Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(1,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, 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("4600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.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: | \(36.7311849298\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 7x^{5} + 24x^{4} + x^{3} - 35x^{2} + 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.356372\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.356372 | −0.205751 | −0.102876 | − | 0.994694i | \(-0.532804\pi\) | ||||
−0.102876 | + | 0.994694i | \(0.532804\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46376 | 0.931212 | 0.465606 | − | 0.884992i | \(-0.345836\pi\) | ||||
0.465606 | + | 0.884992i | \(0.345836\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.87300 | −0.957666 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.61574 | 0.487163 | 0.243581 | − | 0.969880i | \(-0.421678\pi\) | ||||
0.243581 | + | 0.969880i | \(0.421678\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.62553 | −0.728191 | −0.364096 | − | 0.931362i | \(-0.618622\pi\) | ||||
−0.364096 | + | 0.931362i | \(0.618622\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.58924 | −0.627982 | −0.313991 | − | 0.949426i | \(-0.601666\pi\) | ||||
−0.313991 | + | 0.949426i | \(0.601666\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.02550 | 0.923512 | 0.461756 | − | 0.887007i | \(-0.347220\pi\) | ||||
0.461756 | + | 0.887007i | \(0.347220\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.878013 | −0.191598 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.09297 | 0.402793 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.08580 | −1.31580 | −0.657900 | − | 0.753106i | \(-0.728555\pi\) | ||||
−0.657900 | + | 0.753106i | \(0.728555\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.58371 | −0.823258 | −0.411629 | − | 0.911352i | \(-0.635040\pi\) | ||||
−0.411629 | + | 0.911352i | \(0.635040\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.575803 | −0.100234 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.96054 | 0.486710 | 0.243355 | − | 0.969937i | \(-0.421752\pi\) | ||||
0.243355 | + | 0.969937i | \(0.421752\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.935665 | 0.149826 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.71155 | −0.891995 | −0.445997 | − | 0.895034i | \(-0.647151\pi\) | ||||
−0.445997 | + | 0.895034i | \(0.647151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.30448 | −0.351430 | −0.175715 | − | 0.984441i | \(-0.556224\pi\) | ||||
−0.175715 | + | 0.984441i | \(0.556224\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.88317 | 1.00401 | 0.502007 | − | 0.864864i | \(-0.332595\pi\) | ||||
0.502007 | + | 0.864864i | \(0.332595\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.929907 | −0.132844 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.922731 | 0.129208 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.76467 | −0.929199 | −0.464600 | − | 0.885521i | \(-0.653802\pi\) | ||||
−0.464600 | + | 0.885521i | \(0.653802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.43457 | −0.190014 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.53432 | 0.329941 | 0.164970 | − | 0.986299i | \(-0.447247\pi\) | ||||
0.164970 | + | 0.986299i | \(0.447247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.25564 | 1.18506 | 0.592532 | − | 0.805547i | \(-0.298129\pi\) | ||||
0.592532 | + | 0.805547i | \(0.298129\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.07837 | −0.891791 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.7285 | −1.92154 | −0.960770 | − | 0.277347i | \(-0.910545\pi\) | ||||
−0.960770 | + | 0.277347i | \(0.910545\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.356372 | −0.0429021 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.25113 | −0.623194 | −0.311597 | − | 0.950214i | \(-0.600864\pi\) | ||||
−0.311597 | + | 0.950214i | \(0.600864\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.03858 | 0.706762 | 0.353381 | − | 0.935479i | \(-0.385032\pi\) | ||||
0.353381 | + | 0.935479i | \(0.385032\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.98078 | 0.453652 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.35712 | −0.152688 | −0.0763439 | − | 0.997082i | \(-0.524325\pi\) | ||||
−0.0763439 | + | 0.997082i | \(0.524325\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.87312 | 0.874791 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.59500 | −0.943423 | −0.471712 | − | 0.881753i | \(-0.656364\pi\) | ||||
−0.471712 | + | 0.881753i | \(0.656364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.52518 | 0.270727 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.84084 | −0.937127 | −0.468564 | − | 0.883430i | \(-0.655228\pi\) | ||||
−0.468564 | + | 0.883430i | \(0.655228\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.46867 | −0.678100 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.63350 | 0.169386 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.01314 | 0.813611 | 0.406806 | − | 0.913515i | \(-0.366643\pi\) | ||||
0.406806 | + | 0.913515i | \(0.366643\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.64201 | −0.466539 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.33185 | −0.630043 | −0.315021 | − | 0.949085i | \(-0.602012\pi\) | ||||
−0.315021 | + | 0.949085i | \(0.602012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.1901 | 1.29966 | 0.649831 | − | 0.760078i | \(-0.274839\pi\) | ||||
0.649831 | + | 0.760078i | \(0.274839\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.54923 | 0.923159 | 0.461580 | − | 0.887099i | \(-0.347283\pi\) | ||||
