Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7938,2,Mod(1,7938)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7938, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7938.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7938.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: | \(63.3852491245\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7938.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.44949 | 1.54266 | 0.771329 | − | 0.636436i | \(-0.219592\pi\) | ||||
0.771329 | + | 0.636436i | \(0.219592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.44949 | −1.09082 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.89898 | 1.35873 | 0.679366 | − | 0.733799i | \(-0.262255\pi\) | ||||
0.679366 | + | 0.733799i | \(0.262255\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.44949 | −1.70903 | −0.854515 | − | 0.519427i | \(-0.826146\pi\) | ||||
−0.854515 | + | 0.519427i | \(0.826146\pi\) | |||||||
\(20\) | 3.44949 | 0.771329 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | 1.00000 | 0.208514 | 0.104257 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104257 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.89898 | 1.37980 | ||||||||
\(26\) | −4.89898 | −0.960769 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.89898 | −0.538327 | −0.269163 | − | 0.963095i | \(-0.586747\pi\) | ||||
−0.269163 | + | 0.963095i | \(0.586747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.79796 | −1.28198 | −0.640988 | − | 0.767551i | \(-0.721475\pi\) | ||||
−0.640988 | + | 0.767551i | \(0.721475\pi\) | |||||||
\(38\) | 7.44949 | 1.20847 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.44949 | −0.545412 | ||||||||
\(41\) | −9.79796 | −1.53018 | −0.765092 | − | 0.643921i | \(-0.777307\pi\) | ||||
−0.765092 | + | 0.643921i | \(0.777307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.89898 | −0.442090 | −0.221045 | − | 0.975264i | \(-0.570947\pi\) | ||||
−0.221045 | + | 0.975264i | \(0.570947\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −9.79796 | −1.42918 | −0.714590 | − | 0.699544i | \(-0.753387\pi\) | ||||
−0.714590 | + | 0.699544i | \(0.753387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.89898 | −0.975663 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.89898 | 0.679366 | ||||||||
\(53\) | 1.10102 | 0.151237 | 0.0756184 | − | 0.997137i | \(-0.475907\pi\) | ||||
0.0756184 | + | 0.997137i | \(0.475907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.89898 | −0.930258 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.89898 | 0.380655 | ||||||||
\(59\) | −2.00000 | −0.260378 | −0.130189 | − | 0.991489i | \(-0.541558\pi\) | ||||
−0.130189 | + | 0.991489i | \(0.541558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.4495 | −1.46596 | −0.732978 | − | 0.680252i | \(-0.761870\pi\) | ||||
−0.732978 | + | 0.680252i | \(0.761870\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 16.8990 | 2.09606 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.10102 | −0.378850 | −0.189425 | − | 0.981895i | \(-0.560662\pi\) | ||||
−0.189425 | + | 0.981895i | \(0.560662\pi\) | |||||||
\(68\) | 2.00000 | 0.242536 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.89898 | −1.17479 | −0.587396 | − | 0.809299i | \(-0.699847\pi\) | ||||
−0.587396 | + | 0.809299i | \(0.699847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.89898 | −0.339300 | −0.169650 | − | 0.985504i | \(-0.554264\pi\) | ||||
−0.169650 | + | 0.985504i | \(0.554264\pi\) | |||||||
\(74\) | 7.79796 | 0.906494 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.44949 | −0.854515 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.89898 | 0.888705 | 0.444352 | − | 0.895852i | \(-0.353434\pi\) | ||||
0.444352 | + | 0.895852i | \(0.353434\pi\) | |||||||
\(80\) | 3.44949 | 0.385665 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.79796 | 1.08200 | ||||||||
\(83\) | 2.00000 | 0.219529 | 0.109764 | − | 0.993958i | \(-0.464990\pi\) | ||||
0.109764 | + | 0.993958i | \(0.464990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.89898 | 0.748299 | ||||||||
\(86\) | 2.89898 | 0.312605 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | −7.10102 | −0.752707 | −0.376353 | − | 0.926476i | \(-0.622822\pi\) | ||||
−0.376353 | + | 0.926476i | \(0.622822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.79796 | 1.01058 | ||||||||
\(95\) | −25.6969 | −2.63645 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.89898 | 0.700485 | 0.350243 | − | 0.936659i | \(-0.386099\pi\) | ||||
0.350243 | + | 0.936659i | \(0.386099\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.89898 | 0.689898 | ||||||||
\(101\) | 7.24745 | 0.721148 | 0.360574 | − | 0.932731i | \(-0.382581\pi\) | ||||
0.360574 | + | 0.932731i | \(0.382581\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | −1.37946 | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||||
−0.689730 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(104\) | −4.89898 | −0.480384 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.10102 | −0.106941 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.6969 | −1.59928 | −0.799638 | − | 0.600482i | \(-0.794975\pi\) | ||||
−0.799638 | + | 0.600482i | \(0.794975\pi\) | |||||||
\(110\) | 6.89898 | 0.657792 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.8990 | 1.49565 | 0.747825 | − | 0.663896i | \(-0.231098\pi\) | ||||
0.747825 | + | 0.663896i | \(0.231098\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.44949 | 0.321667 | ||||||||
\(116\) | −2.89898 | −0.269163 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00000 | 0.184115 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 11.4495 | 1.03659 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | 6.55051 | 0.585895 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.00000 | −0.266207 | −0.133103 | − | 0.991102i | \(-0.542494\pi\) | ||||
