Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3360,2,Mod(1,3360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3360, 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("3360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.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: | \(26.8297350792\) |
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: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3360.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.80642 | 1.75070 | 0.875351 | − | 0.483487i | \(-0.160630\pi\) | ||||
0.875351 | + | 0.483487i | \(0.160630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.05086 | 1.40086 | 0.700428 | − | 0.713723i | \(-0.252993\pi\) | ||||
0.700428 | + | 0.713723i | \(0.252993\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.755569 | 0.183252 | 0.0916262 | − | 0.995793i | \(-0.470794\pi\) | ||||
0.0916262 | + | 0.995793i | \(0.470794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.80642 | −0.414422 | −0.207211 | − | 0.978296i | \(-0.566439\pi\) | ||||
−0.207211 | + | 0.978296i | \(0.566439\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.85728 | 1.84687 | 0.923435 | − | 0.383754i | \(-0.125369\pi\) | ||||
0.923435 | + | 0.383754i | \(0.125369\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.755569 | 0.140306 | 0.0701528 | − | 0.997536i | \(-0.477651\pi\) | ||||
0.0701528 | + | 0.997536i | \(0.477651\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.6637 | −1.91526 | −0.957629 | − | 0.288005i | \(-0.907008\pi\) | ||||
−0.957629 | + | 0.288005i | \(0.907008\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.80642 | 1.01077 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.755569 | −0.124215 | −0.0621074 | − | 0.998069i | \(-0.519782\pi\) | ||||
−0.0621074 | + | 0.998069i | \(0.519782\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.05086 | 0.808784 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.61285 | −1.50127 | −0.750637 | − | 0.660715i | \(-0.770253\pi\) | ||||
−0.750637 | + | 0.660715i | \(0.770253\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.24443 | 0.189774 | 0.0948870 | − | 0.995488i | \(-0.469751\pi\) | ||||
0.0948870 | + | 0.995488i | \(0.469751\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.85728 | −1.29197 | −0.645983 | − | 0.763351i | \(-0.723553\pi\) | ||||
−0.645983 | + | 0.763351i | \(0.723553\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.755569 | 0.105801 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.80642 | −1.07229 | −0.536147 | − | 0.844124i | \(-0.680121\pi\) | ||||
−0.536147 | + | 0.844124i | \(0.680121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.80642 | 0.782938 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.80642 | −0.239267 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8573 | −1.39013 | −0.695066 | − | 0.718946i | \(-0.744625\pi\) | ||||
−0.695066 | + | 0.718946i | \(0.744625\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.05086 | 0.626481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3684 | 1.26670 | 0.633352 | − | 0.773864i | \(-0.281679\pi\) | ||||
0.633352 | + | 0.773864i | \(0.281679\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.85728 | 1.06629 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.05086 | −0.362070 | −0.181035 | − | 0.983477i | \(-0.557945\pi\) | ||||
−0.181035 | + | 0.983477i | \(0.557945\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.05086 | −0.122993 | −0.0614966 | − | 0.998107i | \(-0.519587\pi\) | ||||
−0.0614966 | + | 0.998107i | \(0.519587\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.80642 | 0.661703 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.61285 | −0.835619 | −0.417809 | − | 0.908535i | \(-0.637202\pi\) | ||||
−0.417809 | + | 0.908535i | \(0.637202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.755569 | 0.0819529 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.755569 | 0.0810055 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.10171 | 0.858780 | 0.429390 | − | 0.903119i | \(-0.358729\pi\) | ||||
0.429390 | + | 0.903119i | \(0.358729\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.05086 | 0.529473 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.6637 | −1.10577 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.80642 | −0.185335 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.05086 | 0.512837 | 0.256418 | − | 0.966566i | \(-0.417458\pi\) | ||||
0.256418 | + | 0.966566i | \(0.417458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.80642 | 0.583568 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.85728 | −0.469571 | −0.234785 | − | 0.972047i | \(-0.575439\pi\) | ||||
−0.234785 | + | 0.972047i | \(0.575439\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.48886 | −0.429955 | −0.214978 | − | 0.976619i | \(-0.568968\pi\) | ||||
−0.214978 | + | 0.976619i | \(0.568968\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.755569 | −0.0717154 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.4193 | −1.07423 | −0.537117 | − | 0.843508i | \(-0.680487\pi\) | ||||
−0.537117 | + | 0.843508i | \(0.680487\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.85728 | 0.825946 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.05086 | 0.466952 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.755569 | 0.0692629 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.7146 | 2.06496 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.61285 | −0.866761 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1017 | 1.25132 | 0.625662 | − | 0.780094i | \(-0.284829\pi\) | ||||
0.625662 | + | 0.780094i | \(0.284829\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.24443 | 0.109566 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1017 | 1.23207 | 0.616036 | − | 0.787718i | \(-0.288738\pi\) | ||||
0.616036 | + | 0.787718i | \(0.288738\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.80642 | −0.156637 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.2953 | −0.879586 | −0.439793 | − | 0.898099i | \(-0.644948\pi\) | ||||
