Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1536,2,Mod(1,1536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1536, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1536.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1536.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: | \(12.2650217505\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1536.1 |
$q$-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 | ||||||||
\(5\) | 0.585786 | 0.261972 | 0.130986 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130986 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.41421 | −1.29045 | −0.645226 | − | 0.763992i | \(-0.723237\pi\) | ||||
−0.645226 | + | 0.763992i | \(0.723237\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843 | 0.784465 | 0.392232 | − | 0.919866i | \(-0.371703\pi\) | ||||
0.392232 | + | 0.919866i | \(0.371703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.585786 | −0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.65685 | 0.886917 | 0.443459 | − | 0.896295i | \(-0.353751\pi\) | ||||
0.443459 | + | 0.896295i | \(0.353751\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.65685 | 1.29777 | 0.648886 | − | 0.760886i | \(-0.275235\pi\) | ||||
0.648886 | + | 0.760886i | \(0.275235\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.41421 | 0.745042 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.17157 | −0.244290 | −0.122145 | − | 0.992512i | \(-0.538977\pi\) | ||||
−0.122145 | + | 0.992512i | \(0.538977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.585786 | 0.108778 | 0.0543889 | − | 0.998520i | \(-0.482679\pi\) | ||||
0.0543889 | + | 0.998520i | \(0.482679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.58579 | −0.823632 | −0.411816 | − | 0.911267i | \(-0.635105\pi\) | ||||
−0.411816 | + | 0.911267i | \(0.635105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.65685 | −1.58758 | −0.793789 | − | 0.608194i | \(-0.791894\pi\) | ||||
−0.793789 | + | 0.608194i | \(0.791894\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.82843 | −0.452911 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.6569 | −1.82049 | −0.910247 | − | 0.414065i | \(-0.864109\pi\) | ||||
−0.910247 | + | 0.414065i | \(0.864109\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.65685 | −0.252668 | −0.126334 | − | 0.991988i | \(-0.540321\pi\) | ||||
−0.126334 | + | 0.991988i | \(0.540321\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.585786 | 0.0873239 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.4853 | −1.82117 | −0.910583 | − | 0.413327i | \(-0.864367\pi\) | ||||
−0.910583 | + | 0.413327i | \(0.864367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.65685 | 0.665265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.65685 | −0.512062 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.8995 | 1.63452 | 0.817261 | − | 0.576268i | \(-0.195492\pi\) | ||||
0.817261 | + | 0.576268i | \(0.195492\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.17157 | −0.157975 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.65685 | −0.749269 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.65685 | −1.23643 | −0.618217 | − | 0.786008i | \(-0.712145\pi\) | ||||
−0.618217 | + | 0.786008i | \(0.712145\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.41421 | −0.430150 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.65685 | 0.205507 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.17157 | 0.141041 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.17157 | −1.08847 | −0.544233 | − | 0.838934i | \(-0.683179\pi\) | ||||
−0.544233 | + | 0.838934i | \(0.683179\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.65685 | −0.193920 | −0.0969601 | − | 0.995288i | \(-0.530912\pi\) | ||||
−0.0969601 | + | 0.995288i | \(0.530912\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.65685 | 0.537727 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.82843 | 0.778171 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.75736 | −0.647754 | −0.323877 | − | 0.946099i | \(-0.604986\pi\) | ||||
−0.323877 | + | 0.946099i | \(0.604986\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.31371 | −1.02231 | −0.511156 | − | 0.859488i | \(-0.670783\pi\) | ||||
−0.511156 | + | 0.859488i | \(0.670783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.14214 | 0.232347 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.585786 | −0.0628029 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.65685 | −1.01231 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.58579 | 0.475524 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.31371 | 0.339979 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3137 | 1.35180 | 0.675901 | − | 0.736992i | \(-0.263755\pi\) | ||||
0.675901 | + | 0.736992i | \(0.263755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.5563 | −1.74692 | −0.873461 | − | 0.486894i | \(-0.838130\pi\) | ||||
−0.873461 | + | 0.486894i | \(0.838130\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.07107 | −0.893799 | −0.446899 | − | 0.894584i | \(-0.647472\pi\) | ||||
−0.446899 | + | 0.894584i | \(0.647472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3137 | 1.48043 | 0.740216 | − | 0.672369i | \(-0.234723\pi\) | ||||
0.740216 | + | 0.672369i | \(0.234723\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1716 | −1.26161 | −0.630804 | − | 0.775942i | \(-0.717275\pi\) | ||||
−0.630804 | + | 0.775942i | \(0.717275\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.65685 | 0.916588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.686292 | −0.0639970 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.82843 | 0.261488 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.4853 | −1.14452 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.6569 | 1.05106 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.72792 | −0.597007 | −0.298503 | − | 0.954409i | \(-0.596487\pi\) | ||||