−0.133103 | + | 0.991102i | \(0.542494\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −16.8990 | −1.48214 | ||||||||
\(131\) | −13.4495 | −1.17509 | −0.587544 | − | 0.809192i | \(-0.699905\pi\) | ||||
−0.587544 | + | 0.809192i | \(0.699905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.10102 | 0.267887 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | 11.7980 | 1.00797 | 0.503984 | − | 0.863713i | \(-0.331867\pi\) | ||||
0.503984 | + | 0.863713i | \(0.331867\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.44949 | −0.801495 | −0.400748 | − | 0.916188i | \(-0.631250\pi\) | ||||
−0.400748 | + | 0.916188i | \(0.631250\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.89898 | 0.830704 | ||||||||
\(143\) | −9.79796 | −0.819346 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.0000 | −0.830455 | ||||||||
\(146\) | 2.89898 | 0.239921 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.79796 | −0.640988 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | −0.406894 | −0.203447 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203447 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(152\) | 7.44949 | 0.604233 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.6969 | −1.66242 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.34847 | −0.506663 | −0.253332 | − | 0.967380i | \(-0.581526\pi\) | ||||
−0.253332 | + | 0.967380i | \(0.581526\pi\) | |||||||
\(158\) | −7.89898 | −0.628409 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.44949 | −0.272706 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.202041 | −0.0158251 | −0.00791254 | − | 0.999969i | \(-0.502519\pi\) | ||||
−0.00791254 | + | 0.999969i | \(0.502519\pi\) | |||||||
\(164\) | −9.79796 | −0.765092 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | 18.6969 | 1.44681 | 0.723406 | − | 0.690423i | \(-0.242575\pi\) | ||||
0.723406 | + | 0.690423i | \(0.242575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000 | 0.846154 | ||||||||
\(170\) | −6.89898 | −0.529128 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.89898 | −0.221045 | ||||||||
\(173\) | −12.8990 | −0.980691 | −0.490346 | − | 0.871528i | \(-0.663129\pi\) | ||||
−0.490346 | + | 0.871528i | \(0.663129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00000 | −0.150756 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.10102 | 0.532244 | ||||||||
\(179\) | 8.69694 | 0.650040 | 0.325020 | − | 0.945707i | \(-0.394629\pi\) | ||||
0.325020 | + | 0.945707i | \(0.394629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.34847 | −0.323219 | −0.161610 | − | 0.986855i | \(-0.551669\pi\) | ||||
−0.161610 | + | 0.986855i | \(0.551669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −26.8990 | −1.97765 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | −9.79796 | −0.714590 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 25.6969 | 1.86425 | ||||||||
\(191\) | −13.8990 | −1.00569 | −0.502847 | − | 0.864375i | \(-0.667714\pi\) | ||||
−0.502847 | + | 0.864375i | \(0.667714\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.10102 | −0.583124 | −0.291562 | − | 0.956552i | \(-0.594175\pi\) | ||||
−0.291562 | + | 0.956552i | \(0.594175\pi\) | |||||||
\(194\) | −6.89898 | −0.495318 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6969 | 0.904619 | 0.452310 | − | 0.891861i | \(-0.350600\pi\) | ||||
0.452310 | + | 0.891861i | \(0.350600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.89898 | −0.489056 | −0.244528 | − | 0.969642i | \(-0.578633\pi\) | ||||
−0.244528 | + | 0.969642i | \(0.578633\pi\) | |||||||
\(200\) | −6.89898 | −0.487832 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.24745 | −0.509929 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −33.7980 | −2.36055 | ||||||||
\(206\) | 14.0000 | 0.975426 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.89898 | 0.339683 | ||||||||
\(209\) | 14.8990 | 1.03058 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.10102 | 0.213483 | 0.106742 | − | 0.994287i | \(-0.465958\pi\) | ||||
0.106742 | + | 0.994287i | \(0.465958\pi\) | |||||||
\(212\) | 1.10102 | 0.0756184 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | −10.0000 | −0.681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 16.6969 | 1.13086 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.89898 | −0.465129 | ||||||||
\(221\) | 9.79796 | 0.659082 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.8990 | 1.39950 | 0.699750 | − | 0.714388i | \(-0.253295\pi\) | ||||
0.699750 | + | 0.714388i | \(0.253295\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.8990 | −1.05758 | ||||||||
\(227\) | −0.550510 | −0.0365386 | −0.0182693 | − | 0.999833i | \(-0.505816\pi\) | ||||
−0.0182693 | + | 0.999833i | \(0.505816\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.2474 | 1.53623 | 0.768117 | − | 0.640309i | \(-0.221194\pi\) | ||||
0.768117 | + | 0.640309i | \(0.221194\pi\) | |||||||
\(230\) | −3.44949 | −0.227453 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.89898 | 0.190327 | ||||||||
\(233\) | 7.00000 | 0.458585 | 0.229293 | − | 0.973358i | \(-0.426359\pi\) | ||||
0.229293 | + | 0.973358i | \(0.426359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −33.7980 | −2.20474 | ||||||||
\(236\) | −2.00000 | −0.130189 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7980 | 0.827831 | 0.413916 | − | 0.910315i | \(-0.364161\pi\) | ||||
0.413916 | + | 0.910315i | \(0.364161\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.89898 | 0.573234 | 0.286617 | − | 0.958045i | \(-0.407469\pi\) | ||||
