Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(1\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | 0.936010 | 0.540406 | 0.270203 | − | 0.962803i | \(-0.412909\pi\) | ||||
0.270203 | + | 0.962803i | \(0.412909\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.25557 | 0.561508 | 0.280754 | − | 0.959780i | \(-0.409416\pi\) | ||||
0.280754 | + | 0.959780i | \(0.409416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.290471 | 0.109788 | 0.0548938 | − | 0.998492i | \(-0.482518\pi\) | ||||
0.0548938 | + | 0.998492i | \(0.482518\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.12388 | −0.707962 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.70893 | 0.515262 | 0.257631 | − | 0.966243i | \(-0.417058\pi\) | ||||
0.257631 | + | 0.966243i | \(0.417058\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.27793 | −0.631783 | −0.315891 | − | 0.948795i | \(-0.602304\pi\) | ||||
−0.315891 | + | 0.948795i | \(0.602304\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.17523 | 0.303442 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.69974 | −1.13985 | −0.569927 | − | 0.821695i | \(-0.693029\pi\) | ||||
−0.569927 | + | 0.821695i | \(0.693029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.709881 | −0.162858 | −0.0814289 | − | 0.996679i | \(-0.525948\pi\) | ||||
−0.0814289 | + | 0.996679i | \(0.525948\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.271884 | 0.0593299 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.51621 | −0.733180 | −0.366590 | − | 0.930383i | \(-0.619475\pi\) | ||||
−0.366590 | + | 0.930383i | \(0.619475\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.42355 | −0.684709 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.79601 | −0.922992 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.26398 | 0.791801 | 0.395900 | − | 0.918293i | \(-0.370433\pi\) | ||||
0.395900 | + | 0.918293i | \(0.370433\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.767574 | 0.137860 | 0.0689302 | − | 0.997621i | \(-0.478041\pi\) | ||||
0.0689302 | + | 0.997621i | \(0.478041\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.59958 | 0.278451 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.364706 | 0.0616466 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00986 | −0.988015 | −0.494007 | − | 0.869458i | \(-0.664468\pi\) | ||||
−0.494007 | + | 0.869458i | \(0.664468\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.13216 | −0.341419 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.17075 | 0.651362 | 0.325681 | − | 0.945480i | \(-0.394406\pi\) | ||||
0.325681 | + | 0.945480i | \(0.394406\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.76221 | 1.33622 | 0.668112 | − | 0.744061i | \(-0.267103\pi\) | ||||
0.668112 | + | 0.744061i | \(0.267103\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.66668 | −0.397526 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.27463 | −0.915249 | −0.457624 | − | 0.889146i | \(-0.651300\pi\) | ||||
−0.457624 | + | 0.889146i | \(0.651300\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91563 | −0.987947 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.39900 | −0.615984 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.14901 | −0.981992 | −0.490996 | − | 0.871162i | \(-0.663367\pi\) | ||||
−0.490996 | + | 0.871162i | \(0.663367\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.14568 | 0.289324 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.664456 | −0.0880093 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.2872 | −1.59966 | −0.799831 | − | 0.600225i | \(-0.795078\pi\) | ||||
−0.799831 | + | 0.600225i | \(0.795078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1274 | −1.42472 | −0.712362 | − | 0.701813i | \(-0.752374\pi\) | ||||
−0.712362 | + | 0.701813i | \(0.752374\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.616927 | −0.0777255 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.86009 | −0.354751 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.16313 | −0.508607 | −0.254303 | − | 0.967124i | \(-0.581846\pi\) | ||||
−0.254303 | + | 0.967124i | \(0.581846\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.29121 | −0.396215 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.56295 | 0.185488 | 0.0927438 | − | 0.995690i | \(-0.470436\pi\) | ||||
0.0927438 | + | 0.995690i | \(0.470436\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5318 | 1.23265 | 0.616325 | − | 0.787492i | \(-0.288621\pi\) | ||||
0.616325 | + | 0.787492i | \(0.288621\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.20447 | −0.370021 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.496395 | 0.0565695 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.666821 | 0.0750232 | 0.0375116 | − | 0.999296i | \(-0.488057\pi\) | ||||
0.0375116 | + | 0.999296i | \(0.488057\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.88254 | 0.209171 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.50047 | −0.603755 | −0.301877 | − | 0.953347i | \(-0.597613\pi\) | ||||
−0.301877 | + | 0.953347i | \(0.597613\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.90085 | −0.640037 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.99113 | 0.427894 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.34861 | 0.248952 | 0.124476 | − | 0.992223i | \(-0.460275\pi\) | ||||
0.124476 | + | 0.992223i | \(0.460275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.661671 | −0.0693620 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.718457 | 0.0745005 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.891304 | −0.0914459 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.71595 | −0.681901 | −0.340951 | − | 0.940081i | \(-0.610749\pi\) | ||||
−0.340951 | + | 0.940081i | \(0.610749\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.62957 | −0.364786 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.4808 | 1.44089 | 0.720446 | − | 0.693511i | \(-0.243937\pi\) | ||||
0.720446 | + | 0.693511i | \(0.243937\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.81736 | 0.868800 | 0.434400 | − | 0.900720i | \(-0.356960\pi\) | ||||
0.434400 | + | 0.900720i | \(0.356960\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.341369 | 0.0333142 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.366441 | 0.0354252 | 0.0177126 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177126 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.633539 | 0.0606820 | 0.0303410 | − | 0.999540i | \(-0.490341\pi\) | ||||
