Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1716,2,Mod(1,1716)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1716, 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("1716.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1716.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: | \(13.7023289869\) |
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 | \(\chi\) | \(=\) | 1716.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.41421 | −1.52688 | −0.763441 | − | 0.645877i | \(-0.776492\pi\) | ||||
−0.763441 | + | 0.645877i | \(0.776492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.41421 | −0.881546 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.24264 | −1.51406 | −0.757031 | − | 0.653379i | \(-0.773351\pi\) | ||||
−0.757031 | + | 0.653379i | \(0.773351\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.82843 | −1.00680 | −0.503398 | − | 0.864054i | \(-0.667917\pi\) | ||||
−0.503398 | + | 0.864054i | \(0.667917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.585786 | −0.108778 | −0.0543889 | − | 0.998520i | \(-0.517321\pi\) | ||||
−0.0543889 | + | 0.998520i | \(0.517321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.41421 | −0.972421 | −0.486211 | − | 0.873842i | \(-0.661621\pi\) | ||||
−0.486211 | + | 0.873842i | \(0.661621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.65685 | −1.63231 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.828427 | 0.136193 | 0.0680963 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680963 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.65685 | 0.571105 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.242641 | −0.0370024 | −0.0185012 | − | 0.999829i | \(-0.505889\pi\) | ||||
−0.0185012 | + | 0.999829i | \(0.505889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.41421 | −0.508961 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.24264 | −0.874145 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.31371 | 1.27934 | 0.639668 | − | 0.768651i | \(-0.279072\pi\) | ||||
0.639668 | + | 0.768651i | \(0.279072\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.41421 | 0.460372 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.82843 | 0.368230 | 0.184115 | − | 0.982905i | \(-0.441058\pi\) | ||||
0.184115 | + | 0.982905i | \(0.441058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.17157 | −0.406078 | −0.203039 | − | 0.979171i | \(-0.565082\pi\) | ||||
−0.203039 | + | 0.979171i | \(0.565082\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.41421 | 0.423481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.24264 | 0.518321 | 0.259161 | − | 0.965834i | \(-0.416554\pi\) | ||||
0.259161 | + | 0.965834i | \(0.416554\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.82843 | −0.581274 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8284 | −1.28510 | −0.642549 | − | 0.766245i | \(-0.722123\pi\) | ||||
−0.642549 | + | 0.766245i | \(0.722123\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.65685 | −0.662085 | −0.331042 | − | 0.943616i | \(-0.607400\pi\) | ||||
−0.331042 | + | 0.943616i | \(0.607400\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.65685 | 0.768667 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.82843 | −0.322329 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.07107 | −0.795557 | −0.397779 | − | 0.917481i | \(-0.630219\pi\) | ||||
−0.397779 | + | 0.917481i | \(0.630219\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.6569 | −1.93809 | −0.969046 | − | 0.246881i | \(-0.920594\pi\) | ||||
−0.969046 | + | 0.246881i | \(0.920594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.3137 | 2.31180 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.585786 | −0.0628029 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8995 | −1.26134 | −0.630672 | − | 0.776050i | \(-0.717221\pi\) | ||||
−0.630672 | + | 0.776050i | \(0.717221\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.41421 | −0.561428 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8284 | −1.30253 | −0.651265 | − | 0.758851i | \(-0.725761\pi\) | ||||
−0.651265 | + | 0.758851i | \(0.725761\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.7279 | −1.86350 | −0.931749 | − | 0.363103i | \(-0.881717\pi\) | ||||
−0.931749 | + | 0.363103i | \(0.881717\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.82843 | −0.278693 | −0.139347 | − | 0.990244i | \(-0.544500\pi\) | ||||
−0.139347 | + | 0.990244i | \(0.544500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.65685 | −0.942412 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.17157 | 0.113260 | 0.0566301 | − | 0.998395i | \(-0.481964\pi\) | ||||
0.0566301 | + | 0.998395i | \(0.481964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.3137 | −1.46679 | −0.733394 | − | 0.679804i | \(-0.762065\pi\) | ||||
−0.733394 | + | 0.679804i | \(0.762065\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.828427 | 0.0786308 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.9706 | 1.78460 | 0.892300 | − | 0.451442i | \(-0.149090\pi\) | ||||
0.892300 | + | 0.451442i | \(0.149090\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.4853 | 1.53726 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.6569 | −1.61860 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.65685 | 0.329727 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.07107 | −0.627456 | −0.313728 | − | 0.949513i | \(-0.601578\pi\) | ||||
−0.313728 | + | 0.949513i | \(0.601578\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.242641 | −0.0213633 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.41421 | −0.293849 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.0711 | 1.11674 | 0.558368 | − | 0.829593i | \(-0.311428\pi\) | ||||
