Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8400,2,Mod(1,8400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8400, 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("8400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8400.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: | \(67.0743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 840) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8400.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.387873 | −0.116948 | −0.0584741 | − | 0.998289i | \(-0.518623\pi\) | ||||
−0.0584741 | + | 0.998289i | \(0.518623\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.96239 | −0.821619 | −0.410809 | − | 0.911721i | \(-0.634754\pi\) | ||||
−0.410809 | + | 0.911721i | \(0.634754\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.35026 | 0.812558 | 0.406279 | − | 0.913749i | \(-0.366826\pi\) | ||||
0.406279 | + | 0.913749i | \(0.366826\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.96239 | 0.679619 | 0.339809 | − | 0.940494i | \(-0.389637\pi\) | ||||
0.339809 | + | 0.940494i | \(0.389637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.962389 | 0.200672 | 0.100336 | − | 0.994954i | \(-0.468008\pi\) | ||||
0.100336 | + | 0.994954i | \(0.468008\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.22425 | 0.227338 | 0.113669 | − | 0.993519i | \(-0.463740\pi\) | ||||
0.113669 | + | 0.993519i | \(0.463740\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.96239 | −0.532061 | −0.266030 | − | 0.963965i | \(-0.585712\pi\) | ||||
−0.266030 | + | 0.963965i | \(0.585712\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.387873 | 0.0675200 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.92478 | 0.974027 | 0.487014 | − | 0.873394i | \(-0.338086\pi\) | ||||
0.487014 | + | 0.873394i | \(0.338086\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.96239 | 0.474362 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.03761 | 0.162048 | 0.0810238 | − | 0.996712i | \(-0.474181\pi\) | ||||
0.0810238 | + | 0.996712i | \(0.474181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7005 | −1.63181 | −0.815907 | − | 0.578183i | \(-0.803762\pi\) | ||||
−0.815907 | + | 0.578183i | \(0.803762\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.22425 | −0.470306 | −0.235153 | − | 0.971958i | \(-0.575559\pi\) | ||||
−0.235153 | + | 0.971958i | \(0.575559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.35026 | −0.469130 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.66291 | −0.777861 | −0.388930 | − | 0.921267i | \(-0.627155\pi\) | ||||
−0.388930 | + | 0.921267i | \(0.627155\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.96239 | −0.392378 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.22425 | −0.419762 | −0.209881 | − | 0.977727i | \(-0.567308\pi\) | ||||
−0.209881 | + | 0.977727i | \(0.567308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6253 | 1.87258 | 0.936289 | − | 0.351231i | \(-0.114237\pi\) | ||||
0.936289 | + | 0.351231i | \(0.114237\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.962389 | −0.115858 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.53690 | −0.657110 | −0.328555 | − | 0.944485i | \(-0.606562\pi\) | ||||
−0.328555 | + | 0.944485i | \(0.606562\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.18664 | 0.724092 | 0.362046 | − | 0.932160i | \(-0.382078\pi\) | ||||
0.362046 | + | 0.932160i | \(0.382078\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.387873 | 0.0442022 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.9248 | 1.56666 | 0.783330 | − | 0.621606i | \(-0.213520\pi\) | ||||
0.783330 | + | 0.621606i | \(0.213520\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.22425 | −0.353908 | −0.176954 | − | 0.984219i | \(-0.556624\pi\) | ||||
−0.176954 | + | 0.984219i | \(0.556624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.22425 | −0.131254 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.73813 | 0.396242 | 0.198121 | − | 0.980178i | \(-0.436516\pi\) | ||||
0.198121 | + | 0.980178i | \(0.436516\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.96239 | 0.310543 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.96239 | 0.307185 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.73813 | −0.785689 | −0.392844 | − | 0.919605i | \(-0.628509\pi\) | ||||
−0.392844 | + | 0.919605i | \(0.628509\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.387873 | −0.0389827 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.58769 | −0.755003 | −0.377502 | − | 0.926009i | \(-0.623217\pi\) | ||||
−0.377502 | + | 0.926009i | \(0.623217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.7005 | −1.44849 | −0.724243 | − | 0.689545i | \(-0.757811\pi\) | ||||
−0.724243 | + | 0.689545i | \(0.757811\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.4387 | −1.58919 | −0.794593 | − | 0.607143i | \(-0.792315\pi\) | ||||
−0.794593 | + | 0.607143i | \(0.792315\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.77575 | −0.265868 | −0.132934 | − | 0.991125i | \(-0.542440\pi\) | ||||
−0.132934 | + | 0.991125i | \(0.542440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.92478 | −0.562355 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.26187 | 0.400923 | 0.200461 | − | 0.979702i | \(-0.435756\pi\) | ||||
