Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5400,2,Mod(1,5400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5400, 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("5400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5400.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: | \(43.1192170915\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 11x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1080) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.31342\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5400.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.418627 | −0.158226 | −0.0791130 | − | 0.996866i | \(-0.525209\pi\) | ||||
−0.0791130 | + | 0.996866i | \(0.525209\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.50958 | −1.96271 | −0.981356 | − | 0.192201i | \(-0.938437\pi\) | ||||
−0.981356 | + | 0.192201i | \(0.938437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62685 | 0.728557 | 0.364278 | − | 0.931290i | \(-0.381316\pi\) | ||||
0.364278 | + | 0.931290i | \(0.381316\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.27492 | −0.551748 | −0.275874 | − | 0.961194i | \(-0.588967\pi\) | ||||
−0.275874 | + | 0.961194i | \(0.588967\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.27492 | 0.980733 | 0.490367 | − | 0.871516i | \(-0.336863\pi\) | ||||
0.490367 | + | 0.871516i | \(0.336863\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.27492 | 0.891382 | 0.445691 | − | 0.895187i | \(-0.352958\pi\) | ||||
0.445691 | + | 0.895187i | \(0.352958\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.62685 | 0.487793 | 0.243897 | − | 0.969801i | \(-0.421574\pi\) | ||||
0.243897 | + | 0.969801i | \(0.421574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.09095 | 1.00135 | 0.500673 | − | 0.865637i | \(-0.333086\pi\) | ||||
0.500673 | + | 0.865637i | \(0.333086\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.71780 | −1.36149 | −0.680746 | − | 0.732520i | \(-0.738344\pi\) | ||||
−0.680746 | + | 0.732520i | \(0.738344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.3923 | −1.58481 | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.5498 | −1.53885 | −0.769426 | − | 0.638736i | \(-0.779458\pi\) | ||||
−0.769426 | + | 0.638736i | \(0.779458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.82475 | −0.974965 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.54983 | 0.762328 | 0.381164 | − | 0.924507i | \(-0.375523\pi\) | ||||
0.381164 | + | 0.924507i | \(0.375523\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.46410 | 0.450988 | 0.225494 | − | 0.974245i | \(-0.427600\pi\) | ||||
0.225494 | + | 0.974245i | \(0.427600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2749 | 1.31557 | 0.657784 | − | 0.753206i | \(-0.271494\pi\) | ||||
0.657784 | + | 0.753206i | \(0.271494\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.09095 | −0.744128 | −0.372064 | − | 0.928207i | \(-0.621350\pi\) | ||||
−0.372064 | + | 0.928207i | \(0.621350\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.62685 | 0.311750 | 0.155875 | − | 0.987777i | \(-0.450180\pi\) | ||||
0.155875 | + | 0.987777i | \(0.450180\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.50958 | 0.761888 | 0.380944 | − | 0.924598i | \(-0.375599\pi\) | ||||
0.380944 | + | 0.924598i | \(0.375599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.72508 | 0.310552 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.27492 | 0.705983 | 0.352992 | − | 0.935626i | \(-0.385164\pi\) | ||||
0.352992 | + | 0.935626i | \(0.385164\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.450166 | −0.0494121 | −0.0247060 | − | 0.999695i | \(-0.507865\pi\) | ||||
−0.0247060 | + | 0.999695i | \(0.507865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3923 | 1.10158 | 0.550791 | − | 0.834643i | \(-0.314326\pi\) | ||||
0.550791 | + | 0.834643i | \(0.314326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.09967 | −0.115277 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.3901 | −1.46110 | −0.730548 | − | 0.682862i | \(-0.760735\pi\) | ||||
−0.730548 | + | 0.682862i | \(0.760735\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.0646 | 1.59849 | 0.799245 | − | 0.601005i | \(-0.205233\pi\) | ||||
0.799245 | + | 0.601005i | \(0.205233\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.76546 | 0.765153 | 0.382577 | − | 0.923924i | \(-0.375037\pi\) | ||||
