Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3864,2,Mod(1,3864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3864, 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("3864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3864.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: | \(30.8541953410\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3864.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.11491 | 0.498602 | 0.249301 | − | 0.968426i | \(-0.419799\pi\) | ||||
0.249301 | + | 0.968426i | \(0.419799\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.94567 | −1.18966 | −0.594832 | − | 0.803850i | \(-0.702781\pi\) | ||||
−0.594832 | + | 0.803850i | \(0.702781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.47283 | −1.51789 | −0.758946 | − | 0.651154i | \(-0.774285\pi\) | ||||
−0.758946 | + | 0.651154i | \(0.774285\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.11491 | 0.287868 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.926221 | −0.224642 | −0.112321 | − | 0.993672i | \(-0.535828\pi\) | ||||
−0.112321 | + | 0.993672i | \(0.535828\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.28415 | −0.524019 | −0.262010 | − | 0.965065i | \(-0.584385\pi\) | ||||
−0.262010 | + | 0.965065i | \(0.584385\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.75698 | −0.751396 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.58774 | 0.480532 | 0.240266 | − | 0.970707i | \(-0.422765\pi\) | ||||
0.240266 | + | 0.970707i | \(0.422765\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.81756 | 1.58368 | 0.791840 | − | 0.610729i | \(-0.209123\pi\) | ||||
0.791840 | + | 0.610729i | \(0.209123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.94567 | −0.686853 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.11491 | 0.188454 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.87189 | 0.307737 | 0.153868 | − | 0.988091i | \(-0.450827\pi\) | ||||
0.153868 | + | 0.988091i | \(0.450827\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.47283 | −0.876355 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.28415 | −0.669071 | −0.334536 | − | 0.942383i | \(-0.608579\pi\) | ||||
−0.334536 | + | 0.942383i | \(0.608579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.70265 | −1.47964 | −0.739820 | − | 0.672805i | \(-0.765089\pi\) | ||||
−0.739820 | + | 0.672805i | \(0.765089\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.11491 | 0.166201 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.81756 | −1.14031 | −0.570154 | − | 0.821538i | \(-0.693116\pi\) | ||||
−0.570154 | + | 0.821538i | \(0.693116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.926221 | −0.129697 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.70265 | 0.645959 | 0.322979 | − | 0.946406i | \(-0.395316\pi\) | ||||
0.322979 | + | 0.946406i | \(0.395316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.39905 | −0.593168 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.28415 | −0.302543 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.93246 | −0.902530 | −0.451265 | − | 0.892390i | \(-0.649027\pi\) | ||||
−0.451265 | + | 0.892390i | \(0.649027\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0606 | −1.67224 | −0.836118 | − | 0.548550i | \(-0.815180\pi\) | ||||
−0.836118 | + | 0.548550i | \(0.815180\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.10170 | −0.756823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.77643 | −1.07221 | −0.536106 | − | 0.844151i | \(-0.680105\pi\) | ||||
−0.536106 | + | 0.844151i | \(0.680105\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.6483 | −1.50108 | −0.750540 | − | 0.660826i | \(-0.770206\pi\) | ||||
−0.750540 | + | 0.660826i | \(0.770206\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.87189 | −0.921335 | −0.460667 | − | 0.887573i | \(-0.652390\pi\) | ||||
−0.460667 | + | 0.887573i | \(0.652390\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.75698 | −0.433819 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.94567 | −0.449651 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.81756 | 0.992053 | 0.496026 | − | 0.868307i | \(-0.334792\pi\) | ||||
0.496026 | + | 0.868307i | \(0.334792\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.04737 | 0.773550 | 0.386775 | − | 0.922174i | \(-0.373589\pi\) | ||||
0.386775 | + | 0.922174i | \(0.373589\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.03265 | −0.112007 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.58774 | 0.277435 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.0411284 | 0.00435961 | 0.00217980 | − | 0.999998i | \(-0.499306\pi\) | ||||
0.00217980 | + | 0.999998i | \(0.499306\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.47283 | −0.573709 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.81756 | 0.914338 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.54661 | −0.261277 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.5613 | 1.68155 | 0.840774 | − | 0.541386i | \(-0.182100\pi\) | ||||
0.840774 | + | 0.541386i | \(0.182100\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.94567 | −0.396555 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1079 | 1.20479 | 0.602393 | − | 0.798200i | \(-0.294214\pi\) | ||||
0.602393 | + | 0.798200i | \(0.294214\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.87189 | −0.874173 | −0.437087 | − | 0.899419i | \(-0.643990\pi\) | ||||
−0.437087 | + | 0.899419i | \(0.643990\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.11491 | 0.108804 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.93246 | −0.380166 | −0.190083 | − | 0.981768i | \(-0.560876\pi\) | ||||
−0.190083 | + | 0.981768i | \(0.560876\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.5202 | −1.58235 | −0.791174 | − | 0.611591i | \(-0.790530\pi\) | ||||
−0.791174 | + | 0.611591i | \(0.790530\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.87189 | 0.177672 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.9130 | 1.49697 | 0.748485 | − | 0.663151i | \(-0.230781\pi\) | ||||
0.748485 | + | 0.663151i | \(0.230781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.11491 | −0.103966 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.47283 | −0.505964 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.926221 | −0.0849065 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.56829 | 0.415300 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.28415 | −0.386289 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.76322 | −0.873249 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.06058 | 0.271582 | 0.135791 | − | 0.990737i | \(-0.456642\pi\) | ||||
0.135791 | + | 0.990737i | \(0.456642\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.70265 | −0.854271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.8913 | −0.951580 | −0.475790 | − | 0.879559i | \(-0.657838\pi\) | ||||
−0.475790 | + | 0.879559i | \(0.657838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.28415 | −0.198061 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.11491 | 0.0959560 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3774 | 0.972035 | 0.486017 | − | 0.873949i | \(-0.338449\pi\) | ||||
0.486017 | + | 0.873949i | \(0.338449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8044 | 1.00123 | 0.500616 | − | 0.865669i | \(-0.333107\pi\) | ||||
0.500616 | + | 0.865669i | \(0.333107\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.81756 | −0.658357 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.5940 | 1.80578 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.88509 | 0.239594 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.35793 | 0.275092 | 0.137546 | − | 0.990495i | \(-0.456079\pi\) | ||||
0.137546 | + | 0.990495i | \(0.456079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.99304 | 0.569085 | 0.284543 | − | 0.958663i | \(-0.408158\pi\) | ||||
0.284543 | + | 0.958663i | \(0.408158\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.926221 | −0.0748805 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.83076 | 0.789626 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.2104 | −1.05430 | −0.527151 | − | 0.849772i | \(-0.676740\pi\) | ||||
−0.527151 | + | 0.849772i | \(0.676740\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.70265 | 0.372944 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.47283 | −0.350339 | −0.175170 | − | 0.984538i | \(-0.556047\pi\) | ||||
−0.175170 | + | 0.984538i | \(0.556047\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.39905 | −0.342466 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.06682 | 0.469465 | 0.234732 | − | 0.972060i | \(-0.424579\pi\) | ||||
0.234732 | + | 0.972060i | \(0.424579\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.9519 | 1.30399 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.28415 | −0.174673 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.735300 | −0.0559038 | −0.0279519 | − | 0.999609i | \(-0.508899\pi\) | ||||
−0.0279519 | + | 0.999609i | \(0.508899\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.75698 | −0.284001 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.93246 | −0.521076 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1428 | 0.907598 | 0.453799 | − | 0.891104i | \(-0.350068\pi\) | ||||
0.453799 | + | 0.891104i | \(0.350068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.99304 | 0.445459 | 0.222730 | − | 0.974880i | \(-0.428503\pi\) | ||||
0.222730 | + | 0.974880i | \(0.428503\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.0606 | −0.965466 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.08698 | 0.153438 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.65456 | 0.267248 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5613 | −0.981264 | −0.490632 | − | 0.871367i | \(-0.663234\pi\) | ||||
−0.490632 | + | 0.871367i | \(0.663234\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.24926 | −0.521813 | −0.260907 | − | 0.965364i | \(-0.584021\pi\) | ||||
−0.260907 | + | 0.965364i | \(0.584021\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.10170 | −0.436952 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.62039 | 0.257942 | 0.128971 | − | 0.991648i | \(-0.458833\pi\) | ||||
0.128971 | + | 0.991648i | \(0.458833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.41850 | −0.384107 | −0.192054 | − | 0.981384i | \(-0.561515\pi\) | ||||
−0.192054 | + | 0.981384i | \(0.561515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.77643 | −0.619042 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.58774 | 0.181624 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.77643 | −0.333600 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.01249 | 0.623407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.5140 | −1.54993 | −0.774963 | − | 0.632007i | \(-0.782231\pi\) | ||||
−0.774963 | + | 0.632007i | \(0.782231\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.6483 | −0.866648 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.8176 | −0.737751 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.81756 | 0.598575 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.87189 | −0.531933 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.06905 | 0.340981 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.7221 | −1.18676 | −0.593380 | − | 0.804923i | \(-0.702207\pi\) | ||||
−0.593380 | + | 0.804923i | \(0.702207\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.75698 | −0.250465 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.00624 | 0.597765 | 0.298883 | − | 0.954290i | \(-0.403386\pi\) | ||||
0.298883 | + | 0.954290i | \(0.403386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.51173 | 0.430307 | 0.215154 | − | 0.976580i | \(-0.430975\pi\) | ||||
0.215154 | + | 0.976580i | \(0.430975\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.94567 | −0.259606 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.93942 | 0.520129 | 0.260065 | − | 0.965591i | \(-0.416256\pi\) | ||||
0.260065 | + | 0.965591i | \(0.416256\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.71585 | −0.568560 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.81756 | 0.572762 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.42698 | −0.480411 | −0.240206 | − | 0.970722i | \(-0.577215\pi\) | ||||
−0.240206 | + | 0.970722i | \(0.577215\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.05433 | 0.132331 | 0.0661656 | − | 0.997809i | \(-0.478923\pi\) | ||||
0.0661656 | + | 0.997809i | \(0.478923\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.11491 | 0.0712288 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.5008 | 0.795404 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.04737 | 0.446609 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.7283 | −1.05588 | −0.527942 | − | 0.849281i | \(-0.677036\pi\) | ||||
−0.527942 | + | 0.849281i | \(0.677036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.94567 | 0.248062 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.03265 | −0.0646671 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.67000 | 0.478441 | 0.239221 | − | 0.970965i | \(-0.423108\pi\) | ||||
0.239221 | + | 0.970965i | \(0.423108\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.87189 | 0.116314 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.58774 | 0.160177 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.35097 | 0.329955 | 0.164977 | − | 0.986297i | \(-0.447245\pi\) | ||||
0.164977 | + | 0.986297i | \(0.447245\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.24302 | 0.322076 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0411284 | 0.00251702 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.5117 | −0.823825 | −0.411912 | − | 0.911223i | \(-0.635139\pi\) | ||||
−0.411912 | + | 0.911223i | \(0.635139\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4402 | −0.634196 | −0.317098 | − | 0.948393i | \(-0.602708\pi\) | ||||
−0.317098 | + | 0.948393i | \(0.602708\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.47283 | −0.331231 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.8238 | 0.893909 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.4379 | 0.927576 | 0.463788 | − | 0.885946i | \(-0.346490\pi\) | ||||
0.463788 | + | 0.885946i | \(0.346490\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.81756 | 0.527893 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.80908 | 0.465851 | 0.232925 | − | 0.972495i | \(-0.425170\pi\) | ||||
0.232925 | + | 0.972495i | \(0.425170\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5466 | −0.626931 | −0.313466 | − | 0.949600i | \(-0.601490\pi\) | ||||
−0.313466 | + | 0.949600i | \(0.601490\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.54661 | −0.150848 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.28415 | −0.252885 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1421 | −0.949536 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.5613 | 0.970843 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.2144 | −0.771992 | −0.385996 | − | 0.922500i | \(-0.626142\pi\) | ||||
−0.385996 | + | 0.922500i | \(0.626142\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.72906 | −0.450003 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.94567 | −0.228951 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.47283 | 0.316502 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.70265 | −0.559251 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.1079 | 0.695583 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.5613 | −0.833780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.92622 | 0.509446 | 0.254723 | − | 0.967014i | \(-0.418016\pi\) | ||||
0.254723 | + | 0.967014i | \(0.418016\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.87189 | −0.504704 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.1817 | −0.860877 | −0.430438 | − | 0.902620i | \(-0.641641\pi\) | ||||
−0.430438 | + | 0.902620i | \(0.641641\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.1560 | 1.25233 | 0.626167 | − | 0.779689i | \(-0.284623\pi\) | ||||
0.626167 | + | 0.779689i | \(0.284623\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.11491 | 0.0628179 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.2081 | 0.685677 | 0.342839 | − | 0.939394i | \(-0.388612\pi\) | ||||
0.342839 | + | 0.939394i | \(0.388612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.2104 | −0.571671 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.93246 | −0.219489 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.11562 | 0.117717 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.5613 | 1.14054 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.5202 | −0.913569 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.81756 | −0.430996 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.4791 | −0.850807 | −0.425404 | − | 0.905004i | \(-0.639868\pi\) | ||||
−0.425404 | + | 0.905004i | \(0.639868\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.87189 | 0.102579 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.78491 | −0.534607 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.6483 | −0.580051 | −0.290025 | − | 0.957019i | \(-0.593664\pi\) | ||||
−0.290025 | + | 0.957019i | \(0.593664\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.9130 | 0.864276 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.7911 | −1.88405 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.11491 | −0.0600246 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.5334 | −1.58544 | −0.792718 | − | 0.609588i | \(-0.791335\pi\) | ||||
−0.792718 | + | 0.609588i | \(0.791335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.4270 | −0.718730 | −0.359365 | − | 0.933197i | \(-0.617007\pi\) | ||||
−0.359365 | + | 0.933197i | \(0.617007\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.47283 | −0.292118 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.3594 | 1.34975 | 0.674873 | − | 0.737933i | \(-0.264198\pi\) | ||||
0.674873 | + | 0.737933i | \(0.264198\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.1017 | −0.748441 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.926221 | −0.0490208 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.9130 | 0.734301 | 0.367150 | − | 0.930162i | \(-0.380333\pi\) | ||||
0.367150 | + | 0.930162i | \(0.380333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7827 | −0.725404 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.56829 | 0.239773 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.77643 | −0.459379 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.2081 | −0.689459 | −0.344729 | − | 0.938702i | \(-0.612029\pi\) | ||||
−0.344729 | + | 0.938702i | \(0.612029\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.28415 | −0.223024 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.70265 | 0.244149 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.93871 | −0.462829 | −0.231414 | − | 0.972855i | \(-0.574335\pi\) | ||||
−0.231414 | + | 0.972855i | \(0.574335\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.76322 | −0.504171 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.1623 | −0.729394 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.60719 | 0.442122 | 0.221061 | − | 0.975260i | \(-0.429048\pi\) | ||||
0.221061 | + | 0.975260i | \(0.429048\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.06058 | 0.156798 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.8998 | 1.06793 | 0.533965 | − | 0.845506i | \(-0.320701\pi\) | ||||
0.533965 | + | 0.845506i | \(0.320701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.39905 | −0.224197 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.70265 | −0.493213 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.7911 | −0.952749 | −0.476375 | − | 0.879242i | \(-0.658049\pi\) | ||||
−0.476375 | + | 0.879242i | \(0.658049\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.926221 | 0.0468410 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.8913 | −0.549395 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.83076 | 0.494639 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.9038 | 1.90234 | 0.951169 | − | 0.308670i | \(-0.0998839\pi\) | ||||
0.951169 | + | 0.308670i | \(0.0998839\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.28415 | −0.114350 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.0558 | 1.55086 | 0.775428 | − | 0.631437i | \(-0.217534\pi\) | ||||
0.775428 | + | 0.631437i | \(0.217534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −48.2570 | −2.40385 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.11491 | 0.0554002 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.38585 | −0.366103 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.53341 | 0.0758222 | 0.0379111 | − | 0.999281i | \(-0.487930\pi\) | ||||
0.0379111 | + | 0.999281i | \(0.487930\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.3774 | 0.561204 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.93246 | −0.341124 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.85717 | 0.385693 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.8044 | 0.578062 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.2361 | 1.13516 | 0.567578 | − | 0.823320i | \(-0.307881\pi\) | ||||
0.567578 | + | 0.823320i | \(0.307881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.4031 | 1.23807 | 0.619035 | − | 0.785364i | \(-0.287524\pi\) | ||||
0.619035 | + | 0.785364i | \(0.287524\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.81756 | −0.380103 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.47979 | 0.168795 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.0606 | −0.632046 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.5940 | 1.04257 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.8712 | 1.24617 | 0.623085 | − | 0.782154i | \(-0.285879\pi\) | ||||
0.623085 | + | 0.782154i | \(0.285879\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.5613 | 1.13229 | 0.566143 | − | 0.824307i | \(-0.308435\pi\) | ||||
0.566143 | + | 0.824307i | \(0.308435\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.88509 | 0.138330 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.28415 | 0.109266 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.10170 | 0.291218 | 0.145609 | − | 0.989342i | \(-0.453486\pi\) | ||||
0.145609 | + | 0.989342i | \(0.453486\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3510 | 0.491789 | 0.245895 | − | 0.969297i | \(-0.420918\pi\) | ||||
0.245895 | + | 0.969297i | \(0.420918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.0458544 | 0.00217371 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.35793 | 0.158824 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.02168 | 0.284181 | 0.142090 | − | 0.989854i | \(-0.454618\pi\) | ||||
0.142090 | + | 0.989854i | \(0.454618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.9038 | 0.795970 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.99304 | 0.328562 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.10170 | −0.286052 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.8448 | −1.44286 | −0.721429 | − | 0.692489i | \(-0.756514\pi\) | ||||
−0.721429 | + | 0.692489i | \(0.756514\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.926221 | −0.0432323 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.3726 | 1.13515 | 0.567574 | − | 0.823323i | \(-0.307882\pi\) | ||||
0.567574 | + | 0.823323i | \(0.307882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.8913 | −1.24975 | −0.624873 | − | 0.780726i | \(-0.714849\pi\) | ||||
−0.624873 | + | 0.780726i | \(0.714849\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.83076 | 0.455891 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.5459 | 1.27467 | 0.637336 | − | 0.770586i | \(-0.280036\pi\) | ||||
0.637336 | + | 0.770586i | \(0.280036\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.77643 | −0.405258 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.2104 | −0.608702 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 38.2834 | 1.76027 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.58150 | 0.393746 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.70265 | 0.215320 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.7368 | −1.45009 | −0.725046 | − | 0.688700i | \(-0.758182\pi\) | ||||
−0.725046 | + | 0.688700i | \(0.758182\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.2445 | −0.467111 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.4644 | 0.838423 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.7911 | −1.12339 | −0.561697 | − | 0.827343i | \(-0.689851\pi\) | ||||
−0.561697 | + | 0.827343i | \(0.689851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.47283 | −0.202269 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.9450 | 1.62217 | 0.811086 | − | 0.584926i | \(-0.198877\pi\) | ||||
0.811086 | + | 0.584926i | \(0.198877\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.39682 | −0.107947 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.39905 | −0.197723 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.6483 | −0.567355 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.4938 | 1.36509 | 0.682545 | − | 0.730844i | \(-0.260873\pi\) | ||||
0.682545 | + | 0.730844i | \(0.260873\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.06682 | 0.271045 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.65679 | −0.430575 | −0.215288 | − | 0.976551i | \(-0.569069\pi\) | ||||
−0.215288 | + | 0.976551i | \(0.569069\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.4992 | 0.600708 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.9519 | 0.752861 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.9123 | 1.41449 | 0.707244 | − | 0.706970i | \(-0.249938\pi\) | ||||
0.707244 | + | 0.706970i | \(0.249938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.87189 | −0.348232 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.28415 | −0.100848 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.89134 | −0.435864 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.8455 | 1.35658 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.735300 | −0.0322761 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.108664 | −0.00476067 | −0.00238034 | − | 0.999997i | \(-0.500758\pi\) | ||||
−0.00238034 | + | 0.999997i | \(0.500758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.2508 | −1.06041 | −0.530206 | − | 0.847869i | \(-0.677886\pi\) | ||||
−0.530206 | + | 0.847869i | \(0.677886\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.75698 | −0.163968 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.16701 | −0.355760 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.93246 | −0.300843 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.4464 | 1.01558 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.38433 | −0.189551 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.1428 | 0.524002 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.94567 | −0.169952 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5334 | 0.624840 | 0.312420 | − | 0.949944i | \(-0.398860\pi\) | ||||
0.312420 | + | 0.949944i | \(0.398860\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.99304 | 0.257186 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.4185 | −0.788962 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.0187 | −1.75383 | −0.876917 | − | 0.480642i | \(-0.840404\pi\) | ||||
−0.876917 | + | 0.480642i | \(0.840404\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.0606 | −0.557412 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.91078 | −0.251808 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.81756 | 0.374961 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.08698 | 0.0885875 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.65055 | −0.366536 | −0.183268 | − | 0.983063i | \(-0.558668\pi\) | ||||
−0.183268 | + | 0.983063i | \(0.558668\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 53.1010 | 2.24593 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.65456 | 0.154296 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.0257 | −0.717547 | −0.358774 | − | 0.933425i | \(-0.616805\pi\) | ||||
−0.358774 | + | 0.933425i | \(0.616805\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.7415 | 0.746392 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.8440 | 1.25112 | 0.625562 | − | 0.780174i | \(-0.284870\pi\) | ||||
0.625562 | + | 0.780174i | \(0.284870\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.7228 | −0.532433 | −0.266217 | − | 0.963913i | \(-0.585774\pi\) | ||||
−0.266217 | + | 0.963913i | \(0.585774\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.5613 | −0.566533 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.75698 | 0.156677 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.5683 | 0.689747 | 0.344874 | − | 0.938649i | \(-0.387922\pi\) | ||||
0.344874 | + | 0.938649i | \(0.387922\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.24926 | −0.301269 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.04737 | 0.292374 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.5551 | −0.768473 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.10170 | −0.252274 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.7779 | −1.27034 | −0.635171 | − | 0.772372i | \(-0.719070\pi\) | ||||
−0.635171 | + | 0.772372i | \(0.719070\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.1406 | −0.829879 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.62039 | 0.148923 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.5698 | −1.05003 | −0.525013 | − | 0.851094i | \(-0.675940\pi\) | ||||
−0.525013 | + | 0.851094i | \(0.675940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.03265 | −0.0423345 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.41850 | −0.221765 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.974310 | −0.0398092 | −0.0199046 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199046 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.0885 | −0.941800 | −0.470900 | − | 0.882187i | \(-0.656071\pi\) | ||||
−0.470900 | + | 0.882187i | \(0.656071\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.77643 | −0.357404 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.09323 | 0.207069 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.93095 | −0.281318 | −0.140659 | − | 0.990058i | \(-0.544922\pi\) | ||||
−0.140659 | + | 0.990058i | \(0.544922\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.58774 | 0.104861 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.7842 | 1.73086 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.5893 | 1.27588 | 0.637939 | − | 0.770087i | \(-0.279787\pi\) | ||||
0.637939 | + | 0.770087i | \(0.279787\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.77643 | −0.192604 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.5676 | 1.43190 | 0.715948 | − | 0.698153i | \(-0.245995\pi\) | ||||
0.715948 | + | 0.698153i | \(0.245995\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.8128 | −1.31886 | −0.659430 | − | 0.751766i | \(-0.729202\pi\) | ||||
