Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 29x^{7} - 7x^{6} + 266x^{5} + 69x^{4} - 901x^{3} - 199x^{2} + 875x + 391 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2004) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.16840\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.16840 | −1.41695 | −0.708476 | − | 0.705735i | \(-0.750617\pi\) | ||||
−0.708476 | + | 0.705735i | \(0.750617\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.230890 | 0.0872681 | 0.0436341 | − | 0.999048i | \(-0.486106\pi\) | ||||
0.0436341 | + | 0.999048i | \(0.486106\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.534912 | −0.161282 | −0.0806411 | − | 0.996743i | \(-0.525697\pi\) | ||||
−0.0806411 | + | 0.996743i | \(0.525697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.40467 | 0.666936 | 0.333468 | − | 0.942761i | \(-0.391781\pi\) | ||||
0.333468 | + | 0.942761i | \(0.391781\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.16840 | 0.818077 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.83643 | 0.930471 | 0.465235 | − | 0.885187i | \(-0.345970\pi\) | ||||
0.465235 | + | 0.885187i | \(0.345970\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.74980 | 1.77793 | 0.888963 | − | 0.457980i | \(-0.151427\pi\) | ||||
0.888963 | + | 0.457980i | \(0.151427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.230890 | −0.0503843 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.14190 | −1.07216 | −0.536080 | − | 0.844167i | \(-0.680095\pi\) | ||||
−0.536080 | + | 0.844167i | \(0.680095\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.03875 | 1.00775 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.602944 | 0.111964 | 0.0559820 | − | 0.998432i | \(-0.482171\pi\) | ||||
0.0559820 | + | 0.998432i | \(0.482171\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.43840 | 0.797161 | 0.398580 | − | 0.917133i | \(-0.369503\pi\) | ||||
0.398580 | + | 0.917133i | \(0.369503\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.534912 | 0.0931163 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.731551 | −0.123655 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.52496 | 1.40149 | 0.700747 | − | 0.713410i | \(-0.252850\pi\) | ||||
0.700747 | + | 0.713410i | \(0.252850\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.40467 | −0.385056 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.40231 | 0.219004 | 0.109502 | − | 0.993987i | \(-0.465074\pi\) | ||||
0.109502 | + | 0.993987i | \(0.465074\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.66794 | 0.559356 | 0.279678 | − | 0.960094i | \(-0.409772\pi\) | ||||
0.279678 | + | 0.960094i | \(0.409772\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.16840 | −0.472317 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.4809 | −1.82052 | −0.910262 | − | 0.414032i | \(-0.864120\pi\) | ||||
−0.910262 | + | 0.414032i | \(0.864120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.94669 | −0.992384 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.83643 | −0.537208 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.85598 | 0.667020 | 0.333510 | − | 0.942747i | \(-0.391767\pi\) | ||||
0.333510 | + | 0.942747i | \(0.391767\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.69482 | 0.228529 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.74980 | −1.02649 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.66413 | −1.25816 | −0.629081 | − | 0.777339i | \(-0.716569\pi\) | ||||
−0.629081 | + | 0.777339i | \(0.716569\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.49131 | −0.190942 | −0.0954712 | − | 0.995432i | \(-0.530436\pi\) | ||||
−0.0954712 | + | 0.995432i | \(0.530436\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.230890 | 0.0290894 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.61896 | −0.945015 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0615 | −1.47355 | −0.736773 | − | 0.676140i | \(-0.763652\pi\) | ||||
−0.736773 | + | 0.676140i | \(0.763652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.14190 | 0.619012 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4038 | −1.35338 | −0.676691 | − | 0.736267i | \(-0.736587\pi\) | ||||
−0.676691 | + | 0.736267i | \(0.736587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.16407 | 0.487368 | 0.243684 | − | 0.969855i | \(-0.421644\pi\) | ||||
0.243684 | + | 0.969855i | \(0.421644\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.03875 | −0.581825 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.123506 | −0.0140748 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.52893 | 0.847071 | 0.423536 | − | 0.905879i | \(-0.360789\pi\) | ||||
0.423536 | + | 0.905879i | \(0.360789\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.44885 | −0.817617 | −0.408809 | − | 0.912620i | \(-0.634056\pi\) | ||||
−0.408809 | + | 0.912620i | \(0.634056\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.1553 | −1.31843 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.602944 | −0.0646424 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.40223 | 0.996635 | 0.498317 | − | 0.866995i | \(-0.333951\pi\) | ||||
0.498317 | + | 0.866995i | \(0.333951\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.555214 | 0.0582022 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.43840 | −0.460241 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.5544 | −2.51923 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2203 | 1.24078 | 0.620391 | − | 0.784293i | \(-0.286974\pi\) | ||||
0.620391 | + | 0.784293i | \(0.286974\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.534912 | −0.0537607 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.01977 | 0.300478 | 0.150239 | − | 0.988650i | \(-0.451996\pi\) | ||||
0.150239 | + | 0.988650i | \(0.451996\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2753 | −1.11099 | −0.555496 | − | 0.831519i | \(-0.687472\pi\) | ||||
−0.555496 | + | 0.831519i | \(0.687472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.731551 | 0.0713920 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 20.1981 | 1.95263 | 0.976314 | − | 0.216360i | \(-0.0694185\pi\) | ||||
0.976314 | + | 0.216360i | \(0.0694185\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.443113 | 0.0424425 | 0.0212212 | − | 0.999775i | \(-0.493245\pi\) | ||||
