Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7360,2,Mod(1,7360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7360 = 2^{6} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7360.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: | \(58.7698958877\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.21208.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 13x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3680) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-3.07664\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7360.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.58604 | 1.49305 | 0.746524 | − | 0.665358i | \(-0.231721\pi\) | ||||
0.746524 | + | 0.665358i | \(0.231721\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.07664 | 0.784895 | 0.392447 | − | 0.919774i | \(-0.371629\pi\) | ||||
0.392447 | + | 0.919774i | \(0.371629\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.68758 | 1.22919 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.19698 | −0.963926 | −0.481963 | − | 0.876192i | \(-0.660076\pi\) | ||||
−0.481963 | + | 0.876192i | \(0.660076\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.95629 | −1.65198 | −0.825989 | − | 0.563686i | \(-0.809383\pi\) | ||||
−0.825989 | + | 0.563686i | \(0.809383\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.58604 | 0.667712 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.46569 | −1.56816 | −0.784080 | − | 0.620659i | \(-0.786865\pi\) | ||||
−0.784080 | + | 0.620659i | \(0.786865\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.07664 | −1.39408 | −0.697038 | − | 0.717034i | \(-0.745499\pi\) | ||||
−0.697038 | + | 0.717034i | \(0.745499\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.37026 | 1.17189 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.77811 | 0.342197 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.87966 | −0.720434 | −0.360217 | − | 0.932869i | \(-0.617297\pi\) | ||||
−0.360217 | + | 0.932869i | \(0.617297\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.56233 | 1.35823 | 0.679117 | − | 0.734030i | \(-0.262363\pi\) | ||||
0.679117 | + | 0.734030i | \(0.262363\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.26751 | −1.43919 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.07664 | 0.351016 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.64387 | −0.434650 | −0.217325 | − | 0.976099i | \(-0.569733\pi\) | ||||
−0.217325 | + | 0.976099i | \(0.569733\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.4032 | −2.46648 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.979997 | −0.153050 | −0.0765249 | − | 0.997068i | \(-0.524382\pi\) | ||||
−0.0765249 | + | 0.997068i | \(0.524382\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.66267 | −0.863549 | −0.431775 | − | 0.901981i | \(-0.642112\pi\) | ||||
−0.431775 | + | 0.901981i | \(0.642112\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.68758 | 0.549712 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.86086 | 0.709029 | 0.354514 | − | 0.935051i | \(-0.384646\pi\) | ||||
0.354514 | + | 0.935051i | \(0.384646\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.68758 | −0.383940 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.7205 | −2.34134 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.53742 | 1.17270 | 0.586352 | − | 0.810056i | \(-0.300563\pi\) | ||||
0.586352 | + | 0.810056i | \(0.300563\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.19698 | −0.431081 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.7144 | −2.08142 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.13447 | 0.408074 | 0.204037 | − | 0.978963i | \(-0.434594\pi\) | ||||
0.204037 | + | 0.978963i | \(0.434594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.38785 | 0.433770 | 0.216885 | − | 0.976197i | \(-0.430410\pi\) | ||||
0.216885 | + | 0.976197i | \(0.430410\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.65777 | 0.964788 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.95629 | −0.738787 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.11544 | −0.136272 | −0.0681362 | − | 0.997676i | \(-0.521705\pi\) | ||||
−0.0681362 | + | 0.997676i | \(0.521705\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.58604 | −0.311322 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.85475 | −1.16954 | −0.584772 | − | 0.811198i | \(-0.698816\pi\) | ||||
−0.584772 | + | 0.811198i | \(0.698816\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3303 | −1.44315 | −0.721573 | − | 0.692338i | \(-0.756581\pi\) | ||||
−0.721573 | + | 0.692338i | \(0.756581\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.58604 | 0.298610 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.63897 | −0.756580 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.874749 | −0.0984169 | −0.0492085 | − | 0.998789i | \(-0.515670\pi\) | ||||
−0.0492085 | + | 0.998789i | \(0.515670\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.46449 | −0.718276 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.5096 | 1.37311 | 0.686555 | − | 0.727077i | \(-0.259122\pi\) | ||||
0.686555 | + | 0.727077i | \(0.259122\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.46569 | −0.701303 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.0329 | −1.07564 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.4506 | 1.10776 | 0.553880 | − | 0.832596i | \(-0.313146\pi\) | ||||
0.553880 | + | 0.832596i | \(0.313146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.3691 | −1.29663 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.5565 | 2.02791 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.07664 | −0.623450 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.54353 | 0.562860 | 0.281430 | − | 0.959582i | \(-0.409191\pi\) | ||||
0.281430 | + | 0.959582i | \(0.409191\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.7891 | −1.18485 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.153273 | 0.0152512 | 0.00762560 | − | 0.999971i | \(-0.497573\pi\) | ||||
0.00762560 | + | 0.999971i | \(0.497573\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.09053 | 0.304519 | 0.152259 | − | 0.988341i | \(-0.451345\pi\) | ||||
0.152259 | + | 0.988341i | \(0.451345\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.37026 | 0.524083 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.26871 | −0.509345 | −0.254673 | − | 0.967027i | \(-0.581968\pi\) | ||||