0.382577 | + | 0.923924i | \(0.375037\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.72508 | −0.263444 | −0.131722 | − | 0.991287i | \(-0.542051\pi\) | ||||
−0.131722 | + | 0.991287i | \(0.542051\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8248 | 1.22839 | 0.614194 | − | 0.789155i | \(-0.289481\pi\) | ||||
0.614194 | + | 0.789155i | \(0.289481\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.952341 | 0.0873010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.3746 | 2.85224 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0646 | 1.42551 | 0.712753 | − | 0.701416i | \(-0.247448\pi\) | ||||
0.712753 | + | 0.701416i | \(0.247448\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.0646 | 1.40357 | 0.701787 | − | 0.712387i | \(-0.252386\pi\) | ||||
0.701787 | + | 0.712387i | \(0.252386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.78959 | −0.155178 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.8248 | 1.43744 | 0.718718 | − | 0.695302i | \(-0.244729\pi\) | ||||
0.718718 | + | 0.695302i | \(0.244729\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.0997 | −1.42995 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.67232 | −0.464695 | −0.232347 | − | 0.972633i | \(-0.574641\pi\) | ||||
−0.232347 | + | 0.972633i | \(0.574641\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7251 | 0.872795 | 0.436397 | − | 0.899754i | \(-0.356254\pi\) | ||||
0.436397 | + | 0.899754i | \(0.356254\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.55505 | −0.762576 | −0.381288 | − | 0.924456i | \(-0.624519\pi\) | ||||
−0.381288 | + | 0.924456i | \(0.624519\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.78959 | −0.141040 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.4356 | −1.36566 | −0.682831 | − | 0.730577i | \(-0.739251\pi\) | ||||
−0.682831 | + | 0.730577i | \(0.739251\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.72508 | −0.288256 | −0.144128 | − | 0.989559i | \(-0.546038\pi\) | ||||
−0.144128 | + | 0.989559i | \(0.546038\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.09967 | −0.469205 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.0997 | −1.83226 | −0.916132 | − | 0.400877i | \(-0.868706\pi\) | ||||
−0.916132 | + | 0.400877i | \(0.868706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.46192 | −0.557730 | −0.278865 | − | 0.960330i | \(-0.589958\pi\) | ||||
−0.278865 | + | 0.960330i | \(0.589958\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.82475 | −0.209962 | −0.104981 | − | 0.994474i | \(-0.533478\pi\) | ||||
−0.104981 | + | 0.994474i | \(0.533478\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.8087 | 1.08292 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8564 | −1.00261 | −0.501307 | − | 0.865269i | \(-0.667147\pi\) | ||||
−0.501307 | + | 0.865269i | \(0.667147\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.9260 | 0.786472 | 0.393236 | − | 0.919438i | \(-0.371356\pi\) | ||||
0.393236 | + | 0.919438i | \(0.371356\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.00000 | 0.641223 | 0.320612 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320612 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.8248 | 1.40534 | 0.702670 | − | 0.711516i | \(-0.251991\pi\) | ||||
0.702670 | + | 0.711516i | \(0.251991\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.09967 | −0.0771816 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.8279 | −1.92490 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8248 | 1.15826 | 0.579132 | − | 0.815234i | \(-0.303392\pi\) | ||||
0.579132 | + | 0.815234i | \(0.303392\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.25588 | −0.0852547 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.97586 | −0.401980 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.2011 | 1.68759 | 0.843794 | − | 0.536668i | \(-0.180317\pi\) | ||||
0.843794 | + | 0.536668i | \(0.180317\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.7251 | −0.910966 | −0.455483 | − | 0.890245i | \(-0.650533\pi\) | ||||
−0.455483 | + | 0.890245i | \(0.650533\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.27492 | 0.546822 | 0.273411 | − | 0.961897i | \(-0.411848\pi\) | ||||
0.273411 | + | 0.961897i | \(0.411848\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.837253 | −0.0541574 | −0.0270787 | − | 0.999633i | \(-0.508620\pi\) | ||||
