Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5600,2,Mod(1,5600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5600 = 2^{5} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5600.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: | \(44.7162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.504568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 3x^{2} + 7x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1120) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.23118\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5600.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.746976 | 0.431267 | 0.215633 | − | 0.976474i | \(-0.430818\pi\) | ||||
0.215633 | + | 0.976474i | \(0.430818\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.44203 | −0.814009 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.90438 | −1.78024 | −0.890119 | − | 0.455728i | \(-0.849379\pi\) | ||||
−0.890119 | + | 0.455728i | \(0.849379\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.20933 | 0.890108 | 0.445054 | − | 0.895504i | \(-0.353184\pi\) | ||||
0.445054 | + | 0.895504i | \(0.353184\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.14941 | −0.521309 | −0.260654 | − | 0.965432i | \(-0.583938\pi\) | ||||
−0.260654 | + | 0.965432i | \(0.583938\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.56597 | 0.818089 | 0.409045 | − | 0.912514i | \(-0.365862\pi\) | ||||
0.409045 | + | 0.912514i | \(0.365862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.746976 | −0.163003 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.75497 | 0.782965 | 0.391483 | − | 0.920185i | \(-0.371962\pi\) | ||||
0.391483 | + | 0.920185i | \(0.371962\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.06506 | −0.782322 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.61177 | −1.22777 | −0.613887 | − | 0.789394i | \(-0.710395\pi\) | ||||
−0.613887 | + | 0.789394i | \(0.710395\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.79278 | 1.04041 | 0.520207 | − | 0.854040i | \(-0.325855\pi\) | ||||
0.520207 | + | 0.854040i | \(0.325855\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.41043 | −0.767757 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.623035 | 0.102426 | 0.0512132 | − | 0.998688i | \(-0.483691\pi\) | ||||
0.0512132 | + | 0.998688i | \(0.483691\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.39729 | 0.383874 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.43076 | −0.848142 | −0.424071 | − | 0.905629i | \(-0.639399\pi\) | ||||
−0.424071 | + | 0.905629i | \(0.639399\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.6768 | 1.93320 | 0.966599 | − | 0.256293i | \(-0.0825011\pi\) | ||||
0.966599 | + | 0.256293i | \(0.0825011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.31294 | −0.629107 | −0.314554 | − | 0.949240i | \(-0.601855\pi\) | ||||
−0.314554 | + | 0.949240i | \(0.601855\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.60556 | −0.224823 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.11699 | 0.290791 | 0.145395 | − | 0.989374i | \(-0.453555\pi\) | ||||
0.145395 | + | 0.989374i | \(0.453555\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.66369 | 0.352815 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.01926 | 0.913830 | 0.456915 | − | 0.889510i | \(-0.348954\pi\) | ||||
0.456915 | + | 0.889510i | \(0.348954\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.86479 | 0.238762 | 0.119381 | − | 0.992849i | \(-0.461909\pi\) | ||||
0.119381 | + | 0.992849i | \(0.461909\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.44203 | 0.307667 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.88405 | −0.841021 | −0.420511 | − | 0.907288i | \(-0.638149\pi\) | ||||
−0.420511 | + | 0.907288i | \(0.638149\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.80487 | 0.337667 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.81816 | 0.215776 | 0.107888 | − | 0.994163i | \(-0.465591\pi\) | ||||
0.107888 | + | 0.994163i | \(0.465591\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.11699 | 0.715939 | 0.357970 | − | 0.933733i | \(-0.383469\pi\) | ||||
0.357970 | + | 0.933733i | \(0.383469\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.90438 | 0.672867 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.35664 | 0.490160 | 0.245080 | − | 0.969503i | \(-0.421186\pi\) | ||||
0.245080 | + | 0.969503i | \(0.421186\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.28958 | 0.476620 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.1675 | −1.44532 | −0.722661 | − | 0.691203i | \(-0.757081\pi\) | ||||
−0.722661 | + | 0.691203i | \(0.757081\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.93883 | −0.529498 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.1708 | 1.29010 | 0.645050 | − | 0.764140i | \(-0.276836\pi\) | ||||
0.645050 | + | 0.764140i | \(0.276836\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.20933 | −0.336429 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.32706 | 0.448696 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.65935 | −0.980759 | −0.490379 | − | 0.871509i | \(-0.663142\pi\) | ||||
−0.490379 | + | 0.871509i | \(0.663142\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.4187 | 1.44913 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.2307 | −1.31650 | −0.658252 | − | 0.752798i | \(-0.728704\pi\) | ||||
−0.658252 | + | 0.752798i | \(0.728704\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.19700 | 0.315010 | 0.157505 | − | 0.987518i | \(-0.449655\pi\) | ||||
0.157505 | + | 0.987518i | \(0.449655\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.5220 | 1.21055 | 0.605276 | − | 0.796016i | \(-0.293063\pi\) | ||||