−0.254673 | + | 0.967027i | \(0.581968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6615 | −1.02118 | −0.510592 | − | 0.859823i | \(-0.670574\pi\) | ||||
−0.510592 | + | 0.859823i | \(0.670574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.83715 | −0.648954 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.68147 | −0.628540 | −0.314270 | − | 0.949334i | \(-0.601760\pi\) | ||||
−0.314270 | + | 0.949334i | \(0.601760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −21.9643 | −2.03060 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.4269 | −1.23084 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.779314 | −0.0708467 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.53431 | −0.228511 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.90827 | 0.613010 | 0.306505 | − | 0.951869i | \(-0.400840\pi\) | ||||
0.306505 | + | 0.951869i | \(0.400840\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.6439 | −1.28932 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.35146 | −0.817041 | −0.408520 | − | 0.912749i | \(-0.633955\pi\) | ||||
−0.408520 | + | 0.912749i | \(0.633955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.6190 | −1.09420 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.77811 | 0.153035 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.92360 | −0.762395 | −0.381197 | − | 0.924494i | \(-0.624488\pi\) | ||||
−0.381197 | + | 0.924494i | \(0.624488\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.4949 | −1.65354 | −0.826769 | − | 0.562542i | \(-0.809823\pi\) | ||||
−0.826769 | + | 0.562542i | \(0.809823\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.5703 | 1.05861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.0422 | 1.59238 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.87966 | −0.322188 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.95018 | −0.573241 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.9114 | −1.38543 | −0.692717 | − | 0.721209i | \(-0.743587\pi\) | ||||
−0.692717 | + | 0.721209i | \(0.743587\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.4232 | 1.41788 | 0.708939 | − | 0.705269i | \(-0.249174\pi\) | ||||
0.708939 | + | 0.705269i | \(0.249174\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −23.8428 | −1.92757 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.56233 | 0.607421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.5565 | 1.80020 | 0.900101 | − | 0.435682i | \(-0.143493\pi\) | ||||
0.900101 | + | 0.435682i | \(0.143493\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.0781 | 1.75091 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.07664 | −0.163662 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.31242 | −0.729405 | −0.364702 | − | 0.931124i | \(-0.618829\pi\) | ||||
−0.364702 | + | 0.931124i | \(0.618829\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.26751 | −0.643625 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.77811 | −0.524506 | −0.262253 | − | 0.964999i | \(-0.584465\pi\) | ||||
−0.262253 | + | 0.964999i | \(0.584465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.4774 | 1.72903 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.4081 | −1.71359 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.7910 | −1.80880 | −0.904399 | − | 0.426687i | \(-0.859681\pi\) | ||||
−0.904399 | + | 0.426687i | \(0.859681\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.07664 | 0.156979 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.10586 | 0.609274 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.45767 | −0.183695 | −0.0918475 | − | 0.995773i | \(-0.529277\pi\) | ||||
−0.0918475 | + | 0.995773i | \(0.529277\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.28871 | −0.244448 | −0.122224 | − | 0.992503i | \(-0.539003\pi\) | ||||
−0.122224 | + | 0.992503i | \(0.539003\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.76111 | 0.647640 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.64387 | −0.194381 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.6707 | 1.51159 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.69249 | 0.268589 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.36535 | −0.388223 | −0.194112 | − | 0.980979i | \(-0.562182\pi\) | ||||
−0.194112 | + | 0.980979i | \(0.562182\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.4671 | 1.40127 | 0.700637 | − | 0.713517i | \(-0.252899\pi\) | ||||
0.700637 | + | 0.713517i | \(0.252899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.4032 | −1.10304 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.05543 | −0.573926 | −0.286963 | − | 0.957942i | \(-0.592646\pi\) | ||||
−0.286963 | + | 0.957942i | \(0.592646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.4596 | 1.52123 | 0.760615 | − | 0.649204i | \(-0.224898\pi\) | ||||
0.760615 | + | 0.649204i | \(0.224898\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.88456 | −0.203461 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.05663 | −0.565465 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.979997 | −0.0684460 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.68758 | −0.256305 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.4269 | 1.34379 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.43397 | −0.167561 | −0.0837806 | − | 0.996484i | \(-0.526699\pi\) | ||||
−0.0837806 | + | 0.996484i | \(0.526699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −25.4847 | −1.74618 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.66267 | −0.386191 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.7042 | 1.06607 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −31.8865 | −2.15469 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 38.5115 | 2.59057 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.33433 | −0.558108 | −0.279054 | − | 0.960275i | \(-0.590021\pi\) | ||||
−0.279054 | + | 0.960275i | \(0.590021\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.68758 | 0.245839 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.1789 | −1.00746 | −0.503729 | − | 0.863862i | \(-0.668039\pi\) | ||||
−0.503729 | + | 0.863862i | \(0.668039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0590 | 0.929048 | 0.464524 | − | 0.885561i | \(-0.346226\pi\) | ||||
0.464524 | + | 0.885561i | \(0.346226\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.1686 | −1.12961 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.31145 | 0.610014 | 0.305007 | − | 0.952350i | \(-0.401341\pi\) | ||||
