Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 950) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.713538\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.69527 | 1.77464 | 0.887322 | − | 0.461151i | \(-0.152563\pi\) | ||||
0.887322 | + | 0.461151i | \(0.152563\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.40880 | −1.93233 | −0.966163 | − | 0.257931i | \(-0.916959\pi\) | ||||
−0.966163 | + | 0.257931i | \(0.916959\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.06379 | −0.295042 | −0.147521 | − | 0.989059i | \(-0.547129\pi\) | ||||
−0.147521 | + | 0.989059i | \(0.547129\pi\) | |||||||
\(14\) | 4.69527 | 1.25486 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.91794 | 0.465169 | 0.232584 | − | 0.972576i | \(-0.425282\pi\) | ||||
0.232584 | + | 0.972576i | \(0.425282\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.40880 | −1.36636 | ||||||||
\(23\) | 1.79560 | 0.374408 | 0.187204 | − | 0.982321i | \(-0.440057\pi\) | ||||
0.187204 | + | 0.982321i | \(0.440057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.06379 | −0.208626 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.69527 | 0.887322 | ||||||||
\(29\) | −2.93621 | −0.545241 | −0.272620 | − | 0.962122i | \(-0.587890\pi\) | ||||
−0.272620 | + | 0.962122i | \(0.587890\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.55465 | −0.997645 | −0.498822 | − | 0.866704i | \(-0.666234\pi\) | ||||
−0.498822 | + | 0.866704i | \(0.666234\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.91794 | 0.328924 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.4088 | 1.87560 | 0.937798 | − | 0.347182i | \(-0.112861\pi\) | ||||
0.937798 | + | 0.347182i | \(0.112861\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.14585 | 0.178951 | 0.0894757 | − | 0.995989i | \(-0.471481\pi\) | ||||
0.0894757 | + | 0.995989i | \(0.471481\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.55465 | 0.542079 | 0.271040 | − | 0.962568i | \(-0.412633\pi\) | ||||
0.271040 | + | 0.962568i | \(0.412633\pi\) | |||||||
\(44\) | −6.40880 | −0.966163 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.79560 | 0.264747 | ||||||||
\(47\) | 10.8359 | 1.58058 | 0.790288 | − | 0.612736i | \(-0.209931\pi\) | ||||
0.790288 | + | 0.612736i | \(0.209931\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.0455 | 2.14936 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.06379 | −0.147521 | ||||||||
\(53\) | −8.69527 | −1.19439 | −0.597193 | − | 0.802097i | \(-0.703717\pi\) | ||||
−0.597193 | + | 0.802097i | \(0.703717\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.69527 | 0.627431 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.93621 | −0.385544 | ||||||||
\(59\) | 5.63148 | 0.733156 | 0.366578 | − | 0.930387i | \(-0.380529\pi\) | ||||
0.366578 | + | 0.930387i | \(0.380529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.39053 | −0.434113 | −0.217056 | − | 0.976159i | \(-0.569646\pi\) | ||||
−0.217056 | + | 0.976159i | \(0.569646\pi\) | |||||||
\(62\) | −5.55465 | −0.705441 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.82284 | 1.07788 | 0.538941 | − | 0.842344i | \(-0.318825\pi\) | ||||
0.538941 | + | 0.842344i | \(0.318825\pi\) | |||||||
\(68\) | 1.91794 | 0.232584 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.42708 | 0.169363 | 0.0846814 | − | 0.996408i | \(-0.473013\pi\) | ||||
0.0846814 | + | 0.996408i | \(0.473013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6132 | 1.47626 | 0.738132 | − | 0.674656i | \(-0.235708\pi\) | ||||
0.738132 | + | 0.674656i | \(0.235708\pi\) | |||||||
\(74\) | 11.4088 | 1.32625 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −30.0910 | −3.42919 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.96345 | −0.220906 | −0.110453 | − | 0.993881i | \(-0.535230\pi\) | ||||
−0.110453 | + | 0.993881i | \(0.535230\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.14585 | 0.126538 | ||||||||
\(83\) | 16.2447 | 1.78309 | 0.891543 | − | 0.452937i | \(-0.149624\pi\) | ||||
0.891543 | + | 0.452937i | \(0.149624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.55465 | 0.383308 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.40880 | −0.683181 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.99477 | −0.523594 | ||||||||
\(92\) | 1.79560 | 0.187204 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.8359 | 1.11764 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9452 | 1.51745 | 0.758727 | − | 0.651409i | \(-0.225822\pi\) | ||||
0.758727 | + | 0.651409i | \(0.225822\pi\) | |||||||
\(98\) | 15.0455 | 1.51983 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.5364 | −1.04841 | −0.524204 | − | 0.851592i | \(-0.675637\pi\) | ||||
−0.524204 | + | 0.851592i | \(0.675637\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9817 | 1.67326 | 0.836630 | − | 0.547769i | \(-0.184523\pi\) | ||||
0.836630 | + | 0.547769i | \(0.184523\pi\) | |||||||
\(104\) | −1.06379 | −0.104313 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.69527 | −0.844559 | ||||||||
\(107\) | −1.79036 | −0.173081 | −0.0865405 | − | 0.996248i | \(-0.527581\pi\) | ||||
−0.0865405 | + | 0.996248i | \(0.527581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.41404 | 0.231223 | 0.115611 | − | 0.993295i | \(-0.463117\pi\) | ||||
0.115611 | + | 0.993295i | \(0.463117\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.69527 | 0.443661 | ||||||||
\(113\) | 7.14585 | 0.672225 | 0.336112 | − | 0.941822i | \(-0.390888\pi\) | ||||
0.336112 | + | 0.941822i | \(0.390888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.93621 | −0.272620 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.63148 | 0.518420 | ||||||||
\(119\) | 9.00523 | 0.825508 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.0728 | 2.73389 | ||||||||
\(122\) | −3.39053 | −0.306964 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.55465 | −0.498822 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.26295 | −0.821954 | −0.410977 | − | 0.911646i | \(-0.634812\pi\) | ||||