0.286617 | + | 0.958045i | \(0.407469\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.4495 | −0.732978 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.4949 | −2.32211 | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.55051 | −0.414291 | ||||||||
\(251\) | 12.5505 | 0.792181 | 0.396091 | − | 0.918211i | \(-0.370367\pi\) | ||||
0.396091 | + | 0.918211i | \(0.370367\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 3.00000 | 0.188237 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.7980 | 1.73399 | 0.866995 | − | 0.498318i | \(-0.166049\pi\) | ||||
0.866995 | + | 0.498318i | \(0.166049\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.8990 | 1.04803 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.4495 | 0.830912 | ||||||||
\(263\) | −16.1010 | −0.992831 | −0.496416 | − | 0.868085i | \(-0.665351\pi\) | ||||
−0.496416 | + | 0.868085i | \(0.665351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.79796 | 0.233307 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.10102 | −0.189425 | ||||||||
\(269\) | −3.65153 | −0.222638 | −0.111319 | − | 0.993785i | \(-0.535507\pi\) | ||||
−0.111319 | + | 0.993785i | \(0.535507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.8990 | −1.02654 | −0.513270 | − | 0.858227i | \(-0.671566\pi\) | ||||
−0.513270 | + | 0.858227i | \(0.671566\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.7980 | −0.712741 | ||||||||
\(275\) | −13.7980 | −0.832048 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6969 | 0.642717 | 0.321358 | − | 0.946958i | \(-0.395861\pi\) | ||||
0.321358 | + | 0.946958i | \(0.395861\pi\) | |||||||
\(278\) | 9.44949 | 0.566743 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.0000 | 1.13344 | 0.566722 | − | 0.823909i | \(-0.308211\pi\) | ||||
0.566722 | + | 0.823909i | \(0.308211\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.5505 | 1.22160 | 0.610801 | − | 0.791785i | \(-0.290848\pi\) | ||||
0.610801 | + | 0.791785i | \(0.290848\pi\) | |||||||
\(284\) | −9.89898 | −0.587396 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.79796 | 0.579365 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 10.0000 | 0.587220 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.89898 | −0.169650 | ||||||||
\(293\) | 27.2474 | 1.59181 | 0.795906 | − | 0.605420i | \(-0.206995\pi\) | ||||
0.795906 | + | 0.605420i | \(0.206995\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.89898 | −0.401674 | ||||||||
\(296\) | 7.79796 | 0.453247 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 4.89898 | 0.283315 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.00000 | 0.287718 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.44949 | −0.427258 | ||||||||
\(305\) | −39.4949 | −2.26147 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.752551 | −0.0429504 | −0.0214752 | − | 0.999769i | \(-0.506836\pi\) | ||||
−0.0214752 | + | 0.999769i | \(0.506836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.6969 | 1.17551 | ||||||||
\(311\) | 1.30306 | 0.0738898 | 0.0369449 | − | 0.999317i | \(-0.488237\pi\) | ||||
0.0369449 | + | 0.999317i | \(0.488237\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.6969 | −1.39595 | −0.697977 | − | 0.716120i | \(-0.745916\pi\) | ||||
−0.697977 | + | 0.716120i | \(0.745916\pi\) | |||||||
\(314\) | 6.34847 | 0.358265 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.89898 | 0.444352 | ||||||||
\(317\) | 8.69694 | 0.488469 | 0.244234 | − | 0.969716i | \(-0.421463\pi\) | ||||
0.244234 | + | 0.969716i | \(0.421463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.79796 | 0.324623 | ||||||||
\(320\) | 3.44949 | 0.192832 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.8990 | −0.829001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.7980 | 1.87477 | ||||||||
\(326\) | 0.202041 | 0.0111900 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.79796 | 0.541002 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6969 | −1.35747 | −0.678733 | − | 0.734385i | \(-0.737471\pi\) | ||||
−0.678733 | + | 0.734385i | \(0.737471\pi\) | |||||||
\(332\) | 2.00000 | 0.109764 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.6969 | −1.02305 | ||||||||
\(335\) | −10.6969 | −0.584436 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.3939 | 1.92803 | 0.964014 | − | 0.265853i | \(-0.0856535\pi\) | ||||
0.964014 | + | 0.265853i | \(0.0856535\pi\) | |||||||
\(338\) | −11.0000 | −0.598321 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.89898 | 0.374150 | ||||||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.89898 | 0.156302 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.8990 | 0.693453 | ||||||||
\(347\) | 19.5959 | 1.05196 | 0.525982 | − | 0.850496i | \(-0.323698\pi\) | ||||
0.525982 | + | 0.850496i | \(0.323698\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.8990 | −1.11870 | −0.559348 | − | 0.828933i | \(-0.688949\pi\) | ||||
−0.559348 | + | 0.828933i | \(0.688949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00000 | 0.106600 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.1464 | −1.81230 | ||||||||
\(356\) | −7.10102 | −0.376353 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.69694 | −0.459647 | ||||||||
\(359\) | −10.7980 | −0.569894 | −0.284947 | − | 0.958543i | \(-0.591976\pi\) | ||||
−0.284947 | + | 0.958543i | \(0.591976\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.4949 | 1.92078 | ||||||||
\(362\) | 4.34847 | 0.228550 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0000 | −0.523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.79796 | −0.302651 | −0.151325 | − | 0.988484i | \(-0.548354\pi\) | ||||
−0.151325 | + | 0.988484i | \(0.548354\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.8990 | 1.39841 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.89898 | 0.150103 | 0.0750517 | − | 0.997180i | \(-0.476088\pi\) | ||||
