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: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.284897.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 5x^{2} + 10x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.759623\) 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 | ||||||||
\(5\) | −0.473647 | −0.211821 | −0.105911 | − | 0.994376i | \(-0.533776\pi\) | ||||
−0.105911 | + | 0.994376i | \(0.533776\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.663349 | −0.250722 | −0.125361 | − | 0.992111i | \(-0.540009\pi\) | ||||
−0.125361 | + | 0.992111i | \(0.540009\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46722 | −1.04541 | −0.522704 | − | 0.852514i | \(-0.675077\pi\) | ||||
−0.522704 | + | 0.852514i | \(0.675077\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.43008 | −0.673983 | −0.336991 | − | 0.941508i | \(-0.609409\pi\) | ||||
−0.336991 | + | 0.941508i | \(0.609409\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.473647 | 0.122295 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.99358 | −1.45366 | −0.726828 | − | 0.686819i | \(-0.759006\pi\) | ||||
−0.726828 | + | 0.686819i | \(0.759006\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.40051 | 0.550716 | 0.275358 | − | 0.961342i | \(-0.411204\pi\) | ||||
0.275358 | + | 0.961342i | \(0.411204\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.663349 | 0.144755 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.17617 | 1.70485 | 0.852425 | − | 0.522850i | \(-0.175131\pi\) | ||||
0.852425 | + | 0.522850i | \(0.175131\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.77566 | −0.955132 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.87701 | 0.719942 | 0.359971 | − | 0.932963i | \(-0.382787\pi\) | ||||
0.359971 | + | 0.932963i | \(0.382787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.70895 | 0.486542 | 0.243271 | − | 0.969958i | \(-0.421780\pi\) | ||||
0.243271 | + | 0.969958i | \(0.421780\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.46722 | 0.603566 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.314193 | 0.0531083 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.48041 | 1.39417 | 0.697086 | − | 0.716988i | \(-0.254480\pi\) | ||||
0.697086 | + | 0.716988i | \(0.254480\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.43008 | 0.389124 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.71876 | 0.580772 | 0.290386 | − | 0.956910i | \(-0.406216\pi\) | ||||
0.290386 | + | 0.956910i | \(0.406216\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5079 | 1.60245 | 0.801223 | − | 0.598365i | \(-0.204183\pi\) | ||||
0.801223 | + | 0.598365i | \(0.204183\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.473647 | −0.0706071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9069 | 1.59094 | 0.795469 | − | 0.605995i | \(-0.207225\pi\) | ||||
0.795469 | + | 0.605995i | \(0.207225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.55997 | −0.937138 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.99358 | 0.839269 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.259988 | 0.0357121 | 0.0178561 | − | 0.999841i | \(-0.494316\pi\) | ||||
0.0178561 | + | 0.999841i | \(0.494316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.64224 | 0.221439 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.40051 | −0.317956 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.16237 | 0.151327 | 0.0756636 | − | 0.997133i | \(-0.475892\pi\) | ||||
0.0756636 | + | 0.997133i | \(0.475892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.55815 | −0.199500 | −0.0997501 | − | 0.995013i | \(-0.531804\pi\) | ||||
−0.0997501 | + | 0.995013i | \(0.531804\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.663349 | −0.0835741 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.15100 | 0.142764 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.52364 | 0.186142 | 0.0930709 | − | 0.995659i | \(-0.470332\pi\) | ||||
0.0930709 | + | 0.995659i | \(0.470332\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.17617 | −0.984296 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.46519 | 0.529921 | 0.264960 | − | 0.964259i | \(-0.414641\pi\) | ||||
0.264960 | + | 0.964259i | \(0.414641\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.44051 | −0.870845 | −0.435423 | − | 0.900226i | \(-0.643401\pi\) | ||||
−0.435423 | + | 0.900226i | \(0.643401\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.77566 | 0.551446 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.29998 | 0.262107 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.68765 | −0.977437 | −0.488718 | − | 0.872442i | \(-0.662535\pi\) | ||||
−0.488718 | + | 0.872442i | \(0.662535\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.7936 | −1.73357 | −0.866785 | − | 0.498681i | \(-0.833818\pi\) | ||||
−0.866785 | + | 0.498681i | \(0.833818\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.83884 | 0.307915 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.87701 | −0.415659 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.88769 | −0.624094 | −0.312047 | − | 0.950067i | \(-0.601015\pi\) | ||||
−0.312047 | + | 0.950067i | \(0.601015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.61199 | 0.168983 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.70895 | −0.280905 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.13700 | −0.116653 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9569 | −1.31557 | −0.657787 | − | 0.753204i | \(-0.728507\pi\) | ||||
−0.657787 | + | 0.753204i | \(0.728507\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.46722 | −0.348469 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.71030 | −0.369188 | −0.184594 | − | 0.982815i | \(-0.559097\pi\) | ||||
−0.184594 | + | 0.982815i | \(0.559097\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.3630 | −1.41523 | −0.707616 | − | 0.706598i | \(-0.750229\pi\) | ||||
−0.707616 | + | 0.706598i | \(0.750229\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.314193 | −0.0306621 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.312825 | 0.0302419 | 0.0151210 | − | 0.999886i | \(-0.495187\pi\) | ||||
0.0151210 | + | 0.999886i | \(0.495187\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.69339 | 0.928458 | 0.464229 | − | 0.885715i | \(-0.346331\pi\) | ||||
0.464229 | + | 0.885715i | \(0.346331\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.48041 | −0.804925 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.03077 | 0.661399 | 0.330700 | − | 0.943736i | \(-0.392715\pi\) | ||||
0.330700 | + | 0.943736i | \(0.392715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.87262 | −0.361123 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.43008 | −0.224661 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.97583 | 0.364464 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.02164 | 0.0928767 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.71876 | −0.335309 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.63021 | 0.414138 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.30843 | −0.293576 | −0.146788 | − | 0.989168i | \(-0.546894\pi\) | ||||
−0.146788 | + | 0.989168i | \(0.546894\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.5079 | −0.925173 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.96333 | −0.783130 | −0.391565 | − | 0.920151i | \(-0.628066\pi\) | ||||
−0.391565 | + | 0.920151i | \(0.628066\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.59238 | −0.138077 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.473647 | 0.0407650 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.77363 | −0.322403 | −0.161201 | − | 0.986922i | \(-0.551537\pi\) | ||||
−0.161201 | + | 0.986922i | \(0.551537\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.16082 | 0.268097 | 0.134049 | − | 0.990975i | \(-0.457202\pi\) | ||||
0.134049 | + | 0.990975i | \(0.457202\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.9069 | −0.918528 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.42563 | 0.704586 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.83633 | −0.152499 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.55997 | 0.541057 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.2900 | 1.41645 | 0.708227 | − | 0.705985i | \(-0.249495\pi\) | ||||
0.708227 | + | 0.705985i | \(0.249495\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.79304 | 0.471431 | 0.235716 | − | 0.971822i | \(-0.424257\pi\) | ||||
0.235716 | + | 0.971822i | \(0.424257\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.99358 | −0.484552 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.28308 | −0.103060 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.9447 | −1.59176 | −0.795881 | − | 0.605453i | \(-0.792992\pi\) | ||||
−0.795881 | + | 0.605453i | \(0.792992\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.259988 | −0.0206184 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.42366 | −0.427444 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2632 | 0.803874 | 0.401937 | − | 0.915667i | \(-0.368337\pi\) | ||||
0.401937 | + | 0.915667i | \(0.368337\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.64224 | −0.127848 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.09472 | −0.545747 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.40051 | 0.183572 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.66098 | −0.734510 | −0.367255 | − | 0.930120i | \(-0.619702\pi\) | ||||
−0.367255 | + | 0.930120i | \(0.619702\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.16793 | 0.239473 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.16237 | −0.0873688 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.0225 | 1.57130 | 0.785649 | − | 0.618672i | \(-0.212329\pi\) | ||||
0.785649 | + | 0.618672i | \(0.212329\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8532 | −0.806711 | −0.403355 | − | 0.915043i | \(-0.632156\pi\) | ||||
−0.403355 | + | 0.915043i | \(0.632156\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.55815 | 0.115181 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.01672 | −0.295315 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.7811 | 1.51966 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.663349 | 0.0482515 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8612 | −0.930601 | −0.465301 | − | 0.885153i | \(-0.654054\pi\) | ||||
−0.465301 | + | 0.885153i | \(0.654054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.46080 | −0.537040 | −0.268520 | − | 0.963274i | \(-0.586535\pi\) | ||||
−0.268520 | + | 0.963274i | \(0.586535\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.15100 | −0.0824247 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.45809 | −0.175131 | −0.0875657 | − | 0.996159i | \(-0.527909\pi\) | ||||
−0.0875657 | + | 0.996159i | \(0.527909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.6699 | −1.32348 | −0.661738 | − | 0.749735i | \(-0.730181\pi\) | ||||
−0.661738 | + | 0.749735i | \(0.730181\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.52364 | −0.107469 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.57181 | −0.180506 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.76138 | −0.123020 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.17617 | 0.568283 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.32312 | −0.575722 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.26671 | −0.293732 | −0.146866 | − | 0.989156i | \(-0.546919\pi\) | ||||
−0.146866 | + | 0.989156i | \(0.546919\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.46519 | −0.305950 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.97705 | −0.339432 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.79698 | −0.121987 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.44051 | 0.502783 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.5649 | 0.979739 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.9512 | 1.33603 | 0.668015 | − | 0.744148i | \(-0.267144\pi\) | ||||
0.668015 | + | 0.744148i | \(0.267144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.77566 | −0.318377 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.5716 | 1.49813 | 0.749065 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749065 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.25689 | −0.611712 | −0.305856 | − | 0.952078i | \(-0.598943\pi\) | ||||
−0.305856 | + | 0.952078i | \(0.598943\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.29998 | −0.151328 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.24492 | 0.0815571 | 0.0407786 | − | 0.999168i | \(-0.487016\pi\) | ||||