−0.298503 | + | 0.954409i | \(0.596487\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.65685 | 0.145878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.3137 | −1.67471 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.585786 | −0.0504165 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.34315 | 0.371060 | 0.185530 | − | 0.982639i | \(-0.440600\pi\) | ||||
0.185530 | + | 0.982639i | \(0.440600\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.3137 | −1.63817 | −0.819084 | − | 0.573674i | \(-0.805518\pi\) | ||||
−0.819084 | + | 0.573674i | \(0.805518\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.4853 | 1.05145 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.65685 | −0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.343146 | 0.0284967 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.65685 | −0.384091 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.2426 | 1.16680 | 0.583401 | − | 0.812184i | \(-0.301722\pi\) | ||||
0.583401 | + | 0.812184i | \(0.301722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.58579 | −0.373186 | −0.186593 | − | 0.982437i | \(-0.559745\pi\) | ||||
−0.186593 | + | 0.982437i | \(0.559745\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.65685 | 0.295639 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.68629 | −0.215768 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0000 | −1.59617 | −0.798087 | − | 0.602542i | \(-0.794154\pi\) | ||||
−0.798087 | + | 0.602542i | \(0.794154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.8995 | −0.943691 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.34315 | −0.496834 | −0.248417 | − | 0.968653i | \(-0.579910\pi\) | ||||
−0.248417 | + | 0.968653i | \(0.579910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.17157 | 0.0912068 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.6569 | 1.67586 | 0.837929 | − | 0.545779i | \(-0.183766\pi\) | ||||
0.837929 | + | 0.545779i | \(0.183766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.65685 | 0.432590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.7279 | 1.42386 | 0.711929 | − | 0.702252i | \(-0.247822\pi\) | ||||
0.711929 | + | 0.702252i | \(0.247822\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.8995 | 1.20189 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.48528 | 0.630706 | 0.315353 | − | 0.948974i | \(-0.397877\pi\) | ||||
0.315353 | + | 0.948974i | \(0.397877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.65685 | 0.713855 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.65685 | −0.415900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.31371 | −0.534831 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.41421 | 0.248347 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9706 | 1.22795 | 0.613973 | − | 0.789327i | \(-0.289570\pi\) | ||||
0.613973 | + | 0.789327i | \(0.289570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.6569 | −1.55889 | −0.779447 | − | 0.626468i | \(-0.784500\pi\) | ||||
−0.779447 | + | 0.626468i | \(0.784500\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.65685 | −0.118650 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.92893 | 0.208678 | 0.104339 | − | 0.994542i | \(-0.466727\pi\) | ||||
0.104339 | + | 0.994542i | \(0.466727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.5563 | 0.960984 | 0.480492 | − | 0.876999i | \(-0.340458\pi\) | ||||
0.480492 | + | 0.876999i | \(0.340458\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.82843 | −0.476918 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.17157 | −0.0814299 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3137 | −0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.3137 | 1.32961 | 0.664805 | − | 0.747017i | \(-0.268515\pi\) | ||||
0.664805 | + | 0.747017i | \(0.268515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.17157 | 0.628426 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.970563 | −0.0661918 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.6569 | 1.06286 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.65685 | 0.111960 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3431 | 0.695755 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.89949 | −0.528989 | −0.264495 | − | 0.964387i | \(-0.585205\pi\) | ||||
−0.264495 | + | 0.964387i | \(0.585205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −29.3137 | −1.94562 | −0.972810 | − | 0.231606i | \(-0.925602\pi\) | ||||
−0.972810 | + | 0.231606i | \(0.925602\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.4853 | −1.08938 | −0.544689 | − | 0.838638i | \(-0.683352\pi\) | ||||
−0.544689 | + | 0.838638i | \(0.683352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.82843 | −0.449278 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.31371 | 0.610161 | 0.305081 | − | 0.952327i | \(-0.401317\pi\) | ||||
0.305081 | + | 0.952327i | \(0.401317\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.31371 | −0.477094 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.75736 | 0.373981 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.9706 | −1.09773 | −0.548867 | − | 0.835910i | \(-0.684941\pi\) | ||||
−0.548867 | + | 0.835910i | \(0.684941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.6569 | −1.13738 | −0.568689 | − | 0.822553i | \(-0.692549\pi\) | ||||
−0.568689 | + | 0.822553i | \(0.692549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.72792 | 0.174281 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.0000 | 1.01806 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.31371 | 0.590232 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.0000 | 1.38863 | 0.694314 | − | 0.719672i | \(-0.255708\pi\) | ||||
0.694314 | + | 0.719672i | \(0.255708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.34315 | 0.147312 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.14214 | −0.134146 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.31371 | −0.0819469 | −0.0409734 | − | 0.999160i | \(-0.513046\pi\) | ||||
−0.0409734 | + | 0.999160i | \(0.513046\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.9706 | 2.04869 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.585786 | 0.0362593 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.6569 | 0.842118 | 0.421059 | − | 0.907033i | \(-0.361659\pi\) | ||||