0.0303410 | + | 0.999540i | \(0.490341\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.62529 | −0.533929 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3160 | 1.25267 | 0.626334 | − | 0.779555i | \(-0.284555\pi\) | ||||
0.626334 | + | 0.779555i | \(0.284555\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.41484 | −0.411686 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.83805 | 0.447278 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.36514 | −0.125142 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.07955 | −0.734505 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.90387 | 0.352000 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5763 | −0.945977 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1982 | −0.904943 | −0.452472 | − | 0.891779i | \(-0.649458\pi\) | ||||
−0.452472 | + | 0.891779i | \(0.649458\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.20152 | 0.722103 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.45611 | −0.651443 | −0.325722 | − | 0.945466i | \(-0.605607\pi\) | ||||
−0.325722 | + | 0.945466i | \(0.605607\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.206200 | −0.0178798 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.02172 | −0.518267 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.3145 | 1.22297 | 0.611484 | − | 0.791257i | \(-0.290573\pi\) | ||||
0.611484 | + | 0.791257i | \(0.290573\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.47919 | −0.464739 | −0.232369 | − | 0.972628i | \(-0.574648\pi\) | ||||
−0.232369 | + | 0.972628i | \(0.574648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.87312 | −0.494606 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.89282 | −0.325534 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.35372 | 0.444602 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.47310 | −0.533892 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.5138 | −1.59863 | −0.799316 | − | 0.600910i | \(-0.794805\pi\) | ||||
−0.799316 | + | 0.600910i | \(0.794805\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.58290 | −0.372951 | −0.186475 | − | 0.982460i | \(-0.559706\pi\) | ||||
−0.186475 | + | 0.982460i | \(0.559706\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.98171 | 0.806973 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.963742 | 0.0774097 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.1432 | 1.04894 | 0.524471 | − | 0.851428i | \(-0.324263\pi\) | ||||
0.524471 | + | 0.851428i | \(0.324263\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.69155 | −0.530674 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.02136 | −0.0804942 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.4414 | −1.44444 | −0.722219 | − | 0.691664i | \(-0.756878\pi\) | ||||
−0.722219 | + | 0.691664i | \(0.756878\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.00838 | 0.156352 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.16414 | −0.322231 | −0.161115 | − | 0.986936i | \(-0.551509\pi\) | ||||
−0.161115 | + | 0.986936i | \(0.551509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.81106 | −0.600851 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50770 | 0.115297 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.47803 | 0.568544 | 0.284272 | − | 0.958744i | \(-0.408248\pi\) | ||||
0.284272 | + | 0.958744i | \(0.408248\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.994440 | −0.0751726 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.5010 | −0.864467 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.31173 | 0.621248 | 0.310624 | − | 0.950533i | \(-0.399462\pi\) | ||||
0.310624 | + | 0.950533i | \(0.399462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.1549 | 1.05212 | 0.526061 | − | 0.850447i | \(-0.323668\pi\) | ||||
0.526061 | + | 0.850447i | \(0.323668\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.4154 | −0.769929 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.54579 | −0.554778 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.03153 | −0.587324 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.39310 | −0.101333 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.24673 | −0.0902106 | −0.0451053 | − | 0.998982i | \(-0.514362\pi\) | ||||
−0.0451053 | + | 0.998982i | \(0.514362\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.6068 | 0.835478 | 0.417739 | − | 0.908567i | \(-0.362823\pi\) | ||||
0.417739 | + | 0.908567i | \(0.362823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.67708 | −0.191709 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.15490 | −0.296024 | −0.148012 | − | 0.988986i | \(-0.547287\pi\) | ||||
−0.148012 | + | 0.988986i | \(0.547287\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.1713 | −1.14636 | −0.573178 | − | 0.819431i | \(-0.694289\pi\) | ||||
−0.573178 | + | 0.819431i | \(0.694289\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.89673 | −0.274854 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.23856 | 0.0869300 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.23667 | 0.365745 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.46802 | 0.519063 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.21314 | −0.0839145 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4455 | 1.06331 | 0.531655 | − | 0.846961i | \(-0.321570\pi\) | ||||
0.531655 | + | 0.846961i | \(0.321570\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.46293 | 0.100239 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.0016 | 0.750300 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.222958 | 0.0151354 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.85784 | 0.666131 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.7057 | 0.720140 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.34164 | −0.223773 | −0.111886 | − | 0.993721i | \(-0.535689\pi\) | ||||
−0.111886 | + | 0.993721i | \(0.535689\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.27122 | 0.484748 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.92232 | 0.193961 | 0.0969806 | − | 0.995286i | \(-0.469082\pi\) | ||||
0.0969806 | + | 0.995286i | \(0.469082\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.59986 | −0.237885 | −0.118943 | − | 0.992901i | \(-0.537950\pi\) | ||||