−0.410977 | + | 0.911646i | \(0.634812\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.5181 | −1.00634 | −0.503171 | − | 0.864187i | \(-0.667833\pi\) | ||||
−0.503171 | + | 0.864187i | \(0.667833\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.69527 | −0.407131 | ||||||||
\(134\) | 8.82284 | 0.762177 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.91794 | 0.164462 | ||||||||
\(137\) | 15.1041 | 1.29043 | 0.645214 | − | 0.764002i | \(-0.276768\pi\) | ||||
0.645214 | + | 0.764002i | \(0.276768\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.700500 | −0.0594156 | −0.0297078 | − | 0.999559i | \(-0.509458\pi\) | ||||
−0.0297078 | + | 0.999559i | \(0.509458\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.42708 | 0.119758 | ||||||||
\(143\) | 6.81761 | 0.570117 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.6132 | 1.04388 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.4088 | 0.937798 | ||||||||
\(149\) | −12.9452 | −1.06051 | −0.530255 | − | 0.847838i | \(-0.677904\pi\) | ||||
−0.530255 | + | 0.847838i | \(0.677904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.70830 | 0.464535 | 0.232268 | − | 0.972652i | \(-0.425385\pi\) | ||||
0.232268 | + | 0.972652i | \(0.425385\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −30.0910 | −2.42480 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.26295 | −0.739264 | −0.369632 | − | 0.929178i | \(-0.620516\pi\) | ||||
−0.369632 | + | 0.929178i | \(0.620516\pi\) | |||||||
\(158\) | −1.96345 | −0.156204 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.43081 | 0.664441 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.28123 | −0.335332 | −0.167666 | − | 0.985844i | \(-0.553623\pi\) | ||||
−0.167666 | + | 0.985844i | \(0.553623\pi\) | |||||||
\(164\) | 1.14585 | 0.0894757 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.2447 | 1.26083 | ||||||||
\(167\) | −15.2264 | −1.17825 | −0.589127 | − | 0.808040i | \(-0.700528\pi\) | ||||
−0.589127 | + | 0.808040i | \(0.700528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8684 | −0.912950 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.55465 | 0.271040 | ||||||||
\(173\) | −12.2630 | −0.932335 | −0.466168 | − | 0.884696i | \(-0.654366\pi\) | ||||
−0.466168 | + | 0.884696i | \(0.654366\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.40880 | −0.483082 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.0000 | 0.749532 | ||||||||
\(179\) | 1.57292 | 0.117566 | 0.0587829 | − | 0.998271i | \(-0.481278\pi\) | ||||
0.0587829 | + | 0.998271i | \(0.481278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4088 | 0.848010 | 0.424005 | − | 0.905660i | \(-0.360624\pi\) | ||||
0.424005 | + | 0.905660i | \(0.360624\pi\) | |||||||
\(182\) | −4.99477 | −0.370237 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.79560 | 0.132373 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.2917 | −0.898858 | ||||||||
\(188\) | 10.8359 | 0.790288 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.35805 | 0.460053 | 0.230026 | − | 0.973184i | \(-0.426119\pi\) | ||||
0.230026 | + | 0.973184i | \(0.426119\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.4998 | −1.04372 | −0.521860 | − | 0.853031i | \(-0.674762\pi\) | ||||
−0.521860 | + | 0.853031i | \(0.674762\pi\) | |||||||
\(194\) | 14.9452 | 1.07300 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.0455 | 1.07468 | ||||||||
\(197\) | −5.14585 | −0.366627 | −0.183313 | − | 0.983055i | \(-0.558682\pi\) | ||||
−0.183313 | + | 0.983055i | \(0.558682\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.87766 | 0.274880 | 0.137440 | − | 0.990510i | \(-0.456113\pi\) | ||||
0.137440 | + | 0.990510i | \(0.456113\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.5364 | −0.741337 | ||||||||
\(203\) | −13.7863 | −0.967608 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.9817 | 1.18317 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.06379 | −0.0737604 | ||||||||
\(209\) | 6.40880 | 0.443306 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.1496 | 1.18063 | 0.590313 | − | 0.807174i | \(-0.299004\pi\) | ||||
0.590313 | + | 0.807174i | \(0.299004\pi\) | |||||||
\(212\) | −8.69527 | −0.597193 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.79036 | −0.122387 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.0806 | −1.77046 | ||||||||
\(218\) | 2.41404 | 0.163499 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.04028 | −0.137244 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.84635 | −0.525430 | −0.262715 | − | 0.964873i | \(-0.584618\pi\) | ||||
−0.262715 | + | 0.964873i | \(0.584618\pi\) | |||||||
\(224\) | 4.69527 | 0.313716 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.14585 | 0.475335 | ||||||||
\(227\) | 6.28646 | 0.417247 | 0.208624 | − | 0.977996i | \(-0.433102\pi\) | ||||
0.208624 | + | 0.977996i | \(0.433102\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.14585 | −0.207884 | −0.103942 | − | 0.994583i | \(-0.533146\pi\) | ||||
−0.103942 | + | 0.994583i | \(0.533146\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.93621 | −0.192772 | ||||||||
\(233\) | 0.182394 | 0.0119490 | 0.00597451 | − | 0.999982i | \(-0.498098\pi\) | ||||
0.00597451 | + | 0.999982i | \(0.498098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.63148 | 0.366578 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.00523 | 0.583723 | ||||||||
\(239\) | 11.5039 | 0.744126 | 0.372063 | − | 0.928208i | \(-0.378651\pi\) | ||||
0.372063 | + | 0.928208i | \(0.378651\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.445349 | −0.0286874 | −0.0143437 | − | 0.999897i | \(-0.504566\pi\) | ||||
−0.0143437 | + | 0.999897i | \(0.504566\pi\) | |||||||
\(242\) | 30.0728 | 1.93315 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.39053 | −0.217056 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.06379 | 0.0676872 | ||||||||