0.305007 | + | 0.952350i | \(0.401341\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.86086 | 0.317087 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.26213 | −0.146941 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.14837 | 0.333020 | 0.166510 | − | 0.986040i | \(-0.446750\pi\) | ||||
0.166510 | + | 0.986040i | \(0.446750\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.9526 | −1.02760 | −0.513798 | − | 0.857911i | \(-0.671762\pi\) | ||||
−0.513798 | + | 0.857911i | \(0.671762\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.0517 | −1.41462 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.68758 | −0.171703 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.1942 | 2.30298 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 32.3504 | 2.05012 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.6021 | 1.61599 | 0.807994 | − | 0.589190i | \(-0.200553\pi\) | ||||
0.807994 | + | 0.589190i | \(0.200553\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.19698 | 0.200992 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.7205 | −1.04708 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.33924 | 0.582566 | 0.291283 | − | 0.956637i | \(-0.405918\pi\) | ||||
0.291283 | + | 0.956637i | \(0.405918\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.49036 | −0.341155 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.3065 | −0.885553 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.612149 | −0.0377467 | −0.0188733 | − | 0.999822i | \(-0.506008\pi\) | ||||
−0.0188733 | + | 0.999822i | \(0.506008\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.53742 | 0.524450 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.0256 | 1.65394 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.70518 | −0.408822 | −0.204411 | − | 0.978885i | \(-0.565528\pi\) | ||||
−0.204411 | + | 0.978885i | \(0.565528\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −31.2277 | −1.89695 | −0.948475 | − | 0.316852i | \(-0.897374\pi\) | ||||
−0.948475 | + | 0.316852i | \(0.897374\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −31.9868 | −1.93593 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.19698 | −0.192785 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.8513 | 1.79359 | 0.896795 | − | 0.442447i | \(-0.145889\pi\) | ||||
0.896795 | + | 0.442447i | \(0.145889\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27.8867 | 1.66953 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.3910 | 1.09711 | 0.548556 | − | 0.836114i | \(-0.315178\pi\) | ||||
0.548556 | + | 0.836114i | \(0.315178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.6319 | 1.28588 | 0.642941 | − | 0.765916i | \(-0.277714\pi\) | ||||
0.642941 | + | 0.765916i | \(0.277714\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.7144 | −0.930841 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.03510 | −0.120128 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.8052 | 1.45913 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.3358 | 0.840378 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.83451 | −0.574538 | −0.287269 | − | 0.957850i | \(-0.592747\pi\) | ||||
−0.287269 | + | 0.957850i | \(0.592747\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.13447 | 0.182496 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.68458 | −0.329853 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.95629 | 0.344461 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.7593 | −0.677795 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.396369 | 0.0227708 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.38785 | 0.193988 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.0031 | 1.31286 | 0.656428 | − | 0.754388i | \(-0.272066\pi\) | ||||
0.656428 | + | 0.754388i | \(0.272066\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.99222 | 0.454661 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.7144 | 0.720967 | 0.360484 | − | 0.932766i | \(-0.382612\pi\) | ||||
0.360484 | + | 0.932766i | \(0.382612\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5583 | −0.992451 | −0.496226 | − | 0.868194i | \(-0.665281\pi\) | ||||
−0.496226 | + | 0.868194i | \(0.665281\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.65777 | 0.431466 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.0924 | 1.29700 | 0.648500 | − | 0.761214i | \(-0.275397\pi\) | ||||
0.648500 | + | 0.761214i | \(0.275397\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4032 | 0.694445 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.6251 | −0.760477 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.2897 | 2.18613 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.95629 | −0.330396 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.5709 | −1.52468 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.0942 | 0.556513 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.51454 | −0.413037 | −0.206518 | − | 0.978443i | \(-0.566213\pi\) | ||||
−0.206518 | + | 0.978443i | \(0.566213\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.74950 | −0.534269 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.11544 | −0.0609429 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.3996 | 1.38360 | 0.691801 | − | 0.722088i | \(-0.256817\pi\) | ||||
0.691801 | + | 0.722088i | \(0.256817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.2785 | −0.938441 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.1766 | −1.30924 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1176 | −1.08625 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.58604 | −0.139227 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.1964 | −0.815785 | −0.407892 | − | 0.913030i | \(-0.633736\pi\) | ||||
−0.407892 | + | 0.913030i | \(0.633736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.32103 | 0.124242 | 0.0621209 | − | 0.998069i | \(-0.480214\pi\) | ||||
0.0621209 | + | 0.998069i | \(0.480214\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.5909 | −0.565303 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.5113 | −0.559460 | −0.279730 | − | 0.960079i | \(-0.590245\pi\) | ||||
−0.279730 | + | 0.960079i | \(0.590245\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.85475 | −0.523036 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −34.7224 | −1.83771 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.6153 | 0.613030 | 0.306515 | − | 0.951866i | \(-0.400837\pi\) | ||||