0.0212212 | + | 0.999775i | \(0.493245\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.52496 | −0.809153 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.4535 | 1.17152 | 0.585762 | − | 0.810483i | \(-0.300795\pi\) | ||||
0.585762 | + | 0.810483i | \(0.300795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.2916 | 1.51920 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.40467 | 0.222312 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.885792 | 0.0812004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7139 | −0.973988 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.40231 | −0.126442 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.122782 | −0.0109819 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.7466 | −1.84096 | −0.920480 | − | 0.390790i | \(-0.872202\pi\) | ||||
−0.920480 | + | 0.390790i | \(0.872202\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.66794 | −0.322944 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.73611 | 0.239055 | 0.119527 | − | 0.992831i | \(-0.461862\pi\) | ||||
0.119527 | + | 0.992831i | \(0.461862\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.78935 | 0.155156 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.16840 | 0.272692 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.01418 | 0.428391 | 0.214195 | − | 0.976791i | \(-0.431287\pi\) | ||||
0.214195 | + | 0.976791i | \(0.431287\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0795501 | 0.00674735 | 0.00337367 | − | 0.999994i | \(-0.498926\pi\) | ||||
0.00337367 | + | 0.999994i | \(0.498926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.4809 | 1.05108 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.28629 | −0.107565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.91037 | −0.158647 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.94669 | 0.572953 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.9835 | −1.22749 | −0.613746 | − | 0.789503i | \(-0.710338\pi\) | ||||
−0.613746 | + | 0.789503i | \(0.710338\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8126 | 1.36819 | 0.684097 | − | 0.729391i | \(-0.260197\pi\) | ||||
0.684097 | + | 0.729391i | \(0.260197\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.83643 | 0.310157 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.0626 | −1.12954 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.50629 | 0.678876 | 0.339438 | − | 0.940628i | \(-0.389763\pi\) | ||||
0.339438 | + | 0.940628i | \(0.389763\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.85598 | −0.385104 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.18721 | −0.0935653 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6607 | 1.22664 | 0.613320 | − | 0.789835i | \(-0.289834\pi\) | ||||
0.613320 | + | 0.789835i | \(0.289834\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.69482 | −0.131941 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.21756 | −0.555197 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.74980 | 0.592642 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.1435 | −1.30340 | −0.651700 | − | 0.758477i | \(-0.725944\pi\) | ||||
−0.651700 | + | 0.758477i | \(0.725944\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.16340 | 0.0879445 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.66413 | 0.726401 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.4251 | 1.97510 | 0.987551 | − | 0.157297i | \(-0.0502779\pi\) | ||||
0.987551 | + | 0.157297i | \(0.0502779\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.49842 | 0.260036 | 0.130018 | − | 0.991512i | \(-0.458497\pi\) | ||||
0.130018 | + | 0.991512i | \(0.458497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.49131 | 0.110241 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −27.0105 | −1.98585 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.05215 | −0.150068 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.230890 | −0.0167948 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6136 | 1.56390 | 0.781952 | − | 0.623339i | \(-0.214224\pi\) | ||||
0.781952 | + | 0.623339i | \(0.214224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.20183 | −0.590381 | −0.295190 | − | 0.955438i | \(-0.595383\pi\) | ||||
−0.295190 | + | 0.955438i | \(0.595383\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.61896 | 0.545605 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.73231 | 0.194669 | 0.0973345 | − | 0.995252i | \(-0.468968\pi\) | ||||
0.0973345 | + | 0.995252i | \(0.468968\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.5661 | −1.74144 | −0.870721 | − | 0.491778i | \(-0.836347\pi\) | ||||
−0.870721 | + | 0.491778i | \(0.836347\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0615 | 0.850753 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.139214 | 0.00977088 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.44308 | −0.310318 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.14190 | −0.357387 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.14546 | −0.286748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.0986 | 0.901748 | 0.450874 | − | 0.892588i | \(-0.351112\pi\) | ||||
0.450874 | + | 0.892588i | \(0.351112\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.4038 | 0.781376 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.6215 | −0.792580 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.02478 | 0.0695667 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.16407 | −0.281382 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.22535 | 0.620564 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.90957 | 0.261804 | 0.130902 | − | 0.991395i | \(-0.458213\pi\) | ||||
0.130902 | + | 0.991395i | \(0.458213\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.03875 | 0.335917 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.24862 | −0.414736 | −0.207368 | − | 0.978263i | \(-0.566490\pi\) | ||||
−0.207368 | + | 0.978263i | \(0.566490\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.5918 | 1.69116 | 0.845578 | − | 0.533851i | \(-0.179256\pi\) | ||||
0.845578 | + | 0.533851i | \(0.179256\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.123506 | 0.00812608 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.0269 | −0.853421 | −0.426711 | − | 0.904388i | \(-0.640328\pi\) | ||||