−0.0270787 | + | 0.999633i | \(0.508620\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2749 | 1.04836 | 0.524180 | − | 0.851608i | \(-0.324372\pi\) | ||||
0.524180 | + | 0.851608i | \(0.324372\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.2296 | 0.714520 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.837253 | 0.0528470 | 0.0264235 | − | 0.999651i | \(-0.491588\pi\) | ||||
0.0264235 | + | 0.999651i | \(0.491588\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.8279 | −1.74953 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.2749 | 1.63898 | 0.819492 | − | 0.573090i | \(-0.194256\pi\) | ||||
0.819492 | + | 0.573090i | \(0.194256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.54983 | −0.158439 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.4502 | −0.829373 | −0.414686 | − | 0.909964i | \(-0.636109\pi\) | ||||
−0.414686 | + | 0.909964i | \(0.636109\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.8564 | −0.844840 | −0.422420 | − | 0.906400i | \(-0.638819\pi\) | ||||
−0.422420 | + | 0.906400i | \(0.638819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.0000 | 1.39715 | 0.698575 | − | 0.715537i | \(-0.253818\pi\) | ||||
0.698575 | + | 0.715537i | \(0.253818\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8087 | 0.889771 | 0.444886 | − | 0.895587i | \(-0.353244\pi\) | ||||
0.444886 | + | 0.895587i | \(0.353244\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.88054 | 0.470114 | 0.235057 | − | 0.971982i | \(-0.424472\pi\) | ||||
0.235057 | + | 0.971982i | \(0.424472\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.46410 | −0.205919 | −0.102960 | − | 0.994686i | \(-0.532831\pi\) | ||||
−0.102960 | + | 0.994686i | \(0.532831\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.64950 | 0.215423 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8248 | −0.695574 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.7251 | 0.684987 | 0.342493 | − | 0.939520i | \(-0.388729\pi\) | ||||
0.342493 | + | 0.939520i | \(0.388729\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.2296 | 0.649422 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.35050 | 0.250758 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.1101 | −1.09067 | −0.545336 | − | 0.838218i | \(-0.683598\pi\) | ||||
−0.545336 | + | 0.838218i | \(0.683598\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.46410 | 0.196431 | 0.0982156 | − | 0.995165i | \(-0.468687\pi\) | ||||
0.0982156 | + | 0.995165i | \(0.468687\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.9019 | 0.955351 | 0.477675 | − | 0.878536i | \(-0.341480\pi\) | ||||
0.477675 | + | 0.878536i | \(0.341480\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0997 | 0.679585 | 0.339793 | − | 0.940500i | \(-0.389643\pi\) | ||||
0.339793 | + | 0.940500i | \(0.389643\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.0997 | −0.957398 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.72508 | −0.541118 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.41644 | 0.243486 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5498 | 0.799731 | 0.399866 | − | 0.916574i | \(-0.369057\pi\) | ||||
0.399866 | + | 0.916574i | \(0.369057\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.4115 | −1.27530 | −0.637652 | − | 0.770325i | \(-0.720094\pi\) | ||||
−0.637652 | + | 0.770325i | \(0.720094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.5287 | −1.05754 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.78741 | 0.312491 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.27492 | 0.0684411 | 0.0342206 | − | 0.999414i | \(-0.489105\pi\) | ||||
0.0342206 | + | 0.999414i | \(0.489105\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.9244 | 1.60182 | 0.800909 | − | 0.598786i | \(-0.204350\pi\) | ||||
0.800909 | + | 0.598786i | \(0.204350\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0997 | −0.803674 | −0.401837 | − | 0.915711i | \(-0.631628\pi\) | ||||
−0.401837 | + | 0.915711i | \(0.631628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.8756 | −1.41844 | −0.709219 | − | 0.704988i | \(-0.750952\pi\) | ||||
−0.709219 | + | 0.704988i | \(0.750952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.725083 | −0.0381623 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.7824 | −1.29363 | −0.646816 | − | 0.762646i | \(-0.723900\pi\) | ||||