0.461580 | + | 0.887099i | \(0.347283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.5622 | −1.68215 | −0.841077 | − | 0.540915i | \(-0.818078\pi\) | ||||
−0.841077 | + | 0.540915i | \(0.818078\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.05505 | −0.100141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.54267 | −0.145122 | −0.0725611 | − | 0.997364i | \(-0.523117\pi\) | ||||
−0.0725611 | + | 0.997364i | \(0.523117\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.54315 | 0.697364 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.37925 | −0.584785 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.38940 | −0.762673 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.03544 | 0.183529 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4256 | −1.10260 | −0.551299 | − | 0.834308i | \(-0.685868\pi\) | ||||
−0.551299 | + | 0.834308i | \(0.685868\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.821251 | 0.0723071 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3191 | −0.988957 | −0.494479 | − | 0.869190i | \(-0.664641\pi\) | ||||
−0.494479 | + | 0.869190i | \(0.664641\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.91784 | 0.859986 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.94093 | −0.422132 | −0.211066 | − | 0.977472i | \(-0.567694\pi\) | ||||
−0.211066 | + | 0.977472i | \(0.567694\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.93101 | −0.248605 | −0.124303 | − | 0.992244i | \(-0.539669\pi\) | ||||
−0.124303 | + | 0.992244i | \(0.539669\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.45297 | −0.206577 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.24216 | −0.354748 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.331393 | 0.0273328 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.09023 | −0.417008 | −0.208504 | − | 0.978022i | \(-0.566859\pi\) | ||||
−0.208504 | + | 0.978022i | \(0.566859\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.3645 | −1.16897 | −0.584485 | − | 0.811405i | \(-0.698703\pi\) | ||||
−0.584485 | + | 0.811405i | \(0.698703\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.43888 | 0.601398 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.34146 | 0.585912 | 0.292956 | − | 0.956126i | \(-0.405361\pi\) | ||||
0.292956 | + | 0.956126i | \(0.405361\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.41074 | 0.191184 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.46376 | 0.194171 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.12762 | 0.166648 | 0.0833240 | − | 0.996523i | \(-0.473446\pi\) | ||||
0.0833240 | + | 0.996523i | \(0.473446\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.16080 | −0.167208 | −0.0836039 | − | 0.996499i | \(-0.526643\pi\) | ||||
−0.0836039 | + | 0.996499i | \(0.526643\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.10659 | −0.469738 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.5652 | −0.884417 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.6210 | 1.41573 | 0.707863 | − | 0.706350i | \(-0.249659\pi\) | ||||
0.707863 | + | 0.706350i | \(0.249659\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.903162 | −0.0678858 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.4670 | −1.00657 | −0.503287 | − | 0.864119i | \(-0.667876\pi\) | ||||
−0.503287 | + | 0.864119i | \(0.667876\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2927 | 0.913706 | 0.456853 | − | 0.889542i | \(-0.348977\pi\) | ||||
0.456853 | + | 0.889542i | \(0.348977\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.29845 | −0.243828 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.18352 | −0.305930 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.15657 | 0.375085 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.07099 | −0.149852 | −0.0749258 | − | 0.997189i | \(-0.523872\pi\) | ||||
−0.0749258 | + | 0.997189i | \(0.523872\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.7996 | 1.85710 | 0.928549 | − | 0.371209i | \(-0.121057\pi\) | ||||
0.928549 | + | 0.371209i | \(0.121057\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.21443 | −0.300266 | −0.150133 | − | 0.988666i | \(-0.547970\pi\) | ||||
−0.150133 | + | 0.988666i | \(0.547970\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.0428 | −1.56257 | −0.781285 | − | 0.624175i | \(-0.785435\pi\) | ||||
−0.781285 | + | 0.624175i | \(0.785435\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.60519 | 0.395359 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.4577 | −1.22529 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.87300 | −0.199687 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.50414 | 0.449901 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.9217 | 1.99105 | 0.995524 | − | 0.0945049i | \(-0.0301268\pi\) | ||||
0.995524 | + | 0.0945049i | \(0.0301268\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.87135 | 0.128223 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.2931 | −0.766628 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.15198 | −0.145417 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.79812 | 0.457291 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.63731 | 0.444467 | 0.222234 | − | 0.974993i | \(-0.428665\pi\) | ||||
0.222234 | + | 0.974993i | \(0.428665\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.370367 | 0.0245821 | 0.0122911 | − | 0.999924i | \(-0.496088\pi\) | ||||
0.0122911 | + | 0.999924i | \(0.496088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.5625 | −0.764073 | −0.382036 | − | 0.924147i | \(-0.624777\pi\) | ||||