\(248\) | −5.55465 | −0.352721 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.2630 | −0.837150 | −0.418575 | − | 0.908182i | \(-0.637470\pi\) | ||||
−0.418575 | + | 0.908182i | \(0.637470\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.5076 | −0.723479 | ||||||||
\(254\) | −9.26295 | −0.581209 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.4816 | −1.46474 | −0.732370 | − | 0.680907i | \(-0.761586\pi\) | ||||
−0.732370 | + | 0.680907i | \(0.761586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 53.5674 | 3.32851 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.5181 | −0.711591 | ||||||||
\(263\) | 27.9269 | 1.72205 | 0.861023 | − | 0.508565i | \(-0.169824\pi\) | ||||
0.861023 | + | 0.508565i | \(0.169824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.69527 | −0.287885 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.82284 | 0.538941 | ||||||||
\(269\) | −16.4816 | −1.00490 | −0.502449 | − | 0.864607i | \(-0.667568\pi\) | ||||
−0.502449 | + | 0.864607i | \(0.667568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.46736 | −0.0891356 | −0.0445678 | − | 0.999006i | \(-0.514191\pi\) | ||||
−0.0445678 | + | 0.999006i | \(0.514191\pi\) | |||||||
\(272\) | 1.91794 | 0.116292 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.1041 | 0.912470 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.8359 | −0.951486 | −0.475743 | − | 0.879584i | \(-0.657821\pi\) | ||||
−0.475743 | + | 0.879584i | \(0.657821\pi\) | |||||||
\(278\) | −0.700500 | −0.0420132 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.25515 | 0.373151 | 0.186576 | − | 0.982441i | \(-0.440261\pi\) | ||||
0.186576 | + | 0.982441i | \(0.440261\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.7005 | 0.992742 | 0.496371 | − | 0.868111i | \(-0.334666\pi\) | ||||
0.496371 | + | 0.868111i | \(0.334666\pi\) | |||||||
\(284\) | 1.42708 | 0.0846814 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.81761 | 0.403134 | ||||||||
\(287\) | 5.38006 | 0.317575 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3215 | −0.783618 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.6132 | 0.738132 | ||||||||
\(293\) | 0.644516 | 0.0376530 | 0.0188265 | − | 0.999823i | \(-0.494007\pi\) | ||||
0.0188265 | + | 0.999823i | \(0.494007\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.4088 | 0.663123 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.9452 | −0.749894 | ||||||||
\(299\) | −1.91014 | −0.110466 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.6900 | 0.961997 | ||||||||
\(302\) | 5.70830 | 0.328476 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.6457 | −1.52075 | −0.760375 | − | 0.649485i | \(-0.774985\pi\) | ||||
−0.760375 | + | 0.649485i | \(0.774985\pi\) | |||||||
\(308\) | −30.0910 | −1.71460 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.5494 | −0.654907 | −0.327454 | − | 0.944867i | \(-0.606191\pi\) | ||||
−0.327454 | + | 0.944867i | \(0.606191\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.0638 | 1.30364 | 0.651821 | − | 0.758373i | \(-0.274005\pi\) | ||||
0.651821 | + | 0.758373i | \(0.274005\pi\) | |||||||
\(314\) | −9.26295 | −0.522739 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.96345 | −0.110453 | ||||||||
\(317\) | −13.9232 | −0.782003 | −0.391002 | − | 0.920390i | \(-0.627871\pi\) | ||||
−0.391002 | + | 0.920390i | \(0.627871\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.8176 | 1.05358 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.43081 | 0.469831 | ||||||||
\(323\) | −1.91794 | −0.106717 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.28123 | −0.237115 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.14585 | 0.0632689 | ||||||||
\(329\) | 50.8773 | 2.80496 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.735546 | −0.0404292 | −0.0202146 | − | 0.999796i | \(-0.506435\pi\) | ||||
−0.0202146 | + | 0.999796i | \(0.506435\pi\) | |||||||
\(332\) | 16.2447 | 0.891543 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.2264 | −0.833152 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.28123 | 0.124266 | 0.0621332 | − | 0.998068i | \(-0.480210\pi\) | ||||
0.0621332 | + | 0.998068i | \(0.480210\pi\) | |||||||
\(338\) | −11.8684 | −0.645553 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.5987 | 1.92778 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 37.7758 | 2.03970 | ||||||||
\(344\) | 3.55465 | 0.191654 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.2630 | −0.659261 | ||||||||
\(347\) | −2.56246 | −0.137560 | −0.0687799 | − | 0.997632i | \(-0.521911\pi\) | ||||
−0.0687799 | + | 0.997632i | \(0.521911\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.67176 | −0.303602 | −0.151801 | − | 0.988411i | \(-0.548507\pi\) | ||||
−0.151801 | + | 0.988411i | \(0.548507\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.40880 | −0.341590 | ||||||||
\(353\) | −23.6665 | −1.25964 | −0.629821 | − | 0.776740i | \(-0.716872\pi\) | ||||
−0.629821 | + | 0.776740i | \(0.716872\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.57292 | 0.0831316 | ||||||||
\(359\) | −31.9724 | −1.68744 | −0.843720 | − | 0.536784i | \(-0.819639\pi\) | ||||
−0.843720 | + | 0.536784i | \(0.819639\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 11.4088 | 0.599633 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.99477 | −0.261797 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.14585 | −0.0598128 | −0.0299064 | − | 0.999553i | \(-0.509521\pi\) | ||||
−0.0299064 | + | 0.999553i | \(0.509521\pi\) | |||||||
\(368\) | 1.79560 | 0.0936020 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −40.8266 | −2.11961 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.8579 | −1.70132 | −0.850658 | − | 0.525719i | \(-0.823796\pi\) | ||||
−0.850658 | + | 0.525719i | \(0.823796\pi\) | |||||||