0.605276 | + | 0.796016i | \(0.293063\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1217 | 1.35261 | 0.676307 | − | 0.736620i | \(-0.263579\pi\) | ||||
0.676307 | + | 0.736620i | \(0.263579\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.465392 | 0.0441731 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.63513 | −0.153820 | −0.0769102 | − | 0.997038i | \(-0.524505\pi\) | ||||
−0.0769102 | + | 0.997038i | \(0.524505\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.83727 | −0.724556 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.14941 | 0.197036 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.8617 | 2.16925 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.05665 | −0.365775 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.79563 | 0.159336 | 0.0796680 | − | 0.996821i | \(-0.474614\pi\) | ||||
0.0796680 | + | 0.996821i | \(0.474614\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.46928 | 0.833724 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.3868 | 1.08224 | 0.541121 | − | 0.840945i | \(-0.318000\pi\) | ||||
0.541121 | + | 0.840945i | \(0.318000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.56597 | −0.309209 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.3940 | 1.22976 | 0.614881 | − | 0.788620i | \(-0.289204\pi\) | ||||
0.614881 | + | 0.788620i | \(0.289204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.7488 | 1.92953 | 0.964766 | − | 0.263110i | \(-0.0847481\pi\) | ||||
0.964766 | + | 0.263110i | \(0.0847481\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.22166 | −0.271313 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.9491 | −1.58460 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.746976 | 0.0616095 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.7560 | −1.53655 | −0.768276 | − | 0.640119i | \(-0.778885\pi\) | ||||
−0.768276 | + | 0.640119i | \(0.778885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.2824 | 1.81332 | 0.906658 | − | 0.421867i | \(-0.138625\pi\) | ||||
0.906658 | + | 0.421867i | \(0.138625\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.24892 | 0.424350 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.7110 | 1.33369 | 0.666843 | − | 0.745198i | \(-0.267645\pi\) | ||||
0.666843 | + | 0.745198i | \(0.267645\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.58134 | 0.125408 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.75497 | −0.295933 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.3555 | 1.28106 | 0.640530 | − | 0.767933i | \(-0.278715\pi\) | ||||
0.640530 | + | 0.767933i | \(0.278715\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.66452 | −0.283569 | −0.141785 | − | 0.989898i | \(-0.545284\pi\) | ||||
−0.141785 | + | 0.989898i | \(0.545284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.70019 | −0.207707 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.70819 | −0.665932 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.37622 | 0.636832 | 0.318416 | − | 0.947951i | \(-0.396849\pi\) | ||||
0.318416 | + | 0.947951i | \(0.396849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.24322 | 0.394105 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.73613 | 0.129764 | 0.0648822 | − | 0.997893i | \(-0.479333\pi\) | ||||
0.0648822 | + | 0.997893i | \(0.479333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.4621 | 1.00063 | 0.500316 | − | 0.865843i | \(-0.333217\pi\) | ||||
0.500316 | + | 0.865843i | \(0.333217\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.39295 | 0.102970 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.6909 | 0.928054 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.06506 | 0.295690 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.91933 | 0.500665 | 0.250333 | − | 0.968160i | \(-0.419460\pi\) | ||||
0.250333 | + | 0.968160i | \(0.419460\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.32421 | −0.599190 | −0.299595 | − | 0.954066i | \(-0.596852\pi\) | ||||
−0.299595 | + | 0.954066i | \(0.596852\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.6044 | −1.25426 | −0.627130 | − | 0.778914i | \(-0.715771\pi\) | ||||
−0.627130 | + | 0.778914i | \(0.715771\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.56924 | 0.323905 | 0.161952 | − | 0.986799i | \(-0.448221\pi\) | ||||
0.161952 | + | 0.986799i | \(0.448221\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.14222 | −0.362704 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.61177 | 0.464055 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.16974 | −0.637341 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.0548 | −1.45639 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.2582 | 1.94537 | 0.972687 | − | 0.232120i | \(-0.0745662\pi\) | ||||
0.972687 | + | 0.232120i | \(0.0745662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.35812 | 0.0930571 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.79278 | −0.393239 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.56924 | 0.308761 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.89817 | −0.464021 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.2130 | −1.68839 | −0.844193 | − | 0.536039i | \(-0.819920\pi\) | ||||
−0.844193 | + | 0.536039i | \(0.819920\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.5030 | 1.16171 | 0.580857 | − | 0.814006i | \(-0.302718\pi\) | ||||
0.580857 | + | 0.814006i | \(0.302718\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.226808 | −0.0149879 | −0.00749394 | − | 0.999972i | \(-0.502385\pi\) | ||||