0.306515 | + | 0.951866i | \(0.400837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.9255 | 0.943448 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.01533 | −0.105778 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.3303 | −0.645395 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.0381 | −1.46358 | −0.731788 | − | 0.681533i | \(-0.761314\pi\) | ||||
−0.731788 | + | 0.681533i | \(0.761314\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.61382 | −0.188128 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.7291 | 0.920450 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.9224 | 1.44577 | 0.722883 | − | 0.690970i | \(-0.242816\pi\) | ||||
0.722883 | + | 0.690970i | \(0.242816\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.58604 | 0.133542 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.1084 | 1.19014 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.5978 | −0.903936 | −0.451968 | − | 0.892034i | \(-0.649278\pi\) | ||||
−0.451968 | + | 0.892034i | \(0.649278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.8650 | 0.915253 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.24333 | −0.165727 | −0.0828633 | − | 0.996561i | \(-0.526406\pi\) | ||||
−0.0828633 | + | 0.996561i | \(0.526406\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.63897 | −0.338353 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.8816 | −1.06147 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.1964 | −1.07470 | −0.537350 | − | 0.843359i | \(-0.680575\pi\) | ||||
−0.537350 | + | 0.843359i | \(0.680575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.46569 | 0.326984 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.1832 | −1.21988 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.874749 | −0.0440134 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.6263 | −1.38652 | −0.693262 | − | 0.720686i | \(-0.743827\pi\) | ||||
−0.693262 | + | 0.720686i | \(0.743827\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −32.6331 | −1.63370 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.2093 | 1.80821 | 0.904103 | − | 0.427314i | \(-0.140540\pi\) | ||||
0.904103 | + | 0.427314i | \(0.140540\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −45.0434 | −2.24377 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.46449 | −0.321223 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.45241 | 0.418971 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.9231 | 1.67739 | 0.838695 | − | 0.544602i | \(-0.183319\pi\) | ||||
0.838695 | + | 0.544602i | \(0.183319\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.0768 | −1.13829 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.50916 | 0.320295 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.5096 | 0.614074 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −50.4146 | −2.46881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.40318 | 0.312816 | 0.156408 | − | 0.987693i | \(-0.450009\pi\) | ||||
0.156408 | + | 0.987693i | \(0.450009\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.2013 | 0.545918 | 0.272959 | − | 0.962026i | \(-0.411998\pi\) | ||||
0.272959 | + | 0.962026i | \(0.411998\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.9248 | 0.871534 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.46569 | −0.313632 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.03534 | 0.340464 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 49.2437 | 2.37751 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.0002 | −1.20422 | −0.602110 | − | 0.798414i | \(-0.705673\pi\) | ||||
−0.602110 | + | 0.798414i | \(0.705673\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.2955 | −0.927284 | −0.463642 | − | 0.886023i | \(-0.653458\pi\) | ||||
−0.463642 | + | 0.886023i | \(0.653458\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.0329 | −0.481042 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.07664 | 0.290685 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.7725 | −1.85051 | −0.925255 | − | 0.379347i | \(-0.876149\pi\) | ||||
−0.925255 | + | 0.379347i | \(0.876149\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.91067 | −0.471937 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.7915 | −1.84304 | −0.921520 | − | 0.388331i | \(-0.873052\pi\) | ||||
−0.921520 | + | 0.388331i | \(0.873052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.4506 | 0.495406 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −43.7334 | −2.06852 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.7398 | −1.78105 | −0.890525 | − | 0.454934i | \(-0.849663\pi\) | ||||
−0.890525 | + | 0.454934i | \(0.849663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.13303 | 0.147529 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 45.0570 | 2.11696 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.3691 | −0.579870 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.6973 | 1.29562 | 0.647812 | − | 0.761800i | \(-0.275684\pi\) | ||||
0.647812 | + | 0.761800i | \(0.275684\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.4967 | −0.536621 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.5590 | 1.56300 | 0.781498 | − | 0.623907i | \(-0.214456\pi\) | ||||
0.781498 | + | 0.623907i | \(0.214456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.7259 | 0.777318 | 0.388659 | − | 0.921382i | \(-0.372938\pi\) | ||||
0.388659 | + | 0.921382i | \(0.372938\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.5565 | 0.906909 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.79033 | −0.406768 | −0.203384 | − | 0.979099i | \(-0.565194\pi\) | ||||
−0.203384 | + | 0.979099i | \(0.565194\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.31636 | −0.106960 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 58.3318 | 2.68779 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.1035 | 0.832398 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.07664 | −0.278815 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.4824 | 1.44148 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.8726 | 0.816619 | 0.408309 | − | 0.912844i | \(-0.366118\pi\) | ||||