\(374\) | −12.2917 | −0.635588 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.8359 | 0.558818 | ||||||||
\(377\) | 3.12351 | 0.160869 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.2865 | −0.939312 | −0.469656 | − | 0.882849i | \(-0.655622\pi\) | ||||
−0.469656 | + | 0.882849i | \(0.655622\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.35805 | 0.325306 | ||||||||
\(383\) | 20.8542 | 1.06560 | 0.532799 | − | 0.846242i | \(-0.321140\pi\) | ||||
0.532799 | + | 0.846242i | \(0.321140\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.4998 | −0.738022 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.9452 | 0.758727 | ||||||||
\(389\) | 24.9086 | 1.26292 | 0.631459 | − | 0.775409i | \(-0.282456\pi\) | ||||
0.631459 | + | 0.775409i | \(0.282456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.44385 | 0.174163 | ||||||||
\(392\) | 15.0455 | 0.759913 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.14585 | −0.259244 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.7445 | 1.24189 | 0.620946 | − | 0.783853i | \(-0.286749\pi\) | ||||
0.620946 | + | 0.783853i | \(0.286749\pi\) | |||||||
\(398\) | 3.87766 | 0.194369 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.6457 | −0.781308 | −0.390654 | − | 0.920538i | \(-0.627751\pi\) | ||||
−0.390654 | + | 0.920538i | \(0.627751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.90897 | 0.294347 | ||||||||
\(404\) | −10.5364 | −0.524204 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.7863 | −0.684202 | ||||||||
\(407\) | −73.1168 | −3.62426 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.5804 | 1.51210 | 0.756052 | − | 0.654512i | \(-0.227126\pi\) | ||||
0.756052 | + | 0.654512i | \(0.227126\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.9817 | 0.836630 | ||||||||
\(413\) | 26.4413 | 1.30109 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.06379 | −0.0521565 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.40880 | 0.313465 | ||||||||
\(419\) | −1.96345 | −0.0959210 | −0.0479605 | − | 0.998849i | \(-0.515272\pi\) | ||||
−0.0479605 | + | 0.998849i | \(0.515272\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.5949 | −1.24742 | −0.623710 | − | 0.781656i | \(-0.714376\pi\) | ||||
−0.623710 | + | 0.781656i | \(0.714376\pi\) | |||||||
\(422\) | 17.1496 | 0.834829 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.69527 | −0.422279 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.9194 | −0.770396 | ||||||||
\(428\) | −1.79036 | −0.0865405 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.3540 | 0.739575 | 0.369788 | − | 0.929116i | \(-0.379430\pi\) | ||||
0.369788 | + | 0.929116i | \(0.379430\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6640 | −0.800819 | −0.400409 | − | 0.916336i | \(-0.631132\pi\) | ||||
−0.400409 | + | 0.916336i | \(0.631132\pi\) | |||||||
\(434\) | −26.0806 | −1.25191 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.41404 | 0.115611 | ||||||||
\(437\) | −1.79560 | −0.0858951 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.5987 | −0.935393 | −0.467697 | − | 0.883889i | \(-0.654916\pi\) | ||||
−0.467697 | + | 0.883889i | \(0.654916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.04028 | −0.0970462 | ||||||||
\(443\) | 13.0183 | 0.618517 | 0.309258 | − | 0.950978i | \(-0.399919\pi\) | ||||
0.309258 | + | 0.950978i | \(0.399919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.84635 | −0.371535 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.69527 | 0.221830 | ||||||||
\(449\) | −6.77359 | −0.319666 | −0.159833 | − | 0.987144i | \(-0.551095\pi\) | ||||
−0.159833 | + | 0.987144i | \(0.551095\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.34352 | −0.345793 | ||||||||
\(452\) | 7.14585 | 0.336112 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.28646 | 0.295038 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.3189 | 1.27793 | 0.638963 | − | 0.769237i | \(-0.279364\pi\) | ||||
0.638963 | + | 0.769237i | \(0.279364\pi\) | |||||||
\(458\) | −3.14585 | −0.146996 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.7993 | 1.29474 | 0.647372 | − | 0.762174i | \(-0.275868\pi\) | ||||
0.647372 | + | 0.762174i | \(0.275868\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.2369 | −1.77702 | −0.888509 | − | 0.458859i | \(-0.848258\pi\) | ||||
−0.888509 | + | 0.458859i | \(0.848258\pi\) | |||||||
\(464\) | −2.93621 | −0.136310 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.182394 | 0.00844923 | ||||||||
\(467\) | 23.4711 | 1.08611 | 0.543056 | − | 0.839696i | \(-0.317267\pi\) | ||||
0.543056 | + | 0.839696i | \(0.317267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 41.4256 | 1.91286 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.63148 | 0.259210 | ||||||||
\(473\) | −22.7811 | −1.04747 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.00523 | 0.412754 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.5039 | 0.526176 | ||||||||
\(479\) | 19.6900 | 0.899660 | 0.449830 | − | 0.893114i | \(-0.351484\pi\) | ||||
0.449830 | + | 0.893114i | \(0.351484\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.1365 | −0.553379 | ||||||||
\(482\) | −0.445349 | −0.0202851 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 30.0728 | 1.36694 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.3357 | −0.740242 | −0.370121 | − | 0.928984i | \(-0.620684\pi\) | ||||
−0.370121 | + | 0.928984i | \(0.620684\pi\) | |||||||
\(488\) | −3.39053 | −0.153482 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.1093 | −1.22343 | −0.611713 | − | 0.791080i | \(-0.709519\pi\) | ||||
−0.611713 | + | 0.791080i | \(0.709519\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.63148 | −0.253629 | ||||||||
\(494\) | 1.06379 | 0.0478621 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.55465 | −0.249411 | ||||||||
\(497\) | 6.70050 | 0.300558 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.69003 | −0.209955 | −0.104977 | − | 0.994475i | \(-0.533477\pi\) | ||||