−0.00749394 | + | 0.999972i | \(0.502385\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.41043 | 0.290185 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.3836 | 1.79396 | 0.896978 | − | 0.442075i | \(-0.145757\pi\) | ||||
0.896978 | + | 0.442075i | \(0.145757\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.25430 | 0.211390 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.2504 | 0.663044 | 0.331522 | − | 0.943448i | \(-0.392438\pi\) | ||||
0.331522 | + | 0.943448i | \(0.392438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.9407 | −1.34891 | −0.674455 | − | 0.738316i | \(-0.735621\pi\) | ||||
−0.674455 | + | 0.738316i | \(0.735621\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3994 | 0.987872 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4444 | 0.728188 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.83581 | −0.623319 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.25670 | 0.268681 | 0.134340 | − | 0.990935i | \(-0.457108\pi\) | ||||
0.134340 | + | 0.990935i | \(0.457108\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.1708 | −1.39387 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.636942 | 0.0397314 | 0.0198657 | − | 0.999803i | \(-0.493676\pi\) | ||||
0.0198657 | + | 0.999803i | \(0.493676\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.623035 | −0.0387135 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.1461 | 0.999419 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.7560 | −1.52652 | −0.763261 | − | 0.646091i | \(-0.776403\pi\) | ||||
−0.763261 | + | 0.646091i | \(0.776403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.09128 | 0.556377 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.594054 | −0.0362201 | −0.0181100 | − | 0.999836i | \(-0.505765\pi\) | ||||
−0.0181100 | + | 0.999836i | \(0.505765\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.4774 | −1.72988 | −0.864939 | − | 0.501877i | \(-0.832643\pi\) | ||||
−0.864939 | + | 0.501877i | \(0.832643\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.39729 | −0.145091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1049 | −0.787397 | −0.393698 | − | 0.919240i | \(-0.628805\pi\) | ||||
−0.393698 | + | 0.919240i | \(0.628805\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.1461 | −0.846906 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.24420 | 0.0742228 | 0.0371114 | − | 0.999311i | \(-0.488184\pi\) | ||||
0.0371114 | + | 0.999311i | \(0.488184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.476558 | −0.0283284 | −0.0141642 | − | 0.999900i | \(-0.504509\pi\) | ||||
−0.0141642 | + | 0.999900i | \(0.504509\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.43076 | 0.320568 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3800 | −0.728237 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.21530 | −0.422969 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.4190 | −1.89394 | −0.946968 | − | 0.321328i | \(-0.895871\pi\) | ||||
−0.946968 | + | 0.321328i | \(0.895871\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.0017 | 1.39272 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0509 | 0.696924 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.6768 | −0.730680 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.88301 | −0.567764 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.718737 | 0.0410205 | 0.0205102 | − | 0.999790i | \(-0.493471\pi\) | ||||
0.0205102 | + | 0.999790i | \(0.493471\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.38808 | 0.135853 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.1237 | 1.08441 | 0.542204 | − | 0.840247i | \(-0.317590\pi\) | ||||
0.542204 | + | 0.840247i | \(0.317590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.4560 | −1.38234 | −0.691168 | − | 0.722694i | \(-0.742904\pi\) | ||||
−0.691168 | + | 0.722694i | \(0.742904\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.08203 | −0.229270 | −0.114635 | − | 0.993408i | \(-0.536570\pi\) | ||||
−0.114635 | + | 0.993408i | \(0.536570\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.0384 | 2.18573 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.35366 | 0.522070 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.66473 | −0.426477 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.5486 | 0.583337 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.31294 | 0.237780 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.70539 | −0.313597 | −0.156798 | − | 0.987631i | \(-0.550117\pi\) | ||||
−0.156798 | + | 0.987631i | \(0.550117\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.52147 | −0.0833760 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.5071 | −1.06262 | −0.531309 | − | 0.847178i | \(-0.678300\pi\) | ||||
−0.531309 | + | 0.847178i | \(0.678300\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.22140 | −0.0663376 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.2028 | −1.85218 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.5488 | 1.63994 | 0.819972 | − | 0.572403i | \(-0.193989\pi\) | ||||
0.819972 | + | 0.572403i | \(0.193989\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.1043 | −1.12969 | −0.564844 | − | 0.825198i | \(-0.691064\pi\) | ||||
−0.564844 | + | 0.825198i | \(0.691064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.0461 | −0.696351 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.4989 | 1.35717 | 0.678584 | − | 0.734523i | \(-0.262594\pi\) | ||||
0.678584 | + | 0.734523i | \(0.262594\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.60556 | 0.0849752 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.3658 | 1.18042 | 0.590210 | − | 0.807250i | \(-0.299045\pi\) | ||||
