418 | −0.101209 | − | 0.994865i | \(-0.532271\pi\) | ||||
−0.101209 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.2969 | 0.406850 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.2364 | 1.48317 | 0.741584 | − | 0.670860i | \(-0.234075\pi\) | ||||
0.741584 | + | 0.670860i | \(0.234075\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.36209 | −0.264454 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.970177 | −0.0348049 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.19804 | 0.114582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.4003 | −0.372153 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.7956 | 0.707435 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.2735 | −0.652211 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.08239 | −0.323752 | −0.161876 | − | 0.986811i | \(-0.551755\pi\) | ||||
−0.161876 | + | 0.986811i | \(0.551755\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.49233 | −0.195532 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.4325 | −0.584273 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.44819 | 0.228982 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.47744 | 0.0523994 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.5216 | −1.32908 | −0.664542 | − | 0.747251i | \(-0.731373\pi\) | ||||
−0.664542 | + | 0.747251i | \(0.731373\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.6016 | 1.18874 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.9893 | −1.05962 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.95921 | 0.245585 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.07392 | −0.249323 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0645 | 0.635900 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.22629 | −0.0782721 | −0.0391360 | − | 0.999234i | \(-0.512461\pi\) | ||||
−0.0391360 | + | 0.999234i | \(0.512461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.05440 | −0.317943 | −0.158971 | − | 0.987283i | \(-0.550818\pi\) | ||||
−0.158971 | + | 0.987283i | \(0.550818\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.4430 | −0.436395 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.4186 | −0.680204 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.58896 | 0.300490 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.41685 | −0.0844515 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.2651 | 1.02136 | 0.510679 | − | 0.859771i | \(-0.329394\pi\) | ||||
0.510679 | + | 0.859771i | \(0.329394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.6067 | 1.79890 | 0.899448 | − | 0.437027i | \(-0.143969\pi\) | ||||
0.899448 | + | 0.437027i | \(0.143969\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.97358 | −0.0687113 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.6269 | −0.612947 | −0.306474 | − | 0.951879i | \(-0.599149\pi\) | ||||
−0.306474 | + | 0.951879i | \(0.599149\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.5997 | 1.23643 | 0.618215 | − | 0.786009i | \(-0.287856\pi\) | ||||
0.618215 | + | 0.786009i | \(0.287856\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.55500 | 0.123321 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.61102 | 0.125114 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38.0518 | 1.31684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.7835 | −0.407297 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.6882 | −1.23209 | −0.616047 | − | 0.787709i | \(-0.711267\pi\) | ||||
−0.616047 | + | 0.787709i | \(0.711267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.09870 | −0.210300 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.49887 | 0.292717 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.55421 | 0.0534665 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.81982 | 0.0967761 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.78243 | 0.198219 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2507 | 0.761849 | 0.380925 | − | 0.924606i | \(-0.375606\pi\) | ||||
0.380925 | + | 0.924606i | \(0.375606\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.86179 | −0.132070 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0586 | 0.616870 | 0.308435 | − | 0.951245i | \(-0.400195\pi\) | ||||
0.308435 | + | 0.951245i | \(0.400195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.3958 | −1.24181 | −0.620905 | − | 0.783886i | \(-0.713235\pi\) | ||||
−0.620905 | + | 0.783886i | \(0.713235\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.37545 | −0.0809551 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.2661 | −1.03027 | −0.515136 | − | 0.857109i | \(-0.672258\pi\) | ||||
−0.515136 | + | 0.857109i | \(0.672258\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.9214 | −1.05136 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.02444 | −0.102716 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.23287 | 0.0757448 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.51850 | 0.220871 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.56655 | −0.0868647 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.7878 | 0.398500 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.1400 | −1.22036 | −0.610181 | − | 0.792262i | \(-0.708903\pi\) | ||||
−0.610181 | + | 0.792262i | \(0.708903\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.5500 | −0.355841 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.936792 | 0.0315613 | 0.0157807 | − | 0.999875i | \(-0.494977\pi\) | ||||
0.0157807 | + | 0.999875i | \(0.494977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.9589 | −1.27742 | −0.638710 | − | 0.769447i | \(-0.720532\pi\) | ||||