0.421059 | + | 0.907033i | \(0.361659\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.97056 | 0.428198 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.00000 | −0.122398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.24264 | −0.380621 | −0.190310 | − | 0.981724i | \(-0.560949\pi\) | ||||
−0.190310 | + | 0.981724i | \(0.560949\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4142 | 1.17933 | 0.589665 | − | 0.807648i | \(-0.299260\pi\) | ||||
0.589665 | + | 0.807648i | \(0.299260\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.65685 | 0.584459 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.31371 | 0.561638 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.51472 | −0.451516 | −0.225758 | − | 0.974183i | \(-0.572486\pi\) | ||||
−0.225758 | + | 0.974183i | \(0.572486\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.58579 | −0.274544 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.3137 | −0.910305 | −0.455153 | − | 0.890413i | \(-0.650415\pi\) | ||||
−0.455153 | + | 0.890413i | \(0.650415\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.31371 | −0.196287 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 39.7990 | 2.34926 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.3137 | −0.780463 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.8995 | 1.62991 | 0.814953 | − | 0.579527i | \(-0.196763\pi\) | ||||
0.814953 | + | 0.579527i | \(0.196763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.34315 | 0.136423 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.31371 | −0.191637 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.65685 | 0.326056 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.5563 | 1.00859 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.65685 | −0.323911 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000 | 0.913168 | 0.456584 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456584 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.07107 | 0.516035 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3137 | −0.641542 | −0.320771 | − | 0.947157i | \(-0.603942\pi\) | ||||
−0.320771 | + | 0.947157i | \(0.603942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.9706 | 0.959233 | 0.479616 | − | 0.877478i | \(-0.340776\pi\) | ||||
0.479616 | + | 0.877478i | \(0.340776\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.00000 | −0.112687 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.07107 | 0.284820 | 0.142410 | − | 0.989808i | \(-0.454515\pi\) | ||||
0.142410 | + | 0.989808i | \(0.454515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.17157 | −0.0655955 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.3137 | −0.854728 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.6863 | 1.15102 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.1716 | −0.730627 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.1716 | 0.728390 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 42.6274 | 2.35013 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.65685 | −0.529192 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.68629 | 0.256039 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.9706 | 1.14234 | 0.571170 | − | 0.820832i | \(-0.306490\pi\) | ||||
0.571170 | + | 0.820832i | \(0.306490\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.17157 | 0.496669 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.686292 | 0.0369487 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.3137 | −1.35891 | −0.679456 | − | 0.733717i | \(-0.737784\pi\) | ||||
−0.679456 | + | 0.733717i | \(0.737784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.686292 | −0.0367363 | −0.0183682 | − | 0.999831i | \(-0.505847\pi\) | ||||
−0.0183682 | + | 0.999831i | \(0.505847\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.82843 | −0.150970 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.3137 | −0.708617 | −0.354309 | − | 0.935129i | \(-0.615284\pi\) | ||||
−0.354309 | + | 0.935129i | \(0.615284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.37258 | −0.285147 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.4853 | 0.660791 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.7990 | 0.833839 | 0.416919 | − | 0.908943i | \(-0.363110\pi\) | ||||
0.416919 | + | 0.908943i | \(0.363110\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.970563 | −0.0508016 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.7279 | 1.18639 | 0.593194 | − | 0.805060i | \(-0.297867\pi\) | ||||
0.593194 | + | 0.805060i | \(0.297867\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.6569 | −0.606832 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −40.6274 | −2.10927 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.2843 | −1.25739 | −0.628696 | − | 0.777651i | \(-0.716411\pi\) | ||||
−0.628696 | + | 0.777651i | \(0.716411\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.65685 | 0.0853323 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3431 | 0.942224 | 0.471112 | − | 0.882073i | \(-0.343853\pi\) | ||||
0.471112 | + | 0.882073i | \(0.343853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.72792 | 0.344682 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.3137 | 0.986884 | 0.493442 | − | 0.869779i | \(-0.335738\pi\) | ||||
0.493442 | + | 0.869779i | \(0.335738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.65685 | −0.0842226 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.2426 | −1.12775 | −0.563873 | − | 0.825861i | \(-0.690689\pi\) | ||||
−0.563873 | + | 0.825861i | \(0.690689\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.28427 | −0.216665 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.37258 | −0.169693 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00000 | −0.200754 | −0.100377 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100377 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.3137 | 0.966895 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.6569 | −1.58087 | −0.790434 | − | 0.612547i | \(-0.790145\pi\) | ||||