0.590210 | + | 0.807250i | \(0.299045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.28388 | −0.330730 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.8241 | 0.935524 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.0126 | −0.940252 | −0.470126 | − | 0.882599i | \(-0.655791\pi\) | ||||
−0.470126 | + | 0.882599i | \(0.655791\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.2621 | 0.690395 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.11699 | −0.109908 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.8397 | 1.18259 | 0.591297 | − | 0.806454i | \(-0.298616\pi\) | ||||
0.591297 | + | 0.806454i | \(0.298616\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.2193 | −1.09285 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.98775 | −0.307570 | −0.153785 | − | 0.988104i | \(-0.549146\pi\) | ||||
−0.153785 | + | 0.988104i | \(0.549146\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.34129 | 0.0687163 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.6298 | −1.30962 | −0.654810 | − | 0.755793i | \(-0.727251\pi\) | ||||
−0.654810 | + | 0.755793i | \(0.727251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.9572 | −1.57364 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.3043 | 1.23228 | 0.616138 | − | 0.787639i | \(-0.288697\pi\) | ||||
0.616138 | + | 0.787639i | \(0.288697\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.07098 | −0.408167 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.25266 | 0.466735 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.65219 | 0.183298 | 0.0916490 | − | 0.995791i | \(-0.470786\pi\) | ||||
0.0916490 | + | 0.995791i | \(0.470786\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.66369 | −0.133351 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.3543 | 0.816696 | 0.408348 | − | 0.912826i | \(-0.366105\pi\) | ||||
0.408348 | + | 0.912826i | \(0.366105\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.5909 | 0.926080 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.67864 | −0.182343 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.8675 | 1.77353 | 0.886767 | − | 0.462217i | \(-0.152946\pi\) | ||||
0.886767 | + | 0.462217i | \(0.152946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.7520 | 0.530355 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.01926 | −0.345395 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.9928 | 0.832143 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.5741 | −1.10282 | −0.551408 | − | 0.834236i | \(-0.685909\pi\) | ||||
−0.551408 | + | 0.834236i | \(0.685909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.5931 | 0.954910 | 0.477455 | − | 0.878656i | \(-0.341559\pi\) | ||||
0.477455 | + | 0.878656i | \(0.341559\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.5323 | 0.512099 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.86479 | −0.0902436 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.1545 | −0.683387 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.32304 | 0.208234 | 0.104117 | − | 0.994565i | \(-0.466798\pi\) | ||||
0.104117 | + | 0.994565i | \(0.466798\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.71479 | −0.178521 | −0.0892606 | − | 0.996008i | \(-0.528450\pi\) | ||||
−0.0892606 | + | 0.996008i | \(0.528450\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.3901 | 0.640535 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.0528 | 0.527519 | 0.263760 | − | 0.964588i | \(-0.415037\pi\) | ||||
0.263760 | + | 0.964588i | \(0.415037\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.44203 | −0.116287 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.538500 | −0.0255849 | −0.0127925 | − | 0.999918i | \(-0.504072\pi\) | ||||
−0.0127925 | + | 0.999918i | \(0.504072\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.0103 | −0.662664 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.38003 | −0.442671 | −0.221335 | − | 0.975198i | \(-0.571042\pi\) | ||||
−0.221335 | + | 0.975198i | \(0.571042\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.0653 | 1.50989 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.6444 | 0.782022 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.7242 | −1.10977 | −0.554886 | − | 0.831926i | \(-0.687238\pi\) | ||||
−0.554886 | + | 0.831926i | \(0.687238\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.73749 | 0.407831 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.8198 | 1.71487 | 0.857435 | − | 0.514592i | \(-0.172057\pi\) | ||||
0.857435 | + | 0.514592i | \(0.172057\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.3287 | −0.665912 | −0.332956 | − | 0.942942i | \(-0.608046\pi\) | ||||
−0.332956 | + | 0.942942i | \(0.608046\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.3887 | −0.850927 | −0.425464 | − | 0.904975i | \(-0.639889\pi\) | ||||
−0.425464 | + | 0.904975i | \(0.639889\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.88405 | 0.317876 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.4827 | 0.575174 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −74.8488 | −3.44155 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.16974 | −0.236706 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.1400 | 1.19437 | 0.597184 | − | 0.802104i | \(-0.296286\pi\) | ||||
0.597184 | + | 0.802104i | \(0.296286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.99953 | 0.0911706 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.80487 | −0.127626 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.27567 | −0.329692 | −0.164846 | − | 0.986319i | \(-0.552713\pi\) | ||||
−0.164846 | + | 0.986319i | \(0.552713\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.2171 | 0.552478 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.73616 | 0.349128 | 0.174564 | − | 0.984646i | \(-0.444148\pi\) | ||||