0.0407786 | + | 0.999168i | \(0.487016\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.16602 | −0.336994 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.68765 | 0.564323 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.50808 | −0.420972 | −0.210486 | − | 0.977597i | \(-0.567505\pi\) | ||||
−0.210486 | + | 0.977597i | \(0.567505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.9256 | 0.897026 | 0.448513 | − | 0.893776i | \(-0.351954\pi\) | ||||
0.448513 | + | 0.893776i | \(0.351954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.10711 | 0.198506 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.83344 | −0.371173 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.7936 | 1.00088 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3433 | −1.09470 | −0.547349 | − | 0.836905i | \(-0.684363\pi\) | ||||
−0.547349 | + | 0.836905i | \(0.684363\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.3486 | −1.78226 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.83884 | −0.177775 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.261552 | −0.0163152 | −0.00815759 | − | 0.999967i | \(-0.502597\pi\) | ||||
−0.00815759 | + | 0.999967i | \(0.502597\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.62547 | −0.349550 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.87701 | 0.239981 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.1235 | −1.54918 | −0.774590 | − | 0.632464i | \(-0.782044\pi\) | ||||
−0.774590 | + | 0.632464i | \(0.782044\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.123143 | −0.00756459 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.88769 | 0.360321 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.26812 | −0.504116 | −0.252058 | − | 0.967712i | \(-0.581107\pi\) | ||||
−0.252058 | + | 0.967712i | \(0.581107\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.04656 | −0.549540 | −0.274770 | − | 0.961510i | \(-0.588602\pi\) | ||||
−0.274770 | + | 0.961510i | \(0.588602\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.61199 | −0.0975621 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.5583 | 0.998502 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.4147 | −1.52702 | −0.763511 | − | 0.645795i | \(-0.776526\pi\) | ||||
−0.763511 | + | 0.645795i | \(0.776526\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.70895 | 0.162181 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.13820 | −0.306519 | −0.153260 | − | 0.988186i | \(-0.548977\pi\) | ||||
−0.153260 | + | 0.988186i | \(0.548977\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.5596 | −0.806036 | −0.403018 | − | 0.915192i | \(-0.632039\pi\) | ||||
−0.403018 | + | 0.915192i | \(0.632039\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.13700 | 0.0673498 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.46683 | −0.145613 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.9230 | 1.11312 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.9569 | 0.759547 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.0838 | 1.23173 | 0.615864 | − | 0.787853i | \(-0.288807\pi\) | ||||
0.615864 | + | 0.787853i | \(0.288807\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.550551 | −0.0320543 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.46722 | 0.201189 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.8687 | −1.14904 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.97044 | −0.401769 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.71030 | 0.213151 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.738011 | 0.0422584 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.4875 | 1.68294 | 0.841471 | − | 0.540302i | \(-0.181690\pi\) | ||||
0.841471 | + | 0.540302i | \(0.181690\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.3630 | 0.817084 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.2057 | −1.08905 | −0.544527 | − | 0.838743i | \(-0.683291\pi\) | ||||
−0.544527 | + | 0.838743i | \(0.683291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.13192 | −0.403120 | −0.201560 | − | 0.979476i | \(-0.564601\pi\) | ||||
−0.201560 | + | 0.979476i | \(0.564601\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.314193 | 0.0177028 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.54451 | 0.423742 | 0.211871 | − | 0.977298i | \(-0.432044\pi\) | ||||
0.211871 | + | 0.977298i | \(0.432044\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.4425 | −0.752633 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.312825 | −0.0174602 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.3877 | −0.800551 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.6052 | 0.643742 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.69339 | −0.536046 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.23509 | −0.398884 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5151 | 1.18258 | 0.591289 | − | 0.806459i | \(-0.298619\pi\) | ||||
0.591289 | + | 0.806459i | \(0.298619\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.48041 | 0.464724 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.721666 | −0.0394288 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0750 | −1.80171 | −0.900856 | − | 0.434118i | \(-0.857060\pi\) | ||||
−0.900856 | + | 0.434118i | \(0.857060\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.03077 | −0.381859 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.39253 | −0.508634 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.99499 | 0.485684 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.87262 | 0.208495 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.38501 | 0.235400 | 0.117700 | − | 0.993049i | \(-0.462448\pi\) | ||||
0.117700 | + | 0.993049i | \(0.462448\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.5821 | −1.52996 | −0.764982 | − | 0.644052i | \(-0.777252\pi\) | ||||
−0.764982 | + | 0.644052i | \(0.777252\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.43008 | 0.129708 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.2891 | −0.547636 | −0.273818 | − | 0.961782i | \(-0.588287\pi\) | ||||
−0.273818 | + | 0.961782i | \(0.588287\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.11492 | −0.112248 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.97583 | −0.210423 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.2335 | 1.22622 | 0.613108 | − | 0.789999i | \(-0.289919\pi\) | ||||