−0.638710 | + | 0.769447i | \(0.720532\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.50736 | −0.117899 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.3329 | 1.72359 | 0.861796 | − | 0.507256i | \(-0.169340\pi\) | ||||
0.861796 | + | 0.507256i | \(0.169340\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.82092 | 0.161689 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.09170 | 0.137077 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.56664 | 0.320135 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.8322 | −0.462358 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.47569 | −0.116050 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.6322 | −0.454660 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.49509 | 0.149753 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.37973 | −0.212304 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.1474 | 0.968892 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.3418 | −0.907870 | −0.453935 | − | 0.891035i | \(-0.649980\pi\) | ||||
−0.453935 | + | 0.891035i | \(0.649980\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.9446 | −0.727858 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.8164 | 1.58423 | 0.792114 | − | 0.610373i | \(-0.208980\pi\) | ||||
0.792114 | + | 0.610373i | \(0.208980\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5278 | −0.348419 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.65313 | −0.253005 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.95281 | −0.130533 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.2920 | −1.39509 | −0.697543 | − | 0.716543i | \(-0.745723\pi\) | ||||
−0.697543 | + | 0.716543i | \(0.745723\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.9563 | −0.393974 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.4003 | 0.342331 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.28340 | −0.107958 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −34.2335 | −1.12438 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.2483 | 0.828369 | 0.414184 | − | 0.910193i | \(-0.364067\pi\) | ||||
0.414184 | + | 0.910193i | \(0.364067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.02809 | 0.0336942 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.3374 | −0.403908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.61229 | 0.183541 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.5207 | −0.572377 | −0.286189 | − | 0.958173i | \(-0.592388\pi\) | ||||
−0.286189 | + | 0.958173i | \(0.592388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.6466 | 0.412707 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.8160 | 0.548186 | 0.274093 | − | 0.961703i | \(-0.411622\pi\) | ||||
0.274093 | + | 0.961703i | \(0.411622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.1581 | 0.461051 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.42906 | 0.209137 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56.9736 | 1.85139 | 0.925697 | − | 0.378266i | \(-0.123479\pi\) | ||||
0.925697 | + | 0.378266i | \(0.123479\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.95921 | −0.225906 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.1117 | 0.684593 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.2538 | 0.882836 | 0.441418 | − | 0.897302i | \(-0.354476\pi\) | ||||
0.441418 | + | 0.897302i | \(0.354476\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.9406 | −0.612904 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.65444 | −0.118131 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.4629 | 0.434738 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.8853 | −0.738235 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.463294 | −0.0149295 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.9323 | 0.738216 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.65503 | −0.117538 | −0.0587689 | − | 0.998272i | \(-0.518717\pi\) | ||||
−0.0587689 | + | 0.998272i | \(0.518717\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.83498 | 0.0910727 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.8780 | −0.637917 | −0.318958 | − | 0.947769i | \(-0.603333\pi\) | ||||
−0.318958 | + | 0.947769i | \(0.603333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.51502 | −0.272979 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.97358 | 0.0632052 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.8678 | 0.763599 | 0.381799 | − | 0.924245i | \(-0.375304\pi\) | ||||
0.381799 | + | 0.924245i | \(0.375304\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.4084 | 0.396575 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.1491 | −1.18608 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.0856 | −0.895791 | −0.447895 | − | 0.894086i | \(-0.647826\pi\) | ||||
−0.447895 | + | 0.894086i | \(0.647826\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.3533 | 0.552921 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.10593 | −0.226184 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.0243 | 1.20910 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.18594 | 0.164737 | 0.0823684 | − | 0.996602i | \(-0.473752\pi\) | ||||
0.0823684 | + | 0.996602i | \(0.473752\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.18696 | 0.259805 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.6152 | 1.31929 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.3344 | −0.580656 | −0.290328 | − | 0.956927i | \(-0.593764\pi\) | ||||
−0.290328 | + | 0.956927i | \(0.593764\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.25530 | −0.166270 |
(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 | 8008.2.a.n.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.n.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial |