Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,3,Mod(53,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.88557371018\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.629407744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 53.4 | ||
Root | \(0.767178 + 1.18804i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.53 |
Dual form | 216.3.h.e.53.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.420861 | + | 1.95522i | −0.210431 | + | 0.977609i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.64575 | − | 1.64575i | −0.911438 | − | 0.411438i | ||||
\(5\) | −2.22699 | −0.445398 | −0.222699 | − | 0.974887i | \(-0.571487\pi\) | ||||
−0.222699 | + | 0.974887i | \(0.571487\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.64575 | −1.23511 | −0.617554 | − | 0.786529i | \(-0.711876\pi\) | ||||
−0.617554 | + | 0.786529i | \(0.711876\pi\) | |||||||
\(8\) | 4.75216 | − | 6.43560i | 0.594020 | − | 0.804450i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.937254 | − | 4.35425i | 0.0937254 | − | 0.435425i | ||||
\(11\) | 19.8504 | 1.80458 | 0.902289 | − | 0.431132i | \(-0.141886\pi\) | ||||
0.902289 | + | 0.431132i | \(0.141886\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 14.5203i | − | 1.11694i | −0.829524 | − | 0.558472i | \(-0.811388\pi\) | ||
0.829524 | − | 0.558472i | \(-0.188612\pi\) | |||||||
\(14\) | 3.63866 | − | 16.9043i | 0.259905 | − | 1.20745i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 10.5830 | + | 12.0000i | 0.661438 | + | 0.750000i | ||||
\(17\) | − | 5.29570i | − | 0.311512i | −0.987796 | − | 0.155756i | \(-0.950219\pi\) | ||
0.987796 | − | 0.155756i | \(-0.0497813\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 24.2915i | − | 1.27850i | −0.768999 | − | 0.639250i | \(-0.779245\pi\) | ||
0.768999 | − | 0.639250i | \(-0.220755\pi\) | |||||||
\(20\) | 8.11905 | + | 3.66507i | 0.405952 | + | 0.183254i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.35425 | + | 38.8118i | −0.379739 | + | 1.76417i | ||||
\(23\) | − | 29.6528i | − | 1.28925i | −0.764497 | − | 0.644627i | \(-0.777013\pi\) | ||
0.764497 | − | 0.644627i | \(-0.222987\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20.0405 | −0.801621 | ||||||||
\(26\) | 28.3903 | + | 6.11102i | 1.09193 | + | 0.235039i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 31.5203 | + | 14.2288i | 1.12572 | + | 0.508170i | ||||
\(29\) | −6.13742 | −0.211635 | −0.105818 | − | 0.994386i | \(-0.533746\pi\) | ||||
−0.105818 | + | 0.994386i | \(0.533746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1255 | 0.326629 | 0.163314 | − | 0.986574i | \(-0.447782\pi\) | ||||
0.163314 | + | 0.986574i | \(0.447782\pi\) | |||||||
\(32\) | −27.9166 | + | 15.6417i | −0.872393 | + | 0.488804i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.3542 | + | 2.22876i | 0.304537 | + | 0.0655517i | ||||
\(35\) | 19.2540 | 0.550114 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 16.6458i | − | 0.449885i | −0.974372 | − | 0.224943i | \(-0.927781\pi\) | ||
0.974372 | − | 0.224943i | \(-0.0722195\pi\) | |||||||
\(38\) | 47.4952 | + | 10.2234i | 1.24987 | + | 0.269036i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.5830 | + | 14.3320i | −0.264575 | + | 0.358301i | ||||
\(41\) | 7.82087i | 0.190753i | 0.995441 | + | 0.0953765i | \(0.0304055\pi\) | ||||
−0.995441 | + | 0.0953765i | \(0.969595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.54249i | 0.0358718i | 0.999839 | + | 0.0179359i | \(0.00570948\pi\) | ||||
−0.999839 | + | 0.0179359i | \(0.994291\pi\) | |||||||
\(44\) | −72.3695 | − | 32.6687i | −1.64476 | − | 0.742472i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 57.9778 | + | 12.4797i | 1.26039 | + | 0.271299i | ||||
\(47\) | 63.7069i | 1.35547i | 0.735308 | + | 0.677733i | \(0.237037\pi\) | ||||
−0.735308 | + | 0.677733i | \(0.762963\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 25.7490 | 0.525490 | ||||||||
\(50\) | 8.43428 | − | 39.1836i | 0.168686 | − | 0.783671i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −23.8967 | + | 52.9373i | −0.459553 | + | 1.01802i | ||||
\(53\) | −76.5253 | −1.44387 | −0.721936 | − | 0.691959i | \(-0.756748\pi\) | ||||
−0.721936 | + | 0.691959i | \(0.756748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −44.2065 | −0.803755 | ||||||||
\(56\) | −41.0860 | + | 55.6406i | −0.733678 | + | 0.993583i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.58301 | − | 12.0000i | 0.0445346 | − | 0.206897i | ||||
\(59\) | 41.0332 | 0.695477 | 0.347739 | − | 0.937592i | \(-0.386950\pi\) | ||||
0.347739 | + | 0.937592i | \(0.386950\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 52.0627i | − | 0.853488i | −0.904373 | − | 0.426744i | \(-0.859661\pi\) | ||
0.904373 | − | 0.426744i | \(-0.140339\pi\) | |||||||
\(62\) | −4.26143 | + | 19.7975i | −0.0687327 | + | 0.319315i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −18.8340 | − | 61.1660i | −0.294281 | − | 0.955719i | ||||
\(65\) | 32.3365i | 0.497484i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 110.247i | − | 1.64548i | −0.568419 | − | 0.822739i | \(-0.692445\pi\) | ||
0.568419 | − | 0.822739i | \(-0.307555\pi\) | |||||||
\(68\) | −8.71541 | + | 19.3068i | −0.128168 | + | 0.283924i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.10326 | + | 37.6458i | −0.115761 | + | 0.537796i | ||||
\(71\) | − | 100.690i | − | 1.41817i | −0.705125 | − | 0.709083i | \(-0.749109\pi\) | ||
0.705125 | − | 0.709083i | \(-0.250891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −93.9150 | −1.28651 | −0.643254 | − | 0.765653i | \(-0.722416\pi\) | ||||
−0.643254 | + | 0.765653i | \(0.722416\pi\) | |||||||
\(74\) | 32.5461 | + | 7.00555i | 0.439812 | + | 0.0946697i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −39.9778 | + | 88.5608i | −0.526023 | + | 1.16527i | ||||
\(77\) | −171.621 | −2.22885 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.7712 | −0.136345 | −0.0681724 | − | 0.997674i | \(-0.521717\pi\) | ||||
−0.0681724 | + | 0.997674i | \(0.521717\pi\) | |||||||
\(80\) | −23.5682 | − | 26.7239i | −0.294603 | − | 0.334048i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.2915 | − | 3.29150i | −0.186482 | − | 0.0401403i | ||||
\(83\) | 118.996 | 1.43369 | 0.716846 | − | 0.697231i | \(-0.245585\pi\) | ||||
0.716846 | + | 0.697231i | \(0.245585\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.7935i | 0.138747i | ||||||||
\(86\) | −3.01590 | − | 0.649173i | −0.0350686 | − | 0.00754853i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 94.3320 | − | 127.749i | 1.07195 | − | 1.45169i | ||||
\(89\) | 146.071i | 1.64125i | 0.571466 | + | 0.820626i | \(0.306375\pi\) | ||||
−0.571466 | + | 0.820626i | \(0.693625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 125.539i | 1.37954i | ||||||||
\(92\) | −48.8012 | + | 108.107i | −0.530448 | + | 1.17508i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −124.561 | − | 26.8118i | −1.32511 | − | 0.285232i | ||||
\(95\) | 54.0969i | 0.569441i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.70850 | −0.0382319 | −0.0191160 | − | 0.999817i | \(-0.506085\pi\) | ||||
−0.0191160 | + | 0.999817i | \(0.506085\pi\) | |||||||
\(98\) | −10.8368 | + | 50.3449i | −0.110579 | + | 0.513724i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 73.0627 | + | 32.9817i | 0.730627 | + | 0.329817i | ||||
\(101\) | −109.598 | −1.08513 | −0.542563 | − | 0.840015i | \(-0.682546\pi\) | ||||
−0.542563 | + | 0.840015i | \(0.682546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 159.391 | 1.54748 | 0.773742 | − | 0.633501i | \(-0.218383\pi\) | ||||
0.773742 | + | 0.633501i | \(0.218383\pi\) | |||||||
\(104\) | −93.4466 | − | 69.0026i | −0.898525 | − | 0.663486i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 32.2065 | − | 149.624i | 0.303835 | − | 1.41154i | ||||
\(107\) | 49.8355 | 0.465752 | 0.232876 | − | 0.972506i | \(-0.425186\pi\) | ||||
0.232876 | + | 0.972506i | \(0.425186\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 115.956i | 1.06381i | 0.846803 | + | 0.531906i | \(0.178524\pi\) | ||||
−0.846803 | + | 0.531906i | \(0.821476\pi\) | |||||||
\(110\) | 18.6048 | − | 86.4334i | 0.169135 | − | 0.785758i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −91.4980 | − | 103.749i | −0.816947 | − | 0.926330i | ||||
\(113\) | − | 170.025i | − | 1.50464i | −0.658796 | − | 0.752322i | \(-0.728934\pi\) | ||
0.658796 | − | 0.752322i | \(-0.271066\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 66.0366i | 0.574231i | ||||||||
\(116\) | 22.3755 | + | 10.1007i | 0.192892 | + | 0.0870748i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.2693 | + | 80.2288i | −0.146350 | + | 0.679905i | ||||
\(119\) | 45.7853i | 0.384751i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 273.037 | 2.25650 | ||||||||
\(122\) | 101.794 | + | 21.9112i | 0.834377 | + | 0.179600i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −36.9150 | − | 16.6640i | −0.297702 | − | 0.134387i | ||||
\(125\) | 100.305 | 0.802438 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −106.583 | −0.839236 | −0.419618 | − | 0.907701i | \(-0.637836\pi\) | ||||
−0.419618 | + | 0.907701i | \(0.637836\pi\) | |||||||
\(128\) | 127.519 | − | 11.0821i | 0.996245 | − | 0.0865792i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −63.2248 | − | 13.6092i | −0.486345 | − | 0.104686i | ||||
\(131\) | 65.5488 | 0.500372 | 0.250186 | − | 0.968198i | \(-0.419508\pi\) | ||||
0.250186 | + | 0.968198i | \(0.419508\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 210.018i | 1.57908i | ||||||||
\(134\) | 215.557 | + | 46.3987i | 1.60863 | + | 0.346259i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −34.0810 | − | 25.1660i | −0.250596 | − | 0.185044i | ||||
\(137\) | − | 141.829i | − | 1.03525i | −0.855609 | − | 0.517623i | \(-0.826817\pi\) | ||
0.855609 | − | 0.517623i | \(-0.173183\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 171.207i | 1.23170i | 0.787863 | + | 0.615851i | \(0.211188\pi\) | ||||
−0.787863 | + | 0.615851i | \(0.788812\pi\) | |||||||
\(140\) | −70.1953 | − | 31.6873i | −0.501395 | − | 0.226338i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 196.871 | + | 42.3765i | 1.38641 | + | 0.298426i | ||||
\(143\) | − | 288.232i | − | 2.01561i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.6680 | 0.0942619 | ||||||||
\(146\) | 39.5252 | − | 183.624i | 0.270721 | − | 1.25770i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −27.3948 | + | 60.6863i | −0.185100 | + | 0.410042i | ||||
\(149\) | 216.916 | 1.45581 | 0.727905 | − | 0.685678i | \(-0.240494\pi\) | ||||
0.727905 | + | 0.685678i | \(0.240494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −60.7268 | −0.402164 | −0.201082 | − | 0.979574i | \(-0.564446\pi\) | ||||
−0.201082 | + | 0.979574i | \(0.564446\pi\) | |||||||
\(152\) | −156.330 | − | 115.437i | −1.02849 | − | 0.759454i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 72.2288 | − | 335.557i | 0.469018 | − | 2.17894i | ||||
\(155\) | −22.5494 | −0.145480 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 192.207i | − | 1.22425i | −0.790763 | − | 0.612123i | \(-0.790316\pi\) | ||
0.790763 | − | 0.612123i | \(-0.209684\pi\) | |||||||
\(158\) | 4.53320 | − | 21.0601i | 0.0286911 | − | 0.133292i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 62.1699 | − | 34.8340i | 0.388562 | − | 0.217712i | ||||
\(161\) | 256.371i | 1.59237i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.29150i | 0.0385982i | 0.999814 | + | 0.0192991i | \(0.00614347\pi\) | ||||
−0.999814 | + | 0.0192991i | \(0.993857\pi\) | |||||||
\(164\) | 12.8712 | − | 28.5129i | 0.0784830 | − | 0.173859i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −50.0810 | + | 232.664i | −0.301693 | + | 1.40159i | ||||
\(167\) | 214.092i | 1.28199i | 0.767545 | + | 0.640995i | \(0.221478\pi\) | ||||
−0.767545 | + | 0.640995i | \(0.778522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −41.8379 | −0.247562 | ||||||||
\(170\) | −23.0588 | − | 4.96342i | −0.135640 | − | 0.0291966i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.53855 | − | 5.62352i | 0.0147590 | − | 0.0326949i | ||||
\(173\) | 44.0491 | 0.254619 | 0.127309 | − | 0.991863i | \(-0.459366\pi\) | ||||
0.127309 | + | 0.991863i | \(0.459366\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 173.265 | 0.990088 | ||||||||
\(176\) | 210.076 | + | 238.204i | 1.19362 | + | 1.35343i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −285.601 | − | 61.4758i | −1.60450 | − | 0.345370i | ||||
\(179\) | −132.570 | −0.740613 | −0.370306 | − | 0.928910i | \(-0.620747\pi\) | ||||
−0.370306 | + | 0.928910i | \(0.620747\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 141.516i | 0.781858i | 0.920421 | + | 0.390929i | \(0.127846\pi\) | ||||
−0.920421 | + | 0.390929i | \(0.872154\pi\) | |||||||
\(182\) | −245.455 | − | 52.8343i | −1.34865 | − | 0.290299i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −190.834 | − | 140.915i | −1.03714 | − | 0.765843i | ||||
\(185\) | 37.0699i | 0.200378i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 105.122i | − | 0.562147i | ||||||
\(188\) | 104.846 | − | 232.259i | 0.557690 | − | 1.23542i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −105.771 | − | 22.7673i | −0.556691 | − | 0.119828i | ||||
\(191\) | − | 1.45679i | − | 0.00762718i | −0.999993 | − | 0.00381359i | \(-0.998786\pi\) | ||
0.999993 | − | 0.00381359i | \(-0.00121391\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −243.539 | −1.26186 | −0.630929 | − | 0.775841i | \(-0.717326\pi\) | ||||
−0.630929 | + | 0.775841i | \(0.717326\pi\) | |||||||
\(194\) | 1.56076 | − | 7.25092i | 0.00804517 | − | 0.0373759i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −93.8745 | − | 42.3765i | −0.478952 | − | 0.216207i | ||||
\(197\) | −4.99752 | −0.0253681 | −0.0126841 | − | 0.999920i | \(-0.504038\pi\) | ||||
−0.0126841 | + | 0.999920i | \(0.504038\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 102.476 | 0.514954 | 0.257477 | − | 0.966284i | \(-0.417109\pi\) | ||||
0.257477 | + | 0.966284i | \(0.417109\pi\) | |||||||
\(200\) | −95.2357 | + | 128.973i | −0.476179 | + | 0.644864i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 46.1255 | − | 214.288i | 0.228344 | − | 1.06083i | ||||
\(203\) | 53.0626 | 0.261392 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 17.4170i | − | 0.0849610i | ||||||
\(206\) | −67.0815 | + | 311.644i | −0.325638 | + | 1.51283i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 174.243 | − | 153.668i | 0.837707 | − | 0.738788i | ||||
\(209\) | − | 482.195i | − | 2.30715i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.54642i | 0.0452437i | 0.999744 | + | 0.0226219i | \(0.00720138\pi\) | ||||
−0.999744 | + | 0.0226219i | \(0.992799\pi\) | |||||||
\(212\) | 278.992 | + | 125.942i | 1.31600 | + | 0.594064i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20.9738 | + | 97.4392i | −0.0980086 | + | 0.455323i | ||||
\(215\) | − | 3.43510i | − | 0.0159772i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −87.5425 | −0.403422 | ||||||||
\(218\) | −226.718 | − | 48.8012i | −1.03999 | − | 0.223859i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 161.166 | + | 72.7530i | 0.732573 | + | 0.330695i | ||||
\(221\) | −76.8950 | −0.347941 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 51.1294 | 0.229280 | 0.114640 | − | 0.993407i | \(-0.463429\pi\) | ||||
0.114640 | + | 0.993407i | \(0.463429\pi\) | |||||||
\(224\) | 241.360 | − | 135.235i | 1.07750 | − | 0.603726i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 332.435 | + | 71.5568i | 1.47095 | + | 0.316623i | ||||
\(227\) | −235.539 | −1.03762 | −0.518809 | − | 0.854890i | \(-0.673624\pi\) | ||||
−0.518809 | + | 0.854890i | \(0.673624\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 206.332i | 0.901013i | 0.892773 | + | 0.450507i | \(0.148757\pi\) | ||||
−0.892773 | + | 0.450507i | \(0.851243\pi\) | |||||||
\(230\) | −129.116 | − | 27.7923i | −0.561373 | − | 0.120836i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −29.1660 | + | 39.4980i | −0.125716 | + | 0.170250i | ||||
\(233\) | 210.356i | 0.902815i | 0.892318 | + | 0.451407i | \(0.149078\pi\) | ||||
−0.892318 | + | 0.451407i | \(0.850922\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 141.875i | − | 0.603721i | ||||||
\(236\) | −149.597 | − | 67.5304i | −0.633884 | − | 0.286146i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −89.5203 | − | 19.2693i | −0.376136 | − | 0.0809633i | ||||
\(239\) | − | 23.1457i | − | 0.0968440i | −0.998827 | − | 0.0484220i | \(-0.984581\pi\) | ||
0.998827 | − | 0.0484220i | \(-0.0154192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 81.6275 | 0.338703 | 0.169352 | − | 0.985556i | \(-0.445833\pi\) | ||||
0.169352 | + | 0.985556i | \(0.445833\pi\) | |||||||
\(242\) | −114.911 | + | 533.846i | −0.474837 | + | 2.20597i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −85.6823 | + | 189.808i | −0.351157 | + | 0.777901i | ||||
\(245\) | −57.3428 | −0.234052 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −352.719 | −1.42801 | ||||||||
\(248\) | 48.1179 | − | 65.1637i | 0.194024 | − | 0.262757i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −42.2144 | + | 196.118i | −0.168858 | + | 0.784470i | ||||
\(251\) | −232.769 | −0.927366 | −0.463683 | − | 0.886001i | \(-0.653472\pi\) | ||||
−0.463683 | + | 0.886001i | \(0.653472\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 588.620i | − | 2.32656i | ||||||
\(254\) | 44.8567 | − | 208.393i | 0.176601 | − | 0.820445i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.0000 | + | 253.992i | −0.125000 | + | 0.992157i | ||||
\(257\) | 298.491i | 1.16145i | 0.814102 | + | 0.580723i | \(0.197230\pi\) | ||||
−0.814102 | + | 0.580723i | \(0.802770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 143.915i | 0.555656i | ||||||||
\(260\) | 53.2178 | − | 117.891i | 0.204684 | − | 0.453426i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −27.5869 | + | 128.162i | −0.105294 | + | 0.489168i | ||||
\(263\) | 400.163i | 1.52153i | 0.649027 | + | 0.760766i | \(0.275176\pi\) | ||||
−0.649027 | + | 0.760766i | \(0.724824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 170.421 | 0.643098 | ||||||||
\(266\) | −410.631 | − | 88.3886i | −1.54373 | − | 0.332288i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −181.439 | + | 401.933i | −0.677012 | + | 1.49975i | ||||
\(269\) | 446.650 | 1.66041 | 0.830205 | − | 0.557459i | \(-0.188224\pi\) | ||||
0.830205 | + | 0.557459i | \(0.188224\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.3503 | −0.111994 | −0.0559969 | − | 0.998431i | \(-0.517834\pi\) | ||||
−0.0559969 | + | 0.998431i | \(0.517834\pi\) | |||||||
\(272\) | 63.5484 | − | 56.0444i | 0.233634 | − | 0.206046i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 277.306 | + | 59.6902i | 1.01207 | + | 0.217847i | ||||
\(275\) | −397.811 | −1.44659 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 149.284i | − | 0.538930i | −0.963010 | − | 0.269465i | \(-0.913153\pi\) | ||
0.963010 | − | 0.269465i | \(-0.0868469\pi\) | |||||||
\(278\) | −334.746 | − | 72.0542i | −1.20412 | − | 0.259188i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 91.4980 | − | 123.911i | 0.326779 | − | 0.442540i | ||||
\(281\) | − | 81.9607i | − | 0.291675i | −0.989309 | − | 0.145838i | \(-0.953412\pi\) | ||
0.989309 | − | 0.145838i | \(-0.0465877\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 462.207i | − | 1.63324i | −0.577177 | − | 0.816619i | \(-0.695846\pi\) | ||
0.577177 | − | 0.816619i | \(-0.304154\pi\) | |||||||
\(284\) | −165.710 | + | 367.090i | −0.583488 | + | 1.29257i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 563.557 | + | 121.306i | 1.97048 | + | 0.424146i | ||||
\(287\) | − | 67.6173i | − | 0.235600i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 260.956 | 0.902960 | ||||||||
\(290\) | −5.75233 | + | 26.7239i | −0.0198356 | + | 0.0921513i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 342.391 | + | 154.561i | 1.17257 | + | 0.529318i | ||||
\(293\) | 335.860 | 1.14628 | 0.573139 | − | 0.819458i | \(-0.305725\pi\) | ||||
0.573139 | + | 0.819458i | \(0.305725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −91.3804 | −0.309764 | ||||||||
\(296\) | −107.125 | − | 79.1032i | −0.361910 | − | 0.267241i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −91.2915 | + | 424.118i | −0.306347 | + | 1.42321i | ||||
\(299\) | −430.567 | −1.44002 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 13.3360i | − | 0.0443055i | ||||||
\(302\) | 25.5576 | − | 118.734i | 0.0846277 | − | 0.393159i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 291.498 | − | 257.077i | 0.958875 | − | 0.845648i | ||||
\(305\) | 115.943i | 0.380142i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 40.6275i | 0.132337i | 0.997808 | + | 0.0661685i | \(0.0210775\pi\) | ||||
−0.997808 | + | 0.0661685i | \(0.978923\pi\) | |||||||
\(308\) | 625.688 | + | 282.446i | 2.03146 | + | 0.917032i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.49016 | − | 44.0889i | 0.0306134 | − | 0.142222i | ||||
\(311\) | 30.9512i | 0.0995215i | 0.998761 | + | 0.0497608i | \(0.0158459\pi\) | ||||
−0.998761 | + | 0.0497608i | \(0.984154\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −285.612 | −0.912497 | −0.456249 | − | 0.889852i | \(-0.650807\pi\) | ||||
−0.456249 | + | 0.889852i | \(0.650807\pi\) | |||||||
\(314\) | 375.806 | + | 80.8923i | 1.19683 | + | 0.257619i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 39.2693 | + | 17.7268i | 0.124270 | + | 0.0560974i | ||||
\(317\) | 173.426 | 0.547084 | 0.273542 | − | 0.961860i | \(-0.411805\pi\) | ||||
0.273542 | + | 0.961860i | \(0.411805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −121.830 | −0.381912 | ||||||||
\(320\) | 41.9431 | + | 136.216i | 0.131072 | + | 0.425675i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −501.261 | − | 107.897i | −1.55671 | − | 0.335083i | ||||
\(323\) | −128.641 | −0.398268 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 290.994i | 0.895365i | ||||||||
\(326\) | −12.3013 | − | 2.64785i | −0.0377339 | − | 0.00812224i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 50.3320 | + | 37.1660i | 0.153451 | + | 0.113311i | ||||
\(329\) | − | 550.794i | − | 1.67414i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 228.705i | − | 0.690950i | −0.938428 | − | 0.345475i | \(-0.887718\pi\) | ||
0.938428 | − | 0.345475i | \(-0.112282\pi\) | |||||||
\(332\) | −433.832 | − | 195.839i | −1.30672 | − | 0.589875i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −418.597 | − | 90.1033i | −1.25329 | − | 0.269770i | ||||
\(335\) | 245.519i | 0.732893i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −403.207 | −1.19646 | −0.598229 | − | 0.801325i | \(-0.704129\pi\) | ||||
−0.598229 | + | 0.801325i | \(0.704129\pi\) | |||||||
\(338\) | 17.6080 | − | 81.8022i | 0.0520946 | − | 0.242018i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.4091 | − | 42.9961i | 0.0570856 | − | 0.126459i | ||||
\(341\) | 200.995 | 0.589427 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 201.022 | 0.586071 | ||||||||
\(344\) | 9.92683 | + | 7.33014i | 0.0288571 | + | 0.0213086i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.5385 | + | 86.1255i | −0.0535796 | + | 0.248918i | ||||
\(347\) | −166.941 | −0.481097 | −0.240548 | − | 0.970637i | \(-0.577327\pi\) | ||||
−0.240548 | + | 0.970637i | \(0.577327\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 552.395i | − | 1.58279i | −0.611303 | − | 0.791397i | \(-0.709354\pi\) | ||
0.611303 | − | 0.791397i | \(-0.290646\pi\) | |||||||
\(350\) | −72.9207 | + | 338.771i | −0.208345 | + | 0.967918i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −554.154 | + | 310.494i | −1.57430 | + | 0.882085i | ||||
\(353\) | − | 54.0815i | − | 0.153205i | −0.997062 | − | 0.0766027i | \(-0.975593\pi\) | ||
0.997062 | − | 0.0766027i | \(-0.0244073\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 224.235i | 0.631649i | ||||||||
\(356\) | 240.397 | − | 532.540i | 0.675273 | − | 1.49590i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 55.7935 | − | 259.203i | 0.155848 | − | 0.724030i | ||||
\(359\) | − | 623.374i | − | 1.73642i | −0.496198 | − | 0.868209i | \(-0.665271\pi\) | ||
0.496198 | − | 0.868209i | \(-0.334729\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −229.077 | −0.634563 | ||||||||
\(362\) | −276.695 | − | 59.5588i | −0.764351 | − | 0.164527i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 206.605 | − | 457.682i | 0.567597 | − | 1.25737i | ||||
\(365\) | 209.148 | 0.573008 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 61.2653 | 0.166936 | 0.0834678 | − | 0.996510i | \(-0.473400\pi\) | ||||
0.0834678 | + | 0.996510i | \(0.473400\pi\) | |||||||
\(368\) | 355.834 | − | 313.816i | 0.966941 | − | 0.852762i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −72.4797 | − | 15.6013i | −0.195891 | − | 0.0421657i | ||||
\(371\) | 661.618 | 1.78334 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 72.7712i | 0.195097i | 0.995231 | + | 0.0975486i | \(0.0311001\pi\) | ||||
−0.995231 | + | 0.0975486i | \(0.968900\pi\) | |||||||
\(374\) | 205.536 | + | 44.2416i | 0.549560 | + | 0.118293i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 409.992 | + | 302.745i | 1.09040 | + | 0.805173i | ||||
\(377\) | 89.1170i | 0.236385i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 341.405i | − | 0.900805i | −0.892826 | − | 0.450403i | \(-0.851280\pi\) | ||
0.892826 | − | 0.450403i | \(-0.148720\pi\) | |||||||
\(380\) | 89.0301 | − | 197.224i | 0.234290 | − | 0.519010i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.84834 | + | 0.613107i | 0.00745640 | + | 0.00160499i | ||||
\(383\) | 318.059i | 0.830441i | 0.909721 | + | 0.415221i | \(0.136296\pi\) | ||||
−0.909721 | + | 0.415221i | \(0.863704\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 382.199 | 0.992724 | ||||||||
\(386\) | 102.496 | − | 476.171i | 0.265534 | − | 1.23360i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.5203 | + | 6.10326i | 0.0348460 | + | 0.0157301i | ||||
\(389\) | 308.645 | 0.793432 | 0.396716 | − | 0.917941i | \(-0.370150\pi\) | ||||
0.396716 | + | 0.917941i | \(0.370150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −157.033 | −0.401618 | ||||||||
\(392\) | 122.363 | − | 165.710i | 0.312152 | − | 0.422731i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.10326 | − | 9.77124i | 0.00533823 | − | 0.0248001i | ||||
\(395\) | 23.9874 | 0.0607277 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 172.044i | − | 0.433361i | −0.976243 | − | 0.216681i | \(-0.930477\pi\) | ||
0.976243 | − | 0.216681i | \(-0.0695230\pi\) | |||||||
\(398\) | −43.1281 | + | 200.362i | −0.108362 | + | 0.503423i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −212.089 | − | 240.486i | −0.530222 | − | 0.601216i | ||||
\(401\) | − | 329.110i | − | 0.820724i | −0.911923 | − | 0.410362i | \(-0.865402\pi\) | ||
0.911923 | − | 0.410362i | \(-0.134598\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 147.025i | − | 0.364826i | ||||||
\(404\) | 399.566 | + | 180.371i | 0.989026 | + | 0.446462i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.3320 | + | 103.749i | −0.0550050 | + | 0.255539i | ||||
\(407\) | − | 330.424i | − | 0.811853i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −353.458 | −0.864199 | −0.432100 | − | 0.901826i | \(-0.642227\pi\) | ||||
−0.432100 | + | 0.901826i | \(0.642227\pi\) | |||||||
\(410\) | 34.0540 | + | 7.33014i | 0.0830586 | + | 0.0178784i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −581.099 | − | 262.318i | −1.41044 | − | 0.636693i | ||||
\(413\) | −354.763 | −0.858989 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −265.004 | −0.638564 | ||||||||
\(416\) | 227.122 | + | 405.356i | 0.545967 | + | 0.974414i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 942.796 | + | 202.937i | 2.25549 | + | 0.485496i | ||||
\(419\) | 327.287 | 0.781115 | 0.390557 | − | 0.920579i | \(-0.372282\pi\) | ||||
0.390557 | + | 0.920579i | \(0.372282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 501.759i | 1.19183i | 0.803048 | + | 0.595914i | \(0.203210\pi\) | ||||
−0.803048 | + | 0.595914i | \(0.796790\pi\) | |||||||
\(422\) | −18.6653 | − | 4.01772i | −0.0442307 | − | 0.00952067i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −363.660 | + | 492.486i | −0.857689 | + | 1.16152i | ||||
\(425\) | 106.129i | 0.249714i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 450.122i | 1.05415i | ||||||||
\(428\) | −181.688 | − | 82.0168i | −0.424504 | − | 0.191628i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.71637 | + | 1.44570i | 0.0156195 | + | 0.00336210i | ||||
\(431\) | − | 29.8267i | − | 0.0692035i | −0.999401 | − | 0.0346017i | \(-0.988984\pi\) | ||
0.999401 | − | 0.0346017i | \(-0.0110163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 519.859 | 1.20060 | 0.600299 | − | 0.799776i | \(-0.295048\pi\) | ||||
0.600299 | + | 0.799776i | \(0.295048\pi\) | |||||||
\(434\) | 36.8433 | − | 171.165i | 0.0848923 | − | 0.394388i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 190.834 | − | 422.745i | 0.437693 | − | 0.969599i | ||||
\(437\) | −720.312 | −1.64831 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 386.450 | 0.880295 | 0.440148 | − | 0.897925i | \(-0.354926\pi\) | ||||
0.440148 | + | 0.897925i | \(0.354926\pi\) | |||||||
\(440\) | −210.076 | + | 284.496i | −0.477446 | + | 0.646581i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 32.3621 | − | 150.346i | 0.0732175 | − | 0.340150i | ||||
\(443\) | 378.527 | 0.854462 | 0.427231 | − | 0.904143i | \(-0.359489\pi\) | ||||
0.427231 | + | 0.904143i | \(0.359489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 325.299i | − | 0.731010i | ||||||
\(446\) | −21.5184 | + | 99.9692i | −0.0482475 | + | 0.224146i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 162.834 | + | 528.826i | 0.363469 | + | 1.18042i | ||||
\(449\) | 289.127i | 0.643935i | 0.946751 | + | 0.321968i | \(0.104344\pi\) | ||||
−0.946751 | + | 0.321968i | \(0.895656\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 155.247i | 0.344228i | ||||||||
\(452\) | −279.818 | + | 619.868i | −0.619067 | + | 1.37139i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 99.1294 | − | 460.531i | 0.218347 | − | 1.01438i | ||||
\(455\) | − | 279.573i | − | 0.614446i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 485.365 | 1.06207 | 0.531034 | − | 0.847351i | \(-0.321804\pi\) | ||||
0.531034 | + | 0.847351i | \(0.321804\pi\) | |||||||
\(458\) | −403.424 | − | 86.8372i | −0.880838 | − | 0.189601i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 108.680 | − | 240.753i | 0.236260 | − | 0.523376i | ||||
\(461\) | −215.037 | −0.466457 | −0.233228 | − | 0.972422i | \(-0.574929\pi\) | ||||
−0.233228 | + | 0.972422i | \(0.574929\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −374.755 | −0.809407 | −0.404704 | − | 0.914448i | \(-0.632625\pi\) | ||||
−0.404704 | + | 0.914448i | \(0.632625\pi\) | |||||||
\(464\) | −64.9524 | − | 73.6491i | −0.139984 | − | 0.158726i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −411.292 | − | 88.5307i | −0.882600 | − | 0.189980i | ||||
\(467\) | −268.050 | −0.573982 | −0.286991 | − | 0.957933i | \(-0.592655\pi\) | ||||
−0.286991 | + | 0.957933i | \(0.592655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 953.169i | 2.03234i | ||||||||
\(470\) | 277.396 | + | 59.7095i | 0.590203 | + | 0.127042i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 194.996 | − | 264.073i | 0.413127 | − | 0.559477i | ||||
\(473\) | 30.6189i | 0.0647334i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 486.814i | 1.02487i | ||||||||
\(476\) | 75.3512 | − | 166.922i | 0.158301 | − | 0.350676i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 45.2549 | + | 9.74114i | 0.0946756 | + | 0.0203790i | ||||
\(479\) | 512.109i | 1.06912i | 0.845130 | + | 0.534560i | \(0.179523\pi\) | ||||
−0.845130 | + | 0.534560i | \(0.820477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −241.701 | −0.502496 | ||||||||
\(482\) | −34.3538 | + | 159.599i | −0.0712735 | + | 0.331119i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −995.423 | − | 449.350i | −2.05666 | − | 0.928410i | ||||
\(485\) | 8.25878 | 0.0170284 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 885.804 | 1.81890 | 0.909450 | − | 0.415814i | \(-0.136503\pi\) | ||||
0.909450 | + | 0.415814i | \(0.136503\pi\) | |||||||
\(488\) | −335.055 | − | 247.410i | −0.686589 | − | 0.506989i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 24.1334 | − | 112.118i | 0.0492518 | − | 0.228811i | ||||
\(491\) | 434.847 | 0.885636 | 0.442818 | − | 0.896612i | \(-0.353979\pi\) | ||||
0.442818 | + | 0.896612i | \(0.353979\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.5020i | 0.0659269i | ||||||||
\(494\) | 148.446 | − | 689.642i | 0.300498 | − | 1.39604i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 107.158 | + | 121.506i | 0.216045 | + | 0.244972i | ||||
\(497\) | 870.539i | 1.75159i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 712.980i | 1.42882i | 0.699728 | + | 0.714409i | \(0.253304\pi\) | ||||
−0.699728 | + | 0.714409i | \(0.746696\pi\) | |||||||
\(500\) | −365.686 | − | 165.077i | −0.731372 | − | 0.330153i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 97.9634 | − | 455.114i | 0.195146 | − | 0.906601i | ||||
\(503\) | − | 68.4403i | − | 0.136064i | −0.997683 | − | 0.0680321i | \(-0.978328\pi\) | ||
0.997683 | − | 0.0680321i | \(-0.0216720\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 244.073 | 0.483313 | ||||||||
\(506\) | 1150.88 | + | 247.727i | 2.27447 | + | 0.489580i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 388.575 | + | 175.409i | 0.764912 | + | 0.345294i | ||||
\(509\) | −7.45117 | −0.0146388 | −0.00731942 | − | 0.999973i | \(-0.502330\pi\) | ||||
−0.00731942 | + | 0.999973i | \(0.502330\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 811.966 | 1.58897 | ||||||||
\(512\) | −483.142 | − | 169.462i | −0.943637 | − | 0.330981i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −583.616 | − | 125.624i | −1.13544 | − | 0.244404i | ||||
\(515\) | −354.962 | −0.689246 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1264.60i | 2.44604i | ||||||||
\(518\) | −281.385 | − | 60.5683i | −0.543215 | − | 0.116927i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 208.105 | + | 153.668i | 0.400201 | + | 0.295515i | ||||
\(521\) | − | 426.007i | − | 0.817673i | −0.912608 | − | 0.408836i | \(-0.865935\pi\) | ||
0.912608 | − | 0.408836i | \(-0.134065\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 270.875i | 0.517924i | 0.965887 | + | 0.258962i | \(0.0833805\pi\) | ||||
−0.965887 | + | 0.258962i | \(0.916619\pi\) | |||||||
\(524\) | −238.974 | − | 107.877i | −0.456058 | − | 0.205872i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −782.405 | − | 168.413i | −1.48746 | − | 0.320177i | ||||
\(527\) | − | 53.6216i | − | 0.101749i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −350.292 | −0.662177 | ||||||||
\(530\) | −71.7236 | + | 333.210i | −0.135328 | + | 0.628698i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 345.638 | − | 765.674i | 0.649695 | − | 1.43924i | ||||
\(533\) | 113.561 | 0.213060 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −110.983 | −0.207445 | ||||||||
\(536\) | −709.506 | − | 523.911i | −1.32371 | − | 0.977447i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −187.978 | + | 873.298i | −0.349401 | + | 1.62323i | ||||
\(539\) | 511.127 | 0.948288 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 964.379i | − | 1.78259i | −0.453428 | − | 0.891293i | \(-0.649799\pi\) | ||
0.453428 | − | 0.891293i | \(-0.350201\pi\) | |||||||
\(542\) | 12.7733 | − | 59.3415i | 0.0235669 | − | 0.109486i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 82.8340 | + | 147.838i | 0.152268 | + | 0.271761i | ||||
\(545\) | − | 258.232i | − | 0.473820i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 485.162i | − | 0.886951i | −0.896287 | − | 0.443475i | \(-0.853745\pi\) | ||
0.896287 | − | 0.443475i | \(-0.146255\pi\) | |||||||
\(548\) | −233.415 | + | 517.072i | −0.425939 | + | 0.943562i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 167.423 | − | 777.808i | 0.304406 | − | 1.41420i | ||||
\(551\) | 149.087i | 0.270576i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 93.1255 | 0.168401 | ||||||||
\(554\) | 291.882 | + | 62.8277i | 0.526863 | + | 0.113407i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 281.763 | − | 624.176i | 0.506769 | − | 1.12262i | ||||
\(557\) | −930.917 | −1.67130 | −0.835652 | − | 0.549259i | \(-0.814910\pi\) | ||||
−0.835652 | + | 0.549259i | \(0.814910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.3973 | 0.0400667 | ||||||||
\(560\) | 203.765 | + | 231.048i | 0.363866 | + | 0.412586i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 160.251 | + | 34.4941i | 0.285144 | + | 0.0613774i | ||||
\(563\) | −511.376 | −0.908305 | −0.454153 | − | 0.890924i | \(-0.650058\pi\) | ||||
−0.454153 | + | 0.890924i | \(0.650058\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 378.643i | 0.670165i | ||||||||
\(566\) | 903.714 | + | 194.525i | 1.59667 | + | 0.343684i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −648.000 | − | 478.494i | −1.14085 | − | 0.842419i | ||||
\(569\) | − | 88.0640i | − | 0.154770i | −0.997001 | − | 0.0773849i | \(-0.975343\pi\) | ||
0.997001 | − | 0.0773849i | \(-0.0246570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 451.288i | − | 0.790346i | −0.918607 | − | 0.395173i | \(-0.870685\pi\) | ||
0.918607 | − | 0.395173i | \(-0.129315\pi\) | |||||||
\(572\) | −474.359 | + | 1050.82i | −0.829298 | + | 1.83710i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 132.207 | + | 28.4575i | 0.230325 | + | 0.0495775i | ||||
\(575\) | 594.258i | 1.03349i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −177.405 | −0.307461 | −0.153731 | − | 0.988113i | \(-0.549129\pi\) | ||||
−0.153731 | + | 0.988113i | \(0.549129\pi\) | |||||||
\(578\) | −109.826 | + | 510.225i | −0.190011 | + | 0.882742i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −49.8301 | − | 22.4941i | −0.0859139 | − | 0.0387829i | ||||
\(581\) | −1028.81 | −1.77076 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1519.05 | −2.60558 | ||||||||
\(584\) | −446.299 | + | 604.400i | −0.764211 | + | 1.03493i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −141.350 | + | 656.678i | −0.241212 | + | 1.12061i | ||||
\(587\) | −74.8077 | −0.127441 | −0.0637204 | − | 0.997968i | \(-0.520297\pi\) | ||||
−0.0637204 | + | 0.997968i | \(0.520297\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 245.963i | − | 0.417595i | ||||||
\(590\) | 38.4585 | − | 178.669i | 0.0651839 | − | 0.302828i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 199.749 | − | 176.162i | 0.337414 | − | 0.297571i | ||||
\(593\) | − | 149.087i | − | 0.251412i | −0.992068 | − | 0.125706i | \(-0.959880\pi\) | ||
0.992068 | − | 0.125706i | \(-0.0401196\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 101.963i | − | 0.171367i | ||||||
\(596\) | −790.821 | − | 356.989i | −1.32688 | − | 0.598976i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 181.209 | − | 841.852i | 0.303025 | − | 1.40778i | ||||
\(599\) | − | 234.452i | − | 0.391406i | −0.980663 | − | 0.195703i | \(-0.937301\pi\) | ||
0.980663 | − | 0.195703i | \(-0.0626989\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.8627 | 0.0347133 | 0.0173567 | − | 0.999849i | \(-0.494475\pi\) | ||||
0.0173567 | + | 0.999849i | \(0.494475\pi\) | |||||||
\(602\) | 26.0747 | + | 5.61259i | 0.0433135 | + | 0.00932324i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 221.395 | + | 99.9412i | 0.366548 | + | 0.165466i | ||||
\(605\) | −608.050 | −1.00504 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 119.103 | 0.196216 | 0.0981081 | − | 0.995176i | \(-0.468721\pi\) | ||||
0.0981081 | + | 0.995176i | \(0.468721\pi\) | |||||||
\(608\) | 379.961 | + | 678.136i | 0.624936 | + | 1.11536i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −226.694 | − | 48.7960i | −0.371630 | − | 0.0799935i | ||||
\(611\) | 925.040 | 1.51398 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 610.586i | − | 0.996061i | −0.867159 | − | 0.498031i | \(-0.834057\pi\) | ||
0.867159 | − | 0.498031i | \(-0.165943\pi\) | |||||||
\(614\) | −79.4355 | − | 17.0985i | −0.129374 | − | 0.0278478i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −815.571 | + | 1104.49i | −1.32398 | + | 1.79300i | ||||
\(617\) | 1199.40i | 1.94393i | 0.235127 | + | 0.971965i | \(0.424449\pi\) | ||||
−0.235127 | + | 0.971965i | \(0.575551\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 982.482i | 1.58721i | 0.608434 | + | 0.793604i | \(0.291798\pi\) | ||||
−0.608434 | + | 0.793604i | \(0.708202\pi\) | |||||||
\(620\) | 82.2094 | + | 37.1106i | 0.132596 | + | 0.0598559i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −60.5163 | − | 13.0262i | −0.0972931 | − | 0.0209424i | ||||
\(623\) | − | 1262.90i | − | 2.02712i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 277.635 | 0.444217 | ||||||||
\(626\) | 120.203 | − | 558.433i | 0.192017 | − | 0.892066i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −316.324 | + | 700.737i | −0.503701 | + | 1.11582i | ||||
\(629\) | −88.1509 | −0.140145 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.8928 | −0.0410345 | −0.0205173 | − | 0.999789i | \(-0.506531\pi\) | ||||
−0.0205173 | + | 0.999789i | \(0.506531\pi\) | |||||||
\(632\) | −51.1867 | + | 69.3195i | −0.0809915 | + | 0.109683i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −72.9882 | + | 339.085i | −0.115123 | + | 0.534834i | ||||
\(635\) | 237.359 | 0.373794 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 373.882i | − | 0.586943i | ||||||
\(638\) | 51.2736 | − | 238.204i | 0.0803661 | − | 0.373361i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −283.984 | + | 24.6798i | −0.443725 | + | 0.0385622i | ||||
\(641\) | 74.7736i | 0.116651i | 0.998298 | + | 0.0583257i | \(0.0185762\pi\) | ||||
−0.998298 | + | 0.0583257i | \(0.981424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 804.936i | − | 1.25184i | −0.779886 | − | 0.625922i | \(-0.784723\pi\) | ||
0.779886 | − | 0.625922i | \(-0.215277\pi\) | |||||||
\(644\) | 421.923 | − | 934.666i | 0.655160 | − | 1.45134i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 54.1398 | − | 251.520i | 0.0838078 | − | 0.389350i | ||||
\(647\) | 1114.00i | 1.72179i | 0.508782 | + | 0.860895i | \(0.330096\pi\) | ||||
−0.508782 | + | 0.860895i | \(0.669904\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 814.523 | 1.25504 | ||||||||
\(650\) | −568.956 | − | 122.468i | −0.875316 | − | 0.188412i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.3542 | − | 22.9373i | 0.0158807 | − | 0.0351798i | ||||
\(653\) | 789.281 | 1.20870 | 0.604350 | − | 0.796719i | \(-0.293433\pi\) | ||||
0.604350 | + | 0.796719i | \(0.293433\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −145.976 | −0.222865 | ||||||||
\(656\) | −93.8504 | + | 82.7683i | −0.143065 | + | 0.126171i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1076.92 | + | 231.808i | 1.63666 | + | 0.352292i | ||||
\(659\) | 1233.28 | 1.87144 | 0.935722 | − | 0.352739i | \(-0.114750\pi\) | ||||
0.935722 | + | 0.352739i | \(0.114750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.49943i | 0.00680700i | 0.999994 | + | 0.00340350i | \(0.00108337\pi\) | ||||
−0.999994 | + | 0.00340350i | \(0.998917\pi\) | |||||||
\(662\) | 447.167 | + | 96.2529i | 0.675479 | + | 0.145397i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 565.490 | − | 765.814i | 0.851642 | − | 1.15333i | ||||
\(665\) | − | 467.709i | − | 0.703321i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 181.992i | 0.272852i | ||||||||
\(668\) | 352.343 | − | 780.528i | 0.527460 | − | 1.16845i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −480.043 | − | 103.329i | −0.716482 | − | 0.154223i | ||||
\(671\) | − | 1033.46i | − | 1.54018i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −163.620 | −0.243120 | −0.121560 | − | 0.992584i | \(-0.538790\pi\) | ||||
−0.121560 | + | 0.992584i | \(0.538790\pi\) | |||||||
\(674\) | 169.694 | − | 788.356i | 0.251772 | − | 1.16967i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 152.531 | + | 68.8548i | 0.225637 | + | 0.101856i | ||||
\(677\) | −686.078 | −1.01341 | −0.506704 | − | 0.862120i | \(-0.669136\pi\) | ||||
−0.506704 | + | 0.862120i | \(0.669136\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.0627 | 0.0472205 | ||||||||
\(680\) | 75.8981 | + | 56.0444i | 0.111615 | + | 0.0824183i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −84.5909 | + | 392.988i | −0.124034 | + | 0.576229i | ||||
\(683\) | 267.879 | 0.392210 | 0.196105 | − | 0.980583i | \(-0.437171\pi\) | ||||
0.196105 | + | 0.980583i | \(0.437171\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 315.851i | 0.461096i | ||||||||
\(686\) | −84.6025 | + | 393.042i | −0.123327 | + | 0.572948i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.5098 | + | 16.3241i | −0.0269038 | + | 0.0237270i | ||||
\(689\) | 1111.17i | 1.61272i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 576.037i | − | 0.833627i | −0.908992 | − | 0.416814i | \(-0.863147\pi\) | ||
0.908992 | − | 0.416814i | \(-0.136853\pi\) | |||||||
\(692\) | −160.592 | − | 72.4938i | −0.232069 | − | 0.104760i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 70.2589 | − | 326.405i | 0.101238 | − | 0.470324i | ||||
\(695\) | − | 381.275i | − | 0.548597i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.4170 | 0.0594218 | ||||||||
\(698\) | 1080.05 | + | 232.482i | 1.54735 | + | 0.333068i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −631.682 | − | 285.152i | −0.902403 | − | 0.407360i | ||||
\(701\) | −356.794 | −0.508978 | −0.254489 | − | 0.967076i | \(-0.581907\pi\) | ||||
−0.254489 | + | 0.967076i | \(0.581907\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −404.350 | −0.575178 | ||||||||
\(704\) | −373.861 | − | 1214.17i | −0.531053 | − | 1.72467i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 105.741 | + | 22.7608i | 0.149775 | + | 0.0322391i | ||||
\(707\) | 947.555 | 1.34025 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1146.88i | 1.61760i | 0.588081 | + | 0.808802i | \(0.299884\pi\) | ||||
−0.588081 | + | 0.808802i | \(0.700116\pi\) | |||||||
\(710\) | −438.429 | − | 94.3720i | −0.617505 | − | 0.132918i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 940.057 | + | 694.154i | 1.32031 | + | 0.974936i | ||||
\(713\) | − | 300.250i | − | 0.421108i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 641.890i | 0.897749i | ||||||||
\(716\) | 483.316 | + | 218.177i | 0.675023 | + | 0.304716i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1218.83 | + | 262.354i | 1.69754 | + | 0.365396i | ||||
\(719\) | − | 79.3640i | − | 0.110381i | −0.998476 | − | 0.0551905i | \(-0.982423\pi\) | ||
0.998476 | − | 0.0551905i | \(-0.0175766\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1378.05 | −1.91131 | ||||||||
\(722\) | 96.4097 | − | 447.896i | 0.133531 | − | 0.620354i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 232.901 | − | 515.933i | 0.321686 | − | 0.712615i | ||||
\(725\) | 122.997 | 0.169651 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 871.940 | 1.19937 | 0.599683 | − | 0.800237i | \(-0.295293\pi\) | ||||
0.599683 | + | 0.800237i | \(0.295293\pi\) | |||||||
\(728\) | 807.916 | + | 596.579i | 1.10978 | + | 0.819477i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −88.0222 | + | 408.929i | −0.120578 | + | 0.560177i | ||||
\(731\) | 8.16855 | 0.0111745 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1266.45i | − | 1.72776i | −0.503696 | − | 0.863881i | \(-0.668027\pi\) | ||
0.503696 | − | 0.863881i | \(-0.331973\pi\) | |||||||
\(734\) | −25.7842 | + | 119.787i | −0.0351284 | + | 0.163198i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 463.822 | + | 827.806i | 0.630193 | + | 1.12474i | ||||
\(737\) | − | 2188.44i | − | 2.96939i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 560.199i | − | 0.758050i | −0.925387 | − | 0.379025i | \(-0.876260\pi\) | ||
0.925387 | − | 0.379025i | \(-0.123740\pi\) | |||||||
\(740\) | 61.0079 | − | 135.148i | 0.0824430 | − | 0.182632i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −278.450 | + | 1293.61i | −0.375269 | + | 1.74341i | ||||
\(743\) | 470.187i | 0.632823i | 0.948622 | + | 0.316411i | \(0.102478\pi\) | ||||
−0.948622 | + | 0.316411i | \(0.897522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −483.069 | −0.648415 | ||||||||
\(746\) | −142.284 | − | 30.6266i | −0.190729 | − | 0.0410544i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −173.004 | + | 383.247i | −0.231289 | + | 0.512362i | ||||