−0.118943 | + | 0.992901i | \(0.537950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.464631 | 0.0305705 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.965058 | −0.0632231 | −0.0316115 | − | 0.999500i | \(-0.510064\pi\) | ||||
−0.0316115 | + | 0.999500i | \(0.510064\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.87823 | −0.513919 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.624151 | 0.0405430 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.1871 | 0.723633 | 0.361816 | − | 0.932249i | \(-0.382157\pi\) | ||||
0.361816 | + | 0.932249i | \(0.382157\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.39157 | 0.0896389 | 0.0448195 | − | 0.998995i | \(-0.485729\pi\) | ||||
0.0448195 | + | 0.998995i | \(0.485729\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1501 | 1.03603 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.68305 | −0.554740 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.61706 | 0.102891 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.14849 | −0.326273 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −31.2138 | −1.97020 | −0.985099 | − | 0.171986i | \(-0.944982\pi\) | ||||
−0.985099 | + | 0.171986i | \(0.944982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00896 | −0.377780 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.52325 | −0.345880 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.3732 | 0.709442 | 0.354721 | − | 0.934972i | \(-0.384576\pi\) | ||||
0.354721 | + | 0.934972i | \(0.384576\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.74569 | −0.108472 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.05620 | −0.560565 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.75811 | 0.416723 | 0.208362 | − | 0.978052i | \(-0.433187\pi\) | ||||
0.208362 | + | 0.978052i | \(0.433187\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.97608 | −0.551396 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.19832 | 0.134535 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.92490 | −0.483189 | −0.241595 | − | 0.970377i | \(-0.577670\pi\) | ||||
−0.241595 | + | 0.970377i | \(0.577670\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.25681 | 0.137092 | 0.0685458 | − | 0.997648i | \(-0.478164\pi\) | ||||
0.0685458 | + | 0.997648i | \(0.478164\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.619331 | −0.0374836 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.85061 | −0.352805 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.7716 | 1.18796 | 0.593981 | − | 0.804479i | \(-0.297555\pi\) | ||||
0.593981 | + | 0.804479i | \(0.297555\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.63024 | −0.0975999 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.0694 | −1.73413 | −0.867067 | − | 0.498191i | \(-0.833998\pi\) | ||||
−0.867067 | + | 0.498191i | \(0.833998\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.6017 | 1.46242 | 0.731210 | − | 0.682152i | \(-0.238956\pi\) | ||||
0.731210 | + | 0.682152i | \(0.238956\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.834270 | −0.0494179 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.21148 | 0.0715116 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.08755 | 0.299268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.28620 | −0.368503 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.770793 | −0.0450302 | −0.0225151 | − | 0.999747i | \(-0.507167\pi\) | ||||
−0.0225151 | + | 0.999747i | \(0.507167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.4275 | −0.898222 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.19605 | −0.475583 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.00966 | 0.463211 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.54517 | 0.146701 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.5542 | 0.778666 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.9713 | −0.799993 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.43283 | −0.424214 | −0.212107 | − | 0.977246i | \(-0.568033\pi\) | ||||
−0.212107 | + | 0.977246i | \(0.568033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.25314 | 0.469505 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.87330 | −0.389749 | −0.194874 | − | 0.980828i | \(-0.562430\pi\) | ||||
−0.194874 | + | 0.980828i | \(0.562430\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.40916 | 0.418790 | 0.209395 | − | 0.977831i | \(-0.432851\pi\) | ||||
0.209395 | + | 0.977831i | \(0.432851\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.774594 | −0.0436434 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.09525 | 0.117681 | 0.0588404 | − | 0.998267i | \(-0.481260\pi\) | ||||
0.0588404 | + | 0.998267i | \(0.481260\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.28685 | 0.407985 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.342993 | 0.0191440 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.33625 | 0.185634 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.79858 | 0.432587 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.592999 | 0.0327929 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.82260 | −0.100483 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.1838 | −1.16437 | −0.582183 | − | 0.813058i | \(-0.697801\pi\) | ||||
−0.582183 | + | 0.813058i | \(0.697801\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.7642 | 0.699476 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.22709 | −0.285587 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6549 | −0.634882 | −0.317441 | − | 0.948278i | \(-0.602824\pi\) | ||||
−0.317441 | + | 0.948278i | \(0.602824\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.4639 | 0.676949 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.31173 | 0.0710343 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.04208 | −0.218252 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.13234 | −0.222478 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0025 | −0.805375 | −0.402688 | − | 0.915337i | \(-0.631924\pi\) | ||||
−0.402688 | + | 0.915337i | \(0.631924\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.8730 | 1.06378 | 0.531888 | − | 0.846814i | \(-0.321483\pi\) | ||||
0.531888 | + | 0.846814i | \(0.321483\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.9249 | 0.583131 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.8372 | 0.896156 | 0.448078 | − | 0.893995i | \(-0.352109\pi\) | ||||