−0.659430 | + | 0.751766i | \(0.729202\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.0411284 | 0.00164778 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.89981 | 0.315993 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.01249 | 0.359924 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.73378 | −0.0691304 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.6825 | −1.30107 | −0.650535 | − | 0.759477i | \(-0.725455\pi\) | ||||
−0.650535 | + | 0.759477i | \(0.725455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.5140 | −0.894850 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.41226 | 0.135411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.47283 | −0.216842 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.6483 | −0.500360 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.6942 | −0.619882 | −0.309941 | − | 0.950756i | \(-0.600309\pi\) | ||||
−0.309941 | + | 0.950756i | \(0.600309\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.62887 | −0.300853 | −0.150427 | − | 0.988621i | \(-0.548065\pi\) | ||||
−0.150427 | + | 0.988621i | \(0.548065\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.8176 | −0.425941 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.64431 | 0.143273 | 0.0716363 | − | 0.997431i | \(-0.477178\pi\) | ||||
0.0716363 | + | 0.997431i | \(0.477178\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.3532 | 1.07371 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.81756 | 0.345587 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.9673 | 1.36838 | 0.684189 | − | 0.729305i | \(-0.260156\pi\) | ||||
0.684189 | + | 0.729305i | \(0.260156\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.1428 | −0.474460 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.87189 | −0.307112 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.7368 | 1.70374 | 0.851872 | − | 0.523750i | \(-0.175467\pi\) | ||||
0.851872 | + | 0.523750i | \(0.175467\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.9986 | −1.82803 | −0.914016 | − | 0.405678i | \(-0.867036\pi\) | ||||
−0.914016 | + | 0.405678i | \(0.867036\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.06905 | 0.196866 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.54661 | −0.0987534 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.58774 | −0.100198 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.7221 | −0.685176 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.5327 | 1.98940 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.245253 | 0.00945382 | 0.00472691 | − | 0.999989i | \(-0.498495\pi\) | ||||
0.00472691 | + | 0.999989i | \(0.498495\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.75698 | −0.144606 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.2819 | 0.664198 | 0.332099 | − | 0.943245i | \(-0.392243\pi\) | ||||
0.332099 | + | 0.943245i | \(0.392243\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.5613 | 0.635566 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00624 | 0.345120 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.1127 | 0.578270 | 0.289135 | − | 0.957288i | \(-0.406632\pi\) | ||||
0.289135 | + | 0.957288i | \(0.406632\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.6847 | 0.484658 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.51173 | 0.248438 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.7368 | −0.980495 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.1234 | 0.537279 | 0.268639 | − | 0.963241i | \(-0.413426\pi\) | ||||
0.268639 | + | 0.963241i | \(0.413426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.94567 | −0.149884 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.1608 | 0.499216 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.96807 | 0.150301 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.93942 | 0.300297 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.1204 | −1.81748 | −0.908742 | − | 0.417359i | \(-0.862956\pi\) | ||||
−0.908742 | + | 0.417359i | \(0.862956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.27567 | −0.161260 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.71585 | −0.328258 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.1079 | 0.455366 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.83772 | −0.144129 | −0.0720643 | − | 0.997400i | \(-0.522959\pi\) | ||||
−0.0720643 | + | 0.997400i | \(0.522959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.81756 | 0.330684 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.81756 | −0.330220 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0753 | 0.900365 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.42698 | −0.277366 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −53.4108 | −1.99189 | −0.995944 | − | 0.0899774i | \(-0.971321\pi\) | ||||
−0.995944 | + | 0.0899774i | \(0.971321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.87189 | −0.330406 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.05433 | 0.0764014 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.72210 | −0.361070 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.20341 | 0.118808 | 0.0594039 | − | 0.998234i | \(-0.481080\pi\) | ||||
0.0594039 | + | 0.998234i | \(0.481080\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.98680 | 0.332389 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.6197 | −1.72194 | −0.860968 | − | 0.508658i | \(-0.830142\pi\) | ||||
−0.860968 | + | 0.508658i | \(0.830142\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.11491 | 0.0411240 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.6289 | 1.27557 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.7787 | −1.27935 | −0.639677 | − | 0.768644i | \(-0.720932\pi\) | ||||
−0.639677 | + | 0.768644i | \(0.720932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.5008 | 0.459227 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.09394 | 0.0401329 | 0.0200664 | − | 0.999799i | \(-0.493612\pi\) | ||||
0.0200664 | + | 0.999799i | \(0.493612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.74378 | 0.137161 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.04737 | 0.257850 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.93246 | −0.143689 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.6009 | 0.423325 | 0.211662 | − | 0.977343i | \(-0.432112\pi\) | ||||