0.613108 | + | 0.789999i | \(0.289919\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.2375 | −0.696712 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.02164 | −0.0536224 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.52417 | 0.184464 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4276 | −0.857512 | −0.428756 | − | 0.903420i | \(-0.641048\pi\) | ||||
−0.428756 | + | 0.903420i | \(0.641048\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.71876 | 0.193591 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.172463 | −0.00895383 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.00351 | −0.155516 | −0.0777579 | − | 0.996972i | \(-0.524776\pi\) | ||||
−0.0777579 | + | 0.996972i | \(0.524776\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.63021 | −0.239103 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.42143 | −0.485229 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.71775 | 0.139601 | 0.0698007 | − | 0.997561i | \(-0.477764\pi\) | ||||
0.0698007 | + | 0.997561i | \(0.477764\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.30843 | 0.169496 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.85264 | 0.145763 | 0.0728816 | − | 0.997341i | \(-0.476780\pi\) | ||||
0.0728816 | + | 0.997341i | \(0.476780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.08938 | −0.0555198 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.5079 | 0.534149 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.22588 | −0.112857 | −0.0564284 | − | 0.998407i | \(-0.517971\pi\) | ||||
−0.0564284 | + | 0.998407i | \(0.517971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −49.0045 | −2.47827 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.96333 | 0.452140 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.11488 | 0.207042 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.2045 | 0.612527 | 0.306264 | − | 0.951947i | \(-0.400921\pi\) | ||||
0.306264 | + | 0.951947i | \(0.400921\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.59238 | 0.0797187 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.7612 | 1.83577 | 0.917883 | − | 0.396852i | \(-0.129897\pi\) | ||||
0.917883 | + | 0.396852i | \(0.129897\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.58296 | −0.327921 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.473647 | −0.0235357 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.4035 | −1.45748 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4370 | 0.713863 | 0.356931 | − | 0.934131i | \(-0.383823\pi\) | ||||
0.356931 | + | 0.934131i | \(0.383823\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.77363 | 0.186139 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.771054 | −0.0379411 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.48058 | 0.367207 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.16082 | −0.154786 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.34434 | 0.114529 | 0.0572643 | − | 0.998359i | \(-0.481762\pi\) | ||||
0.0572643 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3292 | 0.893311 | 0.446655 | − | 0.894706i | \(-0.352615\pi\) | ||||
0.446655 | + | 0.894706i | \(0.352615\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.9069 | 0.530312 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 28.6233 | 1.38843 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.03359 | 0.0500191 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.42563 | −0.406793 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.77531 | −0.278187 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.96341 | −0.190469 | −0.0952346 | − | 0.995455i | \(-0.530360\pi\) | ||||
−0.0952346 | + | 0.995455i | \(0.530360\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.83633 | 0.0880454 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.6270 | 0.938888 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.234378 | 0.0111863 | 0.00559313 | − | 0.999984i | \(-0.498220\pi\) | ||||
0.00559313 | + | 0.999984i | \(0.498220\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.55997 | −0.312379 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.2502 | −1.24718 | −0.623592 | − | 0.781750i | \(-0.714327\pi\) | ||||
−0.623592 | + | 0.781750i | \(0.714327\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.78868 | 0.132196 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.2900 | −0.817790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.7460 | −1.02626 | −0.513128 | − | 0.858312i | \(-0.671513\pi\) | ||||
−0.513128 | + | 0.858312i | \(0.671513\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8938 | −0.607144 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.79304 | −0.272181 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.763514 | −0.0357941 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.0107 | 1.16995 | 0.584975 | − | 0.811051i | \(-0.301104\pi\) | ||||
0.584975 | + | 0.811051i | \(0.301104\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.99358 | 0.279756 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.70398 | −0.125937 | −0.0629684 | − | 0.998016i | \(-0.520057\pi\) | ||||
−0.0629684 | + | 0.998016i | \(0.520057\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.2411 | 0.847734 | 0.423867 | − | 0.905725i | \(-0.360672\pi\) | ||||
0.423867 | + | 0.905725i | \(0.360672\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.28308 | 0.0595016 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.8934 | −0.689183 | −0.344591 | − | 0.938753i | \(-0.611983\pi\) | ||||
−0.344591 | + | 0.938753i | \(0.611983\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.01070 | −0.0466699 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.9447 | 0.919004 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −36.4334 | −1.67521 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.4640 | −0.526006 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.259988 | 0.0119040 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.1271 | 0.508412 | 0.254206 | − | 0.967150i | \(-0.418186\pi\) | ||||
0.254206 | + | 0.967150i | \(0.418186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.6081 | −0.939647 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.42366 | 0.246785 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.13700 | 0.278667 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.0109 | −1.31461 | −0.657304 | − | 0.753625i | \(-0.728303\pi\) | ||||