−0.426711 | + | 0.904388i | \(0.640328\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 39.5444 | 2.57959 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.52893 | −0.489057 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.54827 | −0.552942 | −0.276471 | − | 0.961022i | \(-0.589165\pi\) | ||||
−0.276471 | + | 0.961022i | \(0.589165\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.8836 | −1.08757 | −0.543783 | − | 0.839226i | \(-0.683008\pi\) | ||||
−0.543783 | + | 0.839226i | \(0.683008\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 22.0099 | 1.40616 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.6357 | 1.18576 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.44885 | 0.472051 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.92874 | 0.121741 | 0.0608704 | − | 0.998146i | \(-0.480612\pi\) | ||||
0.0608704 | + | 0.998146i | \(0.480612\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.75046 | 0.172920 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.1553 | 0.761197 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.9215 | 1.18029 | 0.590145 | − | 0.807297i | \(-0.299071\pi\) | ||||
0.590145 | + | 0.807297i | \(0.299071\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.96833 | 0.122306 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.602944 | 0.0373213 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.99207 | 0.554475 | 0.277237 | − | 0.960801i | \(-0.410581\pi\) | ||||
0.277237 | + | 0.960801i | \(0.410581\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.3857 | −0.945135 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.40223 | −0.575407 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.8434 | 0.722102 | 0.361051 | − | 0.932546i | \(-0.382418\pi\) | ||||
0.361051 | + | 0.932546i | \(0.382418\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.28934 | −0.199813 | −0.0999065 | − | 0.994997i | \(-0.531854\pi\) | ||||
−0.0999065 | + | 0.994997i | \(0.531854\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.555214 | −0.0336031 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.69529 | −0.162532 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.25296 | 0.495872 | 0.247936 | − | 0.968776i | \(-0.420248\pi\) | ||||
0.247936 | + | 0.968776i | \(0.420248\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.43840 | 0.265720 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.3602 | 0.916313 | 0.458156 | − | 0.888872i | \(-0.348510\pi\) | ||||
0.458156 | + | 0.888872i | \(0.348510\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.8821 | −0.706320 | −0.353160 | − | 0.935563i | \(-0.614893\pi\) | ||||
−0.353160 | + | 0.935563i | \(0.614893\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.5544 | 1.45448 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.323779 | 0.0191121 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.28181 | −0.134224 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2203 | −0.716366 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.7646 | −1.32992 | −0.664960 | − | 0.746879i | \(-0.731551\pi\) | ||||
−0.664960 | + | 0.746879i | \(0.731551\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.6198 | 1.78276 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.534912 | 0.0310388 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.3646 | −0.715062 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.846890 | 0.0488140 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.01977 | −0.173481 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.72506 | 0.270556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.2061 | 1.89517 | 0.947585 | − | 0.319503i | \(-0.103516\pi\) | ||||
0.947585 | + | 0.319503i | \(0.103516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.2753 | 0.641432 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.8693 | 0.673047 | 0.336523 | − | 0.941675i | \(-0.390749\pi\) | ||||
0.336523 | + | 0.941675i | \(0.390749\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.72134 | −0.492959 | −0.246480 | − | 0.969148i | \(-0.579274\pi\) | ||||
−0.246480 | + | 0.969148i | \(0.579274\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.731551 | −0.0412182 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.0893 | 1.18449 | 0.592246 | − | 0.805757i | \(-0.298241\pi\) | ||||
0.592246 | + | 0.805757i | \(0.298241\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.322522 | −0.0180578 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.1981 | −1.12735 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.7315 | 1.65431 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.1165 | 0.672105 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.443113 | −0.0245042 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.88171 | −0.158874 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9529 | 0.602026 | 0.301013 | − | 0.953620i | \(-0.402675\pi\) | ||||
0.301013 | + | 0.953620i | \(0.402675\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.52496 | 0.467165 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 38.2156 | 2.08794 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.1884 | −0.881839 | −0.440920 | − | 0.897547i | \(-0.645348\pi\) | ||||
−0.440920 | + | 0.897547i | \(0.645348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.4535 | −0.676379 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.37416 | −0.128568 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.22015 | −0.173872 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.2916 | −0.877109 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.29375 | −0.284183 | −0.142092 | − | 0.989854i | \(-0.545383\pi\) | ||||
−0.142092 | + | 0.989854i | \(0.545383\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.7932 | 1.80891 | 0.904453 | − | 0.426573i | \(-0.140279\pi\) | ||||
0.904453 | + | 0.426573i | \(0.140279\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.40467 | −0.128352 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1450 | 0.752864 | 0.376432 | − | 0.926444i | \(-0.377151\pi\) | ||||
0.376432 | + | 0.926444i | \(0.377151\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.1318 | 1.91768 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.885792 | −0.0468811 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.66904 | 0.510312 | 0.255156 | − | 0.966900i | \(-0.417873\pi\) | ||||