0.200461 | + | 0.979702i | \(0.435756\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.96239 | −0.273873 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.35026 | −0.307118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8496 | −0.986323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.03761 | −0.0935583 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.5501 | 1.29111 | 0.645555 | − | 0.763714i | \(-0.276626\pi\) | ||||
0.645555 | + | 0.763714i | \(0.276626\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.7005 | 0.942129 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.96239 | −0.256872 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4387 | 0.891835 | 0.445917 | − | 0.895074i | \(-0.352878\pi\) | ||||
0.445917 | + | 0.895074i | \(0.352878\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.66291 | −0.480322 | −0.240161 | − | 0.970733i | \(-0.577200\pi\) | ||||
−0.240161 | + | 0.970733i | \(0.577200\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.22425 | 0.271531 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.14903 | 0.0960868 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.5501 | 1.68353 | 0.841764 | − | 0.539846i | \(-0.181517\pi\) | ||||
0.841764 | + | 0.539846i | \(0.181517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.7005 | 1.84734 | 0.923671 | − | 0.383186i | \(-0.125173\pi\) | ||||
0.923671 | + | 0.383186i | \(0.125173\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.35026 | 0.270853 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.18664 | −0.174513 | −0.0872565 | − | 0.996186i | \(-0.527810\pi\) | ||||
−0.0872565 | + | 0.996186i | \(0.527810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.66291 | 0.449098 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.962389 | −0.0758468 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.22425 | −0.565847 | −0.282924 | − | 0.959142i | \(-0.591304\pi\) | ||||
−0.282924 | + | 0.959142i | \(0.591304\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8496 | 1.22648 | 0.613238 | − | 0.789898i | \(-0.289867\pi\) | ||||
0.613238 | + | 0.789898i | \(0.289867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.22425 | −0.324943 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.96239 | 0.226540 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.9756 | 1.82283 | 0.911414 | − | 0.411490i | \(-0.134992\pi\) | ||||
0.911414 | + | 0.411490i | \(0.134992\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.22425 | 0.242350 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.2374 | −0.914668 | −0.457334 | − | 0.889295i | \(-0.651196\pi\) | ||||
−0.457334 | + | 0.889295i | \(0.651196\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.70052 | 0.646705 | 0.323352 | − | 0.946279i | \(-0.395190\pi\) | ||||
0.323352 | + | 0.946279i | \(0.395190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.6253 | −1.08113 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.29948 | −0.0950271 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5369 | 0.979496 | 0.489748 | − | 0.871864i | \(-0.337089\pi\) | ||||
0.489748 | + | 0.871864i | \(0.337089\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.92478 | −0.138548 | −0.0692742 | − | 0.997598i | \(-0.522068\pi\) | ||||
−0.0692742 | + | 0.997598i | \(0.522068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.1114 | 1.43288 | 0.716440 | − | 0.697649i | \(-0.245771\pi\) | ||||
0.716440 | + | 0.697649i | \(0.245771\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.26187 | 0.585668 | 0.292834 | − | 0.956163i | \(-0.405402\pi\) | ||||
0.292834 | + | 0.956163i | \(0.405402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.22425 | −0.0859258 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.962389 | 0.0668906 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.14903 | −0.0794801 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1768 | 1.25134 | 0.625671 | − | 0.780087i | \(-0.284825\pi\) | ||||
0.625671 | + | 0.780087i | \(0.284825\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.53690 | 0.379382 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.96239 | 0.201100 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.18664 | −0.418055 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.92478 | −0.667613 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.4010 | −1.43312 | −0.716560 | − | 0.697525i | \(-0.754284\pi\) | ||||
−0.716560 | + | 0.697525i | \(0.754284\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.5501 | −1.23121 | −0.615606 | − | 0.788054i | \(-0.711089\pi\) | ||||
−0.615606 | + | 0.788054i | \(0.711089\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.5501 | −1.88664 | −0.943321 | − | 0.331881i | \(-0.892317\pi\) | ||||
−0.943321 | + | 0.331881i | \(0.892317\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.387873 | −0.0255202 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.9624 | 1.24227 | 0.621134 | − | 0.783705i | \(-0.286672\pi\) | ||||
0.621134 | + | 0.783705i | \(0.286672\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.9248 | −0.904511 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.1622 | 1.17482 | 0.587408 | − | 0.809291i | \(-0.300149\pi\) | ||||
0.587408 | + | 0.809291i | \(0.300149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.3733 | 0.925865 | 0.462932 | − | 0.886394i | \(-0.346797\pi\) | ||||
0.462932 | + | 0.886394i | \(0.346797\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.77575 | −0.558387 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.22425 | 0.204329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.62530 | 0.544424 | 0.272212 | − | 0.962237i | \(-0.412245\pi\) | ||||