−0.439793 | + | 0.898099i | \(0.644948\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.19358 | 0.525332 | 0.262666 | − | 0.964887i | \(-0.415398\pi\) | ||||
0.262666 | + | 0.964887i | \(0.415398\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.85728 | −0.745917 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.3274 | 2.45248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.755569 | 0.0627466 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.14272 | −0.0936154 | −0.0468077 | − | 0.998904i | \(-0.514905\pi\) | ||||
−0.0468077 | + | 0.998904i | \(0.514905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.6128 | 1.27056 | 0.635278 | − | 0.772284i | \(-0.280886\pi\) | ||||
0.635278 | + | 0.772284i | \(0.280886\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.755569 | 0.0610841 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.6637 | −0.856529 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.05086 | −0.722337 | −0.361168 | − | 0.932501i | \(-0.617622\pi\) | ||||
−0.361168 | + | 0.932501i | \(0.617622\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.80642 | −0.619090 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.85728 | 0.698051 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.24443 | −0.724080 | −0.362040 | − | 0.932163i | \(-0.617920\pi\) | ||||
−0.362040 | + | 0.932163i | \(0.617920\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.80642 | 0.452029 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.7556 | −0.832291 | −0.416145 | − | 0.909298i | \(-0.636619\pi\) | ||||
−0.416145 | + | 0.909298i | \(0.636619\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5111 | 0.962395 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.80642 | −0.138141 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.61285 | 0.730851 | 0.365426 | − | 0.930841i | \(-0.380923\pi\) | ||||
0.365426 | + | 0.930841i | \(0.380923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000 | 0.601317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.8064 | 1.62989 | 0.814944 | − | 0.579539i | \(-0.196767\pi\) | ||||
0.814944 | + | 0.579539i | \(0.196767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.2444 | −1.13311 | −0.566555 | − | 0.824024i | \(-0.691724\pi\) | ||||
−0.566555 | + | 0.824024i | \(0.691724\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.8573 | −0.802593 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.755569 | −0.0555505 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.38715 | 0.320820 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.05086 | 0.220752 | 0.110376 | − | 0.993890i | \(-0.464794\pi\) | ||||
0.110376 | + | 0.993890i | \(0.464794\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.48886 | 0.323115 | 0.161558 | − | 0.986863i | \(-0.448348\pi\) | ||||
0.161558 | + | 0.986863i | \(0.448348\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.05086 | 0.361699 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.70471 | −0.121456 | −0.0607279 | − | 0.998154i | \(-0.519342\pi\) | ||||
−0.0607279 | + | 0.998154i | \(0.519342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.5620 | 1.45760 | 0.728801 | − | 0.684726i | \(-0.240078\pi\) | ||||
0.728801 | + | 0.684726i | \(0.240078\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.3684 | 0.731332 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.755569 | 0.0530305 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.61285 | −0.671390 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.85728 | 0.615623 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.4889 | −0.725530 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.7146 | −1.49489 | −0.747446 | − | 0.664323i | \(-0.768720\pi\) | ||||
−0.747446 | + | 0.664323i | \(0.768720\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.05086 | −0.209041 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.24443 | 0.0848695 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.6637 | −0.723899 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.05086 | −0.0710102 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.81627 | 0.256710 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.59057 | −0.575267 | −0.287634 | − | 0.957741i | \(-0.592869\pi\) | ||||
−0.287634 | + | 0.957741i | \(0.592869\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.5906 | 0.835666 | 0.417833 | − | 0.908524i | \(-0.362790\pi\) | ||||
0.417833 | + | 0.908524i | \(0.362790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.8796 | −0.917187 | −0.458593 | − | 0.888646i | \(-0.651647\pi\) | ||||
−0.458593 | + | 0.888646i | \(0.651647\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.80642 | 0.382035 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.31756 | 0.0863163 | 0.0431582 | − | 0.999068i | \(-0.486258\pi\) | ||||
0.0431582 | + | 0.999068i | \(0.486258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.85728 | −0.577785 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.00000 | 0.259828 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.05086 | −0.197343 | −0.0986717 | − | 0.995120i | \(-0.531459\pi\) | ||||
−0.0986717 | + | 0.995120i | \(0.531459\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.6128 | 0.876881 | 0.438440 | − | 0.898760i | \(-0.355531\pi\) | ||||
0.438440 | + | 0.898760i | \(0.355531\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.12399 | −0.580545 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.61285 | −0.482445 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.48886 | −0.157096 | −0.0785478 | − | 0.996910i | \(-0.525028\pi\) | ||||
−0.0785478 | + | 0.996910i | \(0.525028\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 51.4291 | 3.23332 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.755569 | 0.0473155 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.368416 | −0.0229812 | −0.0114906 | − | 0.999934i | \(-0.503658\pi\) | ||||