0.0750517 | + | 0.997180i | \(0.476088\pi\) | |||||||
\(374\) | 4.00000 | 0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.79796 | 0.505291 | ||||||||
\(377\) | −14.2020 | −0.731442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.4949 | −1.36095 | −0.680476 | − | 0.732771i | \(-0.738227\pi\) | ||||
−0.680476 | + | 0.732771i | \(0.738227\pi\) | |||||||
\(380\) | −25.6969 | −1.31823 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.8990 | 0.711134 | ||||||||
\(383\) | 6.89898 | 0.352521 | 0.176261 | − | 0.984344i | \(-0.443600\pi\) | ||||
0.176261 | + | 0.984344i | \(0.443600\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.10102 | 0.412331 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.89898 | 0.350243 | ||||||||
\(389\) | 15.1010 | 0.765652 | 0.382826 | − | 0.923820i | \(-0.374951\pi\) | ||||
0.382826 | + | 0.923820i | \(0.374951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.6969 | −0.639663 | ||||||||
\(395\) | 27.2474 | 1.37097 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.30306 | −0.466907 | −0.233454 | − | 0.972368i | \(-0.575003\pi\) | ||||
−0.233454 | + | 0.972368i | \(0.575003\pi\) | |||||||
\(398\) | 6.89898 | 0.345815 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.89898 | 0.344949 | ||||||||
\(401\) | 10.1010 | 0.504421 | 0.252210 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252210 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.3939 | −1.46421 | ||||||||
\(404\) | 7.24745 | 0.360574 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.5959 | 0.773061 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.79796 | −0.286691 | −0.143345 | − | 0.989673i | \(-0.545786\pi\) | ||||
−0.143345 | + | 0.989673i | \(0.545786\pi\) | |||||||
\(410\) | 33.7980 | 1.66916 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.0000 | −0.689730 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.89898 | 0.338658 | ||||||||
\(416\) | −4.89898 | −0.240192 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14.8990 | −0.728733 | ||||||||
\(419\) | 24.5505 | 1.19937 | 0.599685 | − | 0.800236i | \(-0.295292\pi\) | ||||
0.599685 | + | 0.800236i | \(0.295292\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1010 | 0.638505 | 0.319252 | − | 0.947670i | \(-0.396568\pi\) | ||||
0.319252 | + | 0.947670i | \(0.396568\pi\) | |||||||
\(422\) | −3.10102 | −0.150955 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.10102 | −0.0534703 | ||||||||
\(425\) | 13.7980 | 0.669299 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.0000 | 0.482243 | ||||||||
\(431\) | 7.59592 | 0.365882 | 0.182941 | − | 0.983124i | \(-0.441438\pi\) | ||||
0.182941 | + | 0.983124i | \(0.441438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7980 | −0.566974 | −0.283487 | − | 0.958976i | \(-0.591491\pi\) | ||||
−0.283487 | + | 0.958976i | \(0.591491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.6969 | −0.799638 | ||||||||
\(437\) | −7.44949 | −0.356357 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.7980 | −1.04036 | −0.520180 | − | 0.854057i | \(-0.674135\pi\) | ||||
−0.520180 | + | 0.854057i | \(0.674135\pi\) | |||||||
\(440\) | 6.89898 | 0.328896 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.79796 | −0.466041 | ||||||||
\(443\) | 5.10102 | 0.242357 | 0.121178 | − | 0.992631i | \(-0.461333\pi\) | ||||
0.121178 | + | 0.992631i | \(0.461333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.4949 | −1.16117 | ||||||||
\(446\) | −20.8990 | −0.989595 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.5959 | 0.877596 | 0.438798 | − | 0.898586i | \(-0.355404\pi\) | ||||
0.438798 | + | 0.898586i | \(0.355404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.5959 | 0.922736 | ||||||||
\(452\) | 15.8990 | 0.747825 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.550510 | 0.0258367 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.4949 | 1.47327 | 0.736635 | − | 0.676291i | \(-0.236414\pi\) | ||||
0.736635 | + | 0.676291i | \(0.236414\pi\) | |||||||
\(458\) | −23.2474 | −1.08628 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.44949 | 0.160833 | ||||||||
\(461\) | 20.3485 | 0.947723 | 0.473861 | − | 0.880599i | \(-0.342860\pi\) | ||||
0.473861 | + | 0.880599i | \(0.342860\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.6969 | −1.19424 | −0.597119 | − | 0.802153i | \(-0.703688\pi\) | ||||
−0.597119 | + | 0.802153i | \(0.703688\pi\) | |||||||
\(464\) | −2.89898 | −0.134582 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.00000 | −0.324269 | ||||||||
\(467\) | 10.0000 | 0.462745 | 0.231372 | − | 0.972865i | \(-0.425678\pi\) | ||||
0.231372 | + | 0.972865i | \(0.425678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 33.7980 | 1.55898 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.00000 | 0.0920575 | ||||||||
\(473\) | 5.79796 | 0.266590 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −51.3939 | −2.35811 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.7980 | −0.585365 | ||||||||
\(479\) | −29.5959 | −1.35227 | −0.676136 | − | 0.736777i | \(-0.736347\pi\) | ||||
−0.676136 | + | 0.736777i | \(0.736347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.2020 | −1.74186 | ||||||||
\(482\) | −8.89898 | −0.405337 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 23.7980 | 1.08061 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.3939 | 1.01476 | 0.507382 | − | 0.861721i | \(-0.330613\pi\) | ||||
0.507382 | + | 0.861721i | \(0.330613\pi\) | |||||||
\(488\) | 11.4495 | 0.518294 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.79796 | 0.171399 | 0.0856997 | − | 0.996321i | \(-0.472687\pi\) | ||||
0.0856997 | + | 0.996321i | \(0.472687\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.79796 | −0.261127 | ||||||||