0.272212 | + | 0.962237i | \(0.412245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.373285 | −0.0234682 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.8251 | −1.73568 | −0.867842 | − | 0.496841i | \(-0.834493\pi\) | ||||
−0.867842 | + | 0.496841i | \(0.834493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.92478 | −0.368148 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.22425 | 0.0757794 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.589104 | 0.0363257 | 0.0181629 | − | 0.999835i | \(-0.494218\pi\) | ||||
0.0181629 | + | 0.999835i | \(0.494218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.73813 | −0.228770 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.7381 | 0.959571 | 0.479786 | − | 0.877386i | \(-0.340714\pi\) | ||||
0.479786 | + | 0.877386i | \(0.340714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.11283 | 0.432074 | 0.216037 | − | 0.976385i | \(-0.430687\pi\) | ||||
0.216037 | + | 0.976385i | \(0.430687\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.96239 | −0.179292 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.92478 | 0.355985 | 0.177993 | − | 0.984032i | \(-0.443040\pi\) | ||||
0.177993 | + | 0.984032i | \(0.443040\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.96239 | −0.177354 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.3258 | 1.74943 | 0.874716 | − | 0.484636i | \(-0.161048\pi\) | ||||
0.874716 | + | 0.484636i | \(0.161048\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1016 | 0.957139 | 0.478570 | − | 0.878050i | \(-0.341155\pi\) | ||||
0.478570 | + | 0.878050i | \(0.341155\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.03761 | −0.0612483 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.77575 | −0.339750 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.73813 | 0.453617 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.27504 | 0.541854 | 0.270927 | − | 0.962600i | \(-0.412670\pi\) | ||||
0.270927 | + | 0.962600i | \(0.412670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.387873 | 0.0225067 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.85097 | −0.164876 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.7005 | 0.616768 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.58769 | 0.435901 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.7005 | −0.610711 | −0.305356 | − | 0.952238i | \(-0.598775\pi\) | ||||
−0.305356 | + | 0.952238i | \(0.598775\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.7005 | 0.836284 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.1016 | −0.686217 | −0.343109 | − | 0.939296i | \(-0.611480\pi\) | ||||
−0.343109 | + | 0.939296i | \(0.611480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.3634 | 1.60320 | 0.801598 | − | 0.597863i | \(-0.203983\pi\) | ||||
0.801598 | + | 0.597863i | \(0.203983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.5125 | −0.983598 | −0.491799 | − | 0.870709i | \(-0.663661\pi\) | ||||
−0.491799 | + | 0.870709i | \(0.663661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.474855 | −0.0265868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.4387 | 0.917516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.92478 | 0.552229 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.77575 | 0.153499 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.22425 | 0.177759 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2243 | 1.05666 | 0.528330 | − | 0.849039i | \(-0.322818\pi\) | ||||
0.528330 | + | 0.849039i | \(0.322818\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.92478 | 0.324676 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0000 | 0.871576 | 0.435788 | − | 0.900049i | \(-0.356470\pi\) | ||||
0.435788 | + | 0.900049i | \(0.356470\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.26187 | −0.231473 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.14903 | 0.0622235 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.11283 | 0.0597401 | 0.0298700 | − | 0.999554i | \(-0.490491\pi\) | ||||
0.0298700 | + | 0.999554i | \(0.490491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.0263 | −1.71433 | −0.857166 | − | 0.515041i | \(-0.827777\pi\) | ||||
−0.857166 | + | 0.515041i | \(0.827777\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.96239 | 0.158121 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.20123 | 0.330058 | 0.165029 | − | 0.986289i | \(-0.447228\pi\) | ||||
0.165029 | + | 0.986289i | \(0.447228\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.35026 | 0.177315 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.68735 | 0.0890549 | 0.0445275 | − | 0.999008i | \(-0.485822\pi\) | ||||
0.0445275 | + | 0.999008i | \(0.485822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.2243 | −0.538119 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8496 | 0.569454 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.84955 | −0.200945 | −0.100473 | − | 0.994940i | \(-0.532035\pi\) | ||||
−0.100473 | + | 0.994940i | \(0.532035\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.03761 | 0.0540159 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.66291 | 0.294004 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.8773 | −1.28810 | −0.644049 | − | 0.764984i | \(-0.722747\pi\) | ||||