−0.0114906 | + | 0.999934i | \(0.503658\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.755569 | −0.0469488 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.755569 | 0.0467685 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.1847 | −1.86127 | −0.930634 | − | 0.365952i | \(-0.880743\pi\) | ||||
−0.930634 | + | 0.365952i | \(0.880743\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.80642 | −0.479545 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.10171 | 0.495817 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.7368 | −1.87406 | −0.937029 | − | 0.349252i | \(-0.886436\pi\) | ||||
−0.937029 | + | 0.349252i | \(0.886436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.6637 | 1.13374 | 0.566870 | − | 0.823808i | \(-0.308154\pi\) | ||||
0.566870 | + | 0.823808i | \(0.308154\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.05086 | 0.305692 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.80642 | 0.350141 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2444 | −1.15629 | −0.578143 | − | 0.815936i | \(-0.696222\pi\) | ||||
−0.578143 | + | 0.815936i | \(0.696222\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.6637 | −0.638419 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.61285 | −0.573454 | −0.286727 | − | 0.958012i | \(-0.592567\pi\) | ||||
−0.286727 | + | 0.958012i | \(0.592567\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.2257 | 0.667298 | 0.333649 | − | 0.942697i | \(-0.391720\pi\) | ||||
0.333649 | + | 0.942697i | \(0.391720\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.80642 | −0.107003 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.61285 | −0.567428 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4291 | −0.966419 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.05086 | 0.296086 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.1017 | −1.40804 | −0.704018 | − | 0.710182i | \(-0.748613\pi\) | ||||
−0.704018 | + | 0.710182i | \(0.748613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.80642 | 0.336923 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 44.7368 | 2.58720 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.24443 | 0.0717278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.0000 | −0.574485 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.8573 | −0.621686 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.12399 | 0.292441 | 0.146221 | − | 0.989252i | \(-0.453289\pi\) | ||||
0.146221 | + | 0.989252i | \(0.453289\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2257 | −1.31701 | −0.658504 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658504 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.33630 | 0.188579 | 0.0942893 | − | 0.995545i | \(-0.469942\pi\) | ||||
0.0942893 | + | 0.995545i | \(0.469942\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.0098 | −1.57319 | −0.786595 | − | 0.617470i | \(-0.788158\pi\) | ||||
−0.786595 | + | 0.617470i | \(0.788158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.38715 | 0.245633 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.85728 | −0.271107 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.36488 | −0.0759438 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.05086 | 0.280171 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.48886 | −0.248235 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.85728 | −0.488318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.28544 | −0.125619 | −0.0628096 | − | 0.998026i | \(-0.520006\pi\) | ||||
−0.0628096 | + | 0.998026i | \(0.520006\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.755569 | −0.0414049 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.3684 | 0.566487 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.7146 | 1.50971 | 0.754854 | − | 0.655893i | \(-0.227708\pi\) | ||||
0.754854 | + | 0.655893i | \(0.227708\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.4193 | −0.620210 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −61.9180 | −3.35305 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.85728 | 0.476860 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.24443 | 0.0668046 | 0.0334023 | − | 0.999442i | \(-0.489366\pi\) | ||||
0.0334023 | + | 0.999442i | \(0.489366\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.5718 | −1.52942 | −0.764708 | − | 0.644377i | \(-0.777117\pi\) | ||||
−0.764708 | + | 0.644377i | \(0.777117\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.05086 | 0.269595 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.6958 | 1.79345 | 0.896724 | − | 0.442591i | \(-0.145940\pi\) | ||||
0.896724 | + | 0.442591i | \(0.145940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.05086 | −0.161923 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.755569 | 0.0399889 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.7654 | 1.51818 | 0.759090 | − | 0.650985i | \(-0.225644\pi\) | ||||
0.759090 | + | 0.650985i | \(0.225644\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7368 | −0.828254 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.7146 | 1.19221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.05086 | −0.0550043 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.89829 | 0.516687 | 0.258343 | − | 0.966053i | \(-0.416823\pi\) | ||||
0.258343 | + | 0.966053i | \(0.416823\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.61285 | −0.500425 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.80642 | −0.405289 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.5941 | 1.63588 | 0.817941 | − | 0.575303i | \(-0.195116\pi\) | ||||
0.817941 | + | 0.575303i | \(0.195116\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.81627 | 0.196548 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.8163 | 1.83976 | 0.919879 | − | 0.392202i | \(-0.128287\pi\) | ||||
0.919879 | + | 0.392202i | \(0.128287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1017 | 0.722453 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.9813 | −1.73636 | −0.868181 | − | 0.496248i | \(-0.834711\pi\) | ||||