0.408309 | + | 0.912844i | \(0.366118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7477 | 0.718032 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.37026 | −0.244355 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.54353 | 0.251719 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.1481 | −0.641113 | −0.320556 | − | 0.947229i | \(-0.603870\pi\) | ||||
−0.320556 | + | 0.947229i | \(0.603870\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.0822 | −1.08904 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.829600 | −0.0374393 | −0.0187197 | − | 0.999825i | \(-0.505959\pi\) | ||||
−0.0187197 | + | 0.999825i | \(0.505959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.0847 | 1.12976 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.7891 | −0.529882 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.4647 | −0.917968 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.0634 | −1.74872 | −0.874358 | − | 0.485281i | \(-0.838717\pi\) | ||||
−0.874358 | + | 0.485281i | \(0.838717\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.5284 | −0.783113 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.4202 | −1.08884 | −0.544421 | − | 0.838812i | \(-0.683251\pi\) | ||||
−0.544421 | + | 0.838812i | \(0.683251\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.153273 | 0.00682055 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 58.1274 | 2.58153 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.6488 | −0.959565 | −0.479783 | − | 0.877387i | \(-0.659284\pi\) | ||||
−0.479783 | + | 0.877387i | \(0.659284\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.6054 | −1.13272 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.8049 | −0.477049 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.09053 | 0.136185 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.5401 | −0.683451 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −61.5245 | −2.70062 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.2788 | 0.800807 | 0.400404 | − | 0.916339i | \(-0.368870\pi\) | ||||
0.400404 | + | 0.916339i | \(0.368870\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.671658 | 0.0293695 | 0.0146848 | − | 0.999892i | \(-0.495326\pi\) | ||||
0.0146848 | + | 0.999892i | \(0.495326\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.37026 | 0.234377 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −48.8957 | −2.12993 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.5586 | 0.501602 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.83715 | 0.252835 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.26871 | −0.227786 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.35563 | −0.274266 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.59215 | 0.370090 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.2309 | 1.17075 | 0.585373 | − | 0.810764i | \(-0.300948\pi\) | ||||
0.585373 | + | 0.810764i | \(0.300948\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.50473 | −0.364973 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.6615 | −0.456687 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.12155 | −0.304495 | −0.152248 | − | 0.988342i | \(-0.548651\pi\) | ||||
−0.152248 | + | 0.988342i | \(0.548651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.4930 | 0.533187 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.5753 | 1.00434 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.81654 | −0.0772469 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.83715 | −0.290221 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.32834 | 0.225769 | 0.112885 | − | 0.993608i | \(-0.463991\pi\) | ||||
0.112885 | + | 0.993608i | \(0.463991\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.7285 | 1.42656 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 53.4551 | 2.25688 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.1317 | −1.52277 | −0.761385 | − | 0.648300i | \(-0.775480\pi\) | ||||
−0.761385 | + | 0.648300i | \(0.775480\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.68147 | −0.281092 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.4244 | −0.563771 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.4566 | 1.48642 | 0.743209 | − | 0.669060i | \(-0.233303\pi\) | ||||
0.743209 | + | 0.669060i | \(0.233303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.95365 | −0.165455 | −0.0827275 | − | 0.996572i | \(-0.526363\pi\) | ||||
−0.0827275 | + | 0.996572i | \(0.526363\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.8750 | −0.579636 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.7234 | 1.48718 | 0.743592 | − | 0.668634i | \(-0.233121\pi\) | ||||
0.743592 | + | 0.668634i | \(0.233121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 50.3427 | 2.09217 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.9780 | 1.07775 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.2940 | −1.13040 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21.9643 | −0.908112 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −42.0407 | −1.73520 | −0.867602 | − | 0.497259i | \(-0.834340\pi\) | ||||
−0.867602 | + | 0.497259i | \(0.834340\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −45.9535 | −1.89348 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.8316 | −0.856899 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.71848 | 0.193765 | 0.0968823 | − | 0.995296i | \(-0.469113\pi\) | ||||
0.0968823 | + | 0.995296i | \(0.469113\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.4269 | −0.550449 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 55.4952 | 2.27127 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.0976 | 1.14804 | 0.574018 | − | 0.818843i | \(-0.305384\pi\) | ||||
0.574018 | + | 0.818843i | \(0.305384\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.3995 | 0.668949 | 0.334474 | − | 0.942405i | \(-0.391441\pi\) | ||||
0.334474 | + | 0.942405i | \(0.391441\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.11327 | −0.167505 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.779314 | −0.0316836 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.6973 | −1.69244 | −0.846220 | − | 0.532834i | \(-0.821127\pi\) | ||||
−0.846220 | + | 0.532834i | \(0.821127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.8347 | −0.844266 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.9527 | −1.17130 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.5660 | −0.871044 | −0.435522 | − | 0.900178i | \(-0.643436\pi\) | ||||
