Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 110x^{6} - 154x^{5} - 282x^{4} + 256x^{3} + 253x^{2} - 126x - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.71781\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.71781 | −1.56913 | −0.784565 | − | 0.620047i | \(-0.787114\pi\) | ||||
−0.784565 | + | 0.620047i | \(0.787114\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.521406 | 0.233180 | 0.116590 | − | 0.993180i | \(-0.462804\pi\) | ||||
0.116590 | + | 0.993180i | \(0.462804\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.38650 | 1.46217 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0523876 | −0.0157954 | −0.00789772 | − | 0.999969i | \(-0.502514\pi\) | ||||
−0.00789772 | + | 0.999969i | \(0.502514\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.95553 | 1.65177 | 0.825884 | − | 0.563840i | \(-0.190677\pi\) | ||||
0.825884 | + | 0.563840i | \(0.190677\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41708 | −0.365889 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.06280 | −1.95552 | −0.977758 | − | 0.209736i | \(-0.932740\pi\) | ||||
−0.977758 | + | 0.209736i | \(0.932740\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.41423 | −1.01269 | −0.506346 | − | 0.862330i | \(-0.669004\pi\) | ||||
−0.506346 | + | 0.862330i | \(0.669004\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.28903 | 1.10284 | 0.551420 | − | 0.834228i | \(-0.314086\pi\) | ||||
0.551420 | + | 0.834228i | \(0.314086\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.72814 | −0.945627 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.76825 | −0.725200 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.73584 | 0.879424 | 0.439712 | − | 0.898139i | \(-0.355081\pi\) | ||||
0.439712 | + | 0.898139i | \(0.355081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.03532 | 1.44319 | 0.721593 | − | 0.692317i | \(-0.243410\pi\) | ||||
0.721593 | + | 0.692317i | \(0.243410\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.142380 | 0.0247851 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.28272 | −0.868474 | −0.434237 | − | 0.900799i | \(-0.642982\pi\) | ||||
−0.434237 | + | 0.900799i | \(0.642982\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.1860 | −2.59184 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.65780 | 0.557809 | 0.278904 | − | 0.960319i | \(-0.410029\pi\) | ||||
0.278904 | + | 0.960319i | \(0.410029\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.28715 | 0.340948 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.87355 | −0.710880 | −0.355440 | − | 0.934699i | \(-0.615669\pi\) | ||||
−0.355440 | + | 0.934699i | \(0.615669\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.9132 | 3.06846 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.13119 | −0.155381 | −0.0776907 | − | 0.996978i | \(-0.524755\pi\) | ||||
−0.0776907 | + | 0.996978i | \(0.524755\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0273152 | −0.00368318 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.9970 | 1.58905 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.21861 | −0.679406 | −0.339703 | − | 0.940533i | \(-0.610326\pi\) | ||||
−0.339703 | + | 0.940533i | \(0.610326\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.2952 | −1.31816 | −0.659080 | − | 0.752073i | \(-0.729054\pi\) | ||||
−0.659080 | + | 0.752073i | \(0.729054\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.10525 | 0.385159 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.37745 | 1.14564 | 0.572819 | − | 0.819682i | \(-0.305850\pi\) | ||||
0.572819 | + | 0.819682i | \(0.305850\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.3746 | −1.73050 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.25115 | 1.09791 | 0.548955 | − | 0.835852i | \(-0.315026\pi\) | ||||
0.548955 | + | 0.835852i | \(0.315026\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.6348 | −1.82992 | −0.914959 | − | 0.403547i | \(-0.867777\pi\) | ||||
−0.914959 | + | 0.403547i | \(0.867777\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.8502 | 1.48381 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.46946 | −0.840380 | −0.420190 | − | 0.907436i | \(-0.638037\pi\) | ||||
−0.420190 | + | 0.907436i | \(0.638037\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.91811 | −0.324234 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.66344 | −0.731407 | −0.365704 | − | 0.930731i | \(-0.619172\pi\) | ||||
−0.365704 | + | 0.930731i | \(0.619172\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.20399 | −0.455987 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.8711 | −1.37993 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.1869 | −1.60980 | −0.804902 | − | 0.593408i | \(-0.797782\pi\) | ||||
−0.804902 | + | 0.593408i | \(0.797782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21.8385 | −2.26455 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.30160 | −0.236139 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.41390 | 0.854302 | 0.427151 | − | 0.904180i | \(-0.359517\pi\) | ||||
0.427151 | + | 0.904180i | \(0.359517\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.229798 | −0.0230956 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.66350 | 0.762547 | 0.381273 | − | 0.924462i | \(-0.375486\pi\) | ||||
0.381273 | + | 0.924462i | \(0.375486\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7118 | 1.25253 | 0.626265 | − | 0.779610i | \(-0.284583\pi\) | ||||
0.626265 | + | 0.779610i | \(0.284583\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4948 | 1.30459 | 0.652297 | − | 0.757963i | \(-0.273805\pi\) | ||||
0.652297 | + | 0.757963i | \(0.273805\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.25475 | −0.694879 | −0.347439 | − | 0.937702i | \(-0.612949\pi\) | ||||