0.448078 | + | 0.893995i | \(0.352109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.96239 | 0.104153 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.27778 | −0.0676274 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.1287 | 1.11513 | 0.557566 | − | 0.830132i | \(-0.311735\pi\) | ||||
0.557566 | + | 0.830132i | \(0.311735\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4961 | −0.973477 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.56254 | −0.396931 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.2234 | 0.692142 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.7766 | 1.39773 | 0.698864 | − | 0.715255i | \(-0.253689\pi\) | ||||
0.698864 | + | 0.715255i | \(0.253689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.85820 | −0.461140 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.07658 | −0.107811 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8709 | 0.925322 | 0.462661 | − | 0.886535i | \(-0.346895\pi\) | ||||
0.462661 | + | 0.886535i | \(0.346895\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.89957 | −0.511211 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.71302 | −0.500246 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.6253 | −1.57312 | −0.786559 | − | 0.617515i | \(-0.788139\pi\) | ||||
−0.786559 | + | 0.617515i | \(0.788139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.54561 | −0.489037 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.8178 | −1.06374 | −0.531871 | − | 0.846826i | \(-0.678511\pi\) | ||||
−0.531871 | + | 0.846826i | \(0.678511\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.623258 | 0.0317642 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.6099 | −0.945995 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.6455 | −1.09747 | −0.548736 | − | 0.835996i | \(-0.684891\pi\) | ||||
−0.548736 | + | 0.835996i | \(0.684891\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.5253 | 0.835719 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.97899 | −0.352044 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.837240 | 0.0421261 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2883 | 1.11862 | 0.559308 | − | 0.828960i | \(-0.311067\pi\) | ||||
0.559308 | + | 0.828960i | \(0.311067\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.193005 | −0.00966234 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.13551 | −0.456205 | −0.228103 | − | 0.973637i | \(-0.573252\pi\) | ||||
−0.228103 | + | 0.973637i | \(0.573252\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.74848 | −0.0870978 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.36366 | 0.117451 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2704 | −0.509087 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.18601 | −0.206985 | −0.103492 | − | 0.994630i | \(-0.533002\pi\) | ||||
−0.103492 | + | 0.994630i | \(0.533002\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.3985 | 0.660899 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.56908 | −0.175623 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.90622 | −0.339013 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.12857 | −0.251147 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.2775 | −0.844062 | −0.422031 | − | 0.906581i | \(-0.638683\pi\) | ||||
−0.422031 | + | 0.906581i | \(0.638683\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.19770 | 0.302057 | 0.151029 | − | 0.988529i | \(-0.451741\pi\) | ||||
0.151029 | + | 0.988529i | \(0.451741\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.3266 | 0.647961 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.0898 | 0.780469 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.23220 | −0.156417 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.64372 | −0.175920 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.74998 | −0.180630 | −0.0903152 | − | 0.995913i | \(-0.528787\pi\) | ||||
−0.0903152 | + | 0.995913i | \(0.528787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.2047 | −0.970976 | −0.485488 | − | 0.874243i | \(-0.661358\pi\) | ||||
−0.485488 | + | 0.874243i | \(0.661358\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.01114 | 0.240266 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.49609 | 0.119404 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.5723 | −1.41141 | −0.705704 | − | 0.708506i | \(-0.749369\pi\) | ||||
−0.705704 | + | 0.708506i | \(0.749369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.6880 | 0.699428 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0255 | −0.571349 | −0.285675 | − | 0.958327i | \(-0.592218\pi\) | ||||
−0.285675 | + | 0.958327i | \(0.592218\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.94884 | 0.139788 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.2651 | −0.863910 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.8819 | 1.22144 | 0.610720 | − | 0.791846i | \(-0.290880\pi\) | ||||
0.610720 | + | 0.791846i | \(0.290880\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.12754 | 0.335623 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.28964 | −0.201545 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.830774 | −0.0389473 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.51083 | 0.398120 | 0.199060 | − | 0.979987i | \(-0.436211\pi\) | ||||
0.199060 | + | 0.979987i | \(0.436211\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.5400 | 1.05208 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.08077 | −0.283210 | −0.141605 | − | 0.989923i | \(-0.545226\pi\) | ||||
−0.141605 | + | 0.989923i | \(0.545226\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.35230 | −0.155794 | −0.0778972 | − | 0.996961i | \(-0.524821\pi\) | ||||
−0.0778972 | + | 0.996961i | \(0.524821\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.902073 | 0.0418326 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.233955 | −0.0108261 | −0.00541307 | − | 0.999985i | \(-0.501723\pi\) | ||||
−0.00541307 | + | 0.999985i | \(0.501723\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.20927 | −0.0558388 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.3022 | 0.566854 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.9740 | 0.688506 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.43031 | 0.111510 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.1837 | 0.695213 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.8576 | 1.40992 | 0.704960 | − | 0.709248i | \(-0.250965\pi\) | ||||