0.255156 | + | 0.966900i | \(0.417873\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.0593 | 2.16102 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.7139 | 0.562332 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.1934 | −0.690577 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1304 | −0.685399 | −0.342700 | − | 0.939445i | \(-0.611341\pi\) | ||||
−0.342700 | + | 0.939445i | \(0.611341\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.40231 | 0.0730014 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.12120 | 0.0582096 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.67027 | −0.190039 | −0.0950197 | − | 0.995475i | \(-0.530291\pi\) | ||||
−0.0950197 | + | 0.995475i | \(0.530291\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.122782 | 0.00634042 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.44988 | 0.0746727 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.9612 | −1.12807 | −0.564036 | − | 0.825750i | \(-0.690752\pi\) | ||||
−0.564036 | + | 0.825750i | \(0.690752\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.7466 | 1.06288 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.5332 | −0.691515 | −0.345757 | − | 0.938324i | \(-0.612378\pi\) | ||||
−0.345757 | + | 0.938324i | \(0.612378\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.391315 | 0.0199433 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.66794 | 0.186452 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.09521 | −0.258337 | −0.129169 | − | 0.991623i | \(-0.541231\pi\) | ||||
−0.129169 | + | 0.991623i | \(0.541231\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.7265 | −0.997613 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.73611 | −0.138018 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.8547 | −1.20026 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.9338 | 0.548751 | 0.274376 | − | 0.961623i | \(-0.411529\pi\) | ||||
0.274376 | + | 0.961623i | \(0.411529\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.78935 | −0.0895795 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.6204 | 0.580296 | 0.290148 | − | 0.956982i | \(-0.406295\pi\) | ||||
0.290148 | + | 0.956982i | \(0.406295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.6729 | 0.531655 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.16840 | −0.157439 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.56011 | −0.226036 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.7043 | 1.22155 | 0.610774 | − | 0.791805i | \(-0.290858\pi\) | ||||
0.610774 | + | 0.791805i | \(0.290858\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.01418 | −0.247331 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.23135 | −0.109797 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.6009 | 1.15852 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0795501 | −0.00389558 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.9832 | 0.878535 | 0.439267 | − | 0.898356i | \(-0.355238\pi\) | ||||
0.439267 | + | 0.898356i | \(0.355238\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.8040 | −1.01393 | −0.506963 | − | 0.861968i | \(-0.669232\pi\) | ||||
−0.506963 | + | 0.861968i | \(0.669232\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.4809 | −0.606841 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.3308 | 0.937682 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.344328 | −0.0166632 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.28629 | 0.0621026 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.8156 | −1.62884 | −0.814419 | − | 0.580277i | \(-0.802944\pi\) | ||||
−0.814419 | + | 0.580277i | \(0.802944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3923 | 0.931936 | 0.465968 | − | 0.884802i | \(-0.345706\pi\) | ||||
0.465968 | + | 0.884802i | \(0.345706\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.91037 | 0.0915951 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −39.8486 | −1.90622 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.3827 | 1.16372 | 0.581861 | − | 0.813288i | \(-0.302325\pi\) | ||||
0.581861 | + | 0.813288i | \(0.302325\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.94669 | −0.330795 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.26405 | −0.155080 | −0.0775399 | − | 0.996989i | \(-0.524707\pi\) | ||||
−0.0775399 | + | 0.996989i | \(0.524707\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.7900 | −1.41218 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.9835 | 0.708693 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.62351 | 0.359775 | 0.179888 | − | 0.983687i | \(-0.442427\pi\) | ||||
0.179888 | + | 0.983687i | \(0.442427\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.750113 | −0.0353215 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.8126 | −0.789927 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.75914 | −0.0824697 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.3938 | −0.953980 | −0.476990 | − | 0.878909i | \(-0.658272\pi\) | ||||
−0.476990 | + | 0.878909i | \(0.658272\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.83643 | −0.179069 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.34942 | −0.202573 | −0.101286 | − | 0.994857i | \(-0.532296\pi\) | ||||
−0.101286 | + | 0.994857i | \(0.532296\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.5171 | 1.60415 | 0.802074 | − | 0.597225i | \(-0.203730\pi\) | ||||
0.802074 | + | 0.597225i | \(0.203730\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.0626 | 0.652139 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.4037 | −1.08300 | −0.541498 | − | 0.840702i | \(-0.682142\pi\) | ||||
−0.541498 | + | 0.840702i | \(0.682142\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.78488 | −0.128594 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.50629 | −0.391949 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.96203 | −0.0902141 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 39.0493 | 1.79170 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.85598 | 0.222340 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.86695 | −0.222377 | −0.111188 | − | 0.993799i | \(-0.535466\pi\) | ||||
−0.111188 | + | 0.993799i | \(0.535466\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.4997 | 0.934707 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.18721 | 0.0540200 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −38.7187 | −1.75813 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.2862 | −0.964570 | −0.482285 | − | 0.876014i | \(-0.660193\pi\) | ||||