−0.382036 | + | 0.924147i | \(0.624777\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.41864 | −0.0933395 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.8534 | 1.10410 | 0.552051 | − | 0.833810i | \(-0.313845\pi\) | ||||
0.552051 | + | 0.833810i | \(0.313845\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.483639 | 0.0314157 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.7742 | −1.14972 | −0.574859 | − | 0.818252i | \(-0.694943\pi\) | ||||
−0.574859 | + | 0.818252i | \(0.694943\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.6318 | −1.71551 | −0.857754 | − | 0.514061i | \(-0.828141\pi\) | ||||
−0.857754 | + | 0.514061i | \(0.828141\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.08467 | −0.582782 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.5691 | −0.672493 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.06301 | 0.194111 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.8599 | 1.06419 | 0.532094 | − | 0.846685i | \(-0.321405\pi\) | ||||
0.532094 | + | 0.846685i | \(0.321405\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.61574 | 0.101580 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.33024 | −0.519626 | −0.259813 | − | 0.965659i | \(-0.583661\pi\) | ||||
−0.259813 | + | 0.965659i | \(0.583661\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.29405 | 0.453230 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.3575 | 1.26010 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.0389 | −0.927337 | −0.463669 | − | 0.886009i | \(-0.653467\pi\) | ||||
−0.463669 | + | 0.886009i | \(0.653467\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.15063 | 0.192815 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.01922 | −0.427969 | −0.213985 | − | 0.976837i | \(-0.568644\pi\) | ||||
−0.213985 | + | 0.976837i | \(0.568644\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.40129 | 0.267359 | 0.133680 | − | 0.991025i | \(-0.457321\pi\) | ||||
0.133680 | + | 0.991025i | \(0.457321\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.30525 | 0.139520 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.41544 | −0.505634 | −0.252817 | − | 0.967514i | \(-0.581357\pi\) | ||||
−0.252817 | + | 0.967514i | \(0.581357\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.1690 | 0.788406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0068 | −0.895233 | −0.447617 | − | 0.894226i | \(-0.647727\pi\) | ||||
−0.447617 | + | 0.894226i | \(0.647727\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.09122 | 0.421529 | 0.210765 | − | 0.977537i | \(-0.432405\pi\) | ||||
0.210765 | + | 0.977537i | \(0.432405\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.0719 | −0.830637 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.2958 | −0.605638 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.85566 | −0.167402 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.0567 | −1.63909 | −0.819545 | − | 0.573015i | \(-0.805774\pi\) | ||||
−0.819545 | + | 0.573015i | \(0.805774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.38169 | 0.196225 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.62553 | −0.151838 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.67767 | −0.327256 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.25649 | 0.129632 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.2707 | −1.67057 | −0.835283 | − | 0.549820i | \(-0.814696\pi\) | ||||
−0.835283 | + | 0.549820i | \(0.814696\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.70059 | −0.267407 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.8111 | −0.896563 | −0.448281 | − | 0.893893i | \(-0.647964\pi\) | ||||
−0.448281 | + | 0.893893i | \(0.647964\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.98602 | −0.564443 | −0.282222 | − | 0.959349i | \(-0.591071\pi\) | ||||
−0.282222 | + | 0.959349i | \(0.591071\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.7683 | 0.773302 | 0.386651 | − | 0.922226i | \(-0.373632\pi\) | ||||
0.386651 | + | 0.922226i | \(0.373632\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.4488 | −0.641008 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.40308 | −0.189941 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.4230 | −0.579950 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.25868 | 0.346106 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.9584 | 0.934950 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.6765 | 1.02656 | 0.513278 | − | 0.858223i | \(-0.328431\pi\) | ||||
0.513278 | + | 0.858223i | \(0.328431\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.50564 | −0.466106 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.8915 | 0.756716 | 0.378358 | − | 0.925659i | \(-0.376489\pi\) | ||||
0.378358 | + | 0.925659i | \(0.376489\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.549764 | 0.0298591 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.40606 | −0.401060 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5374 | −1.05492 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.706854 | −0.0379459 | −0.0189730 | − | 0.999820i | \(-0.506040\pi\) | ||||
−0.0189730 | + | 0.999820i | \(0.506040\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.93817 | 0.371392 | 0.185696 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185696 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.49516 | −0.293310 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.413170 | −0.0219908 | −0.0109954 | − | 0.999940i | \(-0.503500\pi\) | ||||