0.558368 | + | 0.829593i | \(0.311428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.24264 | 0.699132 | 0.349566 | − | 0.936912i | \(-0.386329\pi\) | ||||
0.349566 | + | 0.936912i | \(0.386329\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.48528 | 0.203602 | 0.101801 | − | 0.994805i | \(-0.467539\pi\) | ||||
0.101801 | + | 0.994805i | \(0.467539\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.24264 | −0.504688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.4853 | 1.48477 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.34315 | 0.506238 | 0.253119 | − | 0.967435i | \(-0.418544\pi\) | ||||
0.253119 | + | 0.967435i | \(0.418544\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.31371 | 0.738625 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.6569 | −1.07631 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.7279 | −0.996928 | −0.498464 | − | 0.866910i | \(-0.666102\pi\) | ||||
−0.498464 | + | 0.866910i | \(0.666102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.41421 | 0.265796 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3137 | 0.875481 | 0.437741 | − | 0.899101i | \(-0.355779\pi\) | ||||
0.437741 | + | 0.899101i | \(0.355779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.8995 | 1.51293 | 0.756465 | − | 0.654034i | \(-0.226925\pi\) | ||||
0.756465 | + | 0.654034i | \(0.226925\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.8284 | 1.42330 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.82843 | 0.212598 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.82843 | 0.360894 | 0.180447 | − | 0.983585i | \(-0.442246\pi\) | ||||
0.180447 | + | 0.983585i | \(0.442246\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.9706 | 1.85605 | 0.928024 | − | 0.372521i | \(-0.121507\pi\) | ||||
0.928024 | + | 0.372521i | \(0.121507\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.17157 | −0.234449 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.82843 | −0.207950 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.24264 | 0.456507 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.82843 | 0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.34315 | −0.169544 | −0.0847720 | − | 0.996400i | \(-0.527016\pi\) | ||||
−0.0847720 | + | 0.996400i | \(0.527016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.65685 | −0.407189 | −0.203595 | − | 0.979055i | \(-0.565262\pi\) | ||||
−0.203595 | + | 0.979055i | \(0.565262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.41421 | 0.244497 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.1421 | −0.865091 | −0.432546 | − | 0.901612i | \(-0.642385\pi\) | ||||
−0.432546 | + | 0.901612i | \(0.642385\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.48528 | −0.317953 | −0.158977 | − | 0.987282i | \(-0.550819\pi\) | ||||
−0.158977 | + | 0.987282i | \(0.550819\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.24264 | 0.299253 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.65685 | −0.116288 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.4853 | −0.872010 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.82843 | −0.335599 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5858 | 0.728756 | 0.364378 | − | 0.931251i | \(-0.381282\pi\) | ||||
0.364378 | + | 0.931251i | \(0.381282\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.8284 | −0.741952 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.828427 | 0.0564983 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.3137 | −1.03956 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.65685 | −0.382255 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.24264 | 0.419925 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.8995 | −1.46650 | −0.733249 | − | 0.679960i | \(-0.761997\pi\) | ||||
−0.733249 | + | 0.679960i | \(0.761997\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.1421 | 0.805902 | 0.402951 | − | 0.915222i | \(-0.367985\pi\) | ||||
0.402951 | + | 0.915222i | \(0.367985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.31371 | 0.0868123 | 0.0434062 | − | 0.999058i | \(-0.486179\pi\) | ||||
0.0434062 | + | 0.999058i | \(0.486179\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.82843 | −0.186097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.58579 | 0.562474 | 0.281237 | − | 0.959638i | \(-0.409255\pi\) | ||||
0.281237 | + | 0.959638i | \(0.409255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.3137 | 1.78175 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.07107 | −0.459315 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.1421 | 1.30289 | 0.651443 | − | 0.758697i | \(-0.274164\pi\) | ||||
0.651443 | + | 0.758697i | \(0.274164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.343146 | −0.0221040 | −0.0110520 | − | 0.999939i | \(-0.503518\pi\) | ||||
−0.0110520 | + | 0.999939i | \(0.503518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.41421 | −0.218126 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.6569 | −1.11896 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.6569 | 1.61945 | 0.809723 | − | 0.586812i | \(-0.199617\pi\) | ||||
0.809723 | + | 0.586812i | \(0.199617\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.82843 | 0.303561 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.3137 | 1.33472 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.828427 | −0.0516759 | −0.0258379 | − | 0.999666i | \(-0.508225\pi\) | ||||
−0.0258379 | + | 0.999666i | \(0.508225\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.34315 | 0.145596 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.585786 | −0.0362593 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.48528 | 0.523225 | 0.261612 | − | 0.965173i | \(-0.415746\pi\) | ||||