−0.790434 | + | 0.612547i | \(0.790145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.9706 | −0.646110 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.585786 | 0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.3137 | 0.957345 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.31371 | 0.0649587 | 0.0324794 | − | 0.999472i | \(-0.489660\pi\) | ||||
0.0324794 | + | 0.999472i | \(0.489660\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.34315 | −0.214232 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.6569 | −0.672010 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.45584 | −0.267817 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.3137 | 0.945796 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.31371 | 0.0641789 | 0.0320894 | − | 0.999485i | \(-0.489784\pi\) | ||||
0.0320894 | + | 0.999485i | \(0.489784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.1421 | 1.07914 | 0.539571 | − | 0.841940i | \(-0.318587\pi\) | ||||
0.539571 | + | 0.841940i | \(0.318587\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.4853 | −0.607055 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.0294 | −0.826049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.9706 | 1.59556 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.65685 | 0.273115 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.1127 | −1.69132 | −0.845660 | − | 0.533723i | \(-0.820793\pi\) | ||||
−0.845660 | + | 0.533723i | \(0.820793\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6274 | −0.799063 | −0.399531 | − | 0.916720i | \(-0.630827\pi\) | ||||
−0.399531 | + | 0.916720i | \(0.630827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.343146 | −0.0164526 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.62742 | −0.317032 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.8995 | 0.758841 | 0.379421 | − | 0.925224i | \(-0.376123\pi\) | ||||
0.379421 | + | 0.925224i | \(0.376123\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.65685 | 0.221755 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.9411 | 1.32752 | 0.663761 | − | 0.747944i | \(-0.268959\pi\) | ||||
0.663761 | + | 0.747944i | \(0.268959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.17157 | 0.0555379 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.2426 | −0.673654 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.65685 | −0.361349 | −0.180675 | − | 0.983543i | \(-0.557828\pi\) | ||||
−0.180675 | + | 0.983543i | \(0.557828\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.3137 | 1.09780 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.58579 | 0.215459 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.65685 | −0.265197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3137 | −0.809901 | −0.404951 | − | 0.914339i | \(-0.632711\pi\) | ||||
−0.404951 | + | 0.914339i | \(0.632711\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.65685 | −0.170687 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.9289 | −0.509011 | −0.254506 | − | 0.967071i | \(-0.581913\pi\) | ||||
−0.254506 | + | 0.967071i | \(0.581913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.44365 | −0.113566 | −0.0567830 | − | 0.998387i | \(-0.518084\pi\) | ||||
−0.0567830 | + | 0.998387i | \(0.518084\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.68629 | 0.124574 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.31371 | 0.430987 | 0.215494 | − | 0.976505i | \(-0.430864\pi\) | ||||
0.215494 | + | 0.976505i | \(0.430864\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.3137 | −1.26123 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.0000 | 0.921551 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.31371 | 0.152364 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.3431 | −1.20871 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.8995 | 0.544840 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.48528 | 0.204938 | 0.102469 | − | 0.994736i | \(-0.467326\pi\) | ||||
0.102469 | + | 0.994736i | \(0.467326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.3137 | −1.24540 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.79899 | 0.354134 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.55635 | 0.251782 | 0.125891 | − | 0.992044i | \(-0.459821\pi\) | ||||
0.125891 | + | 0.992044i | \(0.459821\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.34315 | 0.286847 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.686292 | 0.0309719 | 0.0154860 | − | 0.999880i | \(-0.495070\pi\) | ||||
0.0154860 | + | 0.999880i | \(0.495070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.14214 | 0.0964769 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.17157 | −0.0526583 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.3137 | 1.40461 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.3137 | −1.04366 | −0.521832 | − | 0.853048i | \(-0.674751\pi\) | ||||
−0.521832 | + | 0.853048i | \(0.674751\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.6569 | −0.967557 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.48528 | 0.199989 | 0.0999944 | − | 0.994988i | \(-0.468118\pi\) | ||||
0.0999944 | + | 0.994988i | \(0.468118\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.2843 | −0.457644 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | 0.222058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.2132 | 1.02891 | 0.514454 | − | 0.857518i | \(-0.327995\pi\) | ||||
0.514454 | + | 0.857518i | \(0.327995\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.65685 | 0.250244 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.65685 | −0.249756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.31371 | −0.234150 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.9706 | 1.09820 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.7279 | −0.822065 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.9706 | −0.480629 | −0.240315 | − | 0.970695i | \(-0.577251\pi\) | ||||