0.704960 | + | 0.709248i | \(0.250965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.6900 | 0.624211 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.956000 | −0.0434995 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.43234 | −0.382893 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.778484 | −0.0352765 | −0.0176382 | − | 0.999844i | \(-0.505615\pi\) | ||||
−0.0176382 | + | 0.999844i | \(0.505615\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.2613 | −0.780583 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.0278 | −1.21975 | −0.609874 | − | 0.792498i | \(-0.708780\pi\) | ||||
−0.609874 | + | 0.792498i | \(0.708780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.0396 | −0.902538 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.55718 | −0.204830 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.453991 | 0.0203643 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.7459 | −1.33161 | −0.665804 | − | 0.746127i | \(-0.731911\pi\) | ||||
−0.665804 | + | 0.746127i | \(0.731911\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.89768 | −0.174135 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.1816 | 0.809071 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.31123 | −0.324703 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.9830 | 1.15168 | 0.575839 | − | 0.817563i | \(-0.304675\pi\) | ||||
0.575839 | + | 0.817563i | \(0.304675\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.05917 | 0.135330 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.40459 | 0.150316 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.0708 | 0.487838 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.7229 | −0.471593 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.99951 | 0.307244 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5399 | 0.549385 | 0.274692 | − | 0.961532i | \(-0.411424\pi\) | ||||
0.274692 | + | 0.961532i | \(0.411424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.1542 | −1.75582 | −0.877910 | − | 0.478826i | \(-0.841062\pi\) | ||||
−0.877910 | + | 0.478826i | \(0.841062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.930806 | −0.0406237 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.60740 | −0.157141 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.6363 | −0.462447 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.0967 | 1.13250 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.50067 | −0.411520 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.460092 | 0.0198915 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.77986 | 0.335726 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.8183 | −0.509052 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.9476 | 0.857614 | 0.428807 | − | 0.903396i | \(-0.358934\pi\) | ||||
0.428807 | + | 0.903396i | \(0.358934\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.2491 | 0.568573 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.795452 | 0.0340734 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.1149 | 1.15935 | 0.579675 | − | 0.814848i | \(-0.303180\pi\) | ||||
0.579675 | + | 0.814848i | \(0.303180\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.6334 | 1.00865 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.02692 | −0.128951 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.193692 | 0.00823663 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.06294 | −0.299805 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.6225 | −0.873802 | −0.436901 | − | 0.899510i | \(-0.643924\pi\) | ||||
−0.436901 | + | 0.899510i | \(0.643924\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.9597 | −0.844203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.51760 | −0.317393 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.60984 | −0.194281 | −0.0971407 | − | 0.995271i | \(-0.530970\pi\) | ||||
−0.0971407 | + | 0.995271i | \(0.530970\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.7192 | 0.703382 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.546824 | 0.0229644 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.1560 | 1.01267 | 0.506335 | − | 0.862337i | \(-0.331000\pi\) | ||||
0.506335 | + | 0.862337i | \(0.331000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.4192 | −1.69149 | −0.845744 | − | 0.533588i | \(-0.820843\pi\) | ||||
−0.845744 | + | 0.533588i | \(0.820843\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.16696 | −0.0487503 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0379 | 0.502015 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.3043 | 1.30321 | 0.651607 | − | 0.758557i | \(-0.274095\pi\) | ||||
0.651607 | + | 0.758557i | \(0.274095\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.8641 | 0.451497 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.59773 | −0.0662848 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.2172 | −0.505984 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.07451 | 0.251150 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.5321 | 0.723628 | 0.361814 | − | 0.932250i | \(-0.382158\pi\) | ||||
0.361814 | + | 0.932250i | \(0.382158\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.544886 | −0.0224516 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.88903 | −0.159973 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.9459 | −0.531626 | −0.265813 | − | 0.964025i | \(-0.585640\pi\) | ||||
−0.265813 | + | 0.964025i | \(0.585640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.71402 | −0.0702682 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.1365 | −0.619497 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.0015 | −0.408651 | −0.204326 | − | 0.978903i | \(-0.565500\pi\) | ||||
−0.204326 | + | 0.978903i | \(0.565500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.7536 | −1.25446 | −0.627232 | − | 0.778832i | \(-0.715812\pi\) | ||||
−0.627232 | + | 0.778832i | \(0.715812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.84200 | 0.360074 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.1444 | −0.412430 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.9574 | −0.972401 | −0.486200 | − | 0.873847i | \(-0.661617\pi\) | ||||
−0.486200 | + | 0.873847i | \(0.661617\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.15931 | 0.0469775 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.2931 | 0.578238 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.1659 | 1.46073 | 0.730363 | − | 0.683059i | \(-0.239351\pi\) | ||||