\(749\) | −430.865 | −0.575254 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1127.93 | 1.50190 | 0.750952 | − | 0.660357i | \(-0.229595\pi\) | ||||
0.750952 | + | 0.660357i | \(0.229595\pi\) | |||||||
\(752\) | −764.482 | + | 674.210i | −1.01660 | + | 0.896556i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −174.243 | − | 37.5059i | −0.231092 | − | 0.0497426i | ||||
\(755\) | 135.238 | 0.179123 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 450.055i | 0.594524i | 0.954796 | + | 0.297262i | \(0.0960735\pi\) | ||||
−0.954796 | + | 0.297262i | \(0.903926\pi\) | |||||||
\(758\) | 667.521 | + | 143.684i | 0.880635 | + | 0.189557i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 348.146 | + | 257.077i | 0.458087 | + | 0.338259i | ||||
\(761\) | − | 223.932i | − | 0.294261i | −0.989117 | − | 0.147130i | \(-0.952996\pi\) | ||
0.989117 | − | 0.147130i | \(-0.0470037\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1002.52i | − | 1.31392i | ||||||
\(764\) | −2.39752 | + | 5.31110i | −0.00313811 | + | 0.00695170i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −621.875 | − | 133.859i | −0.811847 | − | 0.174750i | ||||
\(767\) | − | 595.812i | − | 0.776809i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 562.393 | 0.731331 | 0.365665 | − | 0.930746i | \(-0.380841\pi\) | ||||
0.365665 | + | 0.930746i | \(0.380841\pi\) | |||||||
\(770\) | −160.853 | + | 747.282i | −0.208900 | + | 0.970495i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 887.881 | + | 400.804i | 1.15010 | + | 0.519176i | ||||
\(773\) | 857.103 | 1.10880 | 0.554400 | − | 0.832250i | \(-0.312948\pi\) | ||||
0.554400 | + | 0.832250i | \(0.312948\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −202.920 | −0.261832 | ||||||||
\(776\) | −17.6234 | + | 23.8664i | −0.0227105 | + | 0.0307557i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −129.897 | + | 603.468i | −0.166962 | + | 0.775666i | ||||
\(779\) | 189.981 | 0.243878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1998.73i | − | 2.55919i | ||||||
\(782\) | 66.0890 | − | 307.033i | 0.0845128 | − | 0.392625i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 272.502 | + | 308.988i | 0.347579 | + | 0.394118i | ||||
\(785\) | 428.042i | 0.545276i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 386.624i | − | 0.491262i | −0.969363 | − | 0.245631i | \(-0.921005\pi\) | ||
0.969363 | − | 0.245631i | \(-0.0789952\pi\) | |||||||
\(788\) | 18.2197 | + | 8.22468i | 0.0231215 | + | 0.0104374i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.0954 | + | 46.9007i | −0.0127790 | + | 0.0593679i | ||||
\(791\) | 1469.99i | 1.85840i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −755.965 | −0.953297 | ||||||||
\(794\) | 336.384 | + | 72.4069i | 0.423658 | + | 0.0911925i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −373.601 | − | 168.650i | −0.469348 | − | 0.211871i | ||||
\(797\) | 1049.51 | 1.31682 | 0.658410 | − | 0.752659i | \(-0.271229\pi\) | ||||
0.658410 | + | 0.752659i | \(0.271229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 337.373 | 0.422243 | ||||||||
\(800\) | 559.463 | − | 313.469i | 0.699329 | − | 0.391836i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 643.482 | + | 138.510i | 0.802347 | + | 0.172706i | ||||
\(803\) | −1864.25 | −2.32160 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 570.936i | − | 0.709237i | ||||||
\(806\) | 287.465 | + | 61.8771i | 0.356657 | + | 0.0767705i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −520.826 | + | 705.328i | −0.644587 | + | 0.872931i | ||||
\(809\) | 467.780i | 0.578220i | 0.957296 | + | 0.289110i | \(0.0933593\pi\) | ||||
−0.957296 | + | 0.289110i | \(0.906641\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.80922i | 0.00223085i | 0.999999 | + | 0.00111543i | \(0.000355051\pi\) | ||||
−0.999999 | + | 0.00111543i | \(0.999645\pi\) | |||||||
\(812\) | −193.453 | − | 87.3279i | −0.238243 | − | 0.107547i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 646.051 | + | 139.063i | 0.793674 | + | 0.170839i | ||||
\(815\) | − | 14.0111i | − | 0.0171915i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.4693 | 0.0458621 | ||||||||
\(818\) | 148.757 | − | 691.086i | 0.181854 | − | 0.844849i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −28.6640 | + | 63.4980i | −0.0349561 | + | 0.0774366i | ||||
\(821\) | 737.637 | 0.898462 | 0.449231 | − | 0.893416i | \(-0.351698\pi\) | ||||
0.449231 | + | 0.893416i | \(0.351698\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −290.172 | −0.352579 | −0.176289 | − | 0.984338i | \(-0.556409\pi\) | ||||
−0.176289 | + | 0.984338i | \(0.556409\pi\) | |||||||
\(824\) | 757.450 | − | 1025.78i | 0.919236 | − | 1.24487i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 149.306 | − | 693.638i | 0.180758 | − | 0.839755i | ||||
\(827\) | −429.517 | −0.519368 | −0.259684 | − | 0.965694i | \(-0.583618\pi\) | ||||
−0.259684 | + | 0.965694i | \(0.583618\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 718.136i | 0.866268i | 0.901330 | + | 0.433134i | \(0.142592\pi\) | ||||
−0.901330 | + | 0.433134i | \(0.857408\pi\) | |||||||
\(830\) | 111.530 | − | 518.140i | 0.134373 | − | 0.624265i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −888.146 | + | 273.474i | −1.06748 | + | 0.328695i | ||||
\(833\) | − | 136.359i | − | 0.163696i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 476.782i | − | 0.570996i | ||||||
\(836\) | −793.573 | + | 1757.96i | −0.949250 | + | 2.10283i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −137.743 | + | 639.918i | −0.164371 | + | 0.763625i | ||||
\(839\) | − | 1171.31i | − | 1.39608i | −0.716059 | − | 0.698040i | \(-0.754056\pi\) | ||
0.716059 | − | 0.698040i | \(-0.245944\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −803.332 | −0.955210 | ||||||||
\(842\) | −981.049 | − | 211.171i | −1.16514 | − | 0.250797i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.7110 | − | 34.8039i | 0.0186150 | − | 0.0412368i | ||||
\(845\) | 93.1726 | 0.110263 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2360.61 | −2.78702 | ||||||||
\(848\) | −809.867 | − | 918.303i | −0.955032 | − | 1.08290i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −207.505 | − | 44.6654i | −0.244123 | − | 0.0525476i | ||||
\(851\) | −493.594 | −0.580016 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 94.3059i | 0.110558i | 0.998471 | + | 0.0552789i | \(0.0176048\pi\) | ||||
−0.998471 | + | 0.0552789i | \(0.982395\pi\) | |||||||
\(854\) | −880.086 | − | 189.439i | −1.03055 | − | 0.221825i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 236.826 | − | 320.721i | 0.276666 | − | 0.374675i | ||||
\(857\) | 651.269i | 0.759940i | 0.924999 | + | 0.379970i | \(0.124066\pi\) | ||||
−0.924999 | + | 0.379970i | \(0.875934\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 470.587i | − | 0.547831i | −0.961754 | − | 0.273916i | \(-0.911681\pi\) | ||
0.961754 | − | 0.273916i | \(-0.0883189\pi\) | |||||||
\(860\) | −5.65332 | + | 12.5235i | −0.00657363 | + | 0.0145622i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 58.3177 | + | 12.5529i | 0.0676539 | + | 0.0145625i | ||||
\(863\) | 269.299i | 0.312049i | 0.987753 | + | 0.156025i | \(0.0498679\pi\) | ||||
−0.987753 | + | 0.156025i | \(0.950132\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −98.0968 | −0.113407 | ||||||||
\(866\) | −218.789 | + | 1016.44i | −0.252643 | + | 1.17371i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 319.158 | + | 144.073i | 0.367694 | + | 0.165983i | ||||
\(869\) | −213.813 | −0.246045 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1600.82 | −1.83791 | ||||||||
\(872\) | 746.244 | + | 551.039i | 0.855784 | + | 0.631926i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 303.152 | − | 1408.37i | 0.346855 | − | 1.61140i | ||||
\(875\) | −867.210 | −0.991097 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1011.57i | − | 1.15344i | −0.816942 | − | 0.576719i | \(-0.804333\pi\) | ||
0.816942 | − | 0.576719i | \(-0.195667\pi\) | |||||||
\(878\) | −162.642 | + | 755.593i | −0.185241 | + | 0.860584i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −467.838 | − | 530.478i | −0.531634 | − | 0.602816i | ||||