−0.482285 | + | 0.876014i | \(0.660193\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.6607 | −0.708201 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.1615 | 1.22578 | 0.612891 | − | 0.790168i | \(-0.290007\pi\) | ||||
0.612891 | + | 0.790168i | \(0.290007\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.31315 | 0.104179 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.69482 | 0.0761763 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.63302 | −0.118107 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.7335 | 1.33105 | 0.665526 | − | 0.746375i | \(-0.268207\pi\) | ||||
0.665526 | + | 0.746375i | \(0.268207\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.1206 | −1.12007 | −0.560037 | − | 0.828467i | \(-0.689213\pi\) | ||||
−0.560037 | + | 0.828467i | \(0.689213\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.56783 | −0.425763 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.21756 | 0.320543 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.98009 | −0.442360 | −0.221180 | − | 0.975233i | \(-0.570991\pi\) | ||||
−0.221180 | + | 0.975233i | \(0.570991\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.961442 | 0.0425317 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.74980 | −0.342162 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35.7248 | 1.57422 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.67618 | 0.293618 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.1435 | 0.752518 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.5986 | −1.60341 | −0.801707 | − | 0.597717i | \(-0.796075\pi\) | ||||
−0.801707 | + | 0.597717i | \(0.796075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.5958 | 0.856865 | 0.428433 | − | 0.903574i | \(-0.359066\pi\) | ||||
0.428433 | + | 0.903574i | \(0.359066\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.16340 | −0.0507748 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.0276 | 0.741735 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.43910 | 0.149526 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.66413 | −0.419388 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.37210 | 0.146062 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −63.9957 | −2.76678 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.4251 | −1.14033 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.71587 | 0.160054 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.4214 | 1.73785 | 0.868927 | − | 0.494941i | \(-0.164810\pi\) | ||||
0.868927 | + | 0.494941i | \(0.164810\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.49842 | −0.150132 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.40396 | −0.0601389 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.7069 | 1.27018 | 0.635088 | − | 0.772440i | \(-0.280964\pi\) | ||||
0.635088 | + | 0.772440i | \(0.280964\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.49131 | −0.0636475 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.67269 | 0.199063 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.73835 | 0.0739223 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.0105 | 1.14653 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.9127 | 1.77590 | 0.887950 | − | 0.459940i | \(-0.152129\pi\) | ||||
0.887950 | + | 0.459940i | \(0.152129\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.82020 | 0.373055 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.05215 | 0.0866420 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.6677 | 1.08176 | 0.540882 | − | 0.841099i | \(-0.318091\pi\) | ||||
0.540882 | + | 0.841099i | \(0.318091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.4575 | −1.65999 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.230890 | 0.00969646 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.1215 | 0.843538 | 0.421769 | − | 0.906703i | \(-0.361409\pi\) | ||||
0.421769 | + | 0.906703i | \(0.361409\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.50467 | 0.104817 | 0.0524085 | − | 0.998626i | \(-0.483310\pi\) | ||||
0.0524085 | + | 0.998626i | \(0.483310\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.6136 | −0.902920 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.9087 | −1.08047 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.39885 | 0.349649 | 0.174824 | − | 0.984600i | \(-0.444064\pi\) | ||||
0.174824 | + | 0.984600i | \(0.444064\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.20183 | 0.340857 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.71986 | −0.0713519 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.59752 | −0.107578 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.61896 | −0.315005 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.75584 | 0.237569 | 0.118784 | − | 0.992920i | \(-0.462100\pi\) | ||||
0.118784 | + | 0.992920i | \(0.462100\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.3967 | 1.41729 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.73231 | −0.112392 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.97459 | −0.0810867 | −0.0405434 | − | 0.999178i | \(-0.512909\pi\) | ||||
−0.0405434 | + | 0.999178i | \(0.512909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.80654 | −0.115057 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.5661 | 1.00542 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.4063 | −0.629486 | −0.314743 | − | 0.949177i | \(-0.601918\pi\) | ||||
−0.314743 | + | 0.949177i | \(0.601918\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.5939 | −1.49269 | −0.746347 | − | 0.665557i | \(-0.768194\pi\) | ||||
−0.746347 | + | 0.665557i | \(0.768194\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.0615 | −0.491182 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.9458 | 1.38009 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.4777 | 0.709398 | 0.354699 | − | 0.934981i | \(-0.384583\pi\) | ||||
0.354699 | + | 0.934981i | \(0.384583\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.139214 | −0.00564122 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.0124 | −1.21417 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.2259 | −1.09964 | −0.549821 | − | 0.835282i | \(-0.685304\pi\) | ||||
−0.549821 | + | 0.835282i | \(0.685304\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.44308 | 0.179162 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0487 | −0.887648 | −0.443824 | − | 0.896114i | \(-0.646378\pi\) | ||||