−0.644049 | + | 0.764984i | \(0.722747\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.62672 | −0.186785 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.70052 | −0.138717 | −0.0693583 | − | 0.997592i | \(-0.522095\pi\) | ||||
−0.0693583 | + | 0.997592i | \(0.522095\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.5501 | −0.745423 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.523730 | 0.0267614 | 0.0133807 | − | 0.999910i | \(-0.495741\pi\) | ||||
0.0133807 | + | 0.999910i | \(0.495741\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.7005 | −0.543938 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.77575 | 0.343544 | 0.171772 | − | 0.985137i | \(-0.445051\pi\) | ||||
0.171772 | + | 0.985137i | \(0.445051\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.22425 | 0.163058 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.635150 | 0.0318773 | 0.0159386 | − | 0.999873i | \(-0.494926\pi\) | ||||
0.0159386 | + | 0.999873i | \(0.494926\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.96239 | 0.148305 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3733 | 0.518017 | 0.259009 | − | 0.965875i | \(-0.416604\pi\) | ||||
0.259009 | + | 0.965875i | \(0.416604\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.77575 | 0.437151 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.29806 | −0.113911 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.7743 | 0.779991 | 0.389995 | − | 0.920817i | \(-0.372477\pi\) | ||||
0.389995 | + | 0.920817i | \(0.372477\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.4387 | −0.514901 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.22425 | 0.158655 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.66291 | 0.277314 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.1490 | −1.22861 | −0.614305 | − | 0.789068i | \(-0.710564\pi\) | ||||
−0.614305 | + | 0.789068i | \(0.710564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.1768 | 0.983357 | 0.491678 | − | 0.870777i | \(-0.336384\pi\) | ||||
0.491678 | + | 0.870777i | \(0.336384\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.22425 | −0.156769 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.6253 | −0.707768 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.14903 | −0.0554757 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.3127 | 1.84546 | 0.922728 | − | 0.385452i | \(-0.125955\pi\) | ||||
0.922728 | + | 0.385452i | \(0.125955\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.8872 | −0.619318 | −0.309659 | − | 0.950848i | \(-0.600215\pi\) | ||||
−0.309659 | + | 0.950848i | \(0.600215\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.85097 | 0.136380 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.6629 | 1.41573 | 0.707867 | − | 0.706346i | \(-0.249658\pi\) | ||||
0.707867 | + | 0.706346i | \(0.249658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.8119 | 1.17885 | 0.589425 | − | 0.807823i | \(-0.299354\pi\) | ||||
0.589425 | + | 0.807823i | \(0.299354\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.5501 | −0.971985 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.6516 | −1.72970 | −0.864849 | − | 0.502032i | \(-0.832586\pi\) | ||||
−0.864849 | + | 0.502032i | \(0.832586\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.402462 | −0.0189512 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.7005 | −1.06656 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.4763 | 0.723949 | 0.361975 | − | 0.932188i | \(-0.382103\pi\) | ||||
0.361975 | + | 0.932188i | \(0.382103\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.35026 | −0.156377 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.2605 | 1.92169 | 0.960845 | − | 0.277085i | \(-0.0893684\pi\) | ||||
0.960845 | + | 0.277085i | \(0.0893684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.5975 | −0.724879 | −0.362440 | − | 0.932007i | \(-0.618056\pi\) | ||||
−0.362440 | + | 0.932007i | \(0.618056\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.5501 | 0.858395 | 0.429198 | − | 0.903211i | \(-0.358796\pi\) | ||||
0.429198 | + | 0.903211i | \(0.358796\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.18664 | 0.100755 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.15045 | 0.190838 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.66291 | −0.259287 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.5026 | 1.89630 | 0.948151 | − | 0.317819i | \(-0.102950\pi\) | ||||
0.948151 | + | 0.317819i | \(0.102950\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5515 | −0.800279 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.962389 | 0.0437902 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.6728 | 0.619572 | 0.309786 | − | 0.950806i | \(-0.399743\pi\) | ||||
0.309786 | + | 0.950806i | \(0.399743\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.22425 | 0.326692 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.3404 | −1.05334 | −0.526669 | − | 0.850070i | \(-0.676559\pi\) | ||||
−0.526669 | + | 0.850070i | \(0.676559\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.10157 | 0.184725 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.53690 | 0.248364 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.85097 | 0.306691 | 0.153346 | − | 0.988173i | \(-0.450995\pi\) | ||||
0.153346 | + | 0.988173i | \(0.450995\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.8496 | −0.708106 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.32582 | −0.148291 | −0.0741456 | − | 0.997247i | \(-0.523623\pi\) | ||||