0.174564 | + | 0.984646i | \(0.444148\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.2114 | 0.640050 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.81816 | −0.0815558 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.66694 | −0.387986 | −0.193993 | − | 0.981003i | \(-0.562144\pi\) | ||||
−0.193993 | + | 0.981003i | \(0.562144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.73731 | −0.122294 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.28220 | 0.369285 | 0.184643 | − | 0.982806i | \(-0.440887\pi\) | ||||
0.184643 | + | 0.982806i | \(0.440887\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.01698 | −0.0895772 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.9114 | 1.54742 | 0.773711 | − | 0.633539i | \(-0.218398\pi\) | ||||
0.773711 | + | 0.633539i | \(0.218398\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.11699 | −0.270600 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.4959 | −0.640009 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.4653 | 1.11996 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.25683 | 0.274645 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.9125 | 0.565705 | 0.282853 | − | 0.959163i | \(-0.408719\pi\) | ||||
0.282853 | + | 0.959163i | \(0.408719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.4885 | 1.07081 | 0.535405 | − | 0.844596i | \(-0.320159\pi\) | ||||
0.535405 | + | 0.844596i | \(0.320159\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.4511 | −0.542377 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.90020 | −0.386965 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.1412 | −0.743866 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.4291 | −0.754938 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.29685 | 0.0559631 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.90438 | −0.254320 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0318 | −0.431299 | −0.215650 | − | 0.976471i | \(-0.569187\pi\) | ||||
−0.215650 | + | 0.976471i | \(0.569187\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0559 | 0.431539 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.3310 | −0.912046 | −0.456023 | − | 0.889968i | \(-0.650726\pi\) | ||||
−0.456023 | + | 0.889968i | \(0.650726\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.55387 | −0.194354 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.5773 | −1.00443 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.35664 | −0.185263 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.4179 | −1.37359 | −0.686795 | − | 0.726851i | \(-0.740983\pi\) | ||||
−0.686795 | + | 0.726851i | \(0.740983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.6841 | 1.72076 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.47983 | 0.400239 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 44.8971 | 1.89219 | 0.946093 | − | 0.323894i | \(-0.104992\pi\) | ||||
0.946093 | + | 0.323894i | \(0.104992\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.28958 | −0.180145 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.1454 | −0.676850 | −0.338425 | − | 0.940993i | \(-0.609894\pi\) | ||||
−0.338425 | + | 0.940993i | \(0.609894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1954 | 0.594061 | 0.297031 | − | 0.954868i | \(-0.404004\pi\) | ||||
0.297031 | + | 0.954868i | \(0.404004\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.16857 | 0.215920 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0481 | −0.584831 | −0.292415 | − | 0.956291i | \(-0.594459\pi\) | ||||
−0.292415 | + | 0.956291i | \(0.594459\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.21798 | −0.258411 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.1675 | 0.546280 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.4995 | −0.517676 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.4742 | 0.845061 | 0.422531 | − | 0.906349i | \(-0.361142\pi\) | ||||
0.422531 | + | 0.906349i | \(0.361142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.6568 | 0.851151 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.1501 | −0.540921 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.1372 | 0.662674 | 0.331337 | − | 0.943513i | \(-0.392500\pi\) | ||||
0.331337 | + | 0.943513i | \(0.392500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.41311 | 0.139689 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.5597 | −1.61637 | −0.808183 | − | 0.588931i | \(-0.799549\pi\) | ||||
−0.808183 | + | 0.588931i | \(0.799549\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.4061 | −1.19950 | −0.599750 | − | 0.800188i | \(-0.704733\pi\) | ||||
−0.599750 | + | 0.800188i | \(0.704733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.8110 | 0.684599 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.1165 | −0.897680 | −0.448840 | − | 0.893612i | \(-0.648163\pi\) | ||||
−0.448840 | + | 0.893612i | \(0.648163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.93883 | 0.200131 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.8417 | −0.559974 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.1411 | 1.09622 | 0.548109 | − | 0.836407i | \(-0.315348\pi\) | ||||
0.548109 | + | 0.836407i | \(0.315348\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.66337 | −0.0669648 | −0.0334824 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334824 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.8283 | 0.796969 | 0.398484 | − | 0.917175i | \(-0.369536\pi\) | ||||