−0.347439 | + | 0.937702i | \(0.612949\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.3574 | 1.36275 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.99151 | −0.939923 | −0.469961 | − | 0.882687i | \(-0.655732\pi\) | ||||
−0.469961 | + | 0.882687i | \(0.655732\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.75773 | 0.257160 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 26.1240 | 2.41516 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9973 | −0.999751 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.71781 | 0.245057 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.07230 | −0.453681 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2019 | 1.17147 | 0.585737 | − | 0.810501i | \(-0.300805\pi\) | ||||
0.585737 | + | 0.810501i | \(0.300805\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.94120 | −0.875274 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.0053 | 1.83524 | 0.917619 | − | 0.397460i | \(-0.130108\pi\) | ||||
0.917619 | + | 0.397460i | \(0.130108\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.96479 | −0.169102 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.7936 | 1.43478 | 0.717388 | − | 0.696674i | \(-0.245338\pi\) | ||||
0.717388 | + | 0.696674i | \(0.245338\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3023 | −0.958645 | −0.479323 | − | 0.877639i | \(-0.659118\pi\) | ||||
−0.479323 | + | 0.877639i | \(0.659118\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.2454 | 1.11546 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.311996 | −0.0260904 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.46929 | 0.205064 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.3854 | 1.34234 | 0.671172 | − | 0.741302i | \(-0.265791\pi\) | ||||
0.671172 | + | 0.741302i | \(0.265791\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.53086 | 0.694231 | 0.347116 | − | 0.937822i | \(-0.387161\pi\) | ||||
0.347116 | + | 0.937822i | \(0.387161\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −35.3675 | −2.85929 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.18966 | 0.336522 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.4731 | 1.47432 | 0.737158 | − | 0.675721i | \(-0.236167\pi\) | ||||
0.737158 | + | 0.675721i | \(0.236167\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.07437 | 0.243814 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.1837 | −1.34593 | −0.672965 | − | 0.739674i | \(-0.734980\pi\) | ||||
−0.672965 | + | 0.739674i | \(0.734980\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0742375 | 0.00577938 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.03913 | 0.389939 | 0.194970 | − | 0.980809i | \(-0.437539\pi\) | ||||
0.194970 | + | 0.980809i | \(0.437539\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.4684 | 1.72834 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.3630 | −1.48073 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.34776 | −0.178497 | −0.0892483 | − | 0.996009i | \(-0.528446\pi\) | ||||
−0.0892483 | + | 0.996009i | \(0.528446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.1832 | 1.06608 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.00985 | 0.673428 | 0.336714 | − | 0.941607i | \(-0.390684\pi\) | ||||
0.336714 | + | 0.941607i | \(0.390684\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.24384 | −0.538430 | −0.269215 | − | 0.963080i | \(-0.586764\pi\) | ||||
−0.269215 | + | 0.963080i | \(0.586764\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.9803 | 2.06836 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.75444 | −0.202510 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.422390 | 0.0308882 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3381 | 0.748039 | 0.374020 | − | 0.927421i | \(-0.377979\pi\) | ||||
0.374020 | + | 0.927421i | \(0.377979\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.6485 | −1.70226 | −0.851130 | − | 0.524955i | \(-0.824082\pi\) | ||||
−0.851130 | + | 0.524955i | \(0.824082\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.43948 | −0.604364 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.34901 | 0.594842 | 0.297421 | − | 0.954746i | \(-0.403873\pi\) | ||||
0.297421 | + | 0.954746i | \(0.403873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.31844 | −0.589678 | −0.294839 | − | 0.955547i | \(-0.595266\pi\) | ||||
−0.294839 | + | 0.955547i | \(0.595266\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.4861 | −1.79765 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.521406 | −0.0364165 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 23.2003 | 1.61254 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.231251 | 0.0159959 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.92332 | −0.407778 | −0.203889 | − | 0.978994i | \(-0.565358\pi\) | ||||
−0.203889 | + | 0.978994i | \(0.565358\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −25.1429 | −1.72276 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.90720 | 0.130070 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 42.4925 | 2.87138 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −48.0183 | −3.23006 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.0457 | −1.47629 | −0.738143 | − | 0.674644i | \(-0.764297\pi\) | ||||
−0.738143 | + | 0.674644i | \(0.764297\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.7400 | −1.38267 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.8145 | −1.51425 | −0.757125 | − | 0.653270i | \(-0.773397\pi\) | ||||
−0.757125 | + | 0.653270i | \(0.773397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.11879 | 0.206095 | 0.103048 | − | 0.994676i | \(-0.467141\pi\) | ||||
0.103048 | + | 0.994676i | \(0.467141\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.5258 | 1.73777 | 0.868883 | − | 0.495018i | \(-0.164838\pi\) | ||||