0.261612 | + | 0.965173i | \(0.415746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.7990 | −1.95340 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.8995 | −0.728237 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.82843 | −0.538279 | −0.269139 | − | 0.963101i | \(-0.586739\pi\) | ||||
−0.269139 | + | 0.963101i | \(0.586739\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.65685 | 0.100647 | 0.0503234 | − | 0.998733i | \(-0.483975\pi\) | ||||
0.0503234 | + | 0.998733i | \(0.483975\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.82843 | −0.171184 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.65685 | −0.401423 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.9706 | 0.899494 | 0.449747 | − | 0.893156i | \(-0.351514\pi\) | ||||
0.449747 | + | 0.893156i | \(0.351514\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.41421 | −0.324140 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.6569 | −1.41125 | −0.705625 | − | 0.708586i | \(-0.749334\pi\) | ||||
−0.705625 | + | 0.708586i | \(0.749334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.0711 | 1.60921 | 0.804604 | − | 0.593812i | \(-0.202378\pi\) | ||||
0.804604 | + | 0.593812i | \(0.202378\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3431 | 0.610537 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.9706 | 1.29239 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.8284 | −0.752016 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.51472 | −0.0884908 | −0.0442454 | − | 0.999021i | \(-0.514088\pi\) | ||||
−0.0442454 | + | 0.999021i | \(0.514088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.65685 | −0.562244 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.82843 | 0.279235 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.686292 | −0.0395572 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.7279 | −1.07589 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.8284 | 0.620034 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.82843 | −0.160904 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.8284 | −1.40789 | −0.703945 | − | 0.710254i | \(-0.748580\pi\) | ||||
−0.703945 | + | 0.710254i | \(0.748580\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.6274 | −1.27898 | −0.639489 | − | 0.768801i | \(-0.720854\pi\) | ||||
−0.639489 | + | 0.768801i | \(0.720854\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.65685 | −0.544102 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.92893 | −0.389168 | −0.194584 | − | 0.980886i | \(-0.562336\pi\) | ||||
−0.194584 | + | 0.980886i | \(0.562336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.585786 | 0.0327977 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.17157 | 0.0653908 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.65685 | −0.369256 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.3137 | −0.846850 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.6274 | −1.24749 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.5563 | 1.73449 | 0.867247 | − | 0.497878i | \(-0.165887\pi\) | ||||
0.867247 | + | 0.497878i | \(0.165887\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.828427 | 0.0453975 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.4853 | −0.791415 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.51472 | 0.518300 | 0.259150 | − | 0.965837i | \(-0.416558\pi\) | ||||
0.259150 | + | 0.965837i | \(0.416558\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.9706 | 1.03034 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.41421 | 0.293196 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.4853 | 0.887538 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.6569 | −1.37733 | −0.688666 | − | 0.725079i | \(-0.741803\pi\) | ||||
−0.688666 | + | 0.725079i | \(0.741803\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.9411 | −1.92388 | −0.961942 | − | 0.273253i | \(-0.911900\pi\) | ||||
−0.961942 | + | 0.273253i | \(0.911900\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.7279 | 0.783888 | 0.391944 | − | 0.919989i | \(-0.371803\pi\) | ||||
0.391944 | + | 0.919989i | \(0.371803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.9706 | 1.96219 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.6569 | −0.934500 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.1421 | −0.851949 | −0.425975 | − | 0.904735i | \(-0.640069\pi\) | ||||
−0.425975 | + | 0.904735i | \(0.640069\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.3137 | 1.01093 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.68629 | 0.453421 | 0.226710 | − | 0.973962i | \(-0.427203\pi\) | ||||
0.226710 | + | 0.973962i | \(0.427203\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.65685 | 0.190368 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.3431 | 1.36767 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.4558 | 1.00739 | 0.503693 | − | 0.863883i | \(-0.331974\pi\) | ||||
0.503693 | + | 0.863883i | \(0.331974\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.65685 | −0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.585786 | 0.0301695 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.6985 | 1.52551 | 0.762754 | − | 0.646688i | \(-0.223847\pi\) | ||||
0.762754 | + | 0.646688i | \(0.223847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.07107 | −0.362262 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.7990 | −1.01168 | −0.505841 | − | 0.862627i | \(-0.668818\pi\) | ||||