−0.868181 | + | 0.496248i | \(0.834711\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.80642 | 0.295923 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.24443 | 0.0632580 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.8573 | −1.76733 | −0.883667 | − | 0.468116i | \(-0.844933\pi\) | ||||
−0.883667 | + | 0.468116i | \(0.844933\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.69228 | 0.338443 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.1017 | 0.711337 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.9911 | 1.50521 | 0.752605 | − | 0.658472i | \(-0.228797\pi\) | ||||
0.752605 | + | 0.658472i | \(0.228797\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.80642 | −0.0904343 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.5111 | 1.17409 | 0.587045 | − | 0.809554i | \(-0.300291\pi\) | ||||
0.587045 | + | 0.809554i | \(0.300291\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −53.8608 | −2.68300 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.38715 | −0.217463 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.9180 | 1.97382 | 0.986909 | − | 0.161281i | \(-0.0515626\pi\) | ||||
0.986909 | + | 0.161281i | \(0.0515626\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.2953 | −0.507829 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.61285 | −0.373700 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.19358 | 0.303301 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.12399 | −0.0549103 | −0.0274551 | − | 0.999623i | \(-0.508740\pi\) | ||||
−0.0274551 | + | 0.999623i | \(0.508740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.2257 | 1.42437 | 0.712187 | − | 0.701990i | \(-0.247705\pi\) | ||||
0.712187 | + | 0.701990i | \(0.247705\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.85728 | −0.430656 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.755569 | 0.0366505 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.8573 | −0.525421 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 29.3274 | 1.41594 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.1748 | 1.74248 | 0.871240 | − | 0.490857i | \(-0.163316\pi\) | ||||
0.871240 | + | 0.490857i | \(0.163316\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.46028 | −0.406575 | −0.203288 | − | 0.979119i | \(-0.565163\pi\) | ||||
−0.203288 | + | 0.979119i | \(0.565163\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.755569 | 0.0362267 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | −0.765384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0509 | 0.718338 | 0.359169 | − | 0.933273i | \(-0.383060\pi\) | ||||
0.359169 | + | 0.933273i | \(0.383060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.9813 | −1.80454 | −0.902272 | − | 0.431167i | \(-0.858102\pi\) | ||||
−0.902272 | + | 0.431167i | \(0.858102\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.10171 | 0.384058 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.14272 | −0.0540488 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.7146 | 0.930388 | 0.465194 | − | 0.885209i | \(-0.345985\pi\) | ||||
0.465194 | + | 0.885209i | \(0.345985\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −55.8163 | −2.62829 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.6128 | 0.733556 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.05086 | 0.236788 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.89829 | 0.182354 | 0.0911772 | − | 0.995835i | \(-0.470937\pi\) | ||||
0.0911772 | + | 0.995835i | \(0.470937\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.755569 | 0.0352669 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.285442 | −0.0132944 | −0.00664718 | − | 0.999978i | \(-0.502116\pi\) | ||||
−0.00664718 | + | 0.999978i | \(0.502116\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.8163 | 1.10684 | 0.553418 | − | 0.832904i | \(-0.313323\pi\) | ||||
0.553418 | + | 0.832904i | \(0.313323\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.6637 | −0.494517 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.1017 | 1.20784 | 0.603922 | − | 0.797044i | \(-0.293604\pi\) | ||||
0.603922 | + | 0.797044i | \(0.293604\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.3684 | 0.478769 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.05086 | −0.417041 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.22570 | 0.332238 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.80642 | −0.0828844 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.80642 | −0.357432 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.97773 | 0.227438 | 0.113719 | − | 0.993513i | \(-0.463724\pi\) | ||||
0.113719 | + | 0.993513i | \(0.463724\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.81627 | −0.174007 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.85728 | 0.403020 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.05086 | 0.229348 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.38715 | −0.198801 | −0.0994004 | − | 0.995048i | \(-0.531692\pi\) | ||||
−0.0994004 | + | 0.995048i | \(0.531692\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.24443 | −0.418048 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.21585 | −0.235388 | −0.117694 | − | 0.993050i | \(-0.537550\pi\) | ||||
−0.117694 | + | 0.993050i | \(0.537550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.570884 | 0.0257113 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.80642 | 0.260979 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.05086 | −0.136850 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.5906 | −1.27989 | −0.639945 | − | 0.768421i | \(-0.721043\pi\) | ||||
−0.639945 | + | 0.768421i | \(0.721043\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.7556 | −0.480523 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.1847 | 0.632464 | 0.316232 | − | 0.948682i | \(-0.397582\pi\) | ||||