0.868883 | + | 0.495018i | \(0.164838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.54110 | −0.165763 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.3006 | 1.31866 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.6422 | −1.72334 | −0.861669 | − | 0.507470i | \(-0.830581\pi\) | ||||
−0.861669 | + | 0.507470i | \(0.830581\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.5162 | 1.77248 | 0.886238 | − | 0.463231i | \(-0.153310\pi\) | ||||
0.886238 | + | 0.463231i | \(0.153310\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.2356 | 1.23397 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.2891 | −1.67273 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.1100 | 1.14767 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.34125 | −0.526495 | −0.263248 | − | 0.964728i | \(-0.584794\pi\) | ||||
−0.263248 | + | 0.964728i | \(0.584794\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.277079 | −0.0174198 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.4257 | 0.715502 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.08474 | −0.317177 | −0.158589 | − | 0.987345i | \(-0.550694\pi\) | ||||
−0.158589 | + | 0.987345i | \(0.550694\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.7738 | 1.28586 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.84288 | 0.606938 | 0.303469 | − | 0.952841i | \(-0.401855\pi\) | ||||
0.303469 | + | 0.952841i | \(0.401855\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.589811 | −0.0362318 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 41.2750 | 2.52599 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.97791 | −0.547393 | −0.273696 | − | 0.961816i | \(-0.588246\pi\) | ||||
−0.273696 | + | 0.961816i | \(0.588246\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.29679 | 0.0787741 | 0.0393871 | − | 0.999224i | \(-0.487459\pi\) | ||||
0.0393871 | + | 0.999224i | \(0.487459\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.247696 | 0.0149366 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.86652 | −0.532738 | −0.266369 | − | 0.963871i | \(-0.585824\pi\) | ||||
−0.266369 | + | 0.963871i | \(0.585824\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 35.2470 | 2.11018 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.25681 | −0.0749752 | −0.0374876 | − | 0.999297i | \(-0.511935\pi\) | ||||
−0.0374876 | + | 0.999297i | \(0.511935\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.661785 | −0.0393390 | −0.0196695 | − | 0.999807i | \(-0.506261\pi\) | ||||
−0.0196695 | + | 0.999807i | \(0.506261\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.25532 | 0.370533 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 48.0087 | 2.82404 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.8674 | −1.34051 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.8784 | −1.57025 | −0.785126 | − | 0.619336i | \(-0.787402\pi\) | ||||
−0.785126 | + | 0.619336i | \(0.787402\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.72101 | −0.158424 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.197409 | 0.0114549 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.4990 | 1.82163 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.8280 | −1.19653 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.36796 | −0.307368 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.4296 | −0.937689 | −0.468845 | − | 0.883281i | \(-0.655330\pi\) | ||||
−0.468845 | + | 0.883281i | \(0.655330\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.5483 | −1.96538 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.95638 | 0.337755 | 0.168878 | − | 0.985637i | \(-0.445986\pi\) | ||||
0.168878 | + | 0.985637i | \(0.445986\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.6393 | 0.770937 | 0.385468 | − | 0.922721i | \(-0.374040\pi\) | ||||
0.385468 | + | 0.922721i | \(0.374040\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.1941 | −0.684891 | −0.342446 | − | 0.939538i | \(-0.611255\pi\) | ||||
−0.342446 | + | 0.939538i | \(0.611255\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.248099 | −0.0138909 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −36.6764 | −2.04708 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.5910 | 1.98034 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.1586 | −1.56196 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.7170 | 1.09035 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.4381 | −1.83792 | −0.918962 | − | 0.394345i | \(-0.870971\pi\) | ||||
−0.918962 | + | 0.394345i | \(0.870971\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −23.1727 | −1.26985 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.88945 | 0.267139 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.6785 | −1.12643 | −0.563216 | − | 0.826310i | \(-0.690436\pi\) | ||||
−0.563216 | + | 0.826310i | \(0.690436\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27.1551 | 1.47486 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.420951 | −0.0227958 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.49499 | −0.403517 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.52816 | −0.189401 | −0.0947007 | − | 0.995506i | \(-0.530189\pi\) | ||||
−0.0947007 | + | 0.995506i | \(0.530189\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.8147 | −1.16771 | −0.583857 | − | 0.811856i | \(-0.698457\pi\) | ||||
−0.583857 | + | 0.811856i | \(0.698457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.4419 | −1.19786 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.82379 | −0.522868 | −0.261434 | − | 0.965221i | \(-0.584195\pi\) | ||||
−0.261434 | + | 0.965221i | \(0.584195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.82360 | 0.256010 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.3688 | −1.07503 | −0.537513 | − | 0.843255i | \(-0.680636\pi\) | ||||