\(494\) | 36.4949 | 1.64198 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.3939 | 1.49492 | 0.747458 | − | 0.664309i | \(-0.231274\pi\) | ||||
0.747458 | + | 0.664309i | \(0.231274\pi\) | |||||||
\(500\) | 6.55051 | 0.292948 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.5505 | −0.560157 | ||||||||
\(503\) | 24.4949 | 1.09217 | 0.546087 | − | 0.837729i | \(-0.316117\pi\) | ||||
0.546087 | + | 0.837729i | \(0.316117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.0000 | 1.11249 | ||||||||
\(506\) | 2.00000 | 0.0889108 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.00000 | −0.133103 | ||||||||
\(509\) | −16.8990 | −0.749034 | −0.374517 | − | 0.927220i | \(-0.622191\pi\) | ||||
−0.374517 | + | 0.927220i | \(0.622191\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.7980 | −1.22612 | ||||||||
\(515\) | −48.2929 | −2.12804 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.5959 | 0.861827 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −16.8990 | −0.741069 | ||||||||
\(521\) | −38.6969 | −1.69534 | −0.847672 | − | 0.530521i | \(-0.821996\pi\) | ||||
−0.847672 | + | 0.530521i | \(0.821996\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.348469 | −0.0152375 | −0.00761875 | − | 0.999971i | \(-0.502425\pi\) | ||||
−0.00761875 | + | 0.999971i | \(0.502425\pi\) | |||||||
\(524\) | −13.4495 | −0.587544 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.1010 | 0.702038 | ||||||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | −3.79796 | −0.164973 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −48.0000 | −2.07911 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 41.3939 | 1.78961 | ||||||||
\(536\) | 3.10102 | 0.133944 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.65153 | 0.157429 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.4949 | 1.31108 | 0.655539 | − | 0.755161i | \(-0.272441\pi\) | ||||
0.655539 | + | 0.755161i | \(0.272441\pi\) | |||||||
\(542\) | 16.8990 | 0.725873 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.00000 | −0.0857493 | ||||||||
\(545\) | −57.5959 | −2.46714 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.5959 | 1.35094 | 0.675472 | − | 0.737386i | \(-0.263940\pi\) | ||||
0.675472 | + | 0.737386i | \(0.263940\pi\) | |||||||
\(548\) | 11.7980 | 0.503984 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.7980 | 0.588347 | ||||||||
\(551\) | 21.5959 | 0.920017 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10.6969 | −0.454469 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.44949 | −0.400748 | ||||||||
\(557\) | 3.10102 | 0.131394 | 0.0656972 | − | 0.997840i | \(-0.479073\pi\) | ||||
0.0656972 | + | 0.997840i | \(0.479073\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.2020 | −0.600682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.0000 | −0.801467 | ||||||||
\(563\) | 13.9444 | 0.587686 | 0.293843 | − | 0.955854i | \(-0.405066\pi\) | ||||
0.293843 | + | 0.955854i | \(0.405066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 54.8434 | 2.30728 | ||||||||
\(566\) | −20.5505 | −0.863802 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.89898 | 0.415352 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.2020 | 0.594337 | 0.297168 | − | 0.954825i | \(-0.403958\pi\) | ||||
0.297168 | + | 0.954825i | \(0.403958\pi\) | |||||||
\(572\) | −9.79796 | −0.409673 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.89898 | 0.287707 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.5959 | −0.982311 | −0.491155 | − | 0.871072i | \(-0.663425\pi\) | ||||
−0.491155 | + | 0.871072i | \(0.663425\pi\) | |||||||
\(578\) | 13.0000 | 0.540729 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.0000 | −0.415227 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.20204 | −0.0911992 | ||||||||
\(584\) | 2.89898 | 0.119961 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.2474 | −1.12558 | ||||||||
\(587\) | −18.1464 | −0.748983 | −0.374492 | − | 0.927230i | \(-0.622183\pi\) | ||||
−0.374492 | + | 0.927230i | \(0.622183\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.6969 | 1.84171 | ||||||||
\(590\) | 6.89898 | 0.284026 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.79796 | −0.320494 | ||||||||
\(593\) | −14.6969 | −0.603531 | −0.301765 | − | 0.953382i | \(-0.597576\pi\) | ||||
−0.301765 | + | 0.953382i | \(0.597576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.89898 | −0.200334 | ||||||||
\(599\) | 14.2020 | 0.580280 | 0.290140 | − | 0.956984i | \(-0.406298\pi\) | ||||
0.290140 | + | 0.956984i | \(0.406298\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6969 | 0.517919 | 0.258959 | − | 0.965888i | \(-0.416620\pi\) | ||||
0.258959 | + | 0.965888i | \(0.416620\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.00000 | −0.203447 | ||||||||
\(605\) | −24.1464 | −0.981692 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.69694 | 0.352998 | 0.176499 | − | 0.984301i | \(-0.443523\pi\) | ||||
0.176499 | + | 0.984301i | \(0.443523\pi\) | |||||||
\(608\) | 7.44949 | 0.302117 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39.4949 | 1.59910 | ||||||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6969 | 0.593604 | 0.296802 | − | 0.954939i | \(-0.404080\pi\) | ||||
0.296802 | + | 0.954939i | \(0.404080\pi\) | |||||||
\(614\) | 0.752551 | 0.0303705 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.3939 | −1.74697 | −0.873486 | − | 0.486850i | \(-0.838146\pi\) | ||||
−0.873486 | + | 0.486850i | \(0.838146\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.14643 | 0.166659 | 0.0833295 | − | 0.996522i | \(-0.473445\pi\) | ||||
0.0833295 | + | 0.996522i | \(0.473445\pi\) | |||||||
\(620\) | −20.6969 | −0.831209 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.30306 | −0.0522480 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.8990 | −0.475959 | ||||||||