−0.435522 | + | 0.900178i | \(0.643436\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.53431 | −0.102193 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.5035 | 0.463115 | 0.231557 | − | 0.972821i | \(-0.425618\pi\) | ||||
0.231557 | + | 0.972821i | \(0.425618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.9470 | 1.48503 | 0.742514 | − | 0.669831i | \(-0.233633\pi\) | ||||
0.742514 | + | 0.669831i | \(0.233633\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.77811 | −0.0713531 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.7021 | 0.869476 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 50.2386 | 2.00634 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.0945 | 0.681601 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.6839 | 1.46036 | 0.730181 | − | 0.683254i | \(-0.239436\pi\) | ||||
0.730181 | + | 0.683254i | \(0.239436\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.29433 | −0.250177 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.90827 | 0.274146 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.0080 | 0.634261 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36.3402 | −1.43760 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.7187 | −1.25281 | −0.626407 | − | 0.779496i | \(-0.715475\pi\) | ||||
−0.626407 | + | 0.779496i | \(0.715475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 49.6953 | 1.95979 | 0.979896 | − | 0.199507i | \(-0.0639340\pi\) | ||||
0.979896 | + | 0.199507i | \(0.0639340\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.6439 | −0.576602 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.9197 | −0.704495 | −0.352247 | − | 0.935907i | \(-0.614582\pi\) | ||||
−0.352247 | + | 0.935907i | \(0.614582\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.0209 | −0.393353 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 40.6117 | 1.59170 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.8591 | 1.24674 | 0.623371 | − | 0.781926i | \(-0.285763\pi\) | ||||
0.623371 | + | 0.781926i | \(0.285763\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.35146 | −0.365392 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −45.4688 | −1.77391 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.2689 | −1.64656 | −0.823282 | − | 0.567632i | \(-0.807860\pi\) | ||||
−0.823282 | + | 0.567632i | \(0.807860\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.0251 | −0.973365 | −0.486683 | − | 0.873579i | \(-0.661793\pi\) | ||||
−0.486683 | + | 0.873579i | \(0.661793\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 99.5922 | 3.86784 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.6190 | −0.489342 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.87966 | 0.150221 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.5529 | −0.833282 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.8309 | −0.418122 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.6058 | −0.987030 | −0.493515 | − | 0.869737i | \(-0.664288\pi\) | ||||
−0.493515 | + | 0.869737i | \(0.664288\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.77811 | 0.0684395 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.2689 | 0.471534 | 0.235767 | − | 0.971810i | \(-0.424240\pi\) | ||||
0.235767 | + | 0.971810i | \(0.424240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.5119 | 0.441786 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.2531 | −1.50418 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.0788 | 1.45704 | 0.728522 | − | 0.685022i | \(-0.240208\pi\) | ||||
0.728522 | + | 0.685022i | \(0.240208\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.92360 | −0.340953 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.3572 | 1.38711 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −50.8514 | −1.93728 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.9788 | 0.721987 | 0.360994 | − | 0.932568i | \(-0.382438\pi\) | ||||
0.360994 | + | 0.932568i | \(0.382438\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −24.4817 | −0.929984 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.4949 | −0.739484 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.33636 | 0.240007 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.0797 | 0.910780 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.75834 | −0.217490 | −0.108745 | − | 0.994070i | \(-0.534683\pi\) | ||||
−0.108745 | + | 0.994070i | \(0.534683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0659 | 0.605935 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.5703 | 0.473427 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.318292 | 0.0119706 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.6356 | 1.45099 | 0.725495 | − | 0.688227i | \(-0.241611\pi\) | ||||
0.725495 | + | 0.688227i | \(0.241611\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.22571 | −0.120973 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.56233 | −0.283211 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.0422 | 0.712136 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.3139 | 0.497215 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.30293 | 0.123179 | 0.0615893 | − | 0.998102i | \(-0.480383\pi\) | ||||
0.0615893 | + | 0.998102i | \(0.480383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.41790 | 0.239015 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −41.2540 | −1.53425 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.87966 | −0.144087 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.74362 | −0.361371 | −0.180686 | − | 0.983541i | \(-0.557832\pi\) | ||||
−0.180686 | + | 0.983541i | \(0.557832\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.6331 | −1.39382 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.6131 | 1.35418 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4152 | 0.421629 | 0.210814 | − | 0.977526i | \(-0.432388\pi\) | ||||
0.210814 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.95018 | −0.256361 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.56603 | 0.131357 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −53.6434 | −1.97330 | −0.986652 | − | 0.162845i | \(-0.947933\pi\) | ||||
−0.986652 | + | 0.162845i | \(0.947933\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 93.5996 | 3.43847 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.5457 | 0.900494 | 0.450247 | − | 0.892904i | \(-0.351336\pi\) | ||||