0.398484 | + | 0.917175i | \(0.369536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.2642 | −0.612531 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.1708 | −0.487612 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.7275 | −0.628094 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.33916 | −0.0533958 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.1113 | 0.800619 | 0.400309 | − | 0.916380i | \(-0.368903\pi\) | ||||
0.400309 | + | 0.916380i | \(0.368903\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.1082 | 0.838975 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.20933 | 0.127158 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.44000 | −0.175644 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.5135 | −1.52119 | −0.760597 | − | 0.649225i | \(-0.775093\pi\) | ||||
−0.760597 | + | 0.649225i | \(0.775093\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.3844 | 1.55317 | 0.776584 | − | 0.630013i | \(-0.216951\pi\) | ||||
0.776584 | + | 0.630013i | \(0.216951\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.1010 | 0.868882 | 0.434441 | − | 0.900700i | \(-0.356946\pi\) | ||||
0.434441 | + | 0.900700i | \(0.356946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.4444 | −1.62684 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.32706 | −0.169591 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.5824 | 1.04025 | 0.520124 | − | 0.854090i | \(-0.325886\pi\) | ||||
0.520124 | + | 0.854090i | \(0.325886\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.9378 | −0.582781 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.6953 | 0.494541 | 0.247270 | − | 0.968947i | \(-0.420466\pi\) | ||||
0.247270 | + | 0.968947i | \(0.420466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.67371 | 0.103995 | 0.0519976 | − | 0.998647i | \(-0.483441\pi\) | ||||
0.0519976 | + | 0.998647i | \(0.483441\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.15277 | −0.200117 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.8270 | −0.961305 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.8335 | −0.728145 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.0104 | −0.425053 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.2235 | −0.972296 | −0.486148 | − | 0.873877i | \(-0.661598\pi\) | ||||
−0.486148 | + | 0.873877i | \(0.661598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.88750 | 0.341574 | 0.170787 | − | 0.985308i | \(-0.445369\pi\) | ||||
0.170787 | + | 0.985308i | \(0.445369\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.65935 | 0.370692 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.0743 | 0.501009 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.7217 | 1.40512 | 0.702558 | − | 0.711626i | \(-0.252041\pi\) | ||||
0.702558 | + | 0.711626i | \(0.252041\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.169420 | −0.00646377 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.79411 | 0.258835 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.9721 | 0.873898 | 0.436949 | − | 0.899486i | \(-0.356059\pi\) | ||||
0.436949 | + | 0.899486i | \(0.356059\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.4187 | −0.547720 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.6729 | 0.442144 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.4549 | 0.773674 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.86785 | −0.108317 | −0.0541586 | − | 0.998532i | \(-0.517248\pi\) | ||||
−0.0541586 | + | 0.998532i | \(0.517248\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.22172 | 0.0837939 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.2307 | 0.497592 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.9590 | −1.31291 | −0.656457 | − | 0.754363i | \(-0.727946\pi\) | ||||
−0.656457 | + | 0.754363i | \(0.727946\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.6390 | −0.398995 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.7517 | 0.814608 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.65681 | 0.285949 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.5609 | −1.32620 | −0.663099 | − | 0.748532i | \(-0.730759\pi\) | ||||
−0.663099 | + | 0.748532i | \(0.730759\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.19700 | −0.119062 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.6422 | −0.581740 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.2096 | 1.08333 | 0.541663 | − | 0.840596i | \(-0.317795\pi\) | ||||
0.541663 | + | 0.840596i | \(0.317795\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.36576 | −0.0505836 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.2477 | −1.00779 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.5651 | −0.464103 | −0.232052 | − | 0.972703i | \(-0.574544\pi\) | ||||
−0.232052 | + | 0.972703i | \(0.574544\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.6461 | 1.49722 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.5041 | −0.901398 | −0.450699 | − | 0.892676i | \(-0.648825\pi\) | ||||
−0.450699 | + | 0.892676i | \(0.648825\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.54867 | 0.314043 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.9661 | −0.842544 | −0.421272 | − | 0.906934i | \(-0.638416\pi\) | ||||
−0.421272 | + | 0.906934i | \(0.638416\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.1554 | 1.17650 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.5220 | −0.457545 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.06696 | −0.294368 | −0.147184 | − | 0.989109i | \(-0.547021\pi\) | ||||
−0.147184 | + | 0.989109i | \(0.547021\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.17965 | 0.115873 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.5310 | 1.58216 | 0.791081 | − | 0.611711i | \(-0.209519\pi\) | ||||