0.316232 | + | 0.948682i | \(0.397582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0000 | −0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.5111 | 0.555639 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.7368 | 1.18509 | 0.592545 | − | 0.805538i | \(-0.298123\pi\) | ||||
0.592545 | + | 0.805538i | \(0.298123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.05086 | −0.0464871 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.80642 | −0.0797556 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −51.4291 | −2.26185 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.61285 | 0.421957 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.3274 | −1.54772 | −0.773861 | − | 0.633356i | \(-0.781677\pi\) | ||||
−0.773861 | + | 0.633356i | \(0.781677\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.1017 | −0.441717 | −0.220858 | − | 0.975306i | \(-0.570886\pi\) | ||||
−0.220858 | + | 0.975306i | \(0.570886\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.05716 | −0.350975 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.4514 | 2.41093 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −48.5531 | −2.10307 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.85728 | −0.209998 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.8064 | 0.941017 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.80642 | 0.250100 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.73683 | −0.289639 | −0.144820 | − | 0.989458i | \(-0.546260\pi\) | ||||
−0.144820 | + | 0.989458i | \(0.546260\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.2444 | −0.654201 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.48886 | −0.192282 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.0607 | −1.75563 | −0.877814 | − | 0.479001i | \(-0.840999\pi\) | ||||
−0.877814 | + | 0.479001i | \(0.840999\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.8573 | −0.463377 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.36488 | −0.0581457 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.755569 | −0.0320721 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.0321 | −1.31487 | −0.657437 | − | 0.753510i | \(-0.728359\pi\) | ||||
−0.657437 | + | 0.753510i | \(0.728359\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.28544 | 0.265846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.38715 | 0.185226 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.2034 | −1.35721 | −0.678606 | − | 0.734502i | \(-0.737416\pi\) | ||||
−0.678606 | + | 0.734502i | \(0.737416\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.4193 | −0.480412 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.7368 | −0.785489 | −0.392744 | − | 0.919648i | \(-0.628474\pi\) | ||||
−0.392744 | + | 0.919648i | \(0.628474\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.3872 | −1.02057 | −0.510285 | − | 0.860005i | \(-0.670460\pi\) | ||||
−0.510285 | + | 0.860005i | \(0.670460\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.05086 | 0.127451 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.85728 | 0.369374 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.6637 | −1.19329 | −0.596643 | − | 0.802507i | \(-0.703499\pi\) | ||||
−0.596643 | + | 0.802507i | \(0.703499\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.48886 | 0.186551 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.61285 | −0.315834 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.3274 | −1.87727 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.05086 | 0.208827 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40.2034 | −1.65937 | −0.829686 | − | 0.558230i | \(-0.811481\pi\) | ||||
−0.829686 | + | 0.558230i | \(0.811481\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.2632 | 0.793725 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.70471 | −0.0701225 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.4924 | −0.718327 | −0.359163 | − | 0.933275i | \(-0.616938\pi\) | ||||
−0.359163 | + | 0.933275i | \(0.616938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.755569 | 0.0309753 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.5620 | 0.841546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.15257 | −0.0470925 | −0.0235463 | − | 0.999723i | \(-0.507496\pi\) | ||||
−0.0235463 | + | 0.999723i | \(0.507496\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.1240 | 0.453757 | 0.226878 | − | 0.973923i | \(-0.427148\pi\) | ||||
0.226878 | + | 0.973923i | \(0.427148\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.3684 | 0.422235 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.7146 | 0.923478 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.8385 | 0.764633 | 0.382316 | − | 0.924031i | \(-0.375126\pi\) | ||||
0.382316 | + | 0.924031i | \(0.375126\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.755569 | 0.0306172 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −44.7368 | −1.80986 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.9590 | −0.523409 | −0.261704 | − | 0.965148i | \(-0.584285\pi\) | ||||
−0.261704 | + | 0.965148i | \(0.584285\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.61285 | −0.387627 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.5210 | 1.18847 | 0.594235 | − | 0.804291i | \(-0.297455\pi\) | ||||
0.594235 | + | 0.804291i | \(0.297455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.5210 | −0.463067 | −0.231534 | − | 0.972827i | \(-0.574374\pi\) | ||||
−0.231534 | + | 0.972827i | \(0.574374\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.85728 | 0.355430 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.10171 | 0.324588 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.4889 | −0.418885 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.570884 | −0.0227626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.9180 | −1.35025 | −0.675127 | − | 0.737702i | \(-0.735911\pi\) | ||||