−0.240315 | + | 0.970695i | \(0.577251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.3431 | −1.15191 | −0.575953 | − | 0.817483i | \(-0.695369\pi\) | ||||
−0.575953 | + | 0.817483i | \(0.695369\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.8995 | −0.693911 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.7696 | −0.730493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6274 | −0.940322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.9706 | −1.42811 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.97056 | 0.387831 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.00000 | −0.172613 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.31371 | −0.401170 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.17157 | −0.222343 | −0.111172 | − | 0.993801i | \(-0.535460\pi\) | ||||
−0.111172 | + | 0.993801i | \(0.535460\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.48528 | −0.364138 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.71573 | −0.330506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.9706 | −1.23869 | −0.619346 | − | 0.785118i | \(-0.712602\pi\) | ||||
−0.619346 | + | 0.785118i | \(0.712602\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.65685 | −0.412144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.31371 | 0.141169 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.6569 | 0.835894 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.65685 | 0.240120 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.0711 | −0.553839 | −0.276919 | − | 0.960893i | \(-0.589314\pi\) | ||||
−0.276919 | + | 0.960893i | \(0.589314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.68629 | −0.198209 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.31371 | 0.308785 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.6274 | 1.20650 | 0.603251 | − | 0.797551i | \(-0.293872\pi\) | ||||
0.603251 | + | 0.797551i | \(0.293872\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.51472 | 0.147865 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.41421 | −0.143383 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9706 | 0.795287 | 0.397644 | − | 0.917540i | \(-0.369828\pi\) | ||||
0.397644 | + | 0.917540i | \(0.369828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.9706 | −0.708955 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.45584 | 0.227524 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2843 | 1.17749 | 0.588745 | − | 0.808319i | \(-0.299622\pi\) | ||||
0.588745 | + | 0.808319i | \(0.299622\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.6569 | 0.900028 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.7990 | 1.31924 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.7990 | −0.985653 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.65685 | 0.0685025 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.68629 | 0.358522 | 0.179261 | − | 0.983802i | \(-0.442629\pi\) | ||||
0.179261 | + | 0.983802i | \(0.442629\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.9411 | −1.06889 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.92893 | −0.120480 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.00000 | −0.0821302 | −0.0410651 | − | 0.999156i | \(-0.513075\pi\) | ||||
−0.0410651 | + | 0.999156i | \(0.513075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.31371 | −0.299833 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.5563 | −0.554824 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.4853 | −1.16388 | −0.581939 | − | 0.813233i | \(-0.697706\pi\) | ||||
−0.581939 | + | 0.813233i | \(0.697706\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.65685 | 0.230748 | 0.115374 | − | 0.993322i | \(-0.463193\pi\) | ||||
0.115374 | + | 0.993322i | \(0.463193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.10051 | −0.166709 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.8995 | 0.645341 | 0.322670 | − | 0.946511i | \(-0.395419\pi\) | ||||
0.322670 | + | 0.946511i | \(0.395419\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.3137 | −1.42864 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.6274 | 1.39859 | 0.699294 | − | 0.714834i | \(-0.253498\pi\) | ||||
0.699294 | + | 0.714834i | \(0.253498\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.82843 | 0.275349 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.9411 | −1.76900 | −0.884502 | − | 0.466537i | \(-0.845501\pi\) | ||||
−0.884502 | + | 0.466537i | \(0.845501\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.17157 | 0.0470136 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.82843 | −0.273575 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.3137 | 0.451826 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.3137 | −1.40805 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.0711 | −1.31654 | −0.658269 | − | 0.752783i | \(-0.728711\pi\) | ||||
−0.658269 | + | 0.752783i | \(0.728711\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.3137 | −0.767651 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.94113 | −0.156399 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.1716 | 0.521877 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.17157 | −0.362822 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.9706 | 1.69724 | 0.848618 | − | 0.529007i | \(-0.177435\pi\) | ||||
0.848618 | + | 0.529007i | \(0.177435\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.2843 | −0.957678 | −0.478839 | − | 0.877903i | \(-0.658942\pi\) | ||||
−0.478839 | + | 0.877903i | \(0.658942\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.970563 | 0.0382159 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.1716 | 0.675084 | 0.337542 | − | 0.941310i | \(-0.390404\pi\) | ||||
0.337542 | + | 0.941310i | \(0.390404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.00000 | −0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.6569 | −0.613640 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.4142 | 0.916269 | 0.458134 | − | 0.888883i | \(-0.348518\pi\) | ||||