0.211662 | + | 0.977343i | \(0.432112\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.7283 | −0.609615 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.79659 | 0.283747 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.6825 | 0.969791 | 0.484896 | − | 0.874572i | \(-0.338858\pi\) | ||||
0.484896 | + | 0.874572i | \(0.338858\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.94567 | 0.143219 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.9497 | 0.759425 | 0.379713 | − | 0.925105i | \(-0.376023\pi\) | ||||
0.379713 | + | 0.925105i | \(0.376023\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.5202 | −0.598072 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.03265 | −0.0373356 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.9402 | 1.36994 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.5918 | 0.418009 | 0.209005 | − | 0.977915i | \(-0.432978\pi\) | ||||
0.209005 | + | 0.977915i | \(0.432978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.67000 | 0.276228 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.9277 | −1.65191 | −0.825953 | − | 0.563739i | \(-0.809362\pi\) | ||||
−0.825953 | + | 0.563739i | \(0.809362\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.1274 | −1.18997 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.87189 | 0.0671536 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.78562 | 0.350606 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.9061 | 1.78578 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.58774 | 0.0924783 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.7283 | −0.525677 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.7585 | −1.16771 | −0.583857 | − | 0.811856i | \(-0.698457\pi\) | ||||
−0.583857 | + | 0.811856i | \(0.698457\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.35097 | 0.190499 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.9130 | 0.565802 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 71.4784 | 2.53827 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.24302 | 0.185951 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.1770 | −0.856393 | −0.428197 | − | 0.903686i | \(-0.640851\pi\) | ||||
−0.428197 | + | 0.903686i | \(0.640851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.24078 | 0.256161 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.0411284 | 0.00145320 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.0599 | 1.09608 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.11491 | −0.0392953 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.5117 | −0.475635 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.1777 | −1.02583 | −0.512917 | − | 0.858438i | \(-0.671435\pi\) | ||||
−0.512917 | + | 0.858438i | \(0.671435\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.9915 | 0.596653 | 0.298327 | − | 0.954464i | \(-0.403572\pi\) | ||||
0.298327 | + | 0.954464i | \(0.403572\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.4402 | −0.366153 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.98680 | −0.174680 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.1623 | 0.775360 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.47283 | −0.191236 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.0793 | 1.29408 | 0.647038 | − | 0.762457i | \(-0.276007\pi\) | ||||
0.647038 | + | 0.762457i | \(0.276007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.9450 | −1.14839 | −0.574194 | − | 0.818719i | \(-0.694685\pi\) | ||||
−0.574194 | + | 0.818719i | \(0.694685\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.8238 | 0.516098 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.8936 | 1.07427 | 0.537137 | − | 0.843495i | \(-0.319506\pi\) | ||||
0.537137 | + | 0.843495i | \(0.319506\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.1406 | 0.699512 | 0.349756 | − | 0.936841i | \(-0.386265\pi\) | ||||
0.349756 | + | 0.936841i | \(0.386265\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.4379 | 0.535537 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.926221 | −0.0320917 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.76394 | 0.234076 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.81756 | 0.304779 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.2401 | −1.11305 | −0.556525 | − | 0.830831i | \(-0.687866\pi\) | ||||
−0.556525 | + | 0.830831i | \(0.687866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3036 | −0.769089 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.80908 | 0.268959 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.8998 | 0.650173 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.56829 | 0.156968 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.5466 | −0.361959 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.87189 | −0.0641675 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.8510 | −1.77534 | −0.887672 | − | 0.460476i | \(-0.847679\pi\) | ||||
−0.887672 | + | 0.460476i | \(0.847679\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.54661 | −0.0870923 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.8425 | 1.70259 | 0.851294 | − | 0.524689i | \(-0.175818\pi\) | ||||
0.851294 | + | 0.524689i | \(0.175818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.3121 | −1.44367 | −0.721835 | − | 0.692066i | \(-0.756701\pi\) | ||||
−0.721835 | + | 0.692066i | \(0.756701\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.28415 | −0.146003 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.48604 | 0.288868 | 0.144434 | − | 0.989514i | \(-0.453864\pi\) | ||||
0.144434 | + | 0.989514i | \(0.453864\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.819791 | −0.0278737 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.1421 | −0.548215 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34.7911 | −1.18021 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.0319 | 1.62750 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.5613 | 0.560516 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.76322 | −0.330057 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.5488 | −0.592582 | −0.296291 | − | 0.955098i | \(-0.595750\pi\) | ||||