−0.675127 | + | 0.737702i | \(0.735911\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.7146 | −0.863076 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.1017 | 0.559609 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.05086 | 0.200122 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.05086 | −0.120690 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.3274 | 0.921377 | 0.460689 | − | 0.887562i | \(-0.347603\pi\) | ||||
0.460689 | + | 0.887562i | \(0.347603\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.8163 | 0.465988 | 0.232994 | − | 0.972478i | \(-0.425148\pi\) | ||||
0.232994 | + | 0.972478i | \(0.425148\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.24443 | 0.0489994 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.4701 | −1.11928 | −0.559638 | − | 0.828737i | \(-0.689060\pi\) | ||||
−0.559638 | + | 0.828737i | \(0.689060\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 46.4514 | 1.82338 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.6637 | −0.417943 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.78415 | 0.343750 | 0.171875 | − | 0.985119i | \(-0.445017\pi\) | ||||
0.171875 | + | 0.985119i | \(0.445017\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.1017 | 0.550999 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.05086 | −0.0409978 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.31756 | −0.129234 | −0.0646169 | − | 0.997910i | \(-0.520583\pi\) | ||||
−0.0646169 | + | 0.997910i | \(0.520583\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.7975 | 0.925617 | 0.462808 | − | 0.886458i | \(-0.346842\pi\) | ||||
0.462808 | + | 0.886458i | \(0.346842\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.81627 | 0.148212 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.80642 | −0.0700501 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.69228 | 0.259126 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.59057 | −0.332131 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −63.0420 | −2.43371 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.59057 | −0.254048 | −0.127024 | − | 0.991900i | \(-0.540543\pi\) | ||||
−0.127024 | + | 0.991900i | \(0.540543\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.8163 | 1.14593 | 0.572966 | − | 0.819579i | \(-0.305793\pi\) | ||||
0.572966 | + | 0.819579i | \(0.305793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.05086 | 0.193834 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.5906 | 0.482472 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.1847 | 0.695818 | 0.347909 | − | 0.937528i | \(-0.386892\pi\) | ||||
0.347909 | + | 0.937528i | \(0.386892\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.2953 | −0.393363 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.8796 | −0.529538 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.4291 | −1.50213 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.2355 | 1.11217 | 0.556086 | − | 0.831125i | \(-0.312302\pi\) | ||||
0.556086 | + | 0.831125i | \(0.312302\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.80642 | 0.220568 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.19358 | 0.234936 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.26317 | −0.275112 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.31756 | 0.0498347 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.9813 | 0.905760 | 0.452880 | − | 0.891572i | \(-0.350397\pi\) | ||||
0.452880 | + | 0.891572i | \(0.350397\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.36488 | 0.0514773 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.85728 | −0.333584 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.0000 | −0.376089 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.4889 | 1.22014 | 0.610072 | − | 0.792346i | \(-0.291140\pi\) | ||||
0.610072 | + | 0.792346i | \(0.291140\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.00000 | 0.150012 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −94.4514 | −3.53723 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.3274 | 1.09678 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.05086 | −0.113936 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.3872 | −0.461963 | −0.230981 | − | 0.972958i | \(-0.574194\pi\) | ||||
−0.230981 | + | 0.972958i | \(0.574194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.6128 | 0.506267 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.755569 | 0.0280611 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.1240 | −0.635093 | −0.317547 | − | 0.948243i | \(-0.602859\pi\) | ||||
−0.317547 | + | 0.948243i | \(0.602859\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.940253 | 0.0347765 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.8474 | 0.622274 | 0.311137 | − | 0.950365i | \(-0.399290\pi\) | ||||
0.311137 | + | 0.950365i | \(0.399290\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 60.2034 | 2.21762 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.89829 | −0.216972 | −0.108486 | − | 0.994098i | \(-0.534600\pi\) | ||||
−0.108486 | + | 0.994098i | \(0.534600\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.12399 | −0.335178 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.7556 | −1.27506 | −0.637529 | − | 0.770426i | \(-0.720043\pi\) | ||||
−0.637529 | + | 0.770426i | \(0.720043\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.14272 | −0.0418661 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.61285 | −0.278540 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.85728 | −0.177481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.977725 | −0.0356777 | −0.0178388 | − | 0.999841i | \(-0.505679\pi\) | ||||
−0.0178388 | + | 0.999841i | \(0.505679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.48886 | −0.0906992 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.6128 | 0.568210 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0830 | −1.38415 | −0.692075 | − | 0.721826i | \(-0.743303\pi\) | ||||