−0.646816 | + | 0.762646i | \(0.723900\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.32331 | −0.120620 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.1101 | −0.989484 | −0.494742 | − | 0.869040i | \(-0.664737\pi\) | ||||
−0.494742 | + | 0.869040i | \(0.664737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.90033 | 0.355385 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.2749 | 0.527787 | 0.263894 | − | 0.964552i | \(-0.414993\pi\) | ||||
0.263894 | + | 0.964552i | \(0.414993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.8248 | 1.57507 | 0.787536 | − | 0.616269i | \(-0.211357\pi\) | ||||
0.787536 | + | 0.616269i | \(0.211357\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.3851 | 1.69269 | 0.846347 | − | 0.532632i | \(-0.178797\pi\) | ||||
0.846347 | + | 0.532632i | \(0.178797\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.72508 | −0.491819 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.97586 | 0.299920 | 0.149960 | − | 0.988692i | \(-0.452086\pi\) | ||||
0.149960 | + | 0.988692i | \(0.452086\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.1101 | 0.954313 | 0.477156 | − | 0.878818i | \(-0.341667\pi\) | ||||
0.477156 | + | 0.878818i | \(0.341667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.88054 | 0.392558 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −39.6495 | −1.96535 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0997 | 1.29055 | 0.645273 | − | 0.763952i | \(-0.276744\pi\) | ||||
0.645273 | + | 0.763952i | \(0.276744\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.45017 | −0.0713580 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.2252 | −0.939212 | −0.469606 | − | 0.882876i | \(-0.655604\pi\) | ||||
−0.469606 | + | 0.882876i | \(0.655604\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.37459 | −0.359415 | −0.179708 | − | 0.983720i | \(-0.557515\pi\) | ||||
−0.179708 | + | 0.983720i | \(0.557515\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.30136 | −0.208157 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.5024 | 1.42108 | 0.710540 | − | 0.703656i | \(-0.248451\pi\) | ||||
0.710540 | + | 0.703656i | \(0.248451\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.18408 | −0.393302 | −0.196651 | − | 0.980474i | \(-0.563007\pi\) | ||||
−0.196651 | + | 0.980474i | \(0.563007\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.2749 | 0.874208 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.54983 | −0.360334 | −0.180167 | − | 0.983636i | \(-0.557664\pi\) | ||||
−0.180167 | + | 0.983636i | \(0.557664\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.7251 | −1.03219 | −0.516095 | − | 0.856531i | \(-0.672615\pi\) | ||||
−0.516095 | + | 0.856531i | \(0.672615\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.0816 | 1.56122 | 0.780609 | − | 0.625020i | \(-0.214909\pi\) | ||||
0.780609 | + | 0.625020i | \(0.214909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 56.7492 | 2.67221 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.8492 | 1.72373 | 0.861867 | − | 0.507134i | \(-0.169295\pi\) | ||||
0.861867 | + | 0.507134i | \(0.169295\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.20822 | 0.102847 | 0.0514236 | − | 0.998677i | \(-0.483624\pi\) | ||||
0.0514236 | + | 0.998677i | \(0.483624\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.3901 | −0.668766 | −0.334383 | − | 0.942437i | \(-0.608528\pi\) | ||||
−0.334383 | + | 0.942437i | \(0.608528\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.6495 | −1.60339 | −0.801694 | − | 0.597735i | \(-0.796068\pi\) | ||||
−0.801694 | + | 0.597735i | \(0.796068\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.54983 | 0.117740 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 67.6495 | 3.11053 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.9950 | 0.867904 | 0.433952 | − | 0.900936i | \(-0.357119\pi\) | ||||
0.433952 | + | 0.900936i | \(0.357119\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | 0.729537 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.0668 | −0.546799 | −0.273400 | − | 0.961901i | \(-0.588148\pi\) | ||||
−0.273400 | + | 0.961901i | \(0.588148\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.9019 | −0.762771 | −0.381386 | − | 0.924416i | \(-0.624553\pi\) | ||||