−0.0109954 | + | 0.999940i | \(0.503500\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.27338 | 0.120320 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.6209 | −1.72167 | −0.860834 | − | 0.508886i | \(-0.830057\pi\) | ||||
−0.860834 | + | 0.508886i | \(0.830057\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.79537 | −0.147125 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.98974 | 0.156921 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5293 | −0.706223 | −0.353112 | − | 0.935581i | \(-0.614876\pi\) | ||||
−0.353112 | + | 0.935581i | \(0.614876\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.4093 | 0.854234 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.6665 | −0.865282 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.7690 | 1.07538 | 0.537689 | − | 0.843143i | \(-0.319297\pi\) | ||||
0.537689 | + | 0.843143i | \(0.319297\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.6040 | 0.958153 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0528 | −1.28688 | −0.643438 | − | 0.765498i | \(-0.722493\pi\) | ||||
−0.643438 | + | 0.765498i | \(0.722493\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.42815 | 0.226861 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.51677 | −0.230796 | −0.115398 | − | 0.993319i | \(-0.536814\pi\) | ||||
−0.115398 | + | 0.993319i | \(0.536814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.62076 | 0.336552 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.455188 | 0.0230789 | 0.0115395 | − | 0.999933i | \(-0.496327\pi\) | ||||
0.0115395 | + | 0.999933i | \(0.496327\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.58924 | −0.130943 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.03382 | 0.203479 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.0798 | −0.756832 | −0.378416 | − | 0.925636i | \(-0.623531\pi\) | ||||
−0.378416 | + | 0.925636i | \(0.623531\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.53444 | −0.176943 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.0845 | −1.90185 | −0.950924 | − | 0.309424i | \(-0.899864\pi\) | ||||
−0.950924 | + | 0.309424i | \(0.899864\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0347 | 0.599489 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.78345 | 0.237107 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.3672 | 0.809305 | 0.404653 | − | 0.914470i | \(-0.367392\pi\) | ||||
0.404653 | + | 0.914470i | \(0.367392\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.76081 | 0.0868543 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.24396 | 0.307245 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.04453 | 0.0511509 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.32621 | −0.260202 | −0.130101 | − | 0.991501i | \(-0.541530\pi\) | ||||
−0.130101 | + | 0.991501i | \(0.541530\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.3000 | −0.550730 | −0.275365 | − | 0.961340i | \(-0.588799\pi\) | ||||
−0.275365 | + | 0.961340i | \(0.588799\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.7753 | −0.961510 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.8036 | 1.10355 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.51179 | 0.0729898 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.6364 | 1.62021 | 0.810105 | − | 0.586285i | \(-0.199410\pi\) | ||||
0.810105 | + | 0.586285i | \(0.199410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.3932 | −0.883920 | −0.441960 | − | 0.897035i | \(-0.645717\pi\) | ||||
−0.441960 | + | 0.897035i | \(0.645717\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.02550 | 0.192566 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.7628 | 1.37277 | 0.686387 | − | 0.727236i | \(-0.259196\pi\) | ||||
0.686387 | + | 0.727236i | \(0.259196\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.67162 | 0.127220 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.2359 | −1.05646 | −0.528229 | − | 0.849102i | \(-0.677144\pi\) | ||||
−0.528229 | + | 0.849102i | \(0.677144\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.81401 | 0.0857999 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.4538 | 1.34282 | 0.671409 | − | 0.741087i | \(-0.265689\pi\) | ||||
0.671409 | + | 0.741087i | \(0.265689\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.22836 | −0.434547 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.11912 | 0.240517 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.58512 | −0.354817 | −0.177408 | − | 0.984137i | \(-0.556771\pi\) | ||||
−0.177408 | + | 0.984137i | \(0.556771\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.41920 | −0.252947 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.02951 | 0.280822 | 0.140411 | − | 0.990093i | \(-0.455158\pi\) | ||||
0.140411 | + | 0.990093i | \(0.455158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.2763 | −1.12821 | −0.564107 | − | 0.825701i | \(-0.690780\pi\) | ||||
−0.564107 | + | 0.825701i | \(0.690780\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.99614 | −0.277468 | −0.138734 | − | 0.990330i | \(-0.544303\pi\) | ||||
−0.138734 | + | 0.990330i | \(0.544303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −38.7511 | −1.78936 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.61629 | −0.120552 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.72343 | −0.171203 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.4349 | 0.889863 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.5065 | −0.799892 | −0.399946 | − | 0.916539i | \(-0.630971\pi\) | ||||
−0.399946 | + | 0.916539i | \(0.630971\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.77299 | −0.354418 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.878013 | −0.0399510 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.6269 | 1.43315 | 0.716576 | − | 0.697509i | \(-0.245708\pi\) | ||||