−0.0741456 | + | 0.997247i | \(0.523623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.22425 | 0.187606 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.18664 | −0.274218 | −0.137109 | − | 0.990556i | \(-0.543781\pi\) | ||||
−0.137109 | + | 0.990556i | \(0.543781\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.18664 | −0.273681 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.96239 | −0.130793 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.25060 | 0.0550014 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.9756 | −1.05241 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4387 | 1.50879 | 0.754393 | − | 0.656424i | \(-0.227932\pi\) | ||||
0.754393 | + | 0.656424i | \(0.227932\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.59895 | −0.288552 | −0.144276 | − | 0.989537i | \(-0.546085\pi\) | ||||
−0.144276 | + | 0.989537i | \(0.546085\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.92478 | −0.432330 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0738 | −0.959731 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.22425 | −0.139921 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.07381 | −0.133141 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.2374 | 0.528084 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.387873 | −0.0167069 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.07381 | −0.390113 | −0.195057 | − | 0.980792i | \(-0.562489\pi\) | ||||
−0.195057 | + | 0.980792i | \(0.562489\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.70052 | −0.373375 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.8496 | 0.848706 | 0.424353 | − | 0.905497i | \(-0.360502\pi\) | ||||
0.424353 | + | 0.905497i | \(0.360502\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.6253 | 0.624193 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.62672 | 0.154503 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.9248 | −0.592142 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.785595 | 0.0332867 | 0.0166434 | − | 0.999861i | \(-0.494702\pi\) | ||||
0.0166434 | + | 0.999861i | \(0.494702\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.6991 | 1.34073 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.29948 | 0.0548639 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.2228 | 1.35803 | 0.679015 | − | 0.734124i | \(-0.262407\pi\) | ||||
0.679015 | + | 0.734124i | \(0.262407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.0752 | 0.673908 | 0.336954 | − | 0.941521i | \(-0.390603\pi\) | ||||
0.336954 | + | 0.941521i | \(0.390603\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.8496 | 1.66765 | 0.833826 | − | 0.552027i | \(-0.186146\pi\) | ||||
0.833826 | + | 0.552027i | \(0.186146\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.5369 | −0.565512 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.1378 | −1.25465 | −0.627326 | − | 0.778757i | \(-0.715851\pi\) | ||||
−0.627326 | + | 0.778757i | \(0.715851\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.92478 | 0.0799910 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.22425 | 0.133765 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.19649 | 0.0909694 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.7743 | 1.39402 | 0.697008 | − | 0.717063i | \(-0.254514\pi\) | ||||
0.697008 | + | 0.717063i | \(0.254514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.77575 | −0.361598 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.1114 | −0.827273 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.19982 | 0.295661 | 0.147831 | − | 0.989013i | \(-0.452771\pi\) | ||||
0.147831 | + | 0.989013i | \(0.452771\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.26187 | −0.338136 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.5369 | 1.20685 | 0.603423 | − | 0.797422i | \(-0.293803\pi\) | ||||
0.603423 | + | 0.797422i | \(0.293803\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.59895 | 0.350759 | 0.175379 | − | 0.984501i | \(-0.443885\pi\) | ||||
0.175379 | + | 0.984501i | \(0.443885\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.4010 | −1.51806 | −0.759031 | − | 0.651055i | \(-0.774327\pi\) | ||||
−0.759031 | + | 0.651055i | \(0.774327\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.22425 | 0.0496093 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.55149 | 0.386412 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.5990 | −0.589646 | −0.294823 | − | 0.955552i | \(-0.595261\pi\) | ||||
−0.294823 | + | 0.955552i | \(0.595261\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.8119 | 0.918374 | 0.459187 | − | 0.888340i | \(-0.348141\pi\) | ||||
0.459187 | + | 0.888340i | \(0.348141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.261865 | −0.0105252 | −0.00526262 | − | 0.999986i | \(-0.501675\pi\) | ||||
−0.00526262 | + | 0.999986i | \(0.501675\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.962389 | −0.0386193 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.73813 | −0.149765 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.14903 | 0.0458879 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.8496 | 0.791454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.92478 | 0.235862 | 0.117931 | − | 0.993022i | \(-0.462374\pi\) | ||||