−0.505841 | + | 0.862627i | \(0.668818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.65685 | 0.492159 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.242641 | −0.0123341 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.7990 | −0.902445 | −0.451222 | − | 0.892412i | \(-0.649012\pi\) | ||||
−0.451222 | + | 0.892412i | \(0.649012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.1421 | 1.52435 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.00000 | 0.403547 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.1421 | 1.21472 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.7990 | −1.89708 | −0.948538 | − | 0.316662i | \(-0.897438\pi\) | ||||
−0.948538 | + | 0.316662i | \(0.897438\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.2132 | −0.959462 | −0.479731 | − | 0.877416i | \(-0.659266\pi\) | ||||
−0.479731 | + | 0.877416i | \(0.659266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.41421 | 0.269701 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.41421 | −0.169654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.828427 | −0.0410636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.34315 | 0.115861 | 0.0579306 | − | 0.998321i | \(-0.481550\pi\) | ||||
0.0579306 | + | 0.998321i | \(0.481550\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.0711 | 0.644748 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 60.2843 | 2.95924 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.24264 | 0.403644 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.8284 | 1.40836 | 0.704180 | − | 0.710021i | \(-0.251315\pi\) | ||||
0.704180 | + | 0.710021i | \(0.251315\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.3137 | −1.81856 | −0.909279 | − | 0.416186i | \(-0.863366\pi\) | ||||
−0.909279 | + | 0.416186i | \(0.863366\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.00000 | −0.388973 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −41.5563 | −2.01578 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.97056 | −0.434116 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.6569 | −0.657828 | −0.328914 | − | 0.944360i | \(-0.606683\pi\) | ||||
−0.328914 | + | 0.944360i | \(0.606683\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.00000 | 0.0958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.41421 | 0.449316 | 0.224658 | − | 0.974438i | \(-0.427874\pi\) | ||||
0.224658 | + | 0.974438i | \(0.427874\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.3137 | −1.10767 | −0.553834 | − | 0.832627i | \(-0.686836\pi\) | ||||
−0.553834 | + | 0.832627i | \(0.686836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 40.6274 | 1.92592 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.48528 | 0.117550 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.58579 | 0.405188 | 0.202594 | − | 0.979263i | \(-0.435063\pi\) | ||||
0.202594 | + | 0.979263i | \(0.435063\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.65685 | −0.172195 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0000 | 0.563809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.65685 | 0.452720 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.3137 | 1.18413 | 0.592063 | − | 0.805892i | \(-0.298314\pi\) | ||||
0.592063 | + | 0.805892i | \(0.298314\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.24264 | −0.291382 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.9706 | 0.510950 | 0.255475 | − | 0.966816i | \(-0.417768\pi\) | ||||
0.255475 | + | 0.966816i | \(0.417768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9289 | 0.600858 | 0.300429 | − | 0.953804i | \(-0.402870\pi\) | ||||
0.300429 | + | 0.953804i | \(0.402870\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.4853 | 0.857234 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.4558 | −1.08541 | −0.542704 | − | 0.839924i | \(-0.682599\pi\) | ||||
−0.542704 | + | 0.839924i | \(0.682599\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | 0.554109 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.34315 | 0.292277 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.242641 | 0.0111566 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.31371 | 0.426445 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.1421 | 1.10308 | 0.551541 | − | 0.834148i | \(-0.314040\pi\) | ||||
0.551541 | + | 0.834148i | \(0.314040\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.828427 | −0.0377730 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.6569 | −0.621408 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 43.7990 | 1.98881 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.5563 | −0.523668 | −0.261834 | − | 0.965113i | \(-0.584327\pi\) | ||||
−0.261834 | + | 0.965113i | \(0.584327\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.7279 | −0.575577 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.9706 | 0.946388 | 0.473194 | − | 0.880958i | \(-0.343101\pi\) | ||||
0.473194 | + | 0.880958i | \(0.343101\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.65685 | 0.164696 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.41421 | 0.153457 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.6274 | −1.37383 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.89949 | 0.443162 | 0.221581 | − | 0.975142i | \(-0.428878\pi\) | ||||
0.221581 | + | 0.975142i | \(0.428878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.3137 | 0.505459 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.4853 | −1.09174 | −0.545872 | − | 0.837868i | \(-0.683802\pi\) | ||||
−0.545872 | + | 0.837868i | \(0.683802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 63.9411 | 2.84534 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.55635 | 0.423578 | 0.211789 | − | 0.977315i | \(-0.432071\pi\) | ||||