0.716576 | + | 0.697509i | \(0.245708\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.758224 | −0.0342881 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.7642 | 1.11759 | 0.558797 | − | 0.829305i | \(-0.311263\pi\) | ||||
0.558797 | + | 0.829305i | \(0.311263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.3468 | 0.826299 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.9375 | −0.580326 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.7906 | 1.69174 | 0.845871 | − | 0.533388i | \(-0.179081\pi\) | ||||
0.845871 | + | 0.533388i | \(0.179081\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.770049 | 0.0344032 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.40481 | −0.0626376 | −0.0313188 | − | 0.999509i | \(-0.509971\pi\) | ||||
−0.0313188 | + | 0.999509i | \(0.509971\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.17622 | 0.0966492 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.4044 | 1.34765 | 0.673825 | − | 0.738891i | \(-0.264650\pi\) | ||||
0.673825 | + | 0.738891i | \(0.264650\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.8776 | 0.658146 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.42525 | 0.371984 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.1214 | 0.489118 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.63599 | −0.291288 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.3500 | −0.584873 | −0.292437 | − | 0.956285i | \(-0.594466\pi\) | ||||
−0.292437 | + | 0.956285i | \(0.594466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.71026 | −0.380873 | −0.190437 | − | 0.981699i | \(-0.560990\pi\) | ||||
−0.190437 | + | 0.981699i | \(0.560990\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.8683 | 0.516991 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.28111 | −0.315973 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.9959 | 0.649543 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.79927 | 0.207104 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.50248 | −0.0647166 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.2922 | 0.915423 | 0.457711 | − | 0.889101i | \(-0.348669\pi\) | ||||
0.457711 | + | 0.889101i | \(0.348669\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.38075 | −0.187996 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.27222 | −0.310937 | −0.155469 | − | 0.987841i | \(-0.549689\pi\) | ||||
−0.155469 | + | 0.987841i | \(0.549689\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −26.5914 | −1.13490 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.5238 | −1.21516 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.34361 | −0.142185 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.0665 | 1.14684 | 0.573422 | − | 0.819260i | \(-0.305616\pi\) | ||||
0.573422 | + | 0.819260i | \(0.305616\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.05048 | 0.255908 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.49089 | 0.0629454 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.7921 | −0.539124 | −0.269562 | − | 0.962983i | \(-0.586879\pi\) | ||||
−0.269562 | + | 0.962983i | \(0.586879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.3974 | 0.814616 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.3013 | −0.557621 | −0.278810 | − | 0.960346i | \(-0.589940\pi\) | ||||
−0.278810 | + | 0.960346i | \(0.589940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.8239 | 1.33179 | 0.665894 | − | 0.746046i | \(-0.268050\pi\) | ||||
0.665894 | + | 0.746046i | \(0.268050\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.738043 | 0.0308322 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.0091 | −1.08277 | −0.541386 | − | 0.840774i | \(-0.682100\pi\) | ||||
−0.541386 | + | 0.840774i | \(0.682100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.19426 | −0.382101 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.1760 | −0.878527 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.9299 | −0.452671 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.4259 | 1.62728 | 0.813641 | − | 0.581367i | \(-0.197482\pi\) | ||||
0.813641 | + | 0.581367i | \(0.197482\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.4517 | −0.760289 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.50191 | 0.0617801 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.8918 | −0.857922 | −0.428961 | − | 0.903323i | \(-0.641120\pi\) | ||||
−0.428961 | + | 0.903323i | \(0.641120\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.85542 | 0.321501 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.7986 | 0.522938 | 0.261469 | − | 0.965212i | \(-0.415793\pi\) | ||||
0.261469 | + | 0.965212i | \(0.415793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.7566 | −0.765099 | −0.382550 | − | 0.923935i | \(-0.624954\pi\) | ||||
−0.382550 | + | 0.923935i | \(0.624954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.1879 | 1.84019 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.51153 | 0.0613512 | 0.0306756 | − | 0.999529i | \(-0.490234\pi\) | ||||
0.0306756 | + | 0.999529i | \(0.490234\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.22142 | 0.252105 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.0720 | −0.731114 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.5673 | 1.59811 | 0.799054 | − | 0.601259i | \(-0.205334\pi\) | ||||
0.799054 | + | 0.601259i | \(0.205334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.0023 | −1.65069 | −0.825345 | − | 0.564629i | \(-0.809019\pi\) | ||||