−0.537513 | + | 0.843255i | \(0.680636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.485391 | 0.0255469 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.8885 | 1.56874 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.15208 | −0.426700 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.77124 | −0.0924578 | −0.0462289 | − | 0.998931i | \(-0.514720\pi\) | ||||
−0.0462289 | + | 0.998931i | \(0.514720\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.38650 | −0.228352 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.1930 | −1.35622 | −0.678112 | − | 0.734959i | \(-0.737201\pi\) | ||||
−0.678112 | + | 0.734959i | \(0.737201\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.7856 | 0.711884 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.2045 | 1.45260 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.75824 | −0.398514 | −0.199257 | − | 0.979947i | \(-0.563853\pi\) | ||||
−0.199257 | + | 0.979947i | \(0.563853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.8802 | −1.83820 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.6322 | −1.36084 | −0.680421 | − | 0.732822i | \(-0.738203\pi\) | ||||
−0.680421 | + | 0.732822i | \(0.738203\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.0449 | 0.815610 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.5184 | −0.736110 | −0.368055 | − | 0.929804i | \(-0.619976\pi\) | ||||
−0.368055 | + | 0.929804i | \(0.619976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.6444 | −2.15662 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −57.0884 | −2.87973 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.89462 | −0.195959 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.84163 | 0.142618 | 0.0713088 | − | 0.997454i | \(-0.477282\pi\) | ||||
0.0713088 | + | 0.997454i | \(0.477282\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.1476 | −0.956186 | −0.478093 | − | 0.878309i | \(-0.658672\pi\) | ||||
−0.478093 | + | 0.878309i | \(0.658672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 47.8546 | 2.38381 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.52152 | −0.0756048 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.276749 | 0.0137179 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.5456 | −1.55983 | −0.779915 | − | 0.625886i | \(-0.784738\pi\) | ||||
−0.779915 | + | 0.625886i | \(0.784738\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −45.6419 | −2.25135 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.47435 | −0.170549 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.7174 | 1.50424 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.9308 | −1.70648 | −0.853240 | − | 0.521519i | \(-0.825366\pi\) | ||||
−0.853240 | + | 0.521519i | \(0.825366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.2206 | −1.96023 | −0.980115 | − | 0.198429i | \(-0.936416\pi\) | ||||
−0.980115 | + | 0.198429i | \(0.936416\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.3778 | −1.03943 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.1220 | 1.84919 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.847946 | 0.0409392 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.0998975 | −0.00481190 | −0.00240595 | − | 0.999997i | \(-0.500766\pi\) | ||||
−0.00240595 | + | 0.999997i | \(0.500766\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3357 | 0.929216 | 0.464608 | − | 0.885516i | \(-0.346195\pi\) | ||||
0.464608 | + | 0.885516i | \(0.346195\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.71108 | −0.321772 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.3470 | −1.11684 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.70056 | −0.415255 | −0.207628 | − | 0.978208i | \(-0.566574\pi\) | ||||
−0.207628 | + | 0.978208i | \(0.566574\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.62748 | 0.0773239 | 0.0386619 | − | 0.999252i | \(-0.487690\pi\) | ||||
0.0386619 | + | 0.999252i | \(0.487690\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.91851 | −0.375373 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −44.5324 | −2.10631 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.9660 | 0.517519 | 0.258759 | − | 0.965942i | \(-0.416686\pi\) | ||||
0.258759 | + | 0.965942i | \(0.416686\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0523876 | 0.00246683 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.1853 | −1.08934 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.9173 | −0.791358 | −0.395679 | − | 0.918389i | \(-0.629491\pi\) | ||||
−0.395679 | + | 0.918389i | \(0.629491\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 30.3827 | 1.41814 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.2523 | −0.570648 | −0.285324 | − | 0.958431i | \(-0.592101\pi\) | ||||
−0.285324 | + | 0.958431i | \(0.592101\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.4046 | −0.715911 | −0.357956 | − | 0.933739i | \(-0.616526\pi\) | ||||
−0.357956 | + | 0.933739i | \(0.616526\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.3867 | −0.528046 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.55604 | −0.0720048 | −0.0360024 | − | 0.999352i | \(-0.511462\pi\) | ||||
−0.0360024 | + | 0.999352i | \(0.511462\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −50.2065 | −2.31339 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.191623 | −0.00881084 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.8711 | 0.957630 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.96199 | −0.227194 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.48168 | 0.341847 | 0.170923 | − | 0.985284i | \(-0.445325\pi\) | ||||