0.211789 | + | 0.977315i | \(0.432071\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | −0.707798 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.65685 | 0.425532 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | 0.351840 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.8995 | 0.873491 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.9706 | 0.655872 | 0.327936 | − | 0.944700i | \(-0.393647\pi\) | ||||
0.327936 | + | 0.944700i | \(0.393647\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.10051 | −0.0918487 | −0.0459243 | − | 0.998945i | \(-0.514623\pi\) | ||||
−0.0459243 | + | 0.998945i | \(0.514623\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.8284 | 0.821740 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.7990 | 1.47231 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.82843 | 0.122743 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.65685 | −0.158396 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | −0.172935 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.82843 | 0.208362 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.0000 | 0.773880 | 0.386940 | − | 0.922105i | \(-0.373532\pi\) | ||||
0.386940 | + | 0.922105i | \(0.373532\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.9706 | 1.07159 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 52.2843 | 2.23961 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.1005 | 1.11598 | 0.557989 | − | 0.829849i | \(-0.311573\pi\) | ||||
0.557989 | + | 0.829849i | \(0.311573\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.17157 | −0.135359 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.0000 | −0.850487 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.82843 | −0.120060 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.4853 | 1.12222 | 0.561109 | − | 0.827742i | \(-0.310375\pi\) | ||||
0.561109 | + | 0.827742i | \(0.310375\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.242641 | 0.0102626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.24264 | 0.263564 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.65685 | −0.0698281 | −0.0349140 | − | 0.999390i | \(-0.511116\pi\) | ||||
−0.0349140 | + | 0.999390i | \(0.511116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −64.7696 | −2.72488 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.82843 | 0.118783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.5563 | 0.568312 | 0.284156 | − | 0.958778i | \(-0.408287\pi\) | ||||
0.284156 | + | 0.958778i | \(0.408287\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.0416 | −1.17351 | −0.586753 | − | 0.809766i | \(-0.699594\pi\) | ||||
−0.586753 | + | 0.809766i | \(0.699594\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.34315 | −0.0978863 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.1421 | −1.34042 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.9706 | 1.12280 | 0.561400 | − | 0.827545i | \(-0.310263\pi\) | ||||
0.561400 | + | 0.827545i | \(0.310263\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.65685 | −0.235091 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −49.9411 | −2.07191 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.31371 | −0.385734 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.41421 | 0.141160 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.7990 | −1.31248 | −0.656242 | − | 0.754550i | \(-0.727855\pi\) | ||||
−0.656242 | + | 0.754550i | \(0.727855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.1421 | −0.499461 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.1716 | −0.787282 | −0.393641 | − | 0.919264i | \(-0.628785\pi\) | ||||
−0.393641 | + | 0.919264i | \(0.628785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 60.2843 | 2.47141 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.48528 | −0.183570 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.6569 | −0.558004 | −0.279002 | − | 0.960291i | \(-0.590004\pi\) | ||||
−0.279002 | + | 0.960291i | \(0.590004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.2548 | 1.76440 | 0.882201 | − | 0.470874i | \(-0.156061\pi\) | ||||
0.882201 | + | 0.470874i | \(0.156061\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.24264 | 0.172774 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.41421 | −0.138808 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.2132 | 0.536307 | 0.268154 | − | 0.963376i | \(-0.413586\pi\) | ||||
0.268154 | + | 0.963376i | \(0.413586\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.65685 | −0.0671391 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.9411 | −1.53243 | −0.766214 | − | 0.642586i | \(-0.777862\pi\) | ||||
−0.766214 | + | 0.642586i | \(0.777862\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.4853 | −0.503455 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.9289 | 1.08412 | 0.542059 | − | 0.840340i | \(-0.317645\pi\) | ||||
0.542059 | + | 0.840340i | \(0.317645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.41421 | 0.378389 | 0.189195 | − | 0.981940i | \(-0.439412\pi\) | ||||
0.189195 | + | 0.981940i | \(0.439412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.82843 | −0.193758 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.6569 | −1.34843 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.17157 | −0.206204 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.0711 | −1.71463 | −0.857316 | − | 0.514790i | \(-0.827870\pi\) | ||||
−0.857316 | + | 0.514790i | \(0.827870\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.5858 | 0.420747 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.1421 | 0.958051 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.8284 | −0.428366 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.5980 | 1.48503 | 0.742515 | − | 0.669829i | \(-0.233633\pi\) | ||||