−0.825345 | + | 0.564629i | \(0.809019\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9089 | 0.438464 | 0.219232 | − | 0.975673i | \(-0.429645\pi\) | ||||
0.219232 | + | 0.975673i | \(0.429645\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.09297 | 0.0839880 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.7817 | −0.872664 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.31789 | −0.0925677 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.66555 | −0.305645 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.7516 | −0.985347 | −0.492674 | − | 0.870214i | \(-0.663980\pi\) | ||||
−0.492674 | + | 0.870214i | \(0.663980\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.3069 | −0.409661 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.44150 | 0.0967357 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.0865 | 0.596812 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.5110 | 1.32360 | 0.661802 | − | 0.749679i | \(-0.269792\pi\) | ||||
0.661802 | + | 0.749679i | \(0.269792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.15767 | −0.361143 | −0.180572 | − | 0.983562i | \(-0.557795\pi\) | ||||
−0.180572 | + | 0.983562i | \(0.557795\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.8011 | −1.21092 | −0.605458 | − | 0.795877i | \(-0.707010\pi\) | ||||
−0.605458 | + | 0.795877i | \(0.707010\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.09480 | 0.160735 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.02455 | 0.157735 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.4779 | −0.997026 | −0.498513 | − | 0.866882i | \(-0.666120\pi\) | ||||
−0.498513 | + | 0.866882i | \(0.666120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.3488 | −0.676843 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.34417 | 0.0913159 | 0.0456580 | − | 0.998957i | \(-0.485462\pi\) | ||||
0.0456580 | + | 0.998957i | \(0.485462\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.4164 | 1.68870 | 0.844351 | − | 0.535791i | \(-0.179987\pi\) | ||||
0.844351 | + | 0.535791i | \(0.179987\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.42266 | −0.0940883 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.08580 | −0.274363 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.36535 | −0.0914498 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.9547 | 0.577319 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.4902 | 1.86916 | 0.934580 | − | 0.355754i | \(-0.115776\pi\) | ||||
0.934580 | + | 0.355754i | \(0.115776\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.9213 | 1.80333 | 0.901665 | − | 0.432435i | \(-0.142345\pi\) | ||||
0.901665 | + | 0.432435i | \(0.142345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.7424 | 0.757645 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.131988 | −0.00505780 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.3660 | 0.587965 | 0.293983 | − | 0.955811i | \(-0.405019\pi\) | ||||
0.293983 | + | 0.955811i | \(0.405019\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.12056 | 0.157209 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.7609 | 0.676635 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.0235 | −1.52257 | −0.761283 | − | 0.648419i | \(-0.775430\pi\) | ||||
−0.761283 | + | 0.648419i | \(0.775430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.4368 | −0.434447 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7886 | 0.560157 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.00607 | −0.227171 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.2943 | −1.06866 | −0.534331 | − | 0.845276i | \(-0.679436\pi\) | ||||
−0.534331 | + | 0.845276i | \(0.679436\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.9177 | 0.449483 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.6001 | −0.586703 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.8823 | 1.00959 | 0.504793 | − | 0.863240i | \(-0.331569\pi\) | ||||
0.504793 | + | 0.863240i | \(0.331569\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.89900 | 0.146224 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.58371 | −0.171661 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.33423 | 0.236556 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2624 | 0.420015 | 0.210008 | − | 0.977700i | \(-0.432651\pi\) | ||||
0.210008 | + | 0.977700i | \(0.432651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.4973 | 1.21026 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.49084 | 0.352968 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.07629 | 0.0770054 | 0.0385027 | − | 0.999258i | \(-0.487741\pi\) | ||||
0.0385027 | + | 0.999258i | \(0.487741\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.3818 | −0.754883 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.96684 | 0.220692 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.6294 | 0.614221 | 0.307111 | − | 0.951674i | \(-0.400638\pi\) | ||||
0.307111 | + | 0.951674i | \(0.400638\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.4131 | −0.936103 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.8052 | 1.86890 | 0.934450 | − | 0.356095i | \(-0.115892\pi\) | ||||
0.934450 | + | 0.356095i | \(0.115892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.76652 | 0.138366 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.3667 | 1.15073 | 0.575366 | − | 0.817896i | \(-0.304859\pi\) | ||||
0.575366 | + | 0.817896i | \(0.304859\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.6934 | 0.903485 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.5270 | 0.859657 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.2551 | 1.50542 | 0.752711 | − | 0.658351i | \(-0.228746\pi\) | ||||