0.170923 | + | 0.985284i | \(0.445325\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.4614 | −1.43452 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.38705 | 0.199206 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.12986 | −0.187142 | −0.0935709 | − | 0.995613i | \(-0.529828\pi\) | ||||
−0.0935709 | + | 0.995613i | \(0.529828\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 46.7021 | 2.11194 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.37953 | 0.152516 | 0.0762581 | − | 0.997088i | \(-0.475703\pi\) | ||||
0.0762581 | + | 0.997088i | \(0.475703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.1842 | −1.71973 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.119818 | −0.00538542 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.714451 | 0.0319832 | 0.0159916 | − | 0.999872i | \(-0.494909\pi\) | ||||
0.0159916 | + | 0.999872i | \(0.494909\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.6954 | −0.611865 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.1268 | 1.38788 | 0.693938 | − | 0.720035i | \(-0.255874\pi\) | ||||
0.693938 | + | 0.720035i | \(0.255874\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.99579 | 0.177810 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −61.0648 | −2.71198 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.1459 | 0.804302 | 0.402151 | − | 0.915573i | \(-0.368263\pi\) | ||||
0.402151 | + | 0.915573i | \(0.368263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.6339 | 0.734405 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.62800 | 0.292065 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.255313 | 0.0112287 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.38076 | 0.280084 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.2199 | 0.885851 | 0.442925 | − | 0.896558i | \(-0.353941\pi\) | ||||
0.442925 | + | 0.896558i | \(0.353941\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.7117 | −0.468391 | −0.234196 | − | 0.972189i | \(-0.575246\pi\) | ||||
−0.234196 | + | 0.972189i | \(0.575246\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −64.7872 | −2.82217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.97386 | 0.216255 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.8915 | −0.993405 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.95553 | −0.257963 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.03628 | 0.304205 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.4871 | −1.05670 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.09928 | −0.133248 | −0.0666242 | − | 0.997778i | \(-0.521223\pi\) | ||||
−0.0666242 | + | 0.997778i | \(0.521223\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.6874 | 0.844867 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.78267 | −0.162032 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.4370 | 0.660038 | 0.330019 | − | 0.943974i | \(-0.392945\pi\) | ||||
0.330019 | + | 0.943974i | \(0.392945\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −45.1598 | −1.92737 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.9051 | −0.890586 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.48605 | 0.317765 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.1785 | 1.23633 | 0.618167 | − | 0.786047i | \(-0.287876\pi\) | ||||
0.618167 | + | 0.786047i | \(0.287876\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.7841 | 0.921370 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.14798 | −0.0484677 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.1730 | 1.39808 | 0.699038 | − | 0.715084i | \(-0.253612\pi\) | ||||
0.699038 | + | 0.715084i | \(0.253612\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.20963 | −0.219171 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.0718 | −1.34452 | −0.672261 | − | 0.740315i | \(-0.734677\pi\) | ||||
−0.672261 | + | 0.740315i | \(0.734677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.3618 | 1.52169 | 0.760846 | − | 0.648932i | \(-0.224784\pi\) | ||||
0.760846 | + | 0.648932i | \(0.224784\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.0970 | −1.17377 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.0073 | −1.04287 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.2809 | 1.21898 | 0.609490 | − | 0.792794i | \(-0.291374\pi\) | ||||
0.609490 | + | 0.792794i | \(0.291374\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 64.2723 | 2.67107 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0592605 | 0.00245432 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.6212 | 0.563166 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.283450 | −0.0116992 | −0.00584962 | − | 0.999983i | \(-0.501862\pi\) | ||||
−0.00584962 | + | 0.999983i | \(0.501862\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.4697 | −1.46150 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.6910 | −0.933385 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.9652 | 0.819872 | 0.409936 | − | 0.912114i | \(-0.365551\pi\) | ||||
0.409936 | + | 0.912114i | \(0.365551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.6079 | 0.925282 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.15375 | −0.292294 | −0.146147 | − | 0.989263i | \(-0.546687\pi\) | ||||
−0.146147 | + | 0.989263i | \(0.546687\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.5662 | −0.471794 | −0.235897 | − | 0.971778i | \(-0.575803\pi\) | ||||
−0.235897 | + | 0.971778i | \(0.575803\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 41.1342 | 1.67511 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.73403 | −0.233121 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.37175 | −0.218033 | −0.109016 | − | 0.994040i | \(-0.534770\pi\) | ||||
−0.109016 | + | 0.994040i | \(0.534770\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.0246 | −1.17421 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.5142 | −0.424667 | −0.212333 | − | 0.977197i | \(-0.568106\pi\) | ||||