0.742515 | + | 0.669829i | \(0.233633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.55635 | −0.297993 | −0.148997 | − | 0.988838i | \(-0.547604\pi\) | ||||
−0.148997 | + | 0.988838i | \(0.547604\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.828427 | 0.0326193 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.6569 | 1.16593 | 0.582966 | − | 0.812497i | \(-0.301892\pi\) | ||||
0.582966 | + | 0.812497i | \(0.301892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.82843 | −0.111025 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.3137 | −0.600192 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.8284 | −1.12814 | −0.564072 | − | 0.825726i | \(-0.690766\pi\) | ||||
−0.564072 | + | 0.825726i | \(0.690766\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.3137 | −1.06723 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.65685 | −0.220695 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.1127 | −1.21198 | −0.605989 | − | 0.795473i | \(-0.707223\pi\) | ||||
−0.605989 | + | 0.795473i | \(0.707223\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.82843 | 0.343386 | 0.171693 | − | 0.985151i | \(-0.445076\pi\) | ||||
0.171693 | + | 0.985151i | \(0.445076\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.24264 | 0.242444 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.82843 | 0.109517 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.8995 | −0.846683 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.17157 | 0.122437 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.6569 | −0.449339 | −0.224669 | − | 0.974435i | \(-0.572130\pi\) | ||||
−0.224669 | + | 0.974435i | \(0.572130\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.65685 | 0.256222 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.7574 | −0.528738 | −0.264369 | − | 0.964422i | \(-0.585164\pi\) | ||||
−0.264369 | + | 0.964422i | \(0.585164\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.2843 | −1.39246 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.1421 | 0.465288 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.82843 | 0.261283 | 0.130641 | − | 0.991430i | \(-0.458296\pi\) | ||||
0.130641 | + | 0.991430i | \(0.458296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −44.6274 | −1.70513 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.31371 | 0.0501211 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.31371 | −0.354824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.44365 | −0.321212 | −0.160606 | − | 0.987019i | \(-0.551345\pi\) | ||||
−0.160606 | + | 0.987019i | \(0.551345\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.82843 | −0.107443 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28.1421 | −1.06749 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.8284 | −0.864688 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.58579 | 0.324744 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.2426 | 1.14225 | 0.571124 | − | 0.820864i | \(-0.306507\pi\) | ||||
0.571124 | + | 0.820864i | \(0.306507\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 27.3137 | 1.02869 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −52.9706 | −1.99216 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.6274 | −1.82624 | −0.913120 | − | 0.407690i | \(-0.866334\pi\) | ||||
−0.913120 | + | 0.407690i | \(0.866334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.07107 | −0.265186 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.1421 | 0.979031 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.41421 | −0.127684 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.1421 | 0.752222 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.3137 | −1.31698 | −0.658490 | − | 0.752590i | \(-0.728804\pi\) | ||||
−0.658490 | + | 0.752590i | \(0.728804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.343146 | −0.0127617 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.89949 | −0.144824 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.1716 | −0.636858 | −0.318429 | − | 0.947947i | \(-0.603155\pi\) | ||||
−0.318429 | + | 0.947947i | \(0.603155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.51472 | 0.0560239 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.6274 | 0.540276 | 0.270138 | − | 0.962822i | \(-0.412931\pi\) | ||||
0.270138 | + | 0.962822i | \(0.412931\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.41421 | −0.125935 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.24264 | −0.156280 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.17157 | 0.337382 | 0.168691 | − | 0.985669i | \(-0.446046\pi\) | ||||
0.168691 | + | 0.985669i | \(0.446046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.9411 | 0.951688 | 0.475844 | − | 0.879530i | \(-0.342143\pi\) | ||||
0.475844 | + | 0.879530i | \(0.342143\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.48528 | −0.310877 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.6569 | −0.646031 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.31371 | 0.121080 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.3137 | −0.704767 | −0.352384 | − | 0.935856i | \(-0.614629\pi\) | ||||
−0.352384 | + | 0.935856i | \(0.614629\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.6569 | 0.934988 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.9706 | −1.49107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.2843 | −0.882627 | −0.441313 | − | 0.897353i | \(-0.645487\pi\) | ||||
−0.441313 | + | 0.897353i | \(0.645487\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.82843 | 0.175261 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.1716 | −0.694969 | −0.347484 | − | 0.937686i | \(-0.612964\pi\) | ||||