0.752711 | + | 0.658351i | \(0.228746\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.00839 | −0.218958 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.3081 | 0.411000 | 0.205500 | − | 0.978657i | \(-0.434118\pi\) | ||||
0.205500 | + | 0.978657i | \(0.434118\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.575803 | −0.0209003 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.32880 | −0.156919 | −0.0784594 | − | 0.996917i | \(-0.525000\pi\) | ||||
−0.0784594 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.2690 | −1.56644 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.65395 | −0.240260 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.6517 | 1.46594 | 0.732968 | − | 0.680263i | \(-0.238134\pi\) | ||||
0.732968 | + | 0.680263i | \(0.238134\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.96866 | 0.106914 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.9716 | 1.36574 | 0.682872 | − | 0.730538i | \(-0.260731\pi\) | ||||
0.682872 | + | 0.730538i | \(0.260731\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.59940 | −0.0932528 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.9918 | −0.823768 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.48443 | −0.303597 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.8304 | −0.529994 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −55.1654 | −1.96643 | −0.983216 | − | 0.182443i | \(-0.941599\pi\) | ||||
−0.983216 | + | 0.182443i | \(0.941599\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.35944 | 0.190801 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.80076 | −0.135140 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.3010 | −0.862952 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.0601 | 1.17105 | 0.585524 | − | 0.810655i | \(-0.300889\pi\) | ||||
0.585524 | + | 0.810655i | \(0.300889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.8222 | −0.630503 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.3997 | 0.897455 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.75675 | 0.344308 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.50145 | 0.0880553 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.4318 | −0.929291 | −0.464646 | − | 0.885497i | \(-0.653818\pi\) | ||||
−0.464646 | + | 0.885497i | \(0.653818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.49057 | 0.192800 | 0.0964000 | − | 0.995343i | \(-0.469267\pi\) | ||||
0.0964000 | + | 0.995343i | \(0.469267\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.56850 | −0.0550096 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.27667 | −0.324550 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.5845 | 0.649394 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.2732 | −1.47534 | −0.737672 | − | 0.675160i | \(-0.764075\pi\) | ||||
−0.737672 | + | 0.675160i | \(0.764075\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.2599 | 1.82167 | 0.910833 | − | 0.412774i | \(-0.135440\pi\) | ||||
0.910833 | + | 0.412774i | \(0.135440\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.7667 | −1.62624 | −0.813119 | − | 0.582097i | \(-0.802232\pi\) | ||||
−0.813119 | + | 0.582097i | \(0.802232\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.2175 | 0.528525 | 0.264262 | − | 0.964451i | \(-0.414871\pi\) | ||||
0.264262 | + | 0.964451i | \(0.414871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.99902 | 0.104035 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.40775 | 0.0834236 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.59356 | −0.331602 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.7388 | 1.88979 | 0.944897 | − | 0.327369i | \(-0.106162\pi\) | ||||
0.944897 | + | 0.327369i | \(0.106162\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.2085 | 0.731328 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.34802 | 0.184195 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.6694 | −0.710210 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.52711 | −0.0867302 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.96054 | 0.101486 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.8683 | 0.577559 | 0.288779 | − | 0.957396i | \(-0.406751\pi\) | ||||
0.288779 | + | 0.957396i | \(0.406751\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.9513 | −1.36471 | −0.682355 | − | 0.731021i | \(-0.739044\pi\) | ||||
−0.682355 | + | 0.731021i | \(0.739044\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.5728 | 0.736053 | 0.368027 | − | 0.929815i | \(-0.380034\pi\) | ||||
0.368027 | + | 0.929815i | \(0.380034\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.01482 | 0.170905 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.71384 | −0.0923803 | −0.0461902 | − | 0.998933i | \(-0.514708\pi\) | ||||
−0.0461902 | + | 0.998933i | \(0.514708\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.66915 | 0.124611 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.19275 | −0.0743838 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.2956 | 1.39925 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.0217 | −0.779168 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.8294 | 1.37871 | 0.689355 | − | 0.724423i | \(-0.257894\pi\) | ||||
0.689355 | + | 0.724423i | \(0.257894\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.99862 | 0.337245 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.3676 | 1.22525 | 0.612627 | − | 0.790372i | \(-0.290113\pi\) | ||||