−0.212333 | + | 0.977197i | \(0.568106\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.41708 | 0.0571423 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.5370 | 0.464461 | 0.232231 | − | 0.972661i | \(-0.425398\pi\) | ||||
0.232231 | + | 0.972661i | \(0.425398\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.8935 | −0.799586 | −0.399793 | − | 0.916606i | \(-0.630918\pi\) | ||||
−0.399793 | + | 0.916606i | \(0.630918\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.9304 | −0.799779 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.9960 | 0.839838 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.628495 | −0.0250997 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.5935 | 1.69831 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.58885 | 0.341917 | 0.170958 | − | 0.985278i | \(-0.445314\pi\) | ||||
0.170958 | + | 0.985278i | \(0.445314\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.0985 | 0.639857 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.88352 | 0.273164 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 40.5802 | 1.60533 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.0485 | −1.38433 | −0.692166 | − | 0.721738i | \(-0.743343\pi\) | ||||
−0.692166 | + | 0.721738i | \(0.743343\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.10398 | −0.359026 | −0.179513 | − | 0.983756i | \(-0.557452\pi\) | ||||
−0.179513 | + | 0.983756i | \(0.557452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.18340 | −0.204096 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.6739 | 1.75631 | 0.878156 | − | 0.478375i | \(-0.158774\pi\) | ||||
0.878156 | + | 0.478375i | \(0.158774\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.273390 | 0.0107315 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.524446 | 0.0205232 | 0.0102616 | − | 0.999947i | \(-0.496734\pi\) | ||||
0.0102616 | + | 0.999947i | \(0.496734\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.9523 | 0.427940 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −68.5822 | −2.67565 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.3824 | −1.84576 | −0.922878 | − | 0.385092i | \(-0.874170\pi\) | ||||
−0.922878 | + | 0.385092i | \(0.874170\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8569 | −0.500076 | −0.250038 | − | 0.968236i | \(-0.580443\pi\) | ||||
−0.250038 | + | 0.968236i | \(0.580443\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 130.505 | 5.06838 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.0480 | 0.969863 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 59.9159 | 2.31648 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.539339 | 0.0208209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.1973 | 1.04838 | 0.524189 | − | 0.851602i | \(-0.324369\pi\) | ||||
0.524189 | + | 0.851602i | \(0.324369\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.8168 | 0.685769 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.4835 | −0.710379 | −0.355189 | − | 0.934794i | \(-0.615584\pi\) | ||||
−0.355189 | + | 0.934794i | \(0.615584\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 62.0055 | 2.37606 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.16977 | 0.350872 | 0.175436 | − | 0.984491i | \(-0.443867\pi\) | ||||
0.175436 | + | 0.984491i | \(0.443867\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.75628 | 0.334560 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.47628 | −0.323390 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.73686 | −0.256654 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.4993 | 0.399414 | 0.199707 | − | 0.979856i | \(-0.436001\pi\) | ||||
0.199707 | + | 0.979856i | \(0.436001\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.89306 | −0.223537 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.06280 | 0.305400 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −72.0923 | −2.72678 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.9734 | 1.39647 | 0.698233 | − | 0.715871i | \(-0.253970\pi\) | ||||
0.698233 | + | 0.715871i | \(0.253970\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.3191 | 0.879497 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.90622 | 0.260103 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.6159 | −1.56292 | −0.781460 | − | 0.623956i | \(-0.785525\pi\) | ||||
−0.781460 | + | 0.623956i | \(0.785525\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.7648 | −1.22878 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 42.4991 | 1.59160 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.162676 | −0.00608375 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 72.4084 | 2.70414 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.5108 | −0.988687 | −0.494343 | − | 0.869267i | \(-0.664591\pi\) | ||||
−0.494343 | + | 0.869267i | \(0.664591\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −74.7839 | −2.78124 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.3917 | −0.831607 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.4464 | −1.05502 | −0.527510 | − | 0.849549i | \(-0.676874\pi\) | ||||
−0.527510 | + | 0.849549i | \(0.676874\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.5245 | −1.61202 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.4921 | −1.09080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.9478 | −0.441300 | −0.220650 | − | 0.975353i | \(-0.570818\pi\) | ||||
−0.220650 | + | 0.975353i | \(0.570818\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.491262 | −0.0180959 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.44140 | −0.236951 | −0.118475 | − | 0.992957i | \(-0.537801\pi\) | ||||
−0.118475 | + | 0.992957i | \(0.537801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 71.4487 | 2.62473 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.7507 | −1.45831 | −0.729156 | − | 0.684348i | \(-0.760087\pi\) | ||||