−0.443824 | + | 0.896114i | \(0.646378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.9615 | 0.842513 | 0.421257 | − | 0.906942i | \(-0.361589\pi\) | ||||
0.421257 | + | 0.906942i | \(0.361589\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.14190 | 0.206337 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.17088 | 0.0869744 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.8047 | −0.992190 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.14546 | 0.165554 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.7054 | 1.30405 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.8805 | 0.950668 | 0.475334 | − | 0.879805i | \(-0.342327\pi\) | ||||
0.475334 | + | 0.879805i | \(0.342327\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.0986 | −0.520624 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 65.7334 | 2.60855 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.7045 | −0.661857 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.4038 | −0.451128 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.17791 | 0.204515 | 0.102258 | − | 0.994758i | \(-0.467393\pi\) | ||||
0.102258 | + | 0.994758i | \(0.467393\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0105 | −0.868010 | −0.434005 | − | 0.900911i | \(-0.642900\pi\) | ||||
−0.434005 | + | 0.900911i | \(0.642900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.6215 | 0.457596 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.73591 | 0.304130 | 0.152065 | − | 0.988370i | \(-0.451408\pi\) | ||||
0.152065 | + | 0.988370i | \(0.451408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.16946 | 0.202919 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.02478 | −0.0401644 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.5886 | 0.570896 | 0.285448 | − | 0.958394i | \(-0.407858\pi\) | ||||
0.285448 | + | 0.958394i | \(0.407858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.66908 | −0.338729 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.16407 | 0.162456 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.8462 | 0.812053 | 0.406027 | − | 0.913861i | \(-0.366914\pi\) | ||||
0.406027 | + | 0.913861i | \(0.366914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8177 | −0.848609 | −0.424305 | − | 0.905519i | \(-0.639481\pi\) | ||||
−0.424305 | + | 0.905519i | \(0.639481\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.22535 | −0.358283 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.66937 | −0.219849 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.10028 | −0.120043 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.90957 | −0.151153 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.797719 | 0.0307956 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.9795 | 0.847247 | 0.423623 | − | 0.905838i | \(-0.360758\pi\) | ||||
0.423623 | + | 0.905838i | \(0.360758\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.03875 | −0.193942 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.8610 | −1.22452 | −0.612260 | − | 0.790657i | \(-0.709739\pi\) | ||||
−0.612260 | + | 0.790657i | \(0.709739\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.82154 | 0.108281 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.24862 | 0.239448 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.1729 | −1.11627 | −0.558134 | − | 0.829751i | \(-0.688483\pi\) | ||||
−0.558134 | + | 0.829751i | \(0.688483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.8869 | −0.607009 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.5918 | −0.976390 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.6770 | 0.444859 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.35450 | 0.127611 | 0.0638056 | − | 0.997962i | \(-0.479676\pi\) | ||||
0.0638056 | + | 0.997962i | \(0.479676\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.123506 | −0.00469160 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.252046 | −0.00956066 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.37987 | 0.203777 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.0269 | 0.492723 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.7230 | 1.38701 | 0.693504 | − | 0.720453i | \(-0.256066\pi\) | ||||
0.693504 | + | 0.720453i | \(0.256066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 66.0667 | 2.49175 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −39.5444 | −1.48933 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.697234 | 0.0262222 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.3615 | −0.389136 | −0.194568 | − | 0.980889i | \(-0.562330\pi\) | ||||
−0.194568 | + | 0.980889i | \(0.562330\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.52893 | 0.282357 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.8218 | −0.854684 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.07547 | 0.152414 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.54827 | 0.319241 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.4718 | −0.726175 | −0.363088 | − | 0.931755i | \(-0.618277\pi\) | ||||
−0.363088 | + | 0.931755i | \(0.618277\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.60336 | −0.0969542 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.8836 | 0.627906 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.03809 | 0.112832 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.9158 | 1.48040 | 0.740198 | − | 0.672389i | \(-0.234732\pi\) | ||||
0.740198 | + | 0.672389i | \(0.234732\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.0718 | 0.520464 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.3551 | 1.89684 | 0.948422 | − | 0.317009i | \(-0.102679\pi\) | ||||
0.948422 | + | 0.317009i | \(0.102679\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −22.0099 | −0.811847 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.45184 | 0.237657 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.93272 | −0.291810 | −0.145905 | − | 0.989299i | \(-0.546609\pi\) | ||||
−0.145905 | + | 0.989299i | \(0.546609\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.6357 | −0.684600 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.2211 | 1.14539 | 0.572695 | − | 0.819769i | \(-0.305898\pi\) | ||||