0.791081 | + | 0.611711i | \(0.209519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.5610 | −0.601128 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.5242 | 0.526501 | 0.263250 | − | 0.964728i | \(-0.415205\pi\) | ||||
0.263250 | + | 0.964728i | \(0.415205\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.1217 | −0.511240 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.5271 | 0.813408 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.4577 | −0.449235 | −0.224617 | − | 0.974447i | \(-0.572113\pi\) | ||||
−0.224617 | + | 0.974447i | \(0.572113\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.475780 | 0.0171348 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.8821 | 0.679142 | 0.339571 | − | 0.940580i | \(-0.389718\pi\) | ||||
0.339571 | + | 0.940580i | \(0.389718\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.465392 | −0.0166959 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.3659 | −0.693856 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.7351 | −0.384133 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.8772 | 0.960514 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.1080 | −1.28711 | −0.643555 | − | 0.765399i | \(-0.722541\pi\) | ||||
−0.643555 | + | 0.765399i | \(0.722541\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.4921 | −0.658338 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.63513 | 0.0581386 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.98473 | 0.212524 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.4489 | −0.936866 | −0.468433 | − | 0.883499i | \(-0.655181\pi\) | ||||
−0.468433 | + | 0.883499i | \(0.655181\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.27029 | 0.327959 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.7214 | −1.05015 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.1170 | −1.27454 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.443744 | −0.0156205 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.7779 | 0.906302 | 0.453151 | − | 0.891434i | \(-0.350300\pi\) | ||||
0.453151 | + | 0.891434i | \(0.350300\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.3586 | 0.995805 | 0.497902 | − | 0.867233i | \(-0.334104\pi\) | ||||
0.497902 | + | 0.867233i | \(0.334104\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.2719 | −0.746039 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.2052 | 1.58153 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.83727 | 0.273856 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.00452 | −0.174659 | −0.0873296 | − | 0.996179i | \(-0.527833\pi\) | ||||
−0.0873296 | + | 0.996179i | \(0.527833\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.69074 | 0.302940 | 0.151470 | − | 0.988462i | \(-0.451599\pi\) | ||||
0.151470 | + | 0.988462i | \(0.451599\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.27223 | 0.252880 | 0.126440 | − | 0.991974i | \(-0.459645\pi\) | ||||
0.126440 | + | 0.991974i | \(0.459645\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.68058 | 0.336220 | 0.168110 | − | 0.985768i | \(-0.446234\pi\) | ||||
0.168110 | + | 0.985768i | \(0.446234\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.78904 | −0.339578 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.14941 | −0.0744727 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.5480 | −0.813938 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.4160 | −1.29174 | −0.645872 | − | 0.763446i | \(-0.723506\pi\) | ||||
−0.645872 | + | 0.763446i | \(0.723506\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.7155 | 0.507430 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.929388 | 0.0320098 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.8617 | −0.819899 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.355977 | −0.0122171 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.33948 | 0.0801963 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.3650 | −0.971200 | −0.485600 | − | 0.874181i | \(-0.661399\pi\) | ||||
−0.485600 | + | 0.874181i | \(0.661399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.3622 | −0.456444 | −0.228222 | − | 0.973609i | \(-0.573291\pi\) | ||||
−0.228222 | + | 0.973609i | \(0.573291\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.6961 | −0.399066 | −0.199533 | − | 0.979891i | \(-0.563942\pi\) | ||||
−0.199533 | + | 0.979891i | \(0.563942\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.05665 | 0.138250 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.0895 | −0.615773 | −0.307886 | − | 0.951423i | \(-0.599622\pi\) | ||||
−0.307886 | + | 0.951423i | \(0.599622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.24758 | −0.314064 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.7232 | −0.872601 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.0932 | −0.748600 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.5884 | 0.798346 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.9438 | −1.55141 | −0.775706 | − | 0.631094i | \(-0.782606\pi\) | ||||
−0.775706 | + | 0.631094i | \(0.782606\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.2162 | −0.816791 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.1280 | −0.543368 | −0.271684 | − | 0.962387i | \(-0.587580\pi\) | ||||
−0.271684 | + | 0.962387i | \(0.587580\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.1120 | −0.508558 | −0.254279 | − | 0.967131i | \(-0.581838\pi\) | ||||
−0.254279 | + | 0.967131i | \(0.581838\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.8450 | −1.40502 | −0.702508 | − | 0.711676i | \(-0.747937\pi\) | ||||