−0.729156 | + | 0.684348i | \(0.760087\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.54344 | 0.313007 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.2292 | −1.06944 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.0681 | 0.951240 | 0.475620 | − | 0.879651i | \(-0.342224\pi\) | ||||
0.475620 | + | 0.879651i | \(0.342224\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.6700 | 0.826139 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.44804 | 0.161881 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8431 | −0.648517 | −0.324259 | − | 0.945968i | \(-0.605115\pi\) | ||||
−0.324259 | + | 0.945968i | \(0.605115\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.753050 | 0.0273340 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.9632 | 0.759916 | 0.379958 | − | 0.925004i | \(-0.375938\pi\) | ||||
0.379958 | + | 0.925004i | \(0.375938\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.4408 | −0.666729 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.0796 | −1.12222 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.95390 | −0.286825 | −0.143413 | − | 0.989663i | \(-0.545808\pi\) | ||||
−0.143413 | + | 0.989663i | \(0.545808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.8194 | 0.497692 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.3869 | −0.625364 | −0.312682 | − | 0.949858i | \(-0.601227\pi\) | ||||
−0.312682 | + | 0.949858i | \(0.601227\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.9921 | −1.36472 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.41423 | 0.158156 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.484645 | −0.0173420 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.8458 | −0.637758 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.63199 | 0.343780 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.1912 | −0.541508 | −0.270754 | − | 0.962649i | \(-0.587273\pi\) | ||||
−0.270754 | + | 0.962649i | \(0.587273\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.7511 | −0.952364 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −61.3132 | −2.17729 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.60300 | 0.0568524 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.4142 | 0.404311 | 0.202156 | − | 0.979353i | \(-0.435205\pi\) | ||||
0.202156 | + | 0.979353i | \(0.435205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.2945 | 1.39014 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −66.6172 | −2.35380 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.819070 | 0.0289044 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.4003 | 0.858930 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.40298 | −0.295433 | −0.147716 | − | 0.989030i | \(-0.547192\pi\) | ||||
−0.147716 | + | 0.989030i | \(0.547192\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.3090 | −1.48567 | −0.742835 | − | 0.669474i | \(-0.766519\pi\) | ||||
−0.742835 | + | 0.669474i | \(0.766519\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.52442 | −0.123607 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.95967 | −0.313844 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.1463 | −0.564889 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.23403 | −0.252470 | −0.126235 | − | 0.992000i | \(-0.540289\pi\) | ||||
−0.126235 | + | 0.992000i | \(0.540289\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.5809 | −1.69342 | −0.846712 | − | 0.532052i | \(-0.821421\pi\) | ||||
−0.846712 | + | 0.532052i | \(0.821421\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.673190 | −0.0234375 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.30440 | 0.219225 | 0.109613 | − | 0.993974i | \(-0.465039\pi\) | ||||
0.109613 | + | 0.993974i | \(0.465039\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.8484 | 1.00194 | 0.500972 | − | 0.865463i | \(-0.332976\pi\) | ||||
0.500972 | + | 0.865463i | \(0.332976\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.0975 | 0.835934 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.62743 | 0.0909259 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.2791 | −1.04660 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.912239 | 0.0314940 | 0.0157470 | − | 0.999876i | \(-0.494987\pi\) | ||||
0.0157470 | + | 0.999876i | \(0.494987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.57179 | −0.226613 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.41578 | 0.117646 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.7151 | 0.403013 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.79861 | 0.0617280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.9405 | −0.957787 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.28786 | 0.181053 | 0.0905264 | − | 0.995894i | \(-0.471145\pi\) | ||||
0.0905264 | + | 0.995894i | \(0.471145\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.0960 | −0.345275 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.7176 | 1.22009 | 0.610046 | − | 0.792366i | \(-0.291151\pi\) | ||||
0.610046 | + | 0.792366i | \(0.291151\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.0888 | −0.787778 | −0.393889 | − | 0.919158i | \(-0.628871\pi\) | ||||
−0.393889 | + | 0.919158i | \(0.628871\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.4626 | −0.968879 | −0.484439 | − | 0.874825i | \(-0.660976\pi\) | ||||
−0.484439 | + | 0.874825i | \(0.660976\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.22413 | −0.0416218 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −130.479 | −4.43129 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.391307 | 0.0132742 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.8477 | 1.89233 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.9076 | 1.24913 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.1917 | 0.951967 | 0.475983 | − | 0.879454i | \(-0.342092\pi\) | ||||