−0.657304 | + | 0.753625i | \(0.728303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.2632 | −0.464117 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.0429 | −1.89737 | −0.948685 | − | 0.316223i | \(-0.897585\pi\) | ||||
−0.948685 | + | 0.316223i | \(0.897585\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.2371 | −1.04655 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.64224 | 0.0738132 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.96198 | −0.132863 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.70998 | −0.389912 | −0.194956 | − | 0.980812i | \(-0.562456\pi\) | ||||
−0.194956 | + | 0.980812i | \(0.562456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.952706 | −0.0424791 | −0.0212395 | − | 0.999774i | \(-0.506761\pi\) | ||||
−0.0212395 | + | 0.999774i | \(0.506761\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.75737 | 0.0782019 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.09472 | 0.315087 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.0897 | −0.580191 | −0.290095 | − | 0.956998i | \(-0.593687\pi\) | ||||
−0.290095 | + | 0.956998i | \(0.593687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.93565 | 0.218340 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.40051 | −0.105985 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.80300 | 0.299776 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.8167 | −1.66318 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.66098 | 0.424070 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.0754 | −1.01095 | −0.505475 | − | 0.862841i | \(-0.668683\pi\) | ||||
−0.505475 | + | 0.862841i | \(0.668683\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.3216 | 1.23842 | 0.619210 | − | 0.785226i | \(-0.287453\pi\) | ||||
0.619210 | + | 0.785226i | \(0.287453\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.16793 | −0.138260 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.2363 | −0.707264 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43.8498 | 1.90651 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.16237 | 0.0504424 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.03688 | −0.391431 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.148168 | −0.00640588 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.0225 | −0.907190 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.7449 | 0.979691 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.6244 | −0.886710 | −0.443355 | − | 0.896346i | \(-0.646212\pi\) | ||||
−0.443355 | + | 0.896346i | \(0.646212\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.8532 | 0.465755 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.59124 | −0.196667 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.7328 | −1.39956 | −0.699778 | − | 0.714361i | \(-0.746718\pi\) | ||||
−0.699778 | + | 0.714361i | \(0.746718\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.55815 | −0.0665000 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.30681 | 0.396484 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.76294 | 0.245065 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.01672 | 0.170500 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.834402 | −0.0353548 | −0.0176774 | − | 0.999844i | \(-0.505627\pi\) | ||||
−0.0176774 | + | 0.999844i | \(0.505627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.5351 | −1.08002 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.7811 | −0.877378 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.3371 | 0.435656 | 0.217828 | − | 0.975987i | \(-0.430103\pi\) | ||||
0.217828 | + | 0.975987i | \(0.430103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.33010 | −0.140098 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.663349 | −0.0278580 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.4687 | 1.19347 | 0.596735 | − | 0.802439i | \(-0.296465\pi\) | ||||
0.596735 | + | 0.802439i | \(0.296465\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.5241 | −1.15185 | −0.575924 | − | 0.817503i | \(-0.695358\pi\) | ||||
−0.575924 | + | 0.817503i | \(0.695358\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8612 | 0.537283 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.0466 | −1.62836 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.6801 | −0.819291 | −0.409646 | − | 0.912245i | \(-0.634348\pi\) | ||||
−0.409646 | + | 0.912245i | \(0.634348\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.46080 | 0.310060 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.4767 | 0.434645 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.901438 | −0.0373337 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.15100 | 0.0475879 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.69629 | −0.152562 | −0.0762810 | − | 0.997086i | \(-0.524305\pi\) | ||||
−0.0762810 | + | 0.997086i | \(0.524305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.50287 | 0.267946 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.45809 | 0.101112 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.97065 | 0.286250 | 0.143125 | − | 0.989705i | \(-0.454285\pi\) | ||||
0.143125 | + | 0.989705i | \(0.454285\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.88314 | −0.0772012 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.6699 | 0.764109 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.9392 | −1.67273 | −0.836366 | − | 0.548172i | \(-0.815324\pi\) | ||||
−0.836366 | + | 0.548172i | \(0.815324\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.6168 | −0.881769 | −0.440884 | − | 0.897564i | \(-0.645335\pi\) | ||||
−0.440884 | + | 0.897564i | \(0.645335\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.52364 | 0.0620473 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.483898 | −0.0196733 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.06739 | −0.165090 | −0.0825451 | − | 0.996587i | \(-0.526305\pi\) | ||||
−0.0825451 | + | 0.996587i | \(0.526305\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.57181 | 0.104215 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.5047 | −1.07226 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.06712 | −0.164269 | −0.0821347 | − | 0.996621i | \(-0.526174\pi\) | ||||
−0.0821347 | + | 0.996621i | \(0.526174\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.76138 | 0.0710256 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.9187 | −0.721380 | −0.360690 | − | 0.932686i | \(-0.617459\pi\) | ||||