−0.702508 | + | 0.711676i | \(0.747937\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.79563 | −0.0602234 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.3273 | −0.848497 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.3798 | −0.514666 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.00176 | 0.300560 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.3005 | −1.27739 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.55028 | −0.151592 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.46928 | −0.315118 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.1402 | 0.336701 | 0.168351 | − | 0.985727i | \(-0.446156\pi\) | ||||
0.168351 | + | 0.985727i | \(0.446156\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.3097 | 1.07165 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.7638 | 1.15178 | 0.575888 | − | 0.817529i | \(-0.304656\pi\) | ||||
0.575888 | + | 0.817529i | \(0.304656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 77.7460 | 2.57302 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.3868 | −0.409049 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.8017 | −0.653199 | −0.326599 | − | 0.945163i | \(-0.605903\pi\) | ||||
−0.326599 | + | 0.945163i | \(0.605903\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.536879 | 0.0176908 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.83509 | 0.192064 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.80715 | −0.256421 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.2758 | 0.533992 | 0.266996 | − | 0.963698i | \(-0.413969\pi\) | ||||
0.266996 | + | 0.963698i | \(0.413969\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.56597 | 0.116870 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.2850 | 0.467669 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.52172 | −0.0823809 | −0.0411904 | − | 0.999151i | \(-0.513115\pi\) | ||||
−0.0411904 | + | 0.999151i | \(0.513115\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.2681 | −0.596155 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.7285 | 1.42551 | 0.712755 | − | 0.701413i | \(-0.247447\pi\) | ||||
0.712755 | + | 0.701413i | \(0.247447\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.3923 | −0.664066 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.9743 | 1.33149 | 0.665743 | − | 0.746181i | \(-0.268115\pi\) | ||||
0.665743 | + | 0.746181i | \(0.268115\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.6314 | 0.637263 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.04918 | −0.0988764 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.09948 | −0.165188 | −0.0825942 | − | 0.996583i | \(-0.526321\pi\) | ||||
−0.0825942 | + | 0.996583i | \(0.526321\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.1607 | 0.942633 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.3940 | −0.464806 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.55625 | 0.0824595 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.5792 | −0.985400 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.7426 | 0.699193 | 0.349597 | − | 0.936900i | \(-0.386319\pi\) | ||||
0.349597 | + | 0.936900i | \(0.386319\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.72537 | −0.183925 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.9688 | −1.86031 | −0.930153 | − | 0.367172i | \(-0.880326\pi\) | ||||
−0.930153 | + | 0.367172i | \(0.880326\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.7488 | −0.729295 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.09815 | −0.131111 | −0.0655557 | − | 0.997849i | \(-0.520882\pi\) | ||||
−0.0655557 | + | 0.997849i | \(0.520882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −71.8609 | −2.29669 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.4856 | −1.10104 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.8461 | −0.696781 | −0.348391 | − | 0.937349i | \(-0.613272\pi\) | ||||
−0.348391 | + | 0.937349i | \(0.613272\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.22166 | 0.102547 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.6011 | 1.51363 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.4720 | −0.523250 | −0.261625 | − | 0.965170i | \(-0.584258\pi\) | ||||
−0.261625 | + | 0.965170i | \(0.584258\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.26179 | −0.135244 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.1301 | 0.732539 | 0.366270 | − | 0.930509i | \(-0.380635\pi\) | ||||
0.366270 | + | 0.930509i | \(0.380635\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.53268 | −0.0801304 |
(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 | 5600.2.a.bx.1.3 | 5 | ||
4.3 | odd | 2 | 5600.2.a.bu.1.3 | 5 | |||
5.2 | odd | 4 | 1120.2.g.c.449.5 | yes | 10 | ||
5.3 | odd | 4 | 1120.2.g.c.449.6 | yes | 10 | ||
5.4 | even | 2 | 5600.2.a.bv.1.3 | 5 | |||
20.3 | even | 4 | 1120.2.g.b.449.5 | ✓ | 10 | ||
20.7 | even | 4 | 1120.2.g.b.449.6 | yes | 10 | ||
20.19 | odd | 2 | 5600.2.a.bw.1.3 | 5 | |||
40.3 | even | 4 | 2240.2.g.o.449.6 | 10 | |||
40.13 | odd | 4 | 2240.2.g.n.449.5 | 10 | |||
40.27 | even | 4 | 2240.2.g.o.449.5 | 10 | |||
40.37 | odd | 4 | 2240.2.g.n.449.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.g.b.449.5 | ✓ | 10 | 20.3 | even | 4 | ||
1120.2.g.b.449.6 | yes | 10 | 20.7 | even | 4 | ||
1120.2.g.c.449.5 | yes | 10 | 5.2 | odd | 4 | ||
1120.2.g.c.449.6 | yes | 10 | 5.3 | odd | 4 | ||
2240.2.g.n.449.5 | 10 | 40.13 | odd | 4 | |||
2240.2.g.n.449.6 | 10 | 40.37 | odd | 4 | |||
2240.2.g.o.449.5 | 10 | 40.27 | even | 4 | |||
2240.2.g.o.449.6 | 10 | 40.3 | even | 4 | |||
5600.2.a.bu.1.3 | 5 | 4.3 | odd | 2 | |||
5600.2.a.bv.1.3 | 5 | 5.4 | even | 2 | |||
5600.2.a.bw.1.3 | 5 | 20.19 | odd | 2 | |||
5600.2.a.bx.1.3 | 5 | 1.1 | even | 1 | trivial |