0.612627 | + | 0.790372i | \(0.290113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.2495 | −0.614146 | −0.307073 | − | 0.951686i | \(-0.599350\pi\) | ||||
−0.307073 | + | 0.951686i | \(0.599350\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.33546 | −0.111994 | −0.0559968 | − | 0.998431i | \(-0.517834\pi\) | ||||
−0.0559968 | + | 0.998431i | \(0.517834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.6138 | −1.02675 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.7209 | 0.426166 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.7082 | 0.927219 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.935665 | 0.0312409 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.4792 | 1.08324 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.5153 | 0.583521 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.02336 | 0.0673333 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.50057 | −0.182643 | −0.0913217 | − | 0.995821i | \(-0.529109\pi\) | ||||
−0.0913217 | + | 0.995821i | \(0.529109\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.1914 | 0.603371 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.9531 | 0.396024 | 0.198012 | − | 0.980200i | \(-0.436551\pi\) | ||||
0.198012 | + | 0.980200i | \(0.436551\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.8872 | −0.459601 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.8876 | −0.920929 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.3756 | 0.738102 | 0.369051 | − | 0.929409i | \(-0.379683\pi\) | ||||
0.369051 | + | 0.929409i | \(0.379683\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.4312 | 0.343721 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.7870 | 0.453804 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37.8953 | −1.24464 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.9751 | −1.40997 | −0.704983 | − | 0.709224i | \(-0.749045\pi\) | ||||
−0.704983 | + | 0.709224i | \(0.749045\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.74334 | −0.122683 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.63461 | 0.184469 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.76556 | −0.123015 | −0.0615077 | − | 0.998107i | \(-0.519591\pi\) | ||||
−0.0615077 | + | 0.998107i | \(0.519591\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.55874 | 0.116135 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.9193 | −0.518953 | −0.259477 | − | 0.965749i | \(-0.583550\pi\) | ||||
−0.259477 | + | 0.965749i | \(0.583550\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.71155 | −0.185994 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.8553 | 1.68507 | 0.842535 | − | 0.538642i | \(-0.181062\pi\) | ||||
0.842535 | + | 0.538642i | \(0.181062\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.8545 | −0.514658 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.90662 | −0.159108 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.6848 | 1.44748 | 0.723741 | − | 0.690072i | \(-0.242421\pi\) | ||||
0.723741 | + | 0.690072i | \(0.242421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.08002 | 0.131888 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.1733 | −0.393095 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.98964 | −0.322247 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.4349 | −0.884079 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.5594 | −1.01488 | −0.507440 | − | 0.861687i | \(-0.669408\pi\) | ||||
−0.507440 | + | 0.861687i | \(0.669408\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.71445 | 0.119325 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.6291 | −0.662018 | −0.331009 | − | 0.943628i | \(-0.607389\pi\) | ||||
−0.331009 | + | 0.943628i | \(0.607389\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.22130 | −0.231504 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.76933 | −0.0566058 | −0.0283029 | − | 0.999599i | \(-0.509010\pi\) | ||||
−0.0283029 | + | 0.999599i | \(0.509010\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.2845 | −0.456533 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 50.4562 | 1.61094 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.4073 | 1.38448 | 0.692239 | − | 0.721668i | \(-0.256624\pi\) | ||||
0.692239 | + | 0.721668i | \(0.256624\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.04351 | −0.192367 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.30448 | −0.0732781 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.2222 | 0.515317 | 0.257658 | − | 0.966236i | \(-0.417049\pi\) | ||||
0.257658 | + | 0.966236i | \(0.417049\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.65579 | −0.211215 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.61347 | 0.0827695 | 0.0413847 | − | 0.999143i | \(-0.486823\pi\) | ||||
0.0413847 | + | 0.999143i | \(0.486823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.19633 | 0.196043 |
(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 | 4600.2.a.bh.1.4 | 7 | ||
4.3 | odd | 2 | 9200.2.a.dc.1.4 | 7 | |||
5.2 | odd | 4 | 920.2.e.b.369.9 | yes | 14 | ||
5.3 | odd | 4 | 920.2.e.b.369.6 | ✓ | 14 | ||
5.4 | even | 2 | 4600.2.a.bi.1.4 | 7 | |||
20.3 | even | 4 | 1840.2.e.g.369.9 | 14 | |||
20.7 | even | 4 | 1840.2.e.g.369.6 | 14 | |||
20.19 | odd | 2 | 9200.2.a.cz.1.4 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.6 | ✓ | 14 | 5.3 | odd | 4 | ||
920.2.e.b.369.9 | yes | 14 | 5.2 | odd | 4 | ||
1840.2.e.g.369.6 | 14 | 20.7 | even | 4 | |||
1840.2.e.g.369.9 | 14 | 20.3 | even | 4 | |||
4600.2.a.bh.1.4 | 7 | 1.1 | even | 1 | trivial | ||
4600.2.a.bi.1.4 | 7 | 5.4 | even | 2 | |||
9200.2.a.cz.1.4 | 7 | 20.19 | odd | 2 | |||
9200.2.a.dc.1.4 | 7 | 4.3 | odd | 2 |