−0.692075 | + | 0.721826i | \(0.743303\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 51.4291 | 1.86676 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.8385 | 1.04540 | 0.522698 | − | 0.852518i | \(-0.324925\pi\) | ||||
0.522698 | + | 0.852518i | \(0.324925\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.48886 | −0.162508 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.755569 | 0.0273176 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.4068 | 1.45901 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.63512 | −0.167147 | −0.0835734 | − | 0.996502i | \(-0.526633\pi\) | ||||
−0.0835734 | + | 0.996502i | \(0.526633\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.368416 | −0.0132682 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.5531 | 1.81827 | 0.909134 | − | 0.416503i | \(-0.136744\pi\) | ||||
0.909134 | + | 0.416503i | \(0.136744\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.6637 | −0.383052 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.755569 | −0.0271059 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.3649 | 0.622161 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.7146 | −0.633877 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.755569 | 0.0270018 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.05086 | −0.323039 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.4094 | −0.406702 | −0.203351 | − | 0.979106i | \(-0.565183\pi\) | ||||
−0.203351 | + | 0.979106i | \(0.565183\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.1847 | −1.07460 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.4193 | −0.406023 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −54.8385 | −1.94737 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.80642 | −0.276865 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.61285 | 0.340505 | 0.170252 | − | 0.985401i | \(-0.445542\pi\) | ||||
0.170252 | + | 0.985401i | \(0.445542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.69228 | −0.236756 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.10171 | 0.286260 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.10171 | −0.215325 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.85728 | 0.312178 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.7368 | −1.08199 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.5531 | −1.77735 | −0.888676 | − | 0.458535i | \(-0.848374\pi\) | ||||
−0.888676 | + | 0.458535i | \(0.848374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.2355 | −1.30752 | −0.653758 | − | 0.756703i | \(-0.726809\pi\) | ||||
−0.653758 | + | 0.756703i | \(0.726809\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.6637 | 0.654565 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.24443 | −0.323818 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.24797 | −0.0786465 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.05086 | 0.176491 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.22216 | 0.286955 | 0.143478 | − | 0.989654i | \(-0.454171\pi\) | ||||
0.143478 | + | 0.989654i | \(0.454171\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.83854 | 0.0989454 | 0.0494727 | − | 0.998775i | \(-0.484246\pi\) | ||||
0.0494727 | + | 0.998775i | \(0.484246\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.80642 | 0.202154 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.5718 | −1.06309 | −0.531543 | − | 0.847031i | \(-0.678388\pi\) | ||||
−0.531543 | + | 0.847031i | \(0.678388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.4924 | 1.30216 | 0.651082 | − | 0.759007i | \(-0.274315\pi\) | ||||
0.651082 | + | 0.759007i | \(0.274315\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.2444 | −0.667582 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.755569 | 0.0261789 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.7556 | −0.372212 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.6637 | −0.368591 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.3872 | −0.703843 | −0.351921 | − | 0.936030i | \(-0.614472\pi\) | ||||
−0.351921 | + | 0.936030i | \(0.614472\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4291 | −0.980314 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.61285 | −0.331084 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.5111 | 0.430396 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.7146 | 0.780481 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.2257 | 0.385265 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.69228 | −0.229409 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.23459 | −0.0422715 | −0.0211357 | − | 0.999777i | \(-0.506728\pi\) | ||||
−0.0211357 | + | 0.999777i | \(0.506728\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.80642 | −0.0617784 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.5718 | −1.24927 | −0.624635 | − | 0.780917i | \(-0.714752\pi\) | ||||
−0.624635 | + | 0.780917i | \(0.714752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.09187 | 0.276091 | 0.138045 | − | 0.990426i | \(-0.455918\pi\) | ||||
0.138045 | + | 0.990426i | \(0.455918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.61285 | −0.327605 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.8796 | −0.676708 | −0.338354 | − | 0.941019i | \(-0.609870\pi\) | ||||
−0.338354 | + | 0.941019i | \(0.609870\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.61285 | 0.326847 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.4291 | −0.557962 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.2257 | 0.787878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.3694 | 1.77447 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.05086 | 0.170946 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.9813 | 0.404579 | 0.202289 | − | 0.979326i | \(-0.435162\pi\) | ||||
0.202289 | + | 0.979326i | \(0.435162\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.1017 | −0.812931 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.87601 | −0.164277 | −0.0821386 | − | 0.996621i | \(-0.526175\pi\) | ||||