0.730363 | + | 0.683059i | \(0.239351\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.90158 | 0.197651 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.26460 | −0.0509108 | −0.0254554 | − | 0.999676i | \(-0.508104\pi\) | ||||
−0.0254554 | + | 0.999676i | \(0.508104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.1010 | 1.33044 | 0.665220 | − | 0.746647i | \(-0.268338\pi\) | ||||
0.665220 | + | 0.746647i | \(0.268338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.8638 | 0.676720 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.682201 | 0.0273318 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.83840 | 0.153536 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.13551 | −0.0453479 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.2448 | 1.12619 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.6232 | 0.621948 | 0.310974 | − | 0.950418i | \(-0.399345\pi\) | ||||
0.310974 | + | 0.950418i | \(0.399345\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.4571 | 0.574619 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.8045 | −0.508133 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.7533 | 0.624168 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.31952 | −0.131318 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.6782 | −1.72519 | −0.862593 | − | 0.505898i | \(-0.831161\pi\) | ||||
−0.862593 | + | 0.505898i | \(0.831161\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.2427 | 1.23209 | 0.616046 | − | 0.787710i | \(-0.288734\pi\) | ||||
0.616046 | + | 0.787710i | \(0.288734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.2976 | 0.405466 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.4107 | −1.03831 | −0.519156 | − | 0.854680i | \(-0.673754\pi\) | ||||
−0.519156 | + | 0.854680i | \(0.673754\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.9981 | −0.824246 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.208691 | 0.00817924 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.8022 | −0.774919 | −0.387460 | − | 0.921887i | \(-0.626647\pi\) | ||||
−0.387460 | + | 0.921887i | \(0.626647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.36166 | −0.365790 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.3683 | −0.872669 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.8649 | 0.929644 | 0.464822 | − | 0.885404i | \(-0.346118\pi\) | ||||
0.464822 | + | 0.885404i | \(0.346118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.80754 | 0.225887 | 0.112943 | − | 0.993601i | \(-0.463972\pi\) | ||||
0.112943 | + | 0.993601i | \(0.463972\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.0206 | 0.389168 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.258898 | −0.0100396 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.9930 | −0.580533 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.12781 | −0.120928 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.0160 | −0.734106 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.5299 | 0.907009 | 0.453505 | − | 0.891254i | \(-0.350174\pi\) | ||||
0.453505 | + | 0.891254i | \(0.350174\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.4194 | 0.631981 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.2237 | −0.623528 | −0.311764 | − | 0.950160i | \(-0.600920\pi\) | ||||
−0.311764 | + | 0.950160i | \(0.600920\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.95079 | −0.0748644 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.73532 | 0.104818 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.1880 | 0.466362 | 0.233181 | − | 0.972433i | \(-0.425087\pi\) | ||||
0.233181 | + | 0.972433i | \(0.425087\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.9728 | 0.686706 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.36950 | −0.128555 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.2849 | 0.620406 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.1956 | 0.501986 | 0.250993 | − | 0.967989i | \(-0.419243\pi\) | ||||
0.250993 | + | 0.967989i | \(0.419243\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.05429 | −0.0400490 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.87950 | −0.260954 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.6015 | −0.742458 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.903304 | −0.0341661 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.6611 | 1.53575 | 0.767874 | − | 0.640601i | \(-0.221315\pi\) | ||||
0.767874 | + | 0.640601i | \(0.221315\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.26628 | 0.160906 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.37410 | −0.277725 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.20624 | 0.158192 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.8296 | 1.12027 | 0.560137 | − | 0.828400i | \(-0.310749\pi\) | ||||
0.560137 | + | 0.828400i | \(0.310749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.41625 | −0.0531136 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.69895 | −0.101077 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.88770 | −0.182790 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.4712 | 0.391055 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.19044 | 0.0443958 | 0.0221979 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221979 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.56119 | 0.0953835 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.30252 | 0.0484414 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.5979 | −0.542153 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.8783 | 0.922687 | 0.461343 | − | 0.887222i | \(-0.347368\pi\) | ||||
0.461343 | + | 0.887222i | \(0.347368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.46904 | 0.350705 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.1801 | −1.52310 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.1382 | 0.965435 | 0.482717 | − | 0.875776i | \(-0.339650\pi\) | ||||
0.482717 | + | 0.875776i | \(0.339650\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.12742 | −0.299784 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.11450 | −0.262066 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.5205 | −0.718073 | −0.359036 | − | 0.933324i | \(-0.616895\pi\) | ||||
−0.359036 | + | 0.933324i | \(0.616895\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.51358 | 0.0556028 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.9611 | 1.06248 | 0.531240 | − | 0.847222i | \(-0.321726\pi\) | ||||