0.117931 | + | 0.993022i | \(0.462374\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.1768 | −0.722463 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.96239 | −0.117374 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.53690 | −0.219037 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.87732 | 0.271638 | 0.135819 | − | 0.990734i | \(-0.456633\pi\) | ||||
0.135819 | + | 0.990734i | \(0.456633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.7005 | 0.421987 | 0.210994 | − | 0.977487i | \(-0.432330\pi\) | ||||
0.210994 | + | 0.977487i | \(0.432330\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.2506 | 1.77898 | 0.889492 | − | 0.456950i | \(-0.151058\pi\) | ||||
0.889492 | + | 0.456950i | \(0.151058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.25060 | 0.0490904 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.96239 | −0.116105 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.0625 | 1.41124 | 0.705618 | − | 0.708592i | \(-0.250669\pi\) | ||||
0.705618 | + | 0.708592i | \(0.250669\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.18664 | 0.241364 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.4617 | −1.69303 | −0.846513 | − | 0.532367i | \(-0.821302\pi\) | ||||
−0.846513 | + | 0.532367i | \(0.821302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.4749 | −0.874171 | −0.437085 | − | 0.899420i | \(-0.643989\pi\) | ||||
−0.437085 | + | 0.899420i | \(0.643989\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.92478 | 0.385446 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.17821 | 0.0456204 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.4010 | 0.827412 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.67276 | −0.218995 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.5487 | 1.83287 | 0.916433 | − | 0.400188i | \(-0.131055\pi\) | ||||
0.916433 | + | 0.400188i | \(0.131055\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.67750 | 0.218204 | 0.109102 | − | 0.994031i | \(-0.465202\pi\) | ||||
0.109102 | + | 0.994031i | \(0.465202\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.73813 | 0.296962 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.5501 | 0.710841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.2882 | −0.470195 | −0.235098 | − | 0.971972i | \(-0.575541\pi\) | ||||
−0.235098 | + | 0.971972i | \(0.575541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.5501 | 1.08925 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.7757 | 0.639105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.81336 | 0.0689834 | 0.0344917 | − | 0.999405i | \(-0.489019\pi\) | ||||
0.0344917 | + | 0.999405i | \(0.489019\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.387873 | 0.0147341 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.47627 | 0.131673 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.9624 | −0.717223 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.5778 | 1.11714 | 0.558570 | − | 0.829458i | \(-0.311350\pi\) | ||||
0.558570 | + | 0.829458i | \(0.311350\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.5515 | 0.661967 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.58769 | 0.285364 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.8021 | 0.781239 | 0.390620 | − | 0.920552i | \(-0.372261\pi\) | ||||
0.390620 | + | 0.920552i | \(0.372261\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.9248 | 0.522220 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.85097 | −0.106770 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.1622 | −0.678280 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.3258 | −0.720732 | −0.360366 | − | 0.932811i | \(-0.617348\pi\) | ||||
−0.360366 | + | 0.932811i | \(0.617348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.7005 | 0.547476 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.3733 | −0.534548 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6531 | 0.803068 | 0.401534 | − | 0.915844i | \(-0.368477\pi\) | ||||
0.401534 | + | 0.915844i | \(0.368477\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.8496 | −1.32594 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.0625 | −1.77523 | −0.887615 | − | 0.460586i | \(-0.847639\pi\) | ||||
−0.887615 | + | 0.460586i | \(0.847639\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.2981 | 1.11453 | 0.557266 | − | 0.830334i | \(-0.311850\pi\) | ||||
0.557266 | + | 0.830334i | \(0.311850\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.77575 | 0.322385 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.9624 | 1.50276 | 0.751382 | − | 0.659867i | \(-0.229388\pi\) | ||||
0.751382 | + | 0.659867i | \(0.229388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.22425 | −0.117969 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.4387 | 0.600656 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.52232 | −0.347474 | −0.173737 | − | 0.984792i | \(-0.555584\pi\) | ||||
−0.173737 | + | 0.984792i | \(0.555584\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.62530 | −0.314323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.3258 | 1.13856 | 0.569278 | − | 0.822145i | \(-0.307223\pi\) | ||||
0.569278 | + | 0.822145i | \(0.307223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.373285 | 0.0135494 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −54.2393 | −1.96617 | −0.983087 | − | 0.183138i | \(-0.941375\pi\) | ||||