−0.360690 | + | 0.932686i | \(0.617459\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.24950 | 0.331575 | 0.165788 | − | 0.986161i | \(-0.446983\pi\) | ||||
0.165788 | + | 0.986161i | \(0.446983\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.17617 | −0.328099 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.90559 | 0.156474 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.6852 | 0.867408 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.32312 | 0.332393 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.8280 | −2.02665 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1352 | −0.920997 | −0.460498 | − | 0.887661i | \(-0.652329\pi\) | ||||
−0.460498 | + | 0.887661i | \(0.652329\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.26671 | 0.169586 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.56703 | 0.0621857 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.9412 | 0.631615 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.46519 | 0.176640 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.2103 | −1.46972 | −0.734859 | − | 0.678220i | \(-0.762751\pi\) | ||||
−0.734859 | + | 0.678220i | \(0.762751\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.5078 | −0.414388 | −0.207194 | − | 0.978300i | \(-0.566433\pi\) | ||||
−0.207194 | + | 0.978300i | \(0.566433\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.97705 | 0.195971 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.81698 | 0.385945 | 0.192973 | − | 0.981204i | \(-0.438187\pi\) | ||||
0.192973 | + | 0.981204i | \(0.438187\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.03018 | −0.158199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.79698 | 0.0704291 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.3873 | 1.54134 | 0.770671 | − | 0.637233i | \(-0.219921\pi\) | ||||
0.770671 | + | 0.637233i | \(0.219921\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.24545 | 0.165883 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.44051 | −0.290282 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.1721 | 1.68174 | 0.840872 | − | 0.541234i | \(-0.182043\pi\) | ||||
0.840872 | + | 0.541234i | \(0.182043\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.4626 | 1.06817 | 0.534086 | − | 0.845430i | \(-0.320656\pi\) | ||||
0.534086 | + | 0.845430i | \(0.320656\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.5649 | −0.565653 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.754225 | 0.0292476 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.6991 | 1.22739 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.9512 | −0.771357 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.40244 | 0.208559 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.6060 | −0.563020 | −0.281510 | − | 0.959558i | \(-0.590835\pi\) | ||||
−0.281510 | + | 0.959558i | \(0.590835\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.77566 | 0.183815 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.4195 | 0.823217 | 0.411608 | − | 0.911361i | \(-0.364967\pi\) | ||||
0.411608 | + | 0.911361i | \(0.364967\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.59495 | 0.329844 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.5716 | −0.864946 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.83920 | 0.338223 | 0.169111 | − | 0.985597i | \(-0.445910\pi\) | ||||
0.169111 | + | 0.985597i | \(0.445910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.78737 | 0.0682917 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.25689 | 0.353172 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.631792 | −0.0240694 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.9026 | −1.70818 | −0.854088 | − | 0.520129i | \(-0.825884\pi\) | ||||
−0.854088 | + | 0.520129i | \(0.825884\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.29998 | 0.0873690 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.49711 | −0.0567887 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.2887 | −0.844243 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.24492 | −0.0470870 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.2450 | 1.48226 | 0.741131 | − | 0.671360i | \(-0.234290\pi\) | ||||
0.741131 | + | 0.671360i | \(0.234290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.3574 | 0.767792 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.16602 | 0.194564 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.46122 | 0.0925638 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.10889 | −0.266980 | −0.133490 | − | 0.991050i | \(-0.542618\pi\) | ||||
−0.133490 | + | 0.991050i | \(0.542618\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.68765 | −0.325812 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.1488 | 0.829480 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.99077 | −0.149246 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.50808 | 0.243049 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.8947 | 1.52512 | 0.762558 | − | 0.646919i | \(-0.223943\pi\) | ||||
0.762558 | + | 0.646919i | \(0.223943\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.52770 | 0.354830 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.9256 | −0.517898 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.5153 | −0.687640 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.9140 | 0.738568 | 0.369284 | − | 0.929317i | \(-0.379603\pi\) | ||||
0.369284 | + | 0.929317i | \(0.379603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −62.9802 | −2.32941 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7061 | 0.543182 | 0.271591 | − | 0.962413i | \(-0.412450\pi\) | ||||
0.271591 | + | 0.962413i | \(0.412450\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.10711 | −0.114607 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.28279 | −0.194594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.6497 | 0.759611 | 0.379806 | − | 0.925066i | \(-0.375991\pi\) | ||||
0.379806 | + | 0.925066i | \(0.375991\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.83344 | 0.214297 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.39332 | −0.271235 | −0.135617 | − | 0.990761i | \(-0.543302\pi\) | ||||