0.450247 | + | 0.892904i | \(0.351336\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.9114 | −0.619585 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 46.1303 | 1.68782 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.9412 | −0.399783 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.1797 | 1.10127 | 0.550637 | − | 0.834745i | \(-0.314385\pi\) | ||||
0.550637 | + | 0.834745i | \(0.314385\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 66.2079 | 2.41275 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.4232 | 0.634095 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.1432 | −0.477699 | −0.238849 | − | 0.971057i | \(-0.576770\pi\) | ||||
−0.238849 | + | 0.971057i | \(0.576770\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.26751 | 0.300091 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.39467 | 0.159307 | 0.0796533 | − | 0.996823i | \(-0.474619\pi\) | ||||
0.0796533 | + | 0.996823i | \(0.474619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.1400 | −0.801522 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −23.8428 | −0.862037 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.6698 | −0.674129 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.9380 | −1.00747 | −0.503734 | − | 0.863859i | \(-0.668041\pi\) | ||||
−0.503734 | + | 0.863859i | \(0.668041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.1516 | 0.869799 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.2096 | −1.55414 | −0.777070 | − | 0.629414i | \(-0.783295\pi\) | ||||
−0.777070 | + | 0.629414i | \(0.783295\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.56233 | 0.271647 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.1983 | −0.509360 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.95509 | 0.213363 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.5054 | 1.12735 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.89845 | −0.246531 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.5565 | 0.805074 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.0255 | −1.81886 | −0.909431 | − | 0.415854i | \(-0.863483\pi\) | ||||
−0.909431 | + | 0.415854i | \(0.863483\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.58304 | −0.0563577 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.8750 | −0.493338 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.1790 | −0.716578 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.0781 | 0.783029 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.6701 | 0.696750 | 0.348375 | − | 0.937355i | \(-0.386734\pi\) | ||||
0.348375 | + | 0.937355i | \(0.386734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.4288 | −1.11187 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38.5374 | 1.36165 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.4196 | 1.39109 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.07664 | −0.0731918 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.3398 | −0.610391 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.8691 | −1.61267 | −0.806336 | − | 0.591458i | \(-0.798553\pi\) | ||||
−0.806336 | + | 0.591458i | \(0.798553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.97629 | −0.0693971 | −0.0346985 | − | 0.999398i | \(-0.511047\pi\) | ||||
−0.0346985 | + | 0.999398i | \(0.511047\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −80.7561 | −2.83224 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.31242 | −0.326200 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.4100 | 1.20385 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −45.6119 | −1.59381 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.7778 | −1.17885 | −0.589426 | − | 0.807822i | \(-0.700646\pi\) | ||||
−0.589426 | + | 0.807822i | \(0.700646\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.97189 | 0.0687356 | 0.0343678 | − | 0.999409i | \(-0.489058\pi\) | ||||
0.0343678 | + | 0.999409i | \(0.489058\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.26751 | −0.287838 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.06779 | 0.0719041 | 0.0359520 | − | 0.999354i | \(-0.488554\pi\) | ||||
0.0359520 | + | 0.999354i | \(0.488554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.0659 | −1.04423 | −0.522115 | − | 0.852875i | \(-0.674857\pi\) | ||||
−0.522115 | + | 0.852875i | \(0.674857\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 77.1965 | 2.67792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.3771 | 0.602080 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.77811 | −0.234566 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.4467 | 0.464784 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.4008 | −0.980504 | −0.490252 | − | 0.871581i | \(-0.663095\pi\) | ||||
−0.490252 | + | 0.871581i | \(0.663095\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9483 | −0.480975 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 47.5597 | 1.63804 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.4774 | 0.773247 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.61835 | −0.0556072 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 55.9408 | 1.91988 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.64387 | 0.0906308 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0965 | 0.790809 | 0.395405 | − | 0.918507i | \(-0.370604\pi\) | ||||
0.395405 | + | 0.918507i | \(0.370604\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.4081 | −0.766341 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.1530 | 0.620095 | 0.310048 | − | 0.950721i | \(-0.399655\pi\) | ||||
0.310048 | + | 0.950721i | \(0.399655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.6082 | −1.69261 | −0.846305 | − | 0.532699i | \(-0.821178\pi\) | ||||
−0.846305 | + | 0.532699i | \(0.821178\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.26284 | −0.179357 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.3893 | −0.830221 | −0.415111 | − | 0.909771i | \(-0.636257\pi\) | ||||
−0.415111 | + | 0.909771i | \(0.636257\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.7910 | −0.808919 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 64.1470 | 2.17855 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.79656 | 0.0948666 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.64387 | 0.225119 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.4422 | 0.691864 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.07664 | 0.0702031 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.19639 | 0.107934 | 0.0539672 | − | 0.998543i | \(-0.482813\pi\) | ||||