−0.381386 | + | 0.924416i | \(0.624553\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.97586 | −0.269139 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.09967 | −0.0493269 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.82475 | −0.215986 | −0.107993 | − | 0.994152i | \(-0.534442\pi\) | ||||
−0.107993 | + | 0.994152i | \(0.534442\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.8248 | −0.928530 | −0.464265 | − | 0.885696i | \(-0.653681\pi\) | ||||
−0.464265 | + | 0.885696i | \(0.653681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.3901 | 0.637831 | 0.318915 | − | 0.947783i | \(-0.396681\pi\) | ||||
0.318915 | + | 0.947783i | \(0.396681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.72508 | −0.120551 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 68.6750 | 3.02032 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.20604 | 0.271891 | 0.135946 | − | 0.990716i | \(-0.456593\pi\) | ||||
0.135946 | + | 0.990716i | \(0.456593\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.4833 | 0.720762 | 0.360381 | − | 0.932805i | \(-0.382647\pi\) | ||||
0.360381 | + | 0.932805i | \(0.382647\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.82475 | −0.297291 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.72508 | −0.205438 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.9003 | −0.991923 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 44.4262 | 1.91357 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.5498 | −1.57140 | −0.785700 | − | 0.618608i | \(-0.787697\pi\) | ||||
−0.785700 | + | 0.618608i | \(0.787697\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.3161 | −1.08244 | −0.541220 | − | 0.840881i | \(-0.682037\pi\) | ||||
−0.541220 | + | 0.840881i | \(0.682037\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.2296 | 0.478395 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.62685 | −0.111705 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.3746 | −0.863299 | −0.431649 | − | 0.902041i | \(-0.642068\pi\) | ||||
−0.431649 | + | 0.902041i | \(0.642068\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.2990 | −1.15462 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.17525 | 0.344546 | 0.172273 | − | 0.985049i | \(-0.444889\pi\) | ||||
0.172273 | + | 0.985049i | \(0.444889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.5216 | −1.78260 | −0.891298 | − | 0.453417i | \(-0.850205\pi\) | ||||
−0.891298 | + | 0.453417i | \(0.850205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.4743 | −1.69379 | −0.846897 | − | 0.531756i | \(-0.821532\pi\) | ||||
−0.846897 | + | 0.531756i | \(0.821532\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4115 | −0.974632 | −0.487316 | − | 0.873226i | \(-0.662024\pi\) | ||||
−0.487316 | + | 0.873226i | \(0.662024\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.188451 | 0.00781828 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.1271 | −1.49623 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.0997 | −1.57254 | −0.786271 | − | 0.617882i | \(-0.787991\pi\) | ||||
−0.786271 | + | 0.617882i | \(0.787991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8248 | 0.528435 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.8248 | 1.18369 | 0.591845 | − | 0.806052i | \(-0.298400\pi\) | ||||
0.591845 | + | 0.806052i | \(0.298400\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.4071 | 1.28326 | 0.641629 | − | 0.767015i | \(-0.278259\pi\) | ||||
0.641629 | + | 0.767015i | \(0.278259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.54983 | 0.307964 | 0.153982 | − | 0.988074i | \(-0.450790\pi\) | ||||
0.153982 | + | 0.988074i | \(0.450790\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.4306 | −1.47867 | −0.739336 | − | 0.673336i | \(-0.764861\pi\) | ||||
−0.739336 | + | 0.673336i | \(0.764861\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.7128 | −1.12114 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.6602 | 1.92498 | 0.962488 | − | 0.271324i | \(-0.0874615\pi\) | ||||
0.962488 | + | 0.271324i | \(0.0874615\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.1752 | 0.771966 | 0.385983 | − | 0.922506i | \(-0.373862\pi\) | ||||
0.385983 | + | 0.922506i | \(0.373862\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.09967 | 0.0441994 | 0.0220997 | − | 0.999756i | \(-0.492965\pi\) | ||||