\(626\) | 24.6969 | 0.987088 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.34847 | −0.253332 | ||||||||
\(629\) | −15.5959 | −0.621850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.1010 | 0.720590 | 0.360295 | − | 0.932838i | \(-0.382676\pi\) | ||||
0.360295 | + | 0.932838i | \(0.382676\pi\) | |||||||
\(632\) | −7.89898 | −0.314205 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.69694 | −0.345400 | ||||||||
\(635\) | −10.3485 | −0.410666 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.79796 | −0.229543 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.44949 | −0.136353 | ||||||||
\(641\) | −41.4949 | −1.63895 | −0.819475 | − | 0.573115i | \(-0.805735\pi\) | ||||
−0.819475 | + | 0.573115i | \(0.805735\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.3939 | −0.764820 | −0.382410 | − | 0.923993i | \(-0.624906\pi\) | ||||
−0.382410 | + | 0.923993i | \(0.624906\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.8990 | 0.586193 | ||||||||
\(647\) | −21.3031 | −0.837510 | −0.418755 | − | 0.908099i | \(-0.637533\pi\) | ||||
−0.418755 | + | 0.908099i | \(0.637533\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | −33.7980 | −1.32567 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.202041 | −0.00791254 | ||||||||
\(653\) | 9.79796 | 0.383424 | 0.191712 | − | 0.981451i | \(-0.438596\pi\) | ||||
0.191712 | + | 0.981451i | \(0.438596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −46.3939 | −1.81276 | ||||||||
\(656\) | −9.79796 | −0.382546 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.69694 | −0.182967 | −0.0914834 | − | 0.995807i | \(-0.529161\pi\) | ||||
−0.0914834 | + | 0.995807i | \(0.529161\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.44949 | −0.367543 | −0.183771 | − | 0.982969i | \(-0.558831\pi\) | ||||
−0.183771 | + | 0.982969i | \(0.558831\pi\) | |||||||
\(662\) | 24.6969 | 0.959874 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.00000 | −0.0776151 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.89898 | −0.112249 | ||||||||
\(668\) | 18.6969 | 0.723406 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.6969 | 0.413259 | ||||||||
\(671\) | 22.8990 | 0.884005 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.5959 | 1.17939 | 0.589693 | − | 0.807628i | \(-0.299249\pi\) | ||||
0.589693 | + | 0.807628i | \(0.299249\pi\) | |||||||
\(674\) | −35.3939 | −1.36332 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | 0.423077 | ||||||||
\(677\) | −14.6969 | −0.564849 | −0.282425 | − | 0.959289i | \(-0.591139\pi\) | ||||
−0.282425 | + | 0.959289i | \(0.591139\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.89898 | −0.264564 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.0000 | −0.459504 | ||||||||
\(683\) | −32.2020 | −1.23218 | −0.616088 | − | 0.787677i | \(-0.711284\pi\) | ||||
−0.616088 | + | 0.787677i | \(0.711284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.6969 | 1.55495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.89898 | −0.110523 | ||||||||
\(689\) | 5.39388 | 0.205490 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.95459 | −0.264565 | −0.132283 | − | 0.991212i | \(-0.542231\pi\) | ||||
−0.132283 | + | 0.991212i | \(0.542231\pi\) | |||||||
\(692\) | −12.8990 | −0.490346 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.5959 | −0.743851 | ||||||||
\(695\) | −32.5959 | −1.23643 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.5959 | −0.742248 | ||||||||
\(698\) | 20.8990 | 0.791038 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.3939 | −1.94112 | −0.970560 | − | 0.240860i | \(-0.922571\pi\) | ||||
−0.970560 | + | 0.240860i | \(0.922571\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.0908 | 2.19094 | ||||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | 0.225813 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5959 | −0.435494 | −0.217747 | − | 0.976005i | \(-0.569871\pi\) | ||||
−0.217747 | + | 0.976005i | \(0.569871\pi\) | |||||||
\(710\) | 34.1464 | 1.28149 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.10102 | 0.266122 | ||||||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.7980 | −1.26397 | ||||||||
\(716\) | 8.69694 | 0.325020 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.7980 | 0.402976 | ||||||||
\(719\) | −9.79796 | −0.365402 | −0.182701 | − | 0.983169i | \(-0.558484\pi\) | ||||
−0.182701 | + | 0.983169i | \(0.558484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −36.4949 | −1.35820 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.34847 | −0.161610 | ||||||||
\(725\) | −20.0000 | −0.742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.4949 | −1.50187 | −0.750936 | − | 0.660375i | \(-0.770397\pi\) | ||||
−0.750936 | + | 0.660375i | \(0.770397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.0000 | 0.370117 | ||||||||
\(731\) | −5.79796 | −0.214445 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.5505 | 0.463564 | 0.231782 | − | 0.972768i | \(-0.425544\pi\) | ||||
0.231782 | + | 0.972768i | \(0.425544\pi\) | |||||||
\(734\) | 5.79796 | 0.214007 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 6.20204 | 0.228455 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.5959 | −0.941561 | −0.470781 | − | 0.882250i | \(-0.656028\pi\) | ||||
−0.470781 | + | 0.882250i | \(0.656028\pi\) | |||||||
\(740\) | −26.8990 | −0.988826 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.0000 | −1.32071 | −0.660356 | − | 0.750953i | \(-0.729595\pi\) | ||||
−0.660356 | + | 0.750953i | \(0.729595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.6969 | 0.758277 | ||||||||