0.531240 | + | 0.847222i | \(0.321726\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.5009 | −0.897644 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.6824 | 0.427435 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.106440 | 0.00388925 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.4765 | −0.382291 | −0.191146 | − | 0.981562i | \(-0.561220\pi\) | ||||
−0.191146 | + | 0.981562i | \(0.561220\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.2165 | −1.06471 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.75414 | −0.209415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0106 | 0.363842 | 0.181921 | − | 0.983313i | \(-0.441768\pi\) | ||||
0.181921 | + | 0.983313i | \(0.441768\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.62445 | −0.204155 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.1813 | −0.369070 | −0.184535 | − | 0.982826i | \(-0.559078\pi\) | ||||
−0.184535 | + | 0.982826i | \(0.559078\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.184025 | 0.00666214 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.5327 | 0.453122 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.9894 | 1.01064 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.1908 | 1.73781 | 0.868903 | − | 0.494983i | \(-0.164826\pi\) | ||||
0.868903 | + | 0.494983i | \(0.164826\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6455 | 0.383387 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.5370 | 1.06237 | 0.531186 | − | 0.847255i | \(-0.321746\pi\) | ||||
0.531186 | + | 0.847255i | \(0.321746\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.62783 | −0.0943943 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.63398 | −0.0586188 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.96074 | −0.106079 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.67097 | 0.0955748 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.4501 | −0.730826 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.5022 | 0.588989 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.2406 | 0.792791 | 0.396396 | − | 0.918080i | \(-0.370261\pi\) | ||||
0.396396 | + | 0.918080i | \(0.370261\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.32566 | 0.225200 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.86792 | 0.137527 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.3475 | 0.900116 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.40170 | −0.297978 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.0753 | −1.06532 | −0.532661 | − | 0.846329i | \(-0.678808\pi\) | ||||
−0.532661 | + | 0.846329i | \(0.678808\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.4891 | 1.04325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.98817 | −0.176248 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.9981 | 0.635138 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.28238 | −0.0451981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.41778 | −0.261118 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.1808 | 1.51816 | 0.759078 | − | 0.650999i | \(-0.225650\pi\) | ||||
0.759078 | + | 0.650999i | \(0.225650\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.84533 | 0.345716 | 0.172858 | − | 0.984947i | \(-0.444700\pi\) | ||||
0.172858 | + | 0.984947i | \(0.444700\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.11240 | 0.0740851 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.1544 | −0.811063 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.22012 | −0.217615 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.40531 | 0.0491056 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.9584 | 1.84826 | 0.924131 | − | 0.382076i | \(-0.124791\pi\) | ||||
0.924131 | + | 0.382076i | \(0.124791\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.1156 | 1.50292 | 0.751458 | − | 0.659781i | \(-0.229351\pi\) | ||||
0.751458 | + | 0.659781i | \(0.229351\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.47623 | −0.190658 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.2313 | −1.19034 | −0.595169 | − | 0.803600i | \(-0.702915\pi\) | ||||
−0.595169 | + | 0.803600i | \(0.702915\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.2681 | −1.15545 | −0.577725 | − | 0.816232i | \(-0.696059\pi\) | ||||
−0.577725 | + | 0.816232i | \(0.696059\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.5064 | 0.641981 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.5016 | 1.12612 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.22837 | −0.180935 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.68129 | −0.127244 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.62296 | −0.0560307 | −0.0280153 | − | 0.999607i | \(-0.508919\pi\) | ||||
−0.0280153 | + | 0.999607i | \(0.508919\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8185 | −0.373051 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27.2092 | −0.937136 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.80732 | −0.337382 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.34687 | −0.0806396 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.0275 | 0.790300 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.1319 | 0.724393 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.8985 | 0.475875 | 0.237938 | − | 0.971280i | \(-0.423529\pi\) | ||||
0.237938 | + | 0.971280i | \(0.423529\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.89303 | 0.0647402 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.8506 | 0.438968 | 0.219484 | − | 0.975616i | \(-0.429563\pi\) | ||||
0.219484 | + | 0.975616i | \(0.429563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.7437 | 1.08308 | 0.541541 | − | 0.840674i | \(-0.317841\pi\) | ||||
0.541541 | + | 0.840674i | \(0.317841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.13396 | 0.0386453 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.1302 | −0.515037 | −0.257518 | − | 0.966273i | \(-0.582905\pi\) | ||||
−0.257518 | + | 0.966273i | \(0.582905\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.38918 | 0.319242 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.76200 | 0.161726 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.13955 | 0.0386566 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.48329 | 0.321329 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.2639 | 0.482760 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.07212 | −0.103857 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.1058 | −0.341250 | −0.170625 | − | 0.985336i | \(-0.554579\pi\) | ||||