0.475983 | + | 0.879454i | \(0.342092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 73.0504 | 2.46393 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.41597 | 0.182469 | 0.0912343 | − | 0.995829i | \(-0.470919\pi\) | ||||
0.0912343 | + | 0.995829i | \(0.470919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.811514 | −0.0273096 | −0.0136548 | − | 0.999907i | \(-0.504347\pi\) | ||||
−0.0136548 | + | 0.999907i | \(0.504347\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.39520 | 0.248587 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.7334 | 1.43485 | 0.717424 | − | 0.696636i | \(-0.245321\pi\) | ||||
0.717424 | + | 0.696636i | \(0.245321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.152873 | 0.00512142 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.5130 | 0.719904 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.69779 | 0.157030 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −85.6084 | −2.85838 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.0540 | 1.26917 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.12059 | 0.303851 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.77698 | −0.125551 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.5541 | −0.682487 | −0.341244 | − | 0.939975i | \(-0.610848\pi\) | ||||
−0.341244 | + | 0.939975i | \(0.610848\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33.6160 | 1.11497 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.8456 | 0.856302 | 0.428151 | − | 0.903707i | \(-0.359165\pi\) | ||||
0.428151 | + | 0.903707i | \(0.359165\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.349081 | 0.0115529 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.5891 | 0.482301 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.5311 | −0.809205 | −0.404602 | − | 0.914493i | \(-0.632590\pi\) | ||||
−0.404602 | + | 0.914493i | \(0.632590\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44.6527 | 1.47136 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 55.0955 | 1.81349 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.9774 | 0.821253 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 55.7603 | 1.83141 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.2592 | 0.500639 | 0.250319 | − | 0.968163i | \(-0.419464\pi\) | ||||
0.250319 | + | 0.968163i | \(0.419464\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.1883 | −0.529982 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.220237 | 0.00720251 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6093 | 0.673276 | 0.336638 | − | 0.941634i | \(-0.390710\pi\) | ||||
0.336638 | + | 0.941634i | \(0.390710\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.0689 | −1.20970 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.76678 | −0.187992 | −0.0939958 | − | 0.995573i | \(-0.529964\pi\) | ||||
−0.0939958 | + | 0.995573i | \(0.529964\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.28903 | −0.172235 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.2002 | −0.591427 | −0.295713 | − | 0.955277i | \(-0.595557\pi\) | ||||
−0.295713 | + | 0.955277i | \(0.595557\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −93.1137 | −3.02260 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.1414 | 1.07468 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.8833 | −0.384938 | −0.192469 | − | 0.981303i | \(-0.561649\pi\) | ||||
−0.192469 | + | 0.981303i | \(0.561649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.39035 | 0.174428 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.674287 | 0.0217966 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.5664 | 1.08279 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 59.1951 | 1.90754 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.3305 | −0.396932 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.5653 | 1.94765 | 0.973825 | − | 0.227299i | \(-0.0729894\pi\) | ||||
0.973825 | + | 0.227299i | \(0.0729894\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −96.7297 | −3.10741 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.2238 | 1.67594 | 0.837970 | − | 0.545716i | \(-0.183742\pi\) | ||||
0.837970 | + | 0.545716i | \(0.183742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 76.5297 | 2.45091 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.44437 | −0.110195 | −0.0550976 | − | 0.998481i | \(-0.517547\pi\) | ||||
−0.0550976 | + | 0.998481i | \(0.517547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.795602 | 0.0254276 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.8230 | −1.01603 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.5887 | −1.42216 | −0.711079 | − | 0.703112i | \(-0.751793\pi\) | ||||
−0.711079 | + | 0.703112i | \(0.751793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.35322 | 0.138705 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.3462 | 0.615173 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.3007 | −0.708406 | −0.354203 | − | 0.935169i | \(-0.615248\pi\) | ||||
−0.354203 | + | 0.935169i | \(0.615248\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 90.8785 | 2.88394 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.33728 | −0.137501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.5700 | 0.398097 | 0.199048 | − | 0.979990i | \(-0.436215\pi\) | ||||
0.199048 | + | 0.979990i | \(0.436215\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.9066 | 0.629817 |
(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 | 8036.2.a.o.1.1 | ✓ | 10 | |
7.6 | odd | 2 | 8036.2.a.p.1.10 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.o.1.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8036.2.a.p.1.10 | yes | 10 | 7.6 | odd | 2 |