0.572695 | + | 0.819769i | \(0.305898\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 47.4736 | 1.73930 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.44885 | −0.272539 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.66354 | 0.170402 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5552 | 0.567619 | 0.283810 | − | 0.958881i | \(-0.408402\pi\) | ||||
0.283810 | + | 0.958881i | \(0.408402\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.92874 | −0.0702871 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −53.2692 | −1.93866 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.1429 | 0.441340 | 0.220670 | − | 0.975348i | \(-0.429176\pi\) | ||||
0.220670 | + | 0.975348i | \(0.429176\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.75046 | −0.0998355 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 50.6261 | 1.83519 | 0.917597 | − | 0.397513i | \(-0.130127\pi\) | ||||
0.917597 | + | 0.397513i | \(0.130127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.102310 | 0.00370388 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.1553 | −0.439477 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.2391 | −0.839114 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.38129 | 0.0858716 | 0.0429358 | − | 0.999078i | \(-0.486329\pi\) | ||||
0.0429358 | + | 0.999078i | \(0.486329\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.9215 | −0.681441 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.0022 | 1.54668 | 0.773340 | − | 0.633991i | \(-0.218584\pi\) | ||||
0.773340 | + | 0.633991i | \(0.218584\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.3640 | 0.803339 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.96833 | −0.0706133 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.8676 | 0.389373 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.10003 | 0.218276 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.602944 | −0.0215475 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.9513 | −0.961934 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.51599 | −0.160978 | −0.0804889 | − | 0.996756i | \(-0.525648\pi\) | ||||
−0.0804889 | + | 0.996756i | \(0.525648\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.99207 | −0.320126 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.87538 | 0.102237 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.58611 | −0.127346 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.3857 | 0.545674 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.2925 | −1.32097 | −0.660484 | − | 0.750840i | \(-0.729649\pi\) | ||||
−0.660484 | + | 0.750840i | \(0.729649\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.8820 | −1.69394 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.40223 | 0.332212 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.22741 | −0.0786038 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.76156 | 0.132578 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.8434 | −0.416906 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.4322 | 0.401935 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.1204 | 1.02256 | 0.511278 | − | 0.859415i | \(-0.329172\pi\) | ||||
0.511278 | + | 0.859415i | \(0.329172\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.28934 | 0.115362 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −49.6193 | −1.73809 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.4258 | 0.994493 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.555214 | 0.0194007 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.3833 | −0.850982 | −0.425491 | − | 0.904963i | \(-0.639899\pi\) | ||||
−0.425491 | + | 0.904963i | \(0.639899\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.2495 | −1.15901 | −0.579503 | − | 0.814970i | \(-0.696753\pi\) | ||||
−0.579503 | + | 0.814970i | \(0.696753\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.69529 | 0.0938380 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.7980 | −0.862312 | −0.431156 | − | 0.902277i | \(-0.641894\pi\) | ||||
−0.431156 | + | 0.902277i | \(0.641894\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.0759189 | 0.00263677 | 0.00131839 | − | 0.999999i | \(-0.499580\pi\) | ||||
0.00131839 | + | 0.999999i | \(0.499580\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.25296 | −0.286292 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.6505 | −0.923384 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.16840 | 0.109647 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.43840 | −0.153414 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.3774 | 1.25589 | 0.627944 | − | 0.778259i | \(-0.283897\pi\) | ||||
0.627944 | + | 0.778259i | \(0.283897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6365 | −0.987464 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.3602 | −0.529033 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.8681 | 0.786687 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.47372 | −0.0849981 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.8821 | 0.407794 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.8345 | −1.50263 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.0407 | −0.994334 | −0.497167 | − | 0.867655i | \(-0.665626\pi\) | ||||
−0.497167 | + | 0.867655i | \(0.665626\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.5544 | −0.839744 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.1252 | 1.40481 | 0.702406 | − | 0.711777i | \(-0.252109\pi\) | ||||
0.702406 | + | 0.711777i | \(0.252109\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.21249 | −0.280206 | −0.140103 | − | 0.990137i | \(-0.544743\pi\) | ||||
−0.140103 | + | 0.990137i | \(0.544743\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.323779 | −0.0110344 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.51360 | −0.323847 | −0.161923 | − | 0.986803i | \(-0.551770\pi\) | ||||
−0.161923 | + | 0.986803i | \(0.551770\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.3176 | 1.84685 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.28181 | 0.0774944 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.02732 | −0.136617 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.0039 | −0.982761 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.2203 | 0.413594 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.0283490 | −0.000958372 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.4443 | −0.521517 | −0.260758 | − | 0.965404i | \(-0.583973\pi\) | ||||