\(746\) | −2.89898 | −0.106139 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.00000 | −0.146254 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.5959 | 1.48137 | 0.740683 | − | 0.671855i | \(-0.234502\pi\) | ||||
0.740683 | + | 0.671855i | \(0.234502\pi\) | |||||||
\(752\) | −9.79796 | −0.357295 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.2020 | 0.517208 | ||||||||
\(755\) | −17.2474 | −0.627699 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.3939 | 0.850265 | 0.425132 | − | 0.905131i | \(-0.360228\pi\) | ||||
0.425132 | + | 0.905131i | \(0.360228\pi\) | |||||||
\(758\) | 26.4949 | 0.962338 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 25.6969 | 0.932126 | ||||||||
\(761\) | 2.00000 | 0.0724999 | 0.0362500 | − | 0.999343i | \(-0.488459\pi\) | ||||
0.0362500 | + | 0.999343i | \(0.488459\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.8990 | −0.502847 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.89898 | −0.249270 | ||||||||
\(767\) | −9.79796 | −0.353784 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −54.0908 | −1.95056 | −0.975282 | − | 0.220962i | \(-0.929080\pi\) | ||||
−0.975282 | + | 0.220962i | \(0.929080\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.10102 | −0.291562 | ||||||||
\(773\) | −19.9444 | −0.717350 | −0.358675 | − | 0.933463i | \(-0.616771\pi\) | ||||
−0.358675 | + | 0.933463i | \(0.616771\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −41.3939 | −1.48691 | ||||||||
\(776\) | −6.89898 | −0.247659 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.1010 | −0.541398 | ||||||||
\(779\) | 72.9898 | 2.61513 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.7980 | 0.708427 | ||||||||
\(782\) | −2.00000 | −0.0715199 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.8990 | −0.781608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.3939 | −1.68941 | −0.844705 | − | 0.535233i | \(-0.820224\pi\) | ||||
−0.844705 | + | 0.535233i | \(0.820224\pi\) | |||||||
\(788\) | 12.6969 | 0.452310 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −27.2474 | −0.969421 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.0908 | −1.99184 | ||||||||
\(794\) | 9.30306 | 0.330153 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.89898 | −0.244528 | ||||||||
\(797\) | 35.9444 | 1.27322 | 0.636608 | − | 0.771188i | \(-0.280337\pi\) | ||||
0.636608 | + | 0.771188i | \(0.280337\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.5959 | −0.693254 | ||||||||
\(800\) | −6.89898 | −0.243916 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.1010 | −0.356679 | ||||||||
\(803\) | 5.79796 | 0.204606 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 29.3939 | 1.03536 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.24745 | −0.254964 | ||||||||
\(809\) | 35.7980 | 1.25859 | 0.629295 | − | 0.777167i | \(-0.283344\pi\) | ||||
0.629295 | + | 0.777167i | \(0.283344\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.5959 | −0.546637 | ||||||||
\(815\) | −0.696938 | −0.0244127 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.5959 | 0.755546 | ||||||||
\(818\) | 5.79796 | 0.202721 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −33.7980 | −1.18028 | ||||||||
\(821\) | −39.5959 | −1.38191 | −0.690954 | − | 0.722899i | \(-0.742809\pi\) | ||||
−0.690954 | + | 0.722899i | \(0.742809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.3939 | 1.58233 | 0.791166 | − | 0.611602i | \(-0.209475\pi\) | ||||
0.791166 | + | 0.611602i | \(0.209475\pi\) | |||||||
\(824\) | 14.0000 | 0.487713 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.4949 | −0.434490 | −0.217245 | − | 0.976117i | \(-0.569707\pi\) | ||||
−0.217245 | + | 0.976117i | \(0.569707\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.6969 | −1.06615 | −0.533074 | − | 0.846068i | \(-0.678963\pi\) | ||||
−0.533074 | + | 0.846068i | \(0.678963\pi\) | |||||||
\(830\) | −6.89898 | −0.239467 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.89898 | 0.169842 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.4949 | 2.23194 | ||||||||
\(836\) | 14.8990 | 0.515292 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.5505 | −0.848083 | ||||||||
\(839\) | −44.8990 | −1.55008 | −0.775042 | − | 0.631909i | \(-0.782272\pi\) | ||||
−0.775042 | + | 0.631909i | \(0.782272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5959 | −0.710204 | ||||||||
\(842\) | −13.1010 | −0.451491 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.10102 | 0.106742 | ||||||||
\(845\) | 37.9444 | 1.30533 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.10102 | 0.0378092 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.7980 | −0.473266 | ||||||||
\(851\) | −7.79796 | −0.267311 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.8434 | 1.32997 | 0.664986 | − | 0.746856i | \(-0.268438\pi\) | ||||
0.664986 | + | 0.746856i | \(0.268438\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | −25.1010 | −0.857435 | −0.428717 | − | 0.903439i | \(-0.641034\pi\) | ||||
−0.428717 | + | 0.903439i | \(0.641034\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0000 | 0.341196 | 0.170598 | − | 0.985341i | \(-0.445430\pi\) | ||||
0.170598 | + | 0.985341i | \(0.445430\pi\) | |||||||
\(860\) | −10.0000 | −0.340997 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.59592 | −0.258718 | ||||||||
\(863\) | −2.10102 | −0.0715196 | −0.0357598 | − | 0.999360i | \(-0.511385\pi\) | ||||
−0.0357598 | + | 0.999360i | \(0.511385\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.4949 | −1.51287 | ||||||||
\(866\) | 11.7980 | 0.400911 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.7980 | −0.535909 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.1918 | −0.514756 | ||||||||
\(872\) | 16.6969 | 0.565430 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.44949 | 0.251983 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.4949 | −0.894669 | −0.447335 | − | 0.894367i | \(-0.647627\pi\) | ||||