−0.296291 | + | 0.955098i | \(0.595750\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.2144 | −0.445710 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.7313 | 0.664764 | 0.332382 | − | 0.943145i | \(-0.392148\pi\) | ||||
0.332382 | + | 0.943145i | \(0.392148\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.1873 | 1.55432 | 0.777162 | − | 0.629300i | \(-0.216658\pi\) | ||||
0.777162 | + | 0.629300i | \(0.216658\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.72906 | −0.259809 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.8113 | −1.33673 | −0.668367 | − | 0.743832i | \(-0.733006\pi\) | ||||
−0.668367 | + | 0.743832i | \(0.733006\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.06058 | 0.102648 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.94567 | −0.132185 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.8565 | 0.597543 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.5381 | 0.452530 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.47283 | 0.182733 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.8176 | 0.761008 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.35569 | −0.145109 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.70265 | −0.322884 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.68168 | 0.222107 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.5481 | 1.71163 | 0.855814 | − | 0.517284i | \(-0.173057\pi\) | ||||
0.855814 | + | 0.517284i | \(0.173057\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.1079 | 0.401595 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.7842 | 0.556085 | 0.278042 | − | 0.960569i | \(-0.410314\pi\) | ||||
0.278042 | + | 0.960569i | \(0.410314\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.8066 | −0.920264 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.5613 | −0.481383 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.8913 | −0.359664 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.2508 | −0.898920 | −0.449460 | − | 0.893300i | \(-0.648384\pi\) | ||||
−0.449460 | + | 0.893300i | \(0.648384\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.92622 | 0.294129 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 69.2221 | 2.27847 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.03265 | −0.231232 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.87189 | −0.291391 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.04514 | 0.165526 | 0.0827628 | − | 0.996569i | \(-0.473626\pi\) | ||||
0.0827628 | + | 0.996569i | \(0.473626\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.28415 | −0.0748599 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.1817 | −0.497027 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.07450 | 0.133250 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.64903 | 0.0865402 | 0.0432701 | − | 0.999063i | \(-0.486222\pi\) | ||||
0.0432701 | + | 0.999063i | \(0.486222\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.1560 | 0.723035 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.7019 | −1.06605 | −0.533026 | − | 0.846099i | \(-0.678945\pi\) | ||||
−0.533026 | + | 0.846099i | \(0.678945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.28415 | 0.139511 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.11491 | 0.0362679 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.8216 | −0.514132 | −0.257066 | − | 0.966394i | \(-0.582756\pi\) | ||||
−0.257066 | + | 0.966394i | \(0.582756\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.0815 | 1.39849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.2081 | 0.395876 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.7655 | 0.867018 | 0.433509 | − | 0.901149i | \(-0.357275\pi\) | ||||
0.433509 | + | 0.901149i | \(0.357275\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.1196 | −0.489260 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.2104 | −0.330054 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.3774 | 0.367395 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.7493 | 1.50804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.93246 | −0.126722 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.08226 | −0.260177 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.3400 | 0.943511 | 0.471755 | − | 0.881729i | \(-0.343621\pi\) | ||||
0.471755 | + | 0.881729i | \(0.343621\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.11562 | 0.0679637 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.9309 | 0.671706 | 0.335853 | − | 0.941914i | \(-0.390975\pi\) | ||||
0.335853 | + | 0.941914i | \(0.390975\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.8044 | 0.378430 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.5613 | 0.658490 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.0496 | 0.833401 | 0.416700 | − | 0.909044i | \(-0.363186\pi\) | ||||
0.416700 | + | 0.909044i | \(0.363186\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.162279 | −0.00518646 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.5202 | −0.527450 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 59.7882 | 1.90695 | 0.953474 | − | 0.301476i | \(-0.0974794\pi\) | ||||
0.953474 | + | 0.301476i | \(0.0974794\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.03640 | 0.128610 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.81756 | −0.248836 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.70265 | 0.308526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.0062 | 0.953180 | 0.476590 | − | 0.879126i | \(-0.341873\pi\) | ||||
0.476590 | + | 0.879126i | \(0.341873\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.4791 | −0.491214 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.04113 | −0.191517 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.82853 | 0.247932 | 0.123966 | − | 0.992286i | \(-0.460439\pi\) | ||||
0.123966 | + | 0.992286i | \(0.460439\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.87189 | 0.0592239 |
(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 | 3864.2.a.p.1.3 | ✓ | 3 | |
4.3 | odd | 2 | 7728.2.a.bp.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.p.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
7728.2.a.bp.1.3 | 3 | 4.3 | odd | 2 |