−0.260758 | + | 0.965404i | \(0.583973\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.7646 | 0.767830 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.94074 | 0.301221 | 0.150611 | − | 0.988593i | \(-0.451876\pi\) | ||||
0.150611 | + | 0.988593i | \(0.451876\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.6275 | −1.09800 | −0.549001 | − | 0.835822i | \(-0.684992\pi\) | ||||
−0.549001 | + | 0.835822i | \(0.684992\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −30.6198 | −1.02927 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.4740 | 1.52687 | 0.763434 | − | 0.645886i | \(-0.223512\pi\) | ||||
0.763434 | + | 0.645886i | \(0.223512\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.79017 | −0.160657 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.534912 | −0.0179202 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −96.7243 | −3.23676 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −83.7252 | −2.79862 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.3646 | 0.412841 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.67611 | 0.0892533 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.6296 | 0.620642 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.846890 | −0.0281827 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.0844 | −0.368458 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.4979 | −0.713826 | −0.356913 | − | 0.934138i | \(-0.616171\pi\) | ||||
−0.356913 | + | 0.934138i | \(0.616171\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.01977 | 0.100159 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.8385 | −1.48556 | −0.742782 | − | 0.669533i | \(-0.766494\pi\) | ||||
−0.742782 | + | 0.669533i | \(0.766494\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.98448 | 0.131867 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.72506 | −0.156206 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.631739 | 0.0208619 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.0171 | −1.51796 | −0.758982 | − | 0.651112i | \(-0.774303\pi\) | ||||
−0.758982 | + | 0.651112i | \(0.774303\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.2061 | −1.09418 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.4224 | −0.902619 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.9552 | 1.41236 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.2753 | −0.370331 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.8004 | 0.387159 | 0.193580 | − | 0.981085i | \(-0.437990\pi\) | ||||
0.193580 | + | 0.981085i | \(0.437990\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −53.8354 | −1.76438 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.8693 | −0.388584 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.50204 | 0.212639 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.2945 | 1.38170 | 0.690850 | − | 0.722998i | \(-0.257237\pi\) | ||||
0.690850 | + | 0.722998i | \(0.257237\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.72134 | 0.284610 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.50734 | 0.212133 | 0.106067 | − | 0.994359i | \(-0.466174\pi\) | ||||
0.106067 | + | 0.994359i | \(0.466174\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.21054 | −0.234807 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.731551 | 0.0237973 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.52120 | 0.0819278 | 0.0409639 | − | 0.999161i | \(-0.486957\pi\) | ||||
0.0409639 | + | 0.999161i | \(0.486957\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0132 | 0.325043 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.0893 | −0.683867 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.7358 | 0.768879 | 0.384439 | − | 0.923150i | \(-0.374395\pi\) | ||||
0.384439 | + | 0.923150i | \(0.374395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −68.4804 | −2.21597 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.322522 | 0.0104257 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.15772 | 0.0373848 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3006 | −0.364534 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.1981 | 0.650876 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.9867 | 0.836541 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.9742 | −0.417223 | −0.208612 | − | 0.977999i | \(-0.566894\pi\) | ||||
−0.208612 | + | 0.977999i | \(0.566894\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.7315 | −0.955115 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.0031 | 1.21958 | 0.609789 | − | 0.792564i | \(-0.291254\pi\) | ||||
0.609789 | + | 0.792564i | \(0.291254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0183673 | 0.000588828 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.1165 | −0.388040 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.3943 | 1.03639 | 0.518193 | − | 0.855264i | \(-0.326605\pi\) | ||||
0.518193 | + | 0.855264i | \(0.326605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.02937 | −0.160739 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.443113 | 0.0141475 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.9912 | 0.446249 | 0.223124 | − | 0.974790i | \(-0.428374\pi\) | ||||
0.223124 | + | 0.974790i | \(0.428374\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.65705 | −0.275836 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.88171 | 0.0917258 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.8602 | −0.599719 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.34209 | 0.201463 | 0.100732 | − | 0.994914i | \(-0.467882\pi\) | ||||
0.100732 | + | 0.994914i | \(0.467882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.9529 | −0.347580 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 77.8351 | 2.46754 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.1554 | 1.24006 | 0.620032 | − | 0.784576i | \(-0.287119\pi\) | ||||
0.620032 | + | 0.784576i | \(0.287119\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.52496 | −0.269718 |
(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 | 8016.2.a.bb.1.1 | 9 | ||
4.3 | odd | 2 | 2004.2.a.d.1.1 | ✓ | 9 | ||
12.11 | even | 2 | 6012.2.a.h.1.9 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.d.1.1 | ✓ | 9 | 4.3 | odd | 2 | ||
6012.2.a.h.1.9 | 9 | 12.11 | even | 2 | |||
8016.2.a.bb.1.1 | 9 | 1.1 | even | 1 | trivial |