−0.104977 | + | 0.994475i | \(0.533477\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.2630 | −0.591955 | ||||||||
\(503\) | 5.19136 | 0.231471 | 0.115736 | − | 0.993280i | \(-0.463077\pi\) | ||||
0.115736 | + | 0.993280i | \(0.463077\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.5076 | −0.511577 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.26295 | −0.410977 | ||||||||
\(509\) | 4.51811 | 0.200262 | 0.100131 | − | 0.994974i | \(-0.468074\pi\) | ||||
0.100131 | + | 0.994974i | \(0.468074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 59.2223 | 2.61984 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23.4816 | −1.03573 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −69.4450 | −3.05419 | ||||||||
\(518\) | 53.5674 | 2.35361 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.4453 | −0.632862 | −0.316431 | − | 0.948615i | \(-0.602485\pi\) | ||||
−0.316431 | + | 0.948615i | \(0.602485\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.2134 | 0.796415 | 0.398208 | − | 0.917295i | \(-0.369632\pi\) | ||||
0.398208 | + | 0.917295i | \(0.369632\pi\) | |||||||
\(524\) | −11.5181 | −0.503171 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.9269 | 1.21767 | ||||||||
\(527\) | −10.6535 | −0.464073 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7758 | −0.859819 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.69527 | −0.203566 | ||||||||
\(533\) | −1.21894 | −0.0527981 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.82284 | 0.381089 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.4816 | −0.710571 | ||||||||
\(539\) | −96.4237 | −4.15326 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.3905 | 1.60754 | 0.803772 | − | 0.594937i | \(-0.202823\pi\) | ||||
0.803772 | + | 0.594937i | \(0.202823\pi\) | |||||||
\(542\) | −1.46736 | −0.0630284 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.91794 | 0.0822310 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.5621 | −1.26399 | −0.631993 | − | 0.774974i | \(-0.717763\pi\) | ||||
−0.631993 | + | 0.774974i | \(0.717763\pi\) | |||||||
\(548\) | 15.1041 | 0.645214 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.93621 | 0.125087 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.21894 | −0.392029 | ||||||||
\(554\) | −15.8359 | −0.672802 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.700500 | −0.0297078 | ||||||||
\(557\) | 14.3723 | 0.608972 | 0.304486 | − | 0.952517i | \(-0.401515\pi\) | ||||
0.304486 | + | 0.952517i | \(0.401515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.78139 | −0.159936 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.25515 | 0.263858 | ||||||||
\(563\) | −6.39053 | −0.269329 | −0.134664 | − | 0.990891i | \(-0.542996\pi\) | ||||
−0.134664 | + | 0.990891i | \(0.542996\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16.7005 | 0.701974 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.42708 | 0.0598788 | ||||||||
\(569\) | 44.9086 | 1.88267 | 0.941334 | − | 0.337476i | \(-0.109573\pi\) | ||||
0.941334 | + | 0.337476i | \(0.109573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.4193 | 0.519730 | 0.259865 | − | 0.965645i | \(-0.416322\pi\) | ||||
0.259865 | + | 0.965645i | \(0.416322\pi\) | |||||||
\(572\) | 6.81761 | 0.285058 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.38006 | 0.224559 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.20440 | 0.175032 | 0.0875158 | − | 0.996163i | \(-0.472107\pi\) | ||||
0.0875158 | + | 0.996163i | \(0.472107\pi\) | |||||||
\(578\) | −13.3215 | −0.554102 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 76.2731 | 3.16434 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 55.7262 | 2.30795 | ||||||||
\(584\) | 12.6132 | 0.521938 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.644516 | 0.0266247 | ||||||||
\(587\) | 24.7915 | 1.02326 | 0.511628 | − | 0.859207i | \(-0.329043\pi\) | ||||
0.511628 | + | 0.859207i | \(0.329043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.55465 | 0.228875 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.4088 | 0.468899 | ||||||||
\(593\) | 4.67176 | 0.191846 | 0.0959231 | − | 0.995389i | \(-0.469420\pi\) | ||||
0.0959231 | + | 0.995389i | \(0.469420\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.9452 | −0.530255 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.91014 | −0.0781113 | ||||||||
\(599\) | −39.2369 | −1.60318 | −0.801588 | − | 0.597877i | \(-0.796011\pi\) | ||||
−0.801588 | + | 0.597877i | \(0.796011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.4267 | −1.73062 | −0.865311 | − | 0.501235i | \(-0.832879\pi\) | ||||
−0.865311 | + | 0.501235i | \(0.832879\pi\) | |||||||
\(602\) | 16.6900 | 0.680235 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.70830 | 0.232268 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.98173 | 0.121025 | 0.0605123 | − | 0.998167i | \(-0.480727\pi\) | ||||
0.0605123 | + | 0.998167i | \(0.480727\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.5271 | −0.466336 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.9452 | 1.16908 | 0.584542 | − | 0.811363i | \(-0.301274\pi\) | ||||
0.584542 | + | 0.811363i | \(0.301274\pi\) | |||||||
\(614\) | −26.6457 | −1.07533 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.0910 | −1.21240 | ||||||||
\(617\) | −15.0365 | −0.605349 | −0.302674 | − | 0.953094i | \(-0.597879\pi\) | ||||
−0.302674 | + | 0.953094i | \(0.597879\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.25515 | 0.331803 | 0.165901 | − | 0.986142i | \(-0.446947\pi\) | ||||
0.165901 | + | 0.986142i | \(0.446947\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.5494 | −0.463089 | ||||||||
\(623\) | 46.9527 | 1.88112 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.0638 | 0.921814 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.26295 | −0.369632 | ||||||||