0.0220997 | + | 0.999756i | \(0.492965\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.35050 | −0.174299 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.8564 | −0.552491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.0000 | 0.676759 | 0.338380 | − | 0.941010i | \(-0.390121\pi\) | ||||
0.338380 | + | 0.941010i | \(0.390121\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.9276 | −0.710317 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.9621 | −1.61791 | −0.808954 | − | 0.587872i | \(-0.799966\pi\) | ||||
−0.808954 | + | 0.587872i | \(0.799966\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.4980 | 1.47878 | 0.739389 | − | 0.673278i | \(-0.235114\pi\) | ||||
0.739389 | + | 0.673278i | \(0.235114\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.92442 | 0.311541 | 0.155771 | − | 0.987793i | \(-0.450214\pi\) | ||||
0.155771 | + | 0.987793i | \(0.450214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.5498 | −0.885158 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.5498 | 0.530246 | 0.265123 | − | 0.964215i | \(-0.414587\pi\) | ||||
0.265123 | + | 0.964215i | \(0.414587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.6005 | −0.490847 | −0.245423 | − | 0.969416i | \(-0.578927\pi\) | ||||
−0.245423 | + | 0.969416i | \(0.578927\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.09967 | −0.276145 | −0.138073 | − | 0.990422i | \(-0.544091\pi\) | ||||
−0.138073 | + | 0.990422i | \(0.544091\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.2296 | 0.434810 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −66.8854 | −2.58208 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.1797 | −0.623682 | −0.311841 | − | 0.950134i | \(-0.600946\pi\) | ||||
−0.311841 | + | 0.950134i | \(0.600946\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.02409 | 0.231183 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.4743 | 1.08954 | 0.544769 | − | 0.838586i | \(-0.316618\pi\) | ||||
0.544769 | + | 0.838586i | \(0.316618\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.5786 | 0.555399 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.7251 | −0.826461 | −0.413231 | − | 0.910626i | \(-0.635600\pi\) | ||||
−0.413231 | + | 0.910626i | \(0.635600\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.8323 | 0.751201 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.2274 | −0.575130 | −0.287565 | − | 0.957761i | \(-0.592846\pi\) | ||||
−0.287565 | + | 0.957761i | \(0.592846\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.0383 | 0.982053 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.72508 | −0.252923 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.549834 | −0.0206495 | −0.0103247 | − | 0.999947i | \(-0.503287\pi\) | ||||
−0.0103247 | + | 0.999947i | \(0.503287\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.8248 | 0.480291 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.3638 | −0.908616 | −0.454308 | − | 0.890845i | \(-0.650114\pi\) | ||||
−0.454308 | + | 0.890845i | \(0.650114\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.25083 | −0.121067 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.2657 | 1.53046 | 0.765230 | − | 0.643757i | \(-0.222625\pi\) | ||||
0.765230 | + | 0.643757i | \(0.222625\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.6416 | 0.874417 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.1057 | −1.00117 | −0.500587 | − | 0.865686i | \(-0.666882\pi\) | ||||
−0.500587 | + | 0.865686i | \(0.666882\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.6495 | 1.46051 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.9244 | −1.02722 | −0.513608 | − | 0.858025i | \(-0.671692\pi\) | ||||
−0.513608 | + | 0.858025i | \(0.671692\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.0997 | 1.21431 | 0.607155 | − | 0.794584i | \(-0.292311\pi\) | ||||
0.607155 | + | 0.794584i | \(0.292311\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.14079 | 0.0416837 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.4502 | −0.746237 | −0.373119 | − | 0.927784i | \(-0.621712\pi\) | ||||
−0.373119 | + | 0.927784i | \(0.621712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.18627 | 0.152152 | 0.0760762 | − | 0.997102i | \(-0.475761\pi\) | ||||
0.0760762 | + | 0.997102i | \(0.475761\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.20604 | 0.224969 | 0.112484 | − | 0.993653i | \(-0.464119\pi\) | ||||