−0.347484 | + | 0.937686i | \(0.612964\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.3137 | −1.56806 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.3137 | 0.770599 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.82843 | −0.102129 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.0000 | −0.649097 | −0.324548 | − | 0.945869i | \(-0.605212\pi\) | ||||
−0.324548 | + | 0.945869i | \(0.605212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.828427 | −0.0298351 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.58579 | −0.164939 | −0.0824696 | − | 0.996594i | \(-0.526281\pi\) | ||||
−0.0824696 | + | 0.996594i | \(0.526281\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.0416 | −1.29465 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.34315 | 0.0840599 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.8284 | 0.387472 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.585786 | −0.0209343 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.6569 | −0.772966 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.7990 | −0.563173 | −0.281587 | − | 0.959536i | \(-0.590861\pi\) | ||||
−0.281587 | + | 0.959536i | \(0.590861\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.48528 | 0.302084 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 53.6569 | 1.90782 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.17157 | 0.112626 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −31.7990 | −1.12779 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.51472 | 0.195341 | 0.0976707 | − | 0.995219i | \(-0.468861\pi\) | ||||
0.0976707 | + | 0.995219i | \(0.468861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 49.9411 | 1.76679 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.8995 | −0.420448 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.65685 | 0.199626 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 46.6274 | 1.64340 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.82843 | −0.310775 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.3848 | −0.716691 | −0.358345 | − | 0.933589i | \(-0.616659\pi\) | ||||
−0.358345 | + | 0.933589i | \(0.616659\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.2843 | 0.571818 | 0.285909 | − | 0.958257i | \(-0.407704\pi\) | ||||
0.285909 | + | 0.958257i | \(0.407704\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.65685 | 0.0581084 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.4558 | 1.52219 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.82843 | −0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.6274 | −1.41791 | −0.708953 | − | 0.705255i | \(-0.750832\pi\) | ||||
−0.708953 | + | 0.705255i | \(0.750832\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.45584 | 0.0507475 | 0.0253738 | − | 0.999678i | \(-0.491922\pi\) | ||||
0.0253738 | + | 0.999678i | \(0.491922\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.65685 | −0.231762 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.7696 | 1.48724 | 0.743622 | − | 0.668601i | \(-0.233106\pi\) | ||||
0.743622 | + | 0.668601i | \(0.233106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.3137 | −1.43488 | −0.717442 | − | 0.696618i | \(-0.754687\pi\) | ||||
−0.717442 | + | 0.696618i | \(0.754687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.9706 | 0.519323 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.24264 | −0.216295 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.6274 | −1.33676 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.41421 | −0.187143 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.6569 | −1.43815 | −0.719077 | − | 0.694930i | \(-0.755435\pi\) | ||||
−0.719077 | + | 0.694930i | \(0.755435\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6569 | −0.988167 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.6569 | −0.814785 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.41421 | −0.117453 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.82843 | 0.0971859 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.0711 | 0.929077 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.00000 | −0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.3137 | −0.592810 | −0.296405 | − | 0.955062i | \(-0.595788\pi\) | ||||
−0.296405 | + | 0.955062i | \(0.595788\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.0711 | 0.856411 | 0.428206 | − | 0.903681i | \(-0.359146\pi\) | ||||
0.428206 | + | 0.903681i | \(0.359146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.8284 | −0.778896 | −0.389448 | − | 0.921048i | \(-0.627334\pi\) | ||||
−0.389448 | + | 0.921048i | \(0.627334\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.3431 | 0.352493 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.7696 | 0.707004 | 0.353502 | − | 0.935434i | \(-0.384991\pi\) | ||||
0.353502 | + | 0.935434i | \(0.384991\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −67.9411 | −2.31007 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.9706 | 0.746159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.07107 | 0.239870 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.24264 | −0.143756 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.8284 | −0.434176 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.0000 | −0.540899 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6569 | 0.933906 | 0.466953 | − | 0.884282i | \(-0.345352\pi\) | ||||
0.466953 | + | 0.884282i | \(0.345352\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.51472 | −0.0510902 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.0294 | 0.438973 | 0.219486 | − | 0.975616i | \(-0.429562\pi\) | ||||