−0.0821386 | + | 0.996621i | \(0.526175\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.0607 | 0.843360 | 0.421680 | − | 0.906745i | \(-0.361441\pi\) | ||||
0.421680 | + | 0.906745i | \(0.361441\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.00000 | 0.268917 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.1650 | −0.341307 | −0.170654 | − | 0.985331i | \(-0.554588\pi\) | ||||
−0.170654 | + | 0.985331i | \(0.554588\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.1017 | 0.472956 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.80642 | 0.194523 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.0000 | 0.535420 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.8064 | 0.728908 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 44.7368 | 1.49372 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.05716 | −0.268721 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.89829 | −0.196501 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.24443 | 0.0414121 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.2444 | −0.506742 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.3461 | −1.04083 | −0.520416 | − | 0.853913i | \(-0.674223\pi\) | ||||
−0.520416 | + | 0.853913i | \(0.674223\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.25428 | 0.240345 | 0.120172 | − | 0.992753i | \(-0.461655\pi\) | ||||
0.120172 | + | 0.992753i | \(0.461655\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.2034 | −1.46292 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.8573 | −0.358931 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.1017 | 0.465679 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.2257 | 1.68978 | 0.844890 | − | 0.534940i | \(-0.179666\pi\) | ||||
0.844890 | + | 0.534940i | \(0.179666\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.12399 | 0.168841 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.4094 | −0.507207 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.755569 | −0.0248429 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.8385 | 0.683690 | 0.341845 | − | 0.939756i | \(-0.388948\pi\) | ||||
0.341845 | + | 0.939756i | \(0.388948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.80642 | −0.0592032 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.2257 | −0.760375 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.38715 | 0.143475 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.5620 | −1.52111 | −0.760557 | − | 0.649271i | \(-0.775074\pi\) | ||||
−0.760557 | + | 0.649271i | \(0.775074\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.33630 | 0.108876 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.4068 | −1.38242 | −0.691212 | − | 0.722652i | \(-0.742923\pi\) | ||||
−0.691212 | + | 0.722652i | \(0.742923\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −85.1437 | −2.77266 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.9215 | 1.78471 | 0.892355 | − | 0.451335i | \(-0.149052\pi\) | ||||
0.892355 | + | 0.451335i | \(0.149052\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.30772 | −0.172296 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.0098 | −0.908281 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.03212 | 0.0982200 | 0.0491100 | − | 0.998793i | \(-0.484362\pi\) | ||||
0.0491100 | + | 0.998793i | \(0.484362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.05086 | 0.0987234 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.38715 | 0.141816 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.2953 | −0.332452 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 82.7146 | 2.66821 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.85728 | −0.156524 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.48886 | 0.144502 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.9180 | −1.47662 | −0.738311 | − | 0.674460i | \(-0.764376\pi\) | ||||
−0.738311 | + | 0.674460i | \(0.764376\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.36488 | −0.0438462 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.6548 | −1.62559 | −0.812795 | − | 0.582550i | \(-0.802055\pi\) | ||||
−0.812795 | + | 0.582550i | \(0.802055\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.19358 | 0.198557 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.05086 | 0.161757 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.930409 | −0.0297664 | −0.0148832 | − | 0.999889i | \(-0.504738\pi\) | ||||
−0.0148832 | + | 0.999889i | \(0.504738\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.0420 | 1.50347 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.48886 | −0.143318 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.5496 | −1.00627 | −0.503137 | − | 0.864206i | \(-0.667821\pi\) | ||||
−0.503137 | + | 0.864206i | \(0.667821\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.70471 | −0.0543167 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.85728 | −0.281930 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0223 | 0.350488 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.77430 | 0.151661 | 0.0758304 | − | 0.997121i | \(-0.475839\pi\) | ||||
0.0758304 | + | 0.997121i | \(0.475839\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.28544 | −0.0725263 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.5620 | 0.651859 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.460282 | −0.0145773 | −0.00728864 | − | 0.999973i | \(-0.502320\pi\) | ||||
−0.00728864 | + | 0.999973i | \(0.502320\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.755569 | −0.0239051 |
(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 | 3360.2.a.bj.1.3 | yes | 3 | |
4.3 | odd | 2 | 3360.2.a.bi.1.1 | ✓ | 3 | ||
8.3 | odd | 2 | 6720.2.a.db.1.3 | 3 | |||
8.5 | even | 2 | 6720.2.a.da.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3360.2.a.bi.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
3360.2.a.bj.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
6720.2.a.da.1.1 | 3 | 8.5 | even | 2 | |||
6720.2.a.db.1.3 | 3 | 8.3 | odd | 2 |