0.458134 | + | 0.888883i | \(0.348518\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.34315 | 0.0915543 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.65685 | −0.0646400 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.6863 | 0.650006 | 0.325003 | − | 0.945713i | \(-0.394635\pi\) | ||||
0.325003 | + | 0.945713i | \(0.394635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.6863 | 0.649022 | 0.324511 | − | 0.945882i | \(-0.394800\pi\) | ||||
0.324511 | + | 0.945882i | \(0.394800\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.3431 | −0.401694 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.3137 | −0.438727 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.686292 | −0.0265733 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.89949 | 0.305412 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.3137 | 0.745597 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.6274 | 1.41188 | 0.705942 | − | 0.708270i | \(-0.250524\pi\) | ||||
0.705942 | + | 0.708270i | \(0.250524\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.65685 | 0.179242 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.21320 | 0.277226 | 0.138613 | − | 0.990347i | \(-0.455736\pi\) | ||||
0.138613 | + | 0.990347i | \(0.455736\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.4558 | −1.74444 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.3137 | 1.12330 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.3137 | 0.968602 | 0.484301 | − | 0.874901i | \(-0.339074\pi\) | ||||
0.484301 | + | 0.874901i | \(0.339074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.54416 | 0.0972072 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.4853 | 0.628953 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33.6569 | 1.28222 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6569 | 0.671698 | 0.335849 | − | 0.941916i | \(-0.390977\pi\) | ||||
0.335849 | + | 0.941916i | \(0.390977\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.82843 | 0.259390 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.3137 | −0.429153 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.6274 | −1.61463 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.31371 | −0.352277 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.41421 | 0.280031 | 0.140015 | − | 0.990149i | \(-0.455285\pi\) | ||||
0.140015 | + | 0.990149i | \(0.455285\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.6274 | −2.06031 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.31371 | 0.275450 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 59.9411 | 2.25432 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.1127 | 1.16846 | 0.584231 | − | 0.811587i | \(-0.301396\pi\) | ||||
0.584231 | + | 0.811587i | \(0.301396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.75736 | −0.215918 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.37258 | 0.201205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.31371 | −0.123926 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.9706 | 0.633777 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.1716 | −0.938741 | −0.469371 | − | 0.883001i | \(-0.655519\pi\) | ||||
−0.469371 | + | 0.883001i | \(0.655519\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.9706 | 1.15340 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.6569 | 0.656665 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.72792 | −0.101312 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.7574 | 0.510232 | 0.255116 | − | 0.966910i | \(-0.417886\pi\) | ||||
0.255116 | + | 0.966910i | \(0.417886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.05887 | −0.224096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.4853 | 1.49536 | 0.747679 | − | 0.664060i | \(-0.231168\pi\) | ||||
0.747679 | + | 0.664060i | \(0.231168\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.72792 | −0.100621 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.6274 | −1.27379 | −0.636895 | − | 0.770951i | \(-0.719782\pi\) | ||||
−0.636895 | + | 0.770951i | \(0.719782\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.0000 | −0.587775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.0000 | −1.46746 | −0.733729 | − | 0.679442i | \(-0.762222\pi\) | ||||
−0.733729 | + | 0.679442i | \(0.762222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.34315 | 0.305669 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.31371 | −0.340771 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52.2843 | −1.91043 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.7279 | −1.12128 | −0.560639 | − | 0.828060i | \(-0.689444\pi\) | ||||
−0.560639 | + | 0.828060i | \(0.689444\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.0000 | −0.801725 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.68629 | −0.0977642 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5147 | 0.563892 | 0.281946 | − | 0.959430i | \(-0.409020\pi\) | ||||
0.281946 | + | 0.959430i | \(0.409020\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.34315 | −0.0850508 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.3431 | 0.882438 | 0.441219 | − | 0.897399i | \(-0.354546\pi\) | ||||
0.441219 | + | 0.897399i | \(0.354546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.9706 | 1.62804 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.14214 | 0.0774491 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.3137 | 0.408514 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.6569 | −0.492479 | −0.246239 | − | 0.969209i | \(-0.579195\pi\) | ||||
−0.246239 | + | 0.969209i | \(0.579195\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.31371 | 0.0473121 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.7279 | 0.673597 | 0.336798 | − | 0.941577i | \(-0.390656\pi\) | ||||