0.219486 | + | 0.975616i | \(0.429562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.8284 | −1.17207 | −0.586035 | − | 0.810286i | \(-0.699312\pi\) | ||||
−0.586035 | + | 0.810286i | \(0.699312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.65685 | −0.324612 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.48528 | 0.284908 | 0.142454 | − | 0.989801i | \(-0.454501\pi\) | ||||
0.142454 | + | 0.989801i | \(0.454501\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0000 | −0.670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.4853 | −0.551042 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.82843 | 0.161216 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.17157 | 0.105778 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.1421 | −1.93700 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.686292 | −0.0228384 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −85.2548 | −2.83397 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.3137 | 0.375666 | 0.187833 | − | 0.982201i | \(-0.439854\pi\) | ||||
0.187833 | + | 0.982201i | \(0.439854\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.7279 | −0.621166 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.2843 | 1.46720 | 0.733602 | − | 0.679580i | \(-0.237838\pi\) | ||||
0.733602 | + | 0.679580i | \(0.237838\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.6569 | 0.584357 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.8284 | 0.357977 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.6274 | 0.747223 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.4142 | −1.36613 | −0.683064 | − | 0.730358i | \(-0.739353\pi\) | ||||
−0.683064 | + | 0.730358i | \(0.739353\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.0000 | 0.922631 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.8284 | 0.356422 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.51472 | 0.181323 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.82843 | −0.0928977 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.9289 | −0.621038 | −0.310519 | − | 0.950567i | \(-0.600503\pi\) | ||||
−0.310519 | + | 0.950567i | \(0.600503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.8284 | −0.812846 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.3137 | −0.697033 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.2843 | 0.727995 | 0.363998 | − | 0.931400i | \(-0.381412\pi\) | ||||
0.363998 | + | 0.931400i | \(0.381412\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.6274 | −0.738418 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0000 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.6569 | −0.574986 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.65685 | −0.314137 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.6274 | −0.345345 | −0.172672 | − | 0.984979i | \(-0.555240\pi\) | ||||
−0.172672 | + | 0.984979i | \(0.555240\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.65685 | 0.183629 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.92893 | −0.224686 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.4142 | 1.14718 | 0.573589 | − | 0.819143i | \(-0.305550\pi\) | ||||
0.573589 | + | 0.819143i | \(0.305550\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | 0.258874 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.585786 | 0.0189358 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.9706 | 1.19384 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.68629 | −0.0543965 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.17157 | 0.0377534 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.3137 | 0.621730 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.4264 | 1.49297 | 0.746486 | − | 0.665401i | \(-0.231739\pi\) | ||||
0.746486 | + | 0.665401i | \(0.231739\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.1716 | −1.00034 | −0.500172 | − | 0.865926i | \(-0.666730\pi\) | ||||
−0.500172 | + | 0.865926i | \(0.666730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.3137 | 0.747403 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.65685 | −0.213190 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.5563 | 0.433706 | 0.216853 | − | 0.976204i | \(-0.430421\pi\) | ||||
0.216853 | + | 0.976204i | \(0.430421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.8995 | 0.380310 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.3137 | −0.488929 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.5980 | 0.880239 | 0.440119 | − | 0.897939i | \(-0.354936\pi\) | ||||
0.440119 | + | 0.897939i | \(0.354936\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.4558 | 1.32089 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.6274 | −0.720239 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.17157 | 0.0372539 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4558 | −0.808632 | −0.404316 | − | 0.914619i | \(-0.632490\pi\) | ||||
−0.404316 | + | 0.914619i | \(0.632490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.5563 | 1.00141 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.3137 | 0.485477 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.85786 | −0.122180 | −0.0610899 | − | 0.998132i | \(-0.519458\pi\) | ||||
−0.0610899 | + | 0.998132i | \(0.519458\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.828427 | 0.0262103 |
(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 | 1716.2.a.e.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 5148.2.a.j.1.2 | 2 | |||
4.3 | odd | 2 | 6864.2.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1716.2.a.e.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
5148.2.a.j.1.2 | 2 | 3.2 | odd | 2 | |||
6864.2.a.bb.1.1 | 2 | 4.3 | odd | 2 |