\(629\) | 21.8814 | 0.872468 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.09103 | −0.361908 | −0.180954 | − | 0.983492i | \(-0.557919\pi\) | ||||
−0.180954 | + | 0.983492i | \(0.557919\pi\) | |||||||
\(632\) | −1.96345 | −0.0781020 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.9232 | −0.552960 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.0052 | −0.634150 | ||||||||
\(638\) | 18.8176 | 0.744996 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.1171 | −1.18955 | −0.594777 | − | 0.803891i | \(-0.702760\pi\) | ||||
−0.594777 | + | 0.803891i | \(0.702760\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.3174 | 1.39278 | 0.696392 | − | 0.717662i | \(-0.254788\pi\) | ||||
0.696392 | + | 0.717662i | \(0.254788\pi\) | |||||||
\(644\) | 8.43081 | 0.332220 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.91794 | −0.0754603 | ||||||||
\(647\) | 4.12234 | 0.162066 | 0.0810330 | − | 0.996711i | \(-0.474178\pi\) | ||||
0.0810330 | + | 0.996711i | \(0.474178\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.0910 | −1.41670 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.28123 | −0.167666 | ||||||||
\(653\) | 8.62741 | 0.337617 | 0.168808 | − | 0.985649i | \(-0.446008\pi\) | ||||
0.168808 | + | 0.985649i | \(0.446008\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.14585 | 0.0447379 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 50.8773 | 1.98340 | ||||||||
\(659\) | 37.3853 | 1.45632 | 0.728162 | − | 0.685405i | \(-0.240375\pi\) | ||||
0.728162 | + | 0.685405i | \(0.240375\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8997 | −0.501739 | −0.250869 | − | 0.968021i | \(-0.580716\pi\) | ||||
−0.250869 | + | 0.968021i | \(0.580716\pi\) | |||||||
\(662\) | −0.735546 | −0.0285878 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.2447 | 0.630416 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.27226 | −0.204143 | ||||||||
\(668\) | −15.2264 | −0.589127 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.7292 | 0.838848 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.4349 | −0.402235 | −0.201118 | − | 0.979567i | \(-0.564457\pi\) | ||||
−0.201118 | + | 0.979567i | \(0.564457\pi\) | |||||||
\(674\) | 2.28123 | 0.0878696 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.8684 | −0.456475 | ||||||||
\(677\) | 12.4401 | 0.478112 | 0.239056 | − | 0.971006i | \(-0.423162\pi\) | ||||
0.239056 | + | 0.971006i | \(0.423162\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 70.1716 | 2.69294 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 35.5987 | 1.36314 | ||||||||
\(683\) | 17.5364 | 0.671011 | 0.335505 | − | 0.942038i | \(-0.391093\pi\) | ||||
0.335505 | + | 0.942038i | \(0.391093\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 37.7758 | 1.44229 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.55465 | 0.135520 | ||||||||
\(689\) | 9.24992 | 0.352394 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.2734 | −0.961446 | −0.480723 | − | 0.876872i | \(-0.659626\pi\) | ||||
−0.480723 | + | 0.876872i | \(0.659626\pi\) | |||||||
\(692\) | −12.2630 | −0.466168 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.56246 | −0.0972695 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.19767 | 0.0832426 | ||||||||
\(698\) | −5.67176 | −0.214679 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0545 | 0.606370 | 0.303185 | − | 0.952932i | \(-0.401950\pi\) | ||||
0.303185 | + | 0.952932i | \(0.401950\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.4088 | −0.430291 | ||||||||
\(704\) | −6.40880 | −0.241541 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.6665 | −0.890701 | ||||||||
\(707\) | −49.4711 | −1.86055 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5076 | 0.507290 | 0.253645 | − | 0.967297i | \(-0.418371\pi\) | ||||
0.253645 | + | 0.967297i | \(0.418371\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.0000 | 0.374766 | ||||||||
\(713\) | −9.97392 | −0.373526 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.57292 | 0.0587829 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −31.9724 | −1.19320 | ||||||||
\(719\) | −0.803402 | −0.0299619 | −0.0149809 | − | 0.999888i | \(-0.504769\pi\) | ||||
−0.0149809 | + | 0.999888i | \(0.504769\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 79.7337 | 2.96944 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.4088 | 0.424005 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.6860 | −1.91693 | −0.958463 | − | 0.285217i | \(-0.907934\pi\) | ||||
−0.958463 | + | 0.285217i | \(0.907934\pi\) | |||||||
\(728\) | −4.99477 | −0.185118 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.81761 | 0.252158 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.3723 | 0.826338 | 0.413169 | − | 0.910654i | \(-0.364422\pi\) | ||||
0.413169 | + | 0.910654i | \(0.364422\pi\) | |||||||
\(734\) | −1.14585 | −0.0422940 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.79560 | 0.0661866 | ||||||||
\(737\) | −56.5438 | −2.08282 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.4271 | 1.22963 | 0.614817 | − | 0.788669i | \(-0.289230\pi\) | ||||
0.614817 | + | 0.788669i | \(0.289230\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −40.8266 | −1.49879 | ||||||||
\(743\) | 14.4998 | 0.531947 | 0.265974 | − | 0.963980i | \(-0.414307\pi\) | ||||
0.265974 | + | 0.963980i | \(0.414307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −32.8579 | −1.20301 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.2917 | −0.449429 | ||||||||
\(749\) | −8.40623 | −0.307157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.6169 | −0.971266 | −0.485633 | − | 0.874163i | \(-0.661411\pi\) | ||||
−0.485633 | + | 0.874163i | \(0.661411\pi\) | |||||||
\(752\) | 10.8359 | 0.395144 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.12351 | 0.113751 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.0362 | 1.12803 | 0.564015 | − | 0.825764i | \(-0.309256\pi\) | ||||