0.336798 | + | 0.941577i | \(0.390656\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.3553 | 0.767106 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.9706 | −1.18281 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −65.9411 | −2.36259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.3431 | 0.656369 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.585786 | −0.0209343 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.7157 | −0.418152 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.3431 | −0.368693 | −0.184347 | − | 0.982861i | \(-0.559017\pi\) | ||||
−0.184347 | + | 0.982861i | \(0.559017\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.6569 | −0.486197 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.4853 | −0.728373 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.3137 | −0.969938 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.97056 | −0.247220 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.5858 | 1.15425 | 0.577124 | − | 0.816657i | \(-0.304175\pi\) | ||||
0.577124 | + | 0.816657i | \(0.304175\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.6569 | −1.61522 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.31371 | 0.116938 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.34315 | 0.0825850 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.24264 | 0.219751 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.9706 | −1.37013 | −0.685066 | − | 0.728481i | \(-0.740227\pi\) | ||||
−0.685066 | + | 0.728481i | \(0.740227\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.6569 | 1.04139 | 0.520697 | − | 0.853742i | \(-0.325672\pi\) | ||||
0.520697 | + | 0.853742i | \(0.325672\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.4142 | −0.680886 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.71573 | −0.130156 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.37258 | −0.327905 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.65685 | −0.337438 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.8701 | −1.56598 | −0.782988 | − | 0.622037i | \(-0.786305\pi\) | ||||
−0.782988 | + | 0.622037i | \(0.786305\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.21320 | 0.112005 | 0.0560026 | − | 0.998431i | \(-0.482164\pi\) | ||||
0.0560026 | + | 0.998431i | \(0.482164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.31371 | −0.324262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.9411 | −1.31934 | −0.659671 | − | 0.751554i | \(-0.729304\pi\) | ||||
−0.659671 | + | 0.751554i | \(0.729304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7696 | 0.721356 | 0.360678 | − | 0.932690i | \(-0.382545\pi\) | ||||
0.360678 | + | 0.932690i | \(0.382545\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.51472 | 0.260683 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.0294 | 0.590035 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6863 | 0.439027 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.58579 | 0.158508 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.5147 | −0.397532 | −0.198766 | − | 0.980047i | \(-0.563693\pi\) | ||||
−0.198766 | + | 0.980047i | \(0.563693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6569 | −0.988167 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.00000 | 0.0688837 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.92893 | −0.100758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.8995 | 0.821196 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.3137 | 0.525565 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3137 | 0.387829 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.6274 | −0.363876 | −0.181938 | − | 0.983310i | \(-0.558237\pi\) | ||||
−0.181938 | + | 0.983310i | \(0.558237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.31371 | 0.113326 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.5980 | −1.28432 | −0.642161 | − | 0.766570i | \(-0.721962\pi\) | ||||
−0.642161 | + | 0.766570i | \(0.721962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0294 | −0.376320 | −0.188160 | − | 0.982138i | \(-0.560252\pi\) | ||||
−0.188160 | + | 0.982138i | \(0.560252\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −39.7990 | −1.35635 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.9706 | −1.66698 | −0.833489 | − | 0.552537i | \(-0.813660\pi\) | ||||
−0.833489 | + | 0.552537i | \(0.813660\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.9706 | 0.373010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.62742 | 0.123194 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.5147 | 0.390610 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.6274 | 0.766701 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.3137 | 0.450601 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.3137 | 0.652923 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.686292 | −0.0231744 | −0.0115872 | − | 0.999933i | \(-0.503688\pi\) | ||||
−0.0115872 | + | 0.999933i | \(0.503688\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.8995 | −0.941027 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.6863 | 0.764321 | 0.382160 | − | 0.924096i | \(-0.375180\pi\) | ||||
0.382160 | + | 0.924096i | \(0.375180\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.6569 | −1.40186 | −0.700932 | − | 0.713228i | \(-0.747233\pi\) | ||||
−0.700932 | + | 0.713228i | \(0.747233\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.34315 | −0.0787640 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.3431 | 0.615903 | 0.307951 | − | 0.951402i | \(-0.400357\pi\) | ||||
0.307951 | + | 0.951402i | \(0.400357\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.9706 | 0.770408 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −70.6274 | −2.36346 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.34315 | 0.0783227 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.31371 | 0.110642 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.68629 | −0.0895928 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.5147 | 1.44969 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.65685 | −0.188248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.97056 | 0.165227 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5980 | 0.916376 | 0.458188 | − | 0.888855i | \(-0.348499\pi\) | ||||