−0.983087 | + | 0.183138i | \(0.941375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.77575 | 0.100489 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.55149 | 0.344884 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.1002 | 1.26574 | 0.632872 | − | 0.774256i | \(-0.281876\pi\) | ||||
0.632872 | + | 0.774256i | \(0.281876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.8251 | 1.00210 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.8740 | 0.714818 | 0.357409 | − | 0.933948i | \(-0.383660\pi\) | ||||
0.357409 | + | 0.933948i | \(0.383660\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.92478 | 0.212550 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.07381 | 0.110131 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.14762 | 0.0768478 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.22425 | −0.0437513 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.2506 | −0.472333 | −0.236166 | − | 0.971713i | \(-0.575891\pi\) | ||||
−0.236166 | + | 0.971713i | \(0.575891\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.589104 | −0.0209727 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.26187 | −0.151534 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −43.3258 | −1.53855 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.7235 | −0.556957 | −0.278478 | − | 0.960443i | \(-0.589830\pi\) | ||||
−0.278478 | + | 0.960443i | \(0.589830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.8021 | −0.382151 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.73813 | 0.132081 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.39963 | −0.0846812 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.7381 | −0.554009 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.5040 | −0.650567 | −0.325284 | − | 0.945617i | \(-0.605460\pi\) | ||||
−0.325284 | + | 0.945617i | \(0.605460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.6629 | −1.32252 | −0.661262 | − | 0.750155i | \(-0.729979\pi\) | ||||
−0.661262 | + | 0.750155i | \(0.729979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.11283 | −0.249458 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.6991 | −1.10901 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.96239 | 0.103514 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.9511 | −0.626499 | −0.313249 | − | 0.949671i | \(-0.601418\pi\) | ||||
−0.313249 | + | 0.949671i | \(0.601418\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.1016 | 1.11899 | 0.559495 | − | 0.828834i | \(-0.310995\pi\) | ||||
0.559495 | + | 0.828834i | \(0.310995\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.8594 | 0.899220 | 0.449610 | − | 0.893225i | \(-0.351563\pi\) | ||||
0.449610 | + | 0.893225i | \(0.351563\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.8035 | 0.409953 | 0.204976 | − | 0.978767i | \(-0.434288\pi\) | ||||
0.204976 | + | 0.978767i | \(0.434288\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.92478 | −0.205528 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.35026 | 0.116080 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.96239 | 0.102395 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.5778 | −0.675902 | −0.337951 | − | 0.941164i | \(-0.609734\pi\) | ||||
−0.337951 | + | 0.941164i | \(0.609734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.5012 | −0.948317 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.3258 | −1.01004 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.8496 | 0.372795 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.1016 | −0.552604 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.70194 | 0.195460 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.6155 | −1.39065 | −0.695323 | − | 0.718697i | \(-0.744739\pi\) | ||||
−0.695323 | + | 0.718697i | \(0.744739\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.1246 | 0.994877 | 0.497439 | − | 0.867499i | \(-0.334274\pi\) | ||||
0.497439 | + | 0.867499i | \(0.334274\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.7090 | −1.21837 | −0.609187 | − | 0.793027i | \(-0.708504\pi\) | ||||
−0.609187 | + | 0.793027i | \(0.708504\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.03761 | 0.0353617 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.1852 | −0.721154 | −0.360577 | − | 0.932730i | \(-0.617420\pi\) | ||||
−0.360577 | + | 0.932730i | \(0.617420\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.77575 | 0.196155 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.40105 | −0.183218 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.73813 | −0.261896 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.4485 | −0.893103 | −0.446551 | − | 0.894758i | \(-0.647348\pi\) | ||||
−0.446551 | + | 0.894758i | \(0.647348\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.27504 | −0.312839 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.0362 | −0.877182 | −0.438591 | − | 0.898687i | \(-0.644522\pi\) | ||||
−0.438591 | + | 0.898687i | \(0.644522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.87732 | −0.298745 | −0.149373 | − | 0.988781i | \(-0.547725\pi\) | ||||
−0.149373 | + | 0.988781i | \(0.547725\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.17679 | −0.0730896 | −0.0365448 | − | 0.999332i | \(-0.511635\pi\) | ||||