0.564015 | + | 0.825764i | \(0.309256\pi\) | |||||||
\(758\) | −18.2865 | −0.664194 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.8083 | 1.00805 | 0.504025 | − | 0.863689i | \(-0.331852\pi\) | ||||
0.504025 | + | 0.863689i | \(0.331852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.3345 | 0.410338 | ||||||||
\(764\) | 6.35805 | 0.230026 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.8542 | 0.753491 | ||||||||
\(767\) | −5.99070 | −0.216312 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.2279 | −0.693376 | −0.346688 | − | 0.937980i | \(-0.612694\pi\) | ||||
−0.346688 | + | 0.937980i | \(0.612694\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.4998 | −0.521860 | ||||||||
\(773\) | 6.00373 | 0.215939 | 0.107970 | − | 0.994154i | \(-0.465565\pi\) | ||||
0.107970 | + | 0.994154i | \(0.465565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.9452 | 0.536501 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.9086 | 0.893018 | ||||||||
\(779\) | −1.14585 | −0.0410543 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.14585 | −0.327264 | ||||||||
\(782\) | 3.44385 | 0.123152 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15.0455 | 0.537340 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.2797 | −0.794187 | −0.397093 | − | 0.917778i | \(-0.629981\pi\) | ||||
−0.397093 | + | 0.917778i | \(0.629981\pi\) | |||||||
\(788\) | −5.14585 | −0.183313 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.5517 | 1.19296 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.60680 | 0.128081 | ||||||||
\(794\) | 24.7445 | 0.878150 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.87766 | 0.137440 | ||||||||
\(797\) | 26.6259 | 0.943138 | 0.471569 | − | 0.881829i | \(-0.343688\pi\) | ||||
0.471569 | + | 0.881829i | \(0.343688\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.7826 | 0.735234 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.6457 | −0.552468 | ||||||||
\(803\) | −80.8355 | −2.85262 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.90897 | 0.208135 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.5364 | −0.370669 | ||||||||
\(809\) | −0.651250 | −0.0228967 | −0.0114484 | − | 0.999934i | \(-0.503644\pi\) | ||||
−0.0114484 | + | 0.999934i | \(0.503644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.0780 | −0.459230 | −0.229615 | − | 0.973281i | \(-0.573747\pi\) | ||||
−0.229615 | + | 0.973281i | \(0.573747\pi\) | |||||||
\(812\) | −13.7863 | −0.483804 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −73.1168 | −2.56274 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.55465 | −0.124362 | ||||||||
\(818\) | 30.5804 | 1.06922 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.6640 | −0.511776 | −0.255888 | − | 0.966706i | \(-0.582368\pi\) | ||||
−0.255888 | + | 0.966706i | \(0.582368\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.2850 | 0.637374 | 0.318687 | − | 0.947860i | \(-0.396758\pi\) | ||||
0.318687 | + | 0.947860i | \(0.396758\pi\) | |||||||
\(824\) | 16.9817 | 0.591587 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.4413 | 0.920010 | ||||||||
\(827\) | 40.1910 | 1.39758 | 0.698790 | − | 0.715327i | \(-0.253722\pi\) | ||||
0.698790 | + | 0.715327i | \(0.253722\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.3760 | 0.985539 | 0.492769 | − | 0.870160i | \(-0.335985\pi\) | ||||
0.492769 | + | 0.870160i | \(0.335985\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.06379 | −0.0368802 | ||||||||
\(833\) | 28.8564 | 0.999815 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.40880 | 0.221653 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.96345 | −0.0678264 | ||||||||
\(839\) | −6.93471 | −0.239413 | −0.119706 | − | 0.992809i | \(-0.538195\pi\) | ||||
−0.119706 | + | 0.992809i | \(0.538195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.3787 | −0.702712 | ||||||||
\(842\) | −25.5949 | −0.882060 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.1496 | 0.590313 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 141.200 | 4.85167 | ||||||||
\(848\) | −8.69527 | −0.298597 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.4856 | 0.702238 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.9739 | −0.752373 | −0.376186 | − | 0.926544i | \(-0.622765\pi\) | ||||
−0.376186 | + | 0.926544i | \(0.622765\pi\) | |||||||
\(854\) | −15.9194 | −0.544752 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.79036 | −0.0611934 | ||||||||
\(857\) | 13.6091 | 0.464879 | 0.232440 | − | 0.972611i | \(-0.425329\pi\) | ||||
0.232440 | + | 0.972611i | \(0.425329\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.17192 | 0.176464 | 0.0882319 | − | 0.996100i | \(-0.471878\pi\) | ||||
0.0882319 | + | 0.996100i | \(0.471878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.3540 | 0.522959 | ||||||||
\(863\) | 15.9635 | 0.543402 | 0.271701 | − | 0.962382i | \(-0.412414\pi\) | ||||
0.271701 | + | 0.962382i | \(0.412414\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.6640 | −0.566264 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −26.0806 | −0.885232 | ||||||||
\(869\) | 12.5834 | 0.426862 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.38563 | −0.318020 | ||||||||
\(872\) | 2.41404 | 0.0817496 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.79560 | −0.0607370 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.8866 | 0.536453 | 0.268227 | − | 0.963356i | \(-0.413562\pi\) | ||||
0.268227 | + | 0.963356i | \(0.413562\pi\) | |||||||
\(878\) | −19.5987 | −0.661423 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.1458 | 0.543967 | 0.271984 | − | 0.962302i | \(-0.412320\pi\) | ||||
0.271984 | + | 0.962302i | \(0.412320\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.2887 | −1.28852 | −0.644259 | − | 0.764808i | \(-0.722834\pi\) | ||||
−0.644259 | + | 0.764808i | \(0.722834\pi\) | |||||||