−0.135617 | + | 0.990761i | \(0.543302\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.18936 | −0.300035 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.7936 | −0.577857 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.207512 | −0.00758232 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.9001 | −1.45598 | −0.727988 | − | 0.685590i | \(-0.759544\pi\) | ||||
−0.727988 | + | 0.685590i | \(0.759544\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.3433 | 0.632024 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.74386 | −0.0998591 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.09965 | −0.330733 | −0.165366 | − | 0.986232i | \(-0.552881\pi\) | ||||
−0.165366 | + | 0.986232i | \(0.552881\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.3486 | 1.02899 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.2613 | 0.879472 | 0.439736 | − | 0.898127i | \(-0.355072\pi\) | ||||
0.439736 | + | 0.898127i | \(0.355072\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.43010 | −0.232785 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.83884 | 0.102638 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.82464 | −0.101992 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.0317 | −1.33540 | −0.667699 | − | 0.744431i | \(-0.732721\pi\) | ||||
−0.667699 | + | 0.744431i | \(0.732721\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.261552 | 0.00941958 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.1176 | 0.435841 | 0.217921 | − | 0.975966i | \(-0.430073\pi\) | ||||
0.217921 | + | 0.975966i | \(0.430073\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.9370 | −0.464711 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.62547 | 0.201813 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.92693 | 0.319841 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.4818 | −0.553983 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.87701 | −0.138553 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.44675 | 0.337169 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.4952 | −1.12268 | −0.561341 | − | 0.827585i | \(-0.689714\pi\) | ||||
−0.561341 | + | 0.827585i | \(0.689714\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.1235 | 0.894419 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.66385 | −0.165828 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.78642 | 0.134460 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.123143 | 0.00436742 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.7213 | 1.19447 | 0.597234 | − | 0.802067i | \(-0.296266\pi\) | ||||
0.597234 | + | 0.802067i | \(0.296266\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −65.3714 | −2.31268 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.88769 | −0.208031 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.7979 | 0.910388 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.56890 | 0.0905417 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.26812 | 0.291052 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.2848 | 0.888968 | 0.444484 | − | 0.895787i | \(-0.353387\pi\) | ||||
0.444484 | + | 0.895787i | \(0.353387\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.4610 | 0.823826 | 0.411913 | − | 0.911223i | \(-0.364861\pi\) | ||||
0.411913 | + | 0.911223i | \(0.364861\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.04656 | 0.317277 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.86112 | −0.170278 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.2245 | 0.882493 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.61199 | 0.0563275 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.9196 | −1.11400 | −0.557000 | − | 0.830512i | \(-0.688048\pi\) | ||||
−0.557000 | + | 0.830512i | \(0.688048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.7610 | 1.56027 | 0.780136 | − | 0.625610i | \(-0.215150\pi\) | ||||
0.780136 | + | 0.625610i | \(0.215150\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.5583 | −0.576485 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.36013 | −0.116843 | −0.0584216 | − | 0.998292i | \(-0.518607\pi\) | ||||
−0.0584216 | + | 0.998292i | \(0.518607\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.4683 | 0.606699 | 0.303350 | − | 0.952879i | \(-0.401895\pi\) | ||||
0.303350 | + | 0.952879i | \(0.401895\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.4147 | 0.881627 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 39.3177 | 1.36228 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.473647 | 0.0163912 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.70895 | −0.0936350 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.9496 | −1.82802 | −0.914012 | − | 0.405688i | \(-0.867032\pi\) | ||||
−0.914012 | + | 0.405688i | \(0.867032\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9688 | −0.481683 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.13820 | 0.176969 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.36039 | 0.115601 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.677707 | −0.0232863 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.5596 | 0.465365 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 69.3373 | 2.37685 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −55.3150 | −1.89395 | −0.946975 | − | 0.321308i | \(-0.895878\pi\) | ||||
−0.946975 | + | 0.321308i | \(0.895878\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.13700 | −0.0388844 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.6921 | 1.45834 | 0.729168 | − | 0.684335i | \(-0.239907\pi\) | ||||
0.729168 | + | 0.684335i | \(0.239907\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.8971 | 1.22479 | 0.612397 | − | 0.790550i | \(-0.290205\pi\) | ||||
0.612397 | + | 0.790550i | \(0.290205\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.46683 | 0.0840695 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.29190 | −0.112058 | −0.0560289 | − | 0.998429i | \(-0.517844\pi\) | ||||
−0.0560289 | + | 0.998429i | \(0.517844\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.57589 | 0.155585 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.9230 | −0.642658 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.1220 | 1.02182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.70256 | −0.125456 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.9569 | −0.438525 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.07144 | −0.103834 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.1489 | −0.882985 | −0.441493 | − | 0.897265i | \(-0.645551\pi\) | ||||