−0.0365448 | + | 0.999332i | \(0.511635\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.5501 | −0.487994 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.387873 | −0.0129942 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.55149 | −0.319629 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.85097 | 0.0951911 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.62672 | −0.120958 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.9722 | −0.632057 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.7005 | −0.356091 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.7269 | 1.48513 | 0.742566 | − | 0.669773i | \(-0.233609\pi\) | ||||
0.742566 | + | 0.669773i | \(0.233609\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.58769 | −0.251668 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.4631 | −0.876761 | −0.438381 | − | 0.898789i | \(-0.644448\pi\) | ||||
−0.438381 | + | 0.898789i | \(0.644448\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.25060 | 0.0413889 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 59.2769 | 1.95537 | 0.977683 | − | 0.210085i | \(-0.0673742\pi\) | ||||
0.977683 | + | 0.210085i | \(0.0673742\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.7005 | 0.352594 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.4025 | 0.539894 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.7005 | −0.482829 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.3620 | 0.832101 | 0.416050 | − | 0.909342i | \(-0.363414\pi\) | ||||
0.416050 | + | 0.909342i | \(0.363414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.96239 | 0.0970884 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.1016 | 0.396188 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.85940 | −0.126081 | −0.0630406 | − | 0.998011i | \(-0.520080\pi\) | ||||
−0.0630406 | + | 0.998011i | \(0.520080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.3634 | −0.925606 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.4861 | 0.896022 | 0.448011 | − | 0.894028i | \(-0.352133\pi\) | ||||
0.448011 | + | 0.894028i | \(0.352133\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.998585 | 0.0325184 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.8397 | 0.449730 | 0.224865 | − | 0.974390i | \(-0.427806\pi\) | ||||
0.224865 | + | 0.974390i | \(0.427806\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.3272 | −0.594927 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.5125 | 0.567881 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.2868 | −1.27262 | −0.636312 | − | 0.771432i | \(-0.719541\pi\) | ||||
−0.636312 | + | 0.771432i | \(0.719541\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.474855 | 0.0153499 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.4387 | −0.337082 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2243 | −0.716911 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.4387 | −0.529728 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.67418 | 0.278943 | 0.139471 | − | 0.990226i | \(-0.455460\pi\) | ||||
0.139471 | + | 0.990226i | \(0.455460\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.92478 | −0.318830 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.9248 | 0.831966 | 0.415983 | − | 0.909372i | \(-0.363438\pi\) | ||||
0.415983 | + | 0.909372i | \(0.363438\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.66291 | 0.181545 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.85940 | 0.251445 | 0.125722 | − | 0.992065i | \(-0.459875\pi\) | ||||
0.125722 | + | 0.992065i | \(0.459875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.44992 | −0.0463397 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.77575 | −0.0886228 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.8510 | 0.601253 | 0.300626 | − | 0.953742i | \(-0.402804\pi\) | ||||
0.300626 | + | 0.953742i | \(0.402804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.22425 | −0.102629 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.2981 | −0.327459 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.0738 | 1.36828 | 0.684142 | − | 0.729349i | \(-0.260177\pi\) | ||||
0.684142 | + | 0.729349i | \(0.260177\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.2243 | −0.610063 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.6155 | −0.779579 | −0.389790 | − | 0.920904i | \(-0.627452\pi\) | ||||
−0.389790 | + | 0.920904i | \(0.627452\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.92478 | −0.187452 |
(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 | 8400.2.a.dh.1.2 | 3 | ||
4.3 | odd | 2 | 4200.2.a.bq.1.2 | 3 | |||
5.2 | odd | 4 | 1680.2.t.i.1009.6 | 6 | |||
5.3 | odd | 4 | 1680.2.t.i.1009.3 | 6 | |||
5.4 | even | 2 | 8400.2.a.dk.1.2 | 3 | |||
15.2 | even | 4 | 5040.2.t.ba.1009.1 | 6 | |||
15.8 | even | 4 | 5040.2.t.ba.1009.2 | 6 | |||
20.3 | even | 4 | 840.2.t.e.169.6 | yes | 6 | ||
20.7 | even | 4 | 840.2.t.e.169.3 | ✓ | 6 | ||
20.19 | odd | 2 | 4200.2.a.bo.1.2 | 3 | |||
60.23 | odd | 4 | 2520.2.t.j.1009.2 | 6 | |||
60.47 | odd | 4 | 2520.2.t.j.1009.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.e.169.3 | ✓ | 6 | 20.7 | even | 4 | ||
840.2.t.e.169.6 | yes | 6 | 20.3 | even | 4 | ||
1680.2.t.i.1009.3 | 6 | 5.3 | odd | 4 | |||
1680.2.t.i.1009.6 | 6 | 5.2 | odd | 4 | |||
2520.2.t.j.1009.1 | 6 | 60.47 | odd | 4 | |||
2520.2.t.j.1009.2 | 6 | 60.23 | odd | 4 | |||
4200.2.a.bo.1.2 | 3 | 20.19 | odd | 2 | |||
4200.2.a.bq.1.2 | 3 | 4.3 | odd | 2 | |||
5040.2.t.ba.1009.1 | 6 | 15.2 | even | 4 | |||
5040.2.t.ba.1009.2 | 6 | 15.8 | even | 4 | |||
8400.2.a.dh.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8400.2.a.dk.1.2 | 3 | 5.4 | even | 2 |