0.458188 | + | 0.888855i | \(0.348499\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.5563 | −0.582307 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.3137 | −1.70010 | −0.850050 | − | 0.526703i | \(-0.823428\pi\) | ||||
−0.850050 | + | 0.526703i | \(0.823428\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.6274 | 0.616478 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.65685 | 0.187010 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.6569 | −0.450989 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.3553 | −1.76003 | −0.880015 | − | 0.474946i | \(-0.842468\pi\) | ||||
−0.880015 | + | 0.474946i | \(0.842468\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0000 | −0.527218 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.9411 | −0.853863 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.9706 | 1.47862 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.07107 | −0.297933 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −49.5980 | −1.62726 | −0.813628 | − | 0.581385i | \(-0.802511\pi\) | ||||
−0.813628 | + | 0.581385i | \(0.802511\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.3431 | 0.863362 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.3137 | 0.370394 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.28427 | −0.140111 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.62742 | −0.281845 | −0.140923 | − | 0.990021i | \(-0.545007\pi\) | ||||
−0.140923 | + | 0.990021i | \(0.545007\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.9706 | −0.553813 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.3848 | 0.534128 | 0.267064 | − | 0.963679i | \(-0.413946\pi\) | ||||
0.267064 | + | 0.963679i | \(0.413946\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.6569 | 0.444728 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00000 | 0.0650600 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.6274 | −0.345345 | −0.172672 | − | 0.984979i | \(-0.555240\pi\) | ||||
−0.172672 | + | 0.984979i | \(0.555240\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.68629 | −0.152123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.07107 | −0.164441 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.97056 | −0.0962260 | −0.0481130 | − | 0.998842i | \(-0.515321\pi\) | ||||
−0.0481130 | + | 0.998842i | \(0.515321\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.94113 | 0.321687 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.17157 | 0.0378716 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.8284 | −0.478835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.97056 | −0.321631 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.3137 | 0.493477 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.6863 | −0.408386 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.2426 | −0.329381 | −0.164691 | − | 0.986345i | \(-0.552663\pi\) | ||||
−0.164691 | + | 0.986345i | \(0.552663\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.6863 | −0.664539 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.68629 | −0.214573 | −0.107287 | − | 0.994228i | \(-0.534216\pi\) | ||||
−0.107287 | + | 0.994228i | \(0.534216\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 65.9411 | 2.11398 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.1716 | 0.421828 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.2843 | 0.840908 | 0.420454 | − | 0.907314i | \(-0.361871\pi\) | ||||
0.420454 | + | 0.907314i | \(0.361871\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.00000 | −0.127841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.1716 | −0.420536 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.2843 | −1.66761 | −0.833805 | − | 0.552060i | \(-0.813842\pi\) | ||||
−0.833805 | + | 0.552060i | \(0.813842\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.71573 | 0.0546677 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −42.6274 | −1.35685 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.94113 | 0.0617242 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.89949 | 0.250936 | 0.125468 | − | 0.992098i | \(-0.459957\pi\) | ||||
0.125468 | + | 0.992098i | \(0.459957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.94113 | 0.251751 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.9706 | −0.664144 | −0.332072 | − | 0.943254i | \(-0.607748\pi\) | ||||
−0.332072 | + | 0.943254i | \(0.607748\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.65685 | 0.305529 |
(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 | 1536.2.a.e.1.1 | yes | 2 | |
3.2 | odd | 2 | 4608.2.a.a.1.2 | 2 | |||
4.3 | odd | 2 | 1536.2.a.l.1.1 | yes | 2 | ||
8.3 | odd | 2 | 1536.2.a.b.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 1536.2.a.g.1.2 | yes | 2 | ||
12.11 | even | 2 | 4608.2.a.e.1.2 | 2 | |||
16.3 | odd | 4 | 1536.2.d.a.769.4 | 4 | |||
16.5 | even | 4 | 1536.2.d.f.769.3 | 4 | |||
16.11 | odd | 4 | 1536.2.d.a.769.1 | 4 | |||
16.13 | even | 4 | 1536.2.d.f.769.2 | 4 | |||
24.5 | odd | 2 | 4608.2.a.n.1.1 | 2 | |||
24.11 | even | 2 | 4608.2.a.r.1.1 | 2 | |||
48.5 | odd | 4 | 4608.2.d.o.2305.2 | 4 | |||
48.11 | even | 4 | 4608.2.d.c.2305.2 | 4 | |||
48.29 | odd | 4 | 4608.2.d.o.2305.3 | 4 | |||
48.35 | even | 4 | 4608.2.d.c.2305.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.a.b.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
1536.2.a.e.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1536.2.a.g.1.2 | yes | 2 | 8.5 | even | 2 | ||
1536.2.a.l.1.1 | yes | 2 | 4.3 | odd | 2 | ||
1536.2.d.a.769.1 | 4 | 16.11 | odd | 4 | |||
1536.2.d.a.769.4 | 4 | 16.3 | odd | 4 | |||
1536.2.d.f.769.2 | 4 | 16.13 | even | 4 | |||
1536.2.d.f.769.3 | 4 | 16.5 | even | 4 | |||
4608.2.a.a.1.2 | 2 | 3.2 | odd | 2 | |||
4608.2.a.e.1.2 | 2 | 12.11 | even | 2 | |||
4608.2.a.n.1.1 | 2 | 24.5 | odd | 2 | |||
4608.2.a.r.1.1 | 2 | 24.11 | even | 2 | |||
4608.2.d.c.2305.2 | 4 | 48.11 | even | 4 | |||
4608.2.d.c.2305.3 | 4 | 48.35 | even | 4 | |||
4608.2.d.o.2305.2 | 4 | 48.5 | odd | 4 | |||
4608.2.d.o.2305.3 | 4 | 48.29 | odd | 4 |