−0.441493 | + | 0.897265i | \(0.645551\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.0838 | −0.711138 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.3331 | 1.76315 | 0.881574 | − | 0.472045i | \(-0.156484\pi\) | ||||
0.881574 | + | 0.472045i | \(0.156484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.9420 | −0.435531 | −0.217766 | − | 0.976001i | \(-0.569877\pi\) | ||||
−0.217766 | + | 0.976001i | \(0.569877\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.550551 | 0.0185066 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.4393 | 1.15636 | 0.578180 | − | 0.815909i | \(-0.303763\pi\) | ||||
0.578180 | + | 0.815909i | \(0.303763\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.19465 | 0.0736061 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.46722 | −0.116156 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.1822 | 0.876154 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.95726 | −0.332834 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.8687 | 0.663398 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.5026 | 0.350282 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.55826 | −0.0519132 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.97044 | 0.231962 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.14057 | 0.170878 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.87288 | −0.228210 | −0.114105 | − | 0.993469i | \(-0.536400\pi\) | ||||
−0.114105 | + | 0.993469i | \(0.536400\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.71030 | −0.123063 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.84365 | −0.259872 | −0.129936 | − | 0.991522i | \(-0.541477\pi\) | ||||
−0.129936 | + | 0.991522i | \(0.541477\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54.7599 | 1.81229 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.738011 | −0.0243979 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.94582 | 0.196348 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.78026 | −0.124699 | −0.0623496 | − | 0.998054i | \(-0.519859\pi\) | ||||
−0.0623496 | + | 0.998054i | \(0.519859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.4875 | −0.971647 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.8508 | −0.357157 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.4996 | −1.33162 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.3630 | −0.471744 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.9288 | −1.40845 | −0.704225 | − | 0.709977i | \(-0.748705\pi\) | ||||
−0.704225 | + | 0.709977i | \(0.748705\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.7473 | −0.516097 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.2057 | 0.628766 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.84289 | −0.321897 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.2737 | −0.564307 | −0.282154 | − | 0.959369i | \(-0.591049\pi\) | ||||
−0.282154 | + | 0.959369i | \(0.591049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.13192 | 0.232741 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.76847 | 0.220646 | 0.110323 | − | 0.993896i | \(-0.464812\pi\) | ||||
0.110323 | + | 0.993896i | \(0.464812\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.4052 | 0.990130 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.314193 | −0.0102207 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.9851 | −1.26685 | −0.633423 | − | 0.773806i | \(-0.718351\pi\) | ||||
−0.633423 | + | 0.773806i | \(0.718351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.0810 | 0.586935 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.54451 | −0.244647 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.88392 | −0.125812 | −0.0629062 | − | 0.998019i | \(-0.520037\pi\) | ||||
−0.0629062 | + | 0.998019i | \(0.520037\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.09165 | 0.197121 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.4425 | 0.434533 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.50323 | 0.0808336 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.6616 | −0.763277 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.312825 | 0.0100806 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.53378 | 0.113757 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.3477 | −0.364917 | −0.182459 | − | 0.983214i | \(-0.558406\pi\) | ||||
−0.182459 | + | 0.983214i | \(0.558406\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.3877 | 0.462199 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.4384 | −0.784265 | −0.392132 | − | 0.919909i | \(-0.628262\pi\) | ||||
−0.392132 | + | 0.919909i | \(0.628262\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.09673 | −0.0672180 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.6052 | −0.371665 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.5927 | 1.39465 | 0.697326 | − | 0.716754i | \(-0.254373\pi\) | ||||
0.697326 | + | 0.716754i | \(0.254373\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.4139 | 0.652432 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.69339 | 0.309486 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.69974 | −0.118003 | −0.0590017 | − | 0.998258i | \(-0.518792\pi\) | ||||
−0.0590017 | + | 0.998258i | \(0.518792\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.16426 | 0.0370965 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.23509 | 0.230296 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 85.9148 | 2.73193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.6092 | −1.73472 | −0.867360 | − | 0.497682i | \(-0.834185\pi\) | ||||
−0.867360 | + | 0.497682i | \(0.834185\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.5151 | −0.682762 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.84295 | 0.280340 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.7888 | −0.690057 | −0.345029 | − | 0.938592i | \(-0.612131\pi\) | ||||
−0.345029 | + | 0.938592i | \(0.612131\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.48041 | −0.268308 |
(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.s.1.2 | 5 | ||
4.3 | odd | 2 | 4008.2.a.f.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.f.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
8016.2.a.s.1.2 | 5 | 1.1 | even | 1 | trivial |