0.0539672 | + | 0.998543i | \(0.482813\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.4324 | −0.857813 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.8440 | −0.634869 | −0.317435 | − | 0.948280i | \(-0.602821\pi\) | ||||
−0.317435 | + | 0.948280i | \(0.602821\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.74254 | 0.159599 | 0.0797996 | − | 0.996811i | \(-0.474572\pi\) | ||||
0.0797996 | + | 0.996811i | \(0.474572\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.10586 | 0.272476 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.69296 | 0.0904206 | 0.0452103 | − | 0.998977i | \(-0.485604\pi\) | ||||
0.0452103 | + | 0.998977i | \(0.485604\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.3460 | 0.481148 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.6668 | 0.692365 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.5377 | −0.988440 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.45767 | −0.0821509 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.4032 | 0.514297 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.3392 | −0.978518 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −55.2003 | −1.83899 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.4100 | −1.01198 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.28871 | −0.109321 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.1879 | 1.20160 | 0.600799 | − | 0.799400i | \(-0.294849\pi\) | ||||
0.600799 | + | 0.799400i | \(0.294849\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.565206 | 0.0187467 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.2537 | −1.33367 | −0.666833 | − | 0.745207i | \(-0.732350\pi\) | ||||
−0.666833 | + | 0.745207i | \(0.732350\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.9931 | −1.32358 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.76111 | 0.289633 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.4196 | −0.641291 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.92181 | −0.327290 | −0.163645 | − | 0.986519i | \(-0.552325\pi\) | ||||
−0.163645 | + | 0.986519i | \(0.552325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 59.4869 | 1.96016 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 58.6977 | 1.93206 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.64387 | −0.0869300 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.3966 | 0.374313 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.3155 | −1.06024 | −0.530119 | − | 0.847923i | \(-0.677853\pi\) | ||||
−0.530119 | + | 0.847923i | \(0.677853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3315 | 0.535242 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.8799 | 1.07644 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.6707 | 0.676004 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.1049 | −0.983484 | −0.491742 | − | 0.870741i | \(-0.663640\pi\) | ||||
−0.491742 | + | 0.870741i | \(0.663640\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −45.4063 | −1.48178 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.37205 | 0.207723 | 0.103861 | − | 0.994592i | \(-0.466880\pi\) | ||||
0.103861 | + | 0.994592i | \(0.466880\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.979997 | 0.0319131 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.69249 | 0.120117 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.5664 | 1.25324 | 0.626620 | − | 0.779325i | \(-0.284438\pi\) | ||||
0.626620 | + | 0.779325i | \(0.284438\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 73.4426 | 2.38405 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 59.7179 | 1.93648 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.0322 | 1.42634 | 0.713171 | − | 0.700990i | \(-0.247258\pi\) | ||||
0.713171 | + | 0.700990i | \(0.247258\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.36535 | −0.173619 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.0751 | 1.03684 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.5311 | −0.598400 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.1888 | 0.844801 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.4288 | −0.626084 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.4671 | 0.626669 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3837 | 0.751967 | 0.375984 | − | 0.926626i | \(-0.377305\pi\) | ||||
0.375984 | + | 0.926626i | \(0.377305\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 101.604 | 3.26401 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.4327 | −1.52219 | −0.761095 | − | 0.648641i | \(-0.775338\pi\) | ||||
−0.761095 | + | 0.648641i | \(0.775338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.4839 | −1.29785 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.4032 | −0.493297 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.2961 | −0.873280 | −0.436640 | − | 0.899636i | \(-0.643832\pi\) | ||||
−0.436640 | + | 0.899636i | \(0.643832\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.4104 | −1.06780 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.3150 | −1.25523 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.17601 | 0.228879 | 0.114440 | − | 0.993430i | \(-0.463493\pi\) | ||||
0.114440 | + | 0.993430i | \(0.463493\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.05543 | −0.256667 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.1040 | 0.830901 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.66267 | 0.180063 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.6824 | 1.22879 | 0.614394 | − | 0.789000i | \(-0.289401\pi\) | ||||
0.614394 | + | 0.789000i | \(0.289401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.4329 | −0.616684 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.4596 | 0.680314 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.0184 | 0.697331 | 0.348666 | − | 0.937247i | \(-0.386635\pi\) | ||||
0.348666 | + | 0.937247i | \(0.386635\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.70110 | −0.148736 |
(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 | 7360.2.a.ci.1.4 | 4 | ||
4.3 | odd | 2 | 7360.2.a.ch.1.1 | 4 | |||
8.3 | odd | 2 | 3680.2.a.t.1.4 | yes | 4 | ||
8.5 | even | 2 | 3680.2.a.s.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3680.2.a.s.1.1 | ✓ | 4 | 8.5 | even | 2 | ||
3680.2.a.t.1.4 | yes | 4 | 8.3 | odd | 2 | ||
7360.2.a.ch.1.1 | 4 | 4.3 | odd | 2 | |||
7360.2.a.ci.1.4 | 4 | 1.1 | even | 1 | trivial |