−0.447335 | + | 0.894367i | \(0.647627\pi\) | |||||||
\(878\) | 21.7980 | 0.735645 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.89898 | −0.232565 | ||||||||
\(881\) | −19.5959 | −0.660203 | −0.330102 | − | 0.943945i | \(-0.607083\pi\) | ||||
−0.330102 | + | 0.943945i | \(0.607083\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.202041 | −0.00679922 | −0.00339961 | − | 0.999994i | \(-0.501082\pi\) | ||||
−0.00339961 | + | 0.999994i | \(0.501082\pi\) | |||||||
\(884\) | 9.79796 | 0.329541 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.10102 | −0.171372 | ||||||||
\(887\) | −33.7980 | −1.13482 | −0.567412 | − | 0.823434i | \(-0.692055\pi\) | ||||
−0.567412 | + | 0.823434i | \(0.692055\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.4949 | 0.821071 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.8990 | 0.699750 | ||||||||
\(893\) | 72.9898 | 2.44251 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.0000 | 1.00279 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.5959 | −0.620554 | ||||||||
\(899\) | 17.3939 | 0.580118 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.20204 | 0.0733606 | ||||||||
\(902\) | −19.5959 | −0.652473 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.8990 | −0.528792 | ||||||||
\(905\) | −15.0000 | −0.498617 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.6969 | −0.886457 | −0.443229 | − | 0.896409i | \(-0.646167\pi\) | ||||
−0.443229 | + | 0.896409i | \(0.646167\pi\) | |||||||
\(908\) | −0.550510 | −0.0182693 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.9898 | 1.52371 | 0.761855 | − | 0.647748i | \(-0.224289\pi\) | ||||
0.761855 | + | 0.647748i | \(0.224289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.00000 | −0.132381 | ||||||||
\(914\) | −31.4949 | −1.04176 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.2474 | 0.768117 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.69694 | 0.121951 | 0.0609754 | − | 0.998139i | \(-0.480579\pi\) | ||||
0.0609754 | + | 0.998139i | \(0.480579\pi\) | |||||||
\(920\) | −3.44949 | −0.113726 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.3485 | −0.670141 | ||||||||
\(923\) | −48.4949 | −1.59623 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −53.7980 | −1.76887 | ||||||||
\(926\) | 25.6969 | 0.844454 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.89898 | 0.0951637 | ||||||||
\(929\) | −34.2929 | −1.12511 | −0.562556 | − | 0.826759i | \(-0.690182\pi\) | ||||
−0.562556 | + | 0.826759i | \(0.690182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.00000 | 0.229293 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.0000 | −0.327210 | ||||||||
\(935\) | −13.7980 | −0.451242 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.40408 | −0.209212 | −0.104606 | − | 0.994514i | \(-0.533358\pi\) | ||||
−0.104606 | + | 0.994514i | \(0.533358\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −33.7980 | −1.10237 | ||||||||
\(941\) | 3.44949 | 0.112450 | 0.0562251 | − | 0.998418i | \(-0.482094\pi\) | ||||
0.0562251 | + | 0.998418i | \(0.482094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.79796 | −0.319065 | ||||||||
\(944\) | −2.00000 | −0.0650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.79796 | −0.188508 | ||||||||
\(947\) | −3.50510 | −0.113901 | −0.0569503 | − | 0.998377i | \(-0.518138\pi\) | ||||
−0.0569503 | + | 0.998377i | \(0.518138\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.2020 | −0.461018 | ||||||||
\(950\) | 51.3939 | 1.66744 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55.3939 | −1.79438 | −0.897192 | − | 0.441641i | \(-0.854396\pi\) | ||||
−0.897192 | + | 0.441641i | \(0.854396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47.9444 | −1.55144 | ||||||||
\(956\) | 12.7980 | 0.413916 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.5959 | 0.956201 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 38.2020 | 1.23168 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.89898 | 0.286617 | ||||||||
\(965\) | −27.9444 | −0.899562 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.5959 | −0.469373 | −0.234687 | − | 0.972071i | \(-0.575406\pi\) | ||||
−0.234687 | + | 0.972071i | \(0.575406\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.7980 | −0.764106 | ||||||||
\(971\) | −53.9444 | −1.73116 | −0.865579 | − | 0.500773i | \(-0.833049\pi\) | ||||
−0.865579 | + | 0.500773i | \(0.833049\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.3939 | −0.717546 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.4495 | −0.366489 | ||||||||
\(977\) | −1.59592 | −0.0510579 | −0.0255290 | − | 0.999674i | \(-0.508127\pi\) | ||||
−0.0255290 | + | 0.999674i | \(0.508127\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.2020 | 0.453899 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.79796 | −0.121198 | ||||||||
\(983\) | 45.1918 | 1.44140 | 0.720698 | − | 0.693249i | \(-0.243822\pi\) | ||||
0.720698 | + | 0.693249i | \(0.243822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.7980 | 1.39552 | ||||||||
\(986\) | 5.79796 | 0.184645 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −36.4949 | −1.16106 | ||||||||
\(989\) | −2.89898 | −0.0921822 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7980 | 0.565371 | 0.282685 | − | 0.959213i | \(-0.408775\pi\) | ||||
0.282685 | + | 0.959213i | \(0.408775\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.7980 | −0.754446 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.8536 | −0.565428 | −0.282714 | − | 0.959204i | \(-0.591235\pi\) | ||||
−0.282714 | + | 0.959204i | \(0.591235\pi\) | |||||||
\(998\) | −33.3939 | −1.05706 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))