\(881\) | 803.454i | 0.911979i | 0.889985 | + | 0.455990i | \(0.150715\pi\) | ||||
−0.889985 | + | 0.455990i | \(0.849285\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 458.660i | 0.519434i | 0.965685 | + | 0.259717i | \(0.0836293\pi\) | ||||
−0.965685 | + | 0.259717i | \(0.916371\pi\) | |||||||
\(884\) | 280.340 | + | 126.550i | 0.317127 | + | 0.143156i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −159.307 | + | 740.102i | −0.179805 | + | 0.835329i | ||||
\(887\) | 56.5044i | 0.0637028i | 0.999493 | + | 0.0318514i | \(0.0101403\pi\) | ||||
−0.999493 | + | 0.0318514i | \(0.989860\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 921.490 | 1.03655 | ||||||||
\(890\) | 636.031 | + | 136.906i | 0.714642 | + | 0.153827i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −186.405 | − | 84.1463i | −0.208974 | − | 0.0943344i | ||||
\(893\) | 1547.54 | 1.73296 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 295.231 | 0.329867 | ||||||||
\(896\) | −1102.50 | + | 95.8134i | −1.23047 | + | 0.106935i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −565.306 | − | 121.682i | −0.629517 | − | 0.135504i | ||||
\(899\) | −62.1444 | −0.0691262 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 405.255i | 0.449783i | ||||||||
\(902\) | −303.542 | − | 65.3375i | −0.336521 | − | 0.0724362i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1094.21 | − | 807.984i | −1.21041 | − | 0.893788i | ||||
\(905\) | − | 315.155i | − | 0.348238i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 462.461i | 0.509880i | 0.966957 | + | 0.254940i | \(0.0820558\pi\) | ||||
−0.966957 | + | 0.254940i | \(0.917944\pi\) | |||||||
\(908\) | 858.718 | + | 387.639i | 0.945725 | + | 0.426915i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 546.626 | + | 117.661i | 0.600688 | + | 0.129298i | ||||
\(911\) | − | 199.274i | − | 0.218742i | −0.994001 | − | 0.109371i | \(-0.965116\pi\) | ||
0.994001 | − | 0.109371i | \(-0.0348836\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2362.12 | 2.58721 | ||||||||
\(914\) | −204.271 | + | 948.994i | −0.223492 | + | 1.03829i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 339.571 | − | 752.235i | 0.370711 | − | 0.821218i | ||||
\(917\) | −566.718 | −0.618013 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1663.67 | 1.81031 | 0.905154 | − | 0.425084i | \(-0.139755\pi\) | ||||
0.905154 | + | 0.425084i | \(0.139755\pi\) | |||||||
\(920\) | 424.985 | + | 313.816i | 0.461941 | + | 0.341105i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 90.5006 | − | 420.443i | 0.0981568 | − | 0.456012i | ||||
\(923\) | −1462.04 | −1.58401 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 333.589i | 0.360637i | ||||||||
\(926\) | 157.720 | − | 732.729i | 0.170324 | − | 0.791283i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 171.336 | − | 96.0000i | 0.184629 | − | 0.103448i | ||||
\(929\) | − | 826.068i | − | 0.889201i | −0.895729 | − | 0.444601i | \(-0.853346\pi\) | ||
0.895729 | − | 0.444601i | \(-0.146654\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 625.482i | − | 0.671839i | ||||||
\(932\) | 346.193 | − | 766.905i | 0.371452 | − | 0.822860i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 112.812 | − | 524.095i | 0.120783 | − | 0.561130i | ||||
\(935\) | 234.105i | 0.250379i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −536.859 | −0.572955 | −0.286477 | − | 0.958087i | \(-0.592484\pi\) | ||||
−0.286477 | + | 0.958087i | \(0.592484\pi\) | |||||||
\(938\) | −1863.65 | − | 401.152i | −1.98684 | − | 0.427667i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −233.490 | + | 517.239i | −0.248394 | + | 0.550254i | ||||
\(941\) | −1261.70 | −1.34081 | −0.670406 | − | 0.741995i | \(-0.733880\pi\) | ||||
−0.670406 | + | 0.741995i | \(0.733880\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 231.911 | 0.245929 | ||||||||
\(944\) | 434.254 | + | 492.398i | 0.460015 | + | 0.521608i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −59.8666 | − | 12.8863i | −0.0632840 | − | 0.0136219i | ||||
\(947\) | −173.218 | −0.182912 | −0.0914560 | − | 0.995809i | \(-0.529152\pi\) | ||||
−0.0914560 | + | 0.995809i | \(0.529152\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1363.67i | 1.43696i | ||||||||
\(950\) | −951.828 | − | 204.881i | −1.00192 | − | 0.215665i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 294.656 | + | 217.579i | 0.309513 | + | 0.228549i | ||||
\(953\) | − | 1457.32i | − | 1.52919i | −0.644510 | − | 0.764596i | \(-0.722939\pi\) | ||
0.644510 | − | 0.764596i | \(-0.277061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.24426i | 0.00339713i | ||||||||
\(956\) | −38.0921 | + | 84.3835i | −0.0398453 | + | 0.0882673i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1001.28 | − | 215.527i | −1.04518 | − | 0.224976i | ||||
\(959\) | 1226.22i | 1.27864i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −858.474 | −0.893314 | ||||||||
\(962\) | 101.722 | − | 472.577i | 0.105741 | − | 0.491245i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −297.593 | − | 134.339i | −0.308707 | − | 0.139355i | ||||
\(965\) | 542.358 | 0.562029 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1148.30 | 1.18748 | 0.593742 | − | 0.804655i | \(-0.297650\pi\) | ||||
0.593742 | + | 0.804655i | \(0.297650\pi\) | |||||||
\(968\) | 1297.51 | − | 1757.16i | 1.34041 | − | 1.81524i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.47580 | + | 16.1477i | −0.00358330 | + | 0.0166471i | ||||
\(971\) | −15.1851 | −0.0156386 | −0.00781932 | − | 0.999969i | \(-0.502489\pi\) | ||||
−0.00781932 | + | 0.999969i | \(0.502489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1480.21i | − | 1.52128i | ||||||
\(974\) | −372.801 | + | 1731.94i | −0.382752 | + | 1.77817i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 624.753 | − | 550.980i | 0.640116 | − | 0.564529i | ||||
\(977\) | − | 149.435i | − | 0.152953i | −0.997071 | − | 0.0764764i | \(-0.975633\pi\) | ||
0.997071 | − | 0.0764764i | \(-0.0243670\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2899.57i | 2.96177i | ||||||||
\(980\) | 209.058 | + | 94.3720i | 0.213324 | + | 0.0962979i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −183.010 | + | 850.221i | −0.186365 | + | 0.865805i | ||||
\(983\) | 683.140i | 0.694954i | 0.937688 | + | 0.347477i | \(0.112962\pi\) | ||||
−0.937688 | + | 0.347477i | \(0.887038\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.1294 | 0.0112989 | ||||||||
\(986\) | −63.5484 | − | 13.6788i | −0.0644507 | − | 0.0138730i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1285.93 | + | 580.488i | 1.30154 | + | 0.587538i | ||||
\(989\) | 45.7391 | 0.0462479 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1531.80 | −1.54571 | −0.772854 | − | 0.634584i | \(-0.781171\pi\) | ||||
−0.772854 | + | 0.634584i | \(0.781171\pi\) | |||||||
\(992\) | −282.669 | + | 158.380i | −0.284949 | + | 0.159658i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1702.09 | − | 366.376i | −1.71237 | − | 0.368588i | ||||
\(995\) | −228.213 | −0.229359 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 194.125i | 0.194710i | 0.995250 | + | 0.0973548i | \(0.0310382\pi\) | ||||
−0.995250 | + | 0.0973548i | \(0.968962\pi\) | |||||||
\(998\) | −1394.03 | − | 300.066i | −1.39683 | − | 0.300667i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 216.3.h.e.53.4 | yes | 8 | |
3.2 | odd | 2 | inner | 216.3.h.e.53.5 | yes | 8 | |
4.3 | odd | 2 | 864.3.h.f.593.3 | 8 | |||
8.3 | odd | 2 | 864.3.h.f.593.6 | 8 | |||
8.5 | even | 2 | inner | 216.3.h.e.53.6 | yes | 8 | |
12.11 | even | 2 | 864.3.h.f.593.5 | 8 | |||
24.5 | odd | 2 | inner | 216.3.h.e.53.3 | ✓ | 8 | |
24.11 | even | 2 | 864.3.h.f.593.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.3.h.e.53.3 | ✓ | 8 | 24.5 | odd | 2 | inner | |
216.3.h.e.53.4 | yes | 8 | 1.1 | even | 1 | trivial | |
216.3.h.e.53.5 | yes | 8 | 3.2 | odd | 2 | inner | |
216.3.h.e.53.6 | yes | 8 | 8.5 | even | 2 | inner | |
864.3.h.f.593.3 | 8 | 4.3 | odd | 2 | |||
864.3.h.f.593.4 | 8 | 24.11 | even | 2 | |||
864.3.h.f.593.5 | 8 | 12.11 | even | 2 | |||
864.3.h.f.593.6 | 8 | 8.3 | odd | 2 |