0.112484 | + | 0.993653i | \(0.464119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.36878 | −0.194363 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.09967 | 0.328570 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.00000 | 0.0360609 | 0.0180305 | − | 0.999837i | \(-0.494260\pi\) | ||||
0.0180305 | + | 0.999837i | \(0.494260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.8248 | −1.46836 | −0.734182 | − | 0.678953i | \(-0.762434\pi\) | ||||
−0.734182 | + | 0.678953i | \(0.762434\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −37.2679 | −1.33526 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0997 | −0.611874 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.0290 | 1.89028 | 0.945139 | − | 0.326668i | \(-0.105926\pi\) | ||||
0.945139 | + | 0.326668i | \(0.105926\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.86077 | −0.208385 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.9906 | 0.958466 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.0996689 | −0.00353045 | −0.00176523 | − | 0.999998i | \(-0.500562\pi\) | ||||
−0.00176523 | + | 0.999998i | \(0.500562\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −42.3746 | −1.49537 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.46410 | 0.121791 | 0.0608957 | − | 0.998144i | \(-0.480604\pi\) | ||||
0.0608957 | + | 0.998144i | \(0.480604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.5498 | −0.370455 | −0.185227 | − | 0.982696i | \(-0.559302\pi\) | ||||
−0.185227 | + | 0.982696i | \(0.559302\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −44.4262 | −1.55428 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.7611 | −0.550066 | −0.275033 | − | 0.961435i | \(-0.588689\pi\) | ||||
−0.275033 | + | 0.961435i | \(0.588689\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.0553 | −1.50081 | −0.750406 | − | 0.660977i | \(-0.770142\pi\) | ||||
−0.750406 | + | 0.660977i | \(0.770142\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.3746 | −0.812814 | −0.406407 | − | 0.913692i | \(-0.633218\pi\) | ||||
−0.406407 | + | 0.913692i | \(0.633218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.1993 | −1.53511 | −0.767553 | − | 0.640985i | \(-0.778526\pi\) | ||||
−0.767553 | + | 0.640985i | \(0.778526\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.5257 | 0.537935 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.7611 | 0.544133 | 0.272067 | − | 0.962278i | \(-0.412293\pi\) | ||||
0.272067 | + | 0.962278i | \(0.412293\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.0997 | −0.762058 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.1342 | −0.451298 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.0383 | 0.892582 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.4065 | −1.45197 | −0.725985 | − | 0.687711i | \(-0.758616\pi\) | ||||
−0.725985 | + | 0.687711i | \(0.758616\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.9244 | 0.407330 | 0.203665 | − | 0.979041i | \(-0.434715\pi\) | ||||
0.203665 | + | 0.979041i | \(0.434715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.4743 | 1.24449 | 0.622243 | − | 0.782824i | \(-0.286222\pi\) | ||||
0.622243 | + | 0.782824i | \(0.286222\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.4743 | −1.10544 | −0.552718 | − | 0.833368i | \(-0.686409\pi\) | ||||
−0.552718 | + | 0.833368i | \(0.686409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.8471 | −1.38564 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0000 | −0.542139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.4454 | −1.93979 | −0.969897 | − | 0.243517i | \(-0.921699\pi\) | ||||
−0.969897 | + | 0.243517i | \(0.921699\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.0860 | 0.845168 | 0.422584 | − | 0.906324i | \(-0.361123\pi\) | ||||
0.422584 | + | 0.906324i | \(0.361123\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.3588 | 1.45914 | 0.729570 | − | 0.683906i | \(-0.239720\pi\) | ||||
0.729570 | + | 0.683906i | \(0.239720\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.3746 | −0.784842 | −0.392421 | − | 0.919786i | \(-0.628362\pi\) | ||||