\(884\) | −2.04028 | −0.0686221 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.0183 | 0.437357 | ||||||||
\(887\) | 19.2809 | 0.647389 | 0.323695 | − | 0.946162i | \(-0.395075\pi\) | ||||
0.323695 | + | 0.946162i | \(0.395075\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43.4920 | −1.45868 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.84635 | −0.262715 | ||||||||
\(893\) | −10.8359 | −0.362609 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.69527 | 0.156858 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.77359 | −0.226038 | ||||||||
\(899\) | 16.3096 | 0.543957 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.6770 | −0.555591 | ||||||||
\(902\) | −7.34352 | −0.244512 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.14585 | 0.237667 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.0205 | −1.42847 | −0.714236 | − | 0.699905i | \(-0.753226\pi\) | ||||
−0.714236 | + | 0.699905i | \(0.753226\pi\) | |||||||
\(908\) | 6.28646 | 0.208624 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.7733 | 0.853906 | 0.426953 | − | 0.904274i | \(-0.359587\pi\) | ||||
0.426953 | + | 0.904274i | \(0.359587\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −104.109 | −3.44550 | ||||||||
\(914\) | 27.3189 | 0.903630 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.14585 | −0.103942 | ||||||||
\(917\) | −54.0806 | −1.78590 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.5897 | −0.976074 | −0.488037 | − | 0.872823i | \(-0.662287\pi\) | ||||
−0.488037 | + | 0.872823i | \(0.662287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.7993 | 0.915522 | ||||||||
\(923\) | −1.51811 | −0.0499691 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −38.2369 | −1.25654 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.93621 | −0.0963859 | ||||||||
\(929\) | 1.42334 | 0.0466983 | 0.0233491 | − | 0.999727i | \(-0.492567\pi\) | ||||
0.0233491 | + | 0.999727i | \(0.492567\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0455 | −0.493097 | ||||||||
\(932\) | 0.182394 | 0.00597451 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.4711 | 0.767998 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.2276 | −0.922155 | −0.461077 | − | 0.887360i | \(-0.652537\pi\) | ||||
−0.461077 | + | 0.887360i | \(0.652537\pi\) | |||||||
\(938\) | 41.4256 | 1.35259 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.8672 | 0.517256 | 0.258628 | − | 0.965977i | \(-0.416730\pi\) | ||||
0.258628 | + | 0.965977i | \(0.416730\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.05748 | 0.0670009 | ||||||||
\(944\) | 5.63148 | 0.183289 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.7811 | −0.740676 | ||||||||
\(947\) | 43.6718 | 1.41914 | 0.709571 | − | 0.704634i | \(-0.248889\pi\) | ||||
0.709571 | + | 0.704634i | \(0.248889\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.4178 | −0.435559 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.00523 | 0.291861 | ||||||||
\(953\) | 16.0261 | 0.519136 | 0.259568 | − | 0.965725i | \(-0.416420\pi\) | ||||
0.259568 | + | 0.965725i | \(0.416420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.5039 | 0.372063 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.6900 | 0.636156 | ||||||||
\(959\) | 70.9176 | 2.29005 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.145848 | −0.00470478 | ||||||||
\(962\) | −12.1365 | −0.391298 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.445349 | −0.0143437 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.5987 | 0.372988 | 0.186494 | − | 0.982456i | \(-0.440288\pi\) | ||||
0.186494 | + | 0.982456i | \(0.440288\pi\) | |||||||
\(968\) | 30.0728 | 0.966575 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.0362 | 0.867633 | 0.433817 | − | 0.901001i | \(-0.357167\pi\) | ||||
0.433817 | + | 0.901001i | \(0.357167\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.28903 | −0.105442 | ||||||||
\(974\) | −16.3357 | −0.523430 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.39053 | −0.108528 | ||||||||
\(977\) | 14.1537 | 0.452815 | 0.226408 | − | 0.974033i | \(-0.427302\pi\) | ||||
0.226408 | + | 0.974033i | \(0.427302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −64.0880 | −2.04826 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.1093 | −0.865093 | ||||||||
\(983\) | −32.8542 | −1.04788 | −0.523942 | − | 0.851754i | \(-0.675539\pi\) | ||||
−0.523942 | + | 0.851754i | \(0.675539\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.63148 | −0.179343 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.06379 | 0.0338436 | ||||||||
\(989\) | 6.38273 | 0.202959 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.9709 | 1.52385 | 0.761923 | − | 0.647667i | \(-0.224255\pi\) | ||||
0.761923 | + | 0.647667i | \(0.224255\pi\) | |||||||
\(992\) | −5.55465 | −0.176360 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.70050 | 0.212527 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.1716 | −1.39893 | −0.699464 | − | 0.714668i | \(-0.746578\pi\) | ||||
−0.699464 | + | 0.714668i | \(0.746578\pi\) | |||||||
\(998\) | −4.69003 | −0.148460 | ||||||||
\(999\) | 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 | 8550.2.a.co.1.3 | 3 | ||
3.2 | odd | 2 | 950.2.a.k.1.1 | ✓ | 3 | ||
5.4 | even | 2 | 8550.2.a.cj.1.1 | 3 | |||
12.11 | even | 2 | 7600.2.a.cb.1.3 | 3 | |||
15.2 | even | 4 | 950.2.b.g.799.3 | 6 | |||
15.8 | even | 4 | 950.2.b.g.799.4 | 6 | |||
15.14 | odd | 2 | 950.2.a.m.1.3 | yes | 3 | ||
60.59 | even | 2 | 7600.2.a.bm.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.k.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
950.2.a.m.1.3 | yes | 3 | 15.14 | odd | 2 | ||
950.2.b.g.799.3 | 6 | 15.2 | even | 4 | |||
950.2.b.g.799.4 | 6 | 15.8 | even | 4 | |||
7600.2.a.bm.1.1 | 3 | 60.59 | even | 2 | |||
7600.2.a.cb.1.3 | 3 | 12.11 | even | 2 | |||
8550.2.a.cj.1.1 | 3 | 5.4 | even | 2 | |||
8550.2.a.co.1.3 | 3 | 1.1 | even | 1 | trivial |