−0.170625 | + | 0.985336i | \(0.554579\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.721471 | −0.0243346 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.6025 | −1.30055 | −0.650276 | − | 0.759698i | \(-0.725347\pi\) | ||||
−0.650276 | + | 0.759698i | \(0.725347\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.9608 | 0.671733 | 0.335867 | − | 0.941910i | \(-0.390971\pi\) | ||||
0.335867 | + | 0.941910i | \(0.390971\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.4403 | −0.485405 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.7899 | −1.33601 | −0.668007 | − | 0.744155i | \(-0.732852\pi\) | ||||
−0.668007 | + | 0.744155i | \(0.732852\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.96228 | −0.0993516 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.21714 | 0.107778 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.45424 | 0.149055 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.4359 | 0.348835 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.49712 | 0.250322 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.27292 | 0.109158 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.5985 | 1.11933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.38230 | 0.0792780 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.7724 | 0.590775 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.5622 | 1.74530 | 0.872650 | − | 0.488346i | \(-0.162400\pi\) | ||||
0.872650 | + | 0.488346i | \(0.162400\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −30.7555 | −1.02010 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.4983 | 1.37490 | 0.687450 | − | 0.726232i | \(-0.258730\pi\) | ||||
0.687450 | + | 0.726232i | \(0.258730\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.39992 | −0.311092 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.0773 | −0.432321 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.16578 | −0.0715204 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.47490 | 0.147613 | 0.0738066 | − | 0.997273i | \(-0.476485\pi\) | ||||
0.0738066 | + | 0.997273i | \(0.476485\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.95721 | −0.229248 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.56028 | −0.117188 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.5750 | 0.676503 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.7271 | −0.615077 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.1963 | 0.498574 | 0.249287 | − | 0.968430i | \(-0.419804\pi\) | ||||
0.249287 | + | 0.968430i | \(0.419804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.90927 | 0.160895 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.43348 | −0.210623 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.0841 | −0.329787 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.9845 | 1.14289 | 0.571447 | − | 0.820639i | \(-0.306382\pi\) | ||||
0.571447 | + | 0.820639i | \(0.306382\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.93505 | 0.226317 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.83994 | −0.320773 | −0.160386 | − | 0.987054i | \(-0.551274\pi\) | ||||
−0.160386 | + | 0.987054i | \(0.551274\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.6652 | −0.477566 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.74913 | −0.0568993 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.5404 | −1.73983 | −0.869915 | − | 0.493201i | \(-0.835827\pi\) | ||||
−0.869915 | + | 0.493201i | \(0.835827\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.9906 | −0.778767 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.96117 | 0.0635954 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.8848 | −1.29199 | −0.645997 | − | 0.763340i | \(-0.723558\pi\) | ||||
−0.645997 | + | 0.763340i | \(0.723558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.56536 | −0.0506539 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.82056 | 0.220478 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.15794 | 0.134267 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4108 | −0.980995 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.778279 | −0.0250797 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.5732 | 0.469128 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.2254 | −0.714720 | −0.357360 | − | 0.933967i | \(-0.616323\pi\) | ||||
−0.357360 | + | 0.933967i | \(0.616323\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.12277 | 0.100318 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.4266 | −0.687613 | −0.343807 | − | 0.939040i | \(-0.611716\pi\) | ||||
−0.343807 | + | 0.939040i | \(0.611716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.59154 | −0.0510226 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.29955 | 0.233773 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.5064 | −0.624066 | −0.312033 | − | 0.950071i | \(-0.601010\pi\) | ||||
−0.312033 | + | 0.950071i | \(0.601010\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.01361 | 0.128275 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.34556 | −0.0429606 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.2728 | −1.79482 | −0.897412 | − | 0.441192i | \(-0.854556\pi\) | ||||
−0.897412 | + | 0.441192i | \(0.854556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.21676 | −0.166220 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.70597 | −0.0543016 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.8097 | −0.979693 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.17225 | −0.0690037 | −0.0345018 | − | 0.999405i | \(-0.510984\pi\) | ||||
−0.0345018 | + | 0.999405i | \(0.510984\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.8282 | −0.629230 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.3042 | −0.643687 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.8431 | −1.00848 | −0.504240 | − | 0.863563i | \(-0.668227\pi\) | ||||
−0.504240 | + | 0.863563i | \(0.668227\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.8233 | 0.911930 |
(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 | 4024.2.a.e.1.19 | ✓ | 29 | |
4.3 | odd | 2 | 8048.2.a.w.1.11 | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.e.1.19 | ✓ | 29 | 1.1 | even | 1 | trivial | |
8048.2.a.w.1.11 | 29 | 4.3 | odd | 2 |