−0.392421 | + | 0.919786i | \(0.628362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.72508 | −0.225552 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45.0997 | −1.50920 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.88054 | 0.262831 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.6254 | −0.420614 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.09095 | 0.202247 | 0.101123 | − | 0.994874i | \(-0.467756\pi\) | ||||
0.101123 | + | 0.994874i | \(0.467756\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3923 | 0.344312 | 0.172156 | − | 0.985070i | \(-0.444927\pi\) | ||||
0.172156 | + | 0.985070i | \(0.444927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.93039 | 0.0969817 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.72508 | −0.222082 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.4743 | 1.17019 | 0.585094 | − | 0.810966i | \(-0.301058\pi\) | ||||
0.585094 | + | 0.810966i | \(0.301058\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.90033 | 0.227127 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.2443 | 1.05790 | 0.528951 | − | 0.848652i | \(-0.322585\pi\) | ||||
0.528951 | + | 0.848652i | \(0.322585\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.1752 | −0.956180 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.6673 | −0.805847 | −0.402923 | − | 0.915234i | \(-0.632006\pi\) | ||||
−0.402923 | + | 0.915234i | \(0.632006\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.0838 | 0.948104 | 0.474052 | − | 0.880497i | \(-0.342791\pi\) | ||||
0.474052 | + | 0.880497i | \(0.342791\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37.2679 | −1.21361 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.7492 | 0.836736 | 0.418368 | − | 0.908278i | \(-0.362602\pi\) | ||||
0.418368 | + | 0.908278i | \(0.362602\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.0997 | 0.555079 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.3505 | 0.335285 | 0.167643 | − | 0.985848i | \(-0.446384\pi\) | ||||
0.167643 | + | 0.985848i | \(0.446384\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.04329 | −0.227440 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.3183 | 0.685551 | 0.342776 | − | 0.939417i | \(-0.388633\pi\) | ||||
0.342776 | + | 0.939417i | \(0.388633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0881 | 0.676751 | 0.338375 | − | 0.941011i | \(-0.390123\pi\) | ||||
0.338375 | + | 0.941011i | \(0.390123\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.67451 | −0.0536822 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.0997 | 0.611053 | 0.305526 | − | 0.952184i | \(-0.401168\pi\) | ||||
0.305526 | + | 0.952184i | \(0.401168\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −67.6495 | −2.16209 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.0241 | −1.49984 | −0.749918 | − | 0.661531i | \(-0.769907\pi\) | ||||
−0.749918 | + | 0.661531i | \(0.769907\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.4262 | −1.41267 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.6495 | 0.655953 | 0.327977 | − | 0.944686i | \(-0.393633\pi\) | ||||
0.327977 | + | 0.944686i | \(0.393633\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.952341 | −0.0301609 | −0.0150805 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150805 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5400.2.a.ch.1.2 | 4 | ||
3.2 | odd | 2 | 5400.2.a.cg.1.2 | 4 | |||
5.2 | odd | 4 | 1080.2.f.g.649.7 | yes | 8 | ||
5.3 | odd | 4 | 1080.2.f.g.649.8 | yes | 8 | ||
5.4 | even | 2 | 5400.2.a.cg.1.3 | 4 | |||
15.2 | even | 4 | 1080.2.f.g.649.2 | yes | 8 | ||
15.8 | even | 4 | 1080.2.f.g.649.1 | ✓ | 8 | ||
15.14 | odd | 2 | inner | 5400.2.a.ch.1.3 | 4 | ||
20.3 | even | 4 | 2160.2.f.o.1729.8 | 8 | |||
20.7 | even | 4 | 2160.2.f.o.1729.7 | 8 | |||
60.23 | odd | 4 | 2160.2.f.o.1729.1 | 8 | |||
60.47 | odd | 4 | 2160.2.f.o.1729.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.f.g.649.1 | ✓ | 8 | 15.8 | even | 4 | ||
1080.2.f.g.649.2 | yes | 8 | 15.2 | even | 4 | ||
1080.2.f.g.649.7 | yes | 8 | 5.2 | odd | 4 | ||
1080.2.f.g.649.8 | yes | 8 | 5.3 | odd | 4 | ||
2160.2.f.o.1729.1 | 8 | 60.23 | odd | 4 | |||
2160.2.f.o.1729.2 | 8 | 60.47 | odd | 4 | |||
2160.2.f.o.1729.7 | 8 | 20.7 | even | 4 | |||
2160.2.f.o.1729.8 | 8 | 20.3 | even | 4 | |||
5400.2.a.cg.1.2 | 4 | 3.2 | odd | 2 | |||
5400.2.a.cg.1.3 | 4 | 5.4 | even | 2 | |||
5400.2.a.ch.1.2 | 4 | 1.1 | even | 1 | trivial | ||
5400.2.a.ch.1.3 | 4 | 15.14 | odd | 2 | inner |