Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | −0.452441 | −0.261217 | −0.130609 | − | 0.991434i | \(-0.541693\pi\) | ||||
−0.130609 | + | 0.991434i | \(0.541693\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.91039 | 0.854354 | 0.427177 | − | 0.904168i | \(-0.359508\pi\) | ||||
0.427177 | + | 0.904168i | \(0.359508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.96124 | −0.741279 | −0.370640 | − | 0.928777i | \(-0.620862\pi\) | ||||
−0.370640 | + | 0.928777i | \(0.620862\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.79530 | −0.931766 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.787387 | −0.237406 | −0.118703 | − | 0.992930i | \(-0.537874\pi\) | ||||
−0.118703 | + | 0.992930i | \(0.537874\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.79638 | 1.60763 | 0.803814 | − | 0.594881i | \(-0.202801\pi\) | ||||
0.803814 | + | 0.594881i | \(0.202801\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.864341 | −0.223172 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.13249 | −0.759740 | −0.379870 | − | 0.925040i | \(-0.624031\pi\) | ||||
−0.379870 | + | 0.925040i | \(0.624031\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.63676 | −1.06375 | −0.531873 | − | 0.846824i | \(-0.678512\pi\) | ||||
−0.531873 | + | 0.846824i | \(0.678512\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.887346 | 0.193635 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.51256 | −0.523906 | −0.261953 | − | 0.965081i | \(-0.584367\pi\) | ||||
−0.261953 | + | 0.965081i | \(0.584367\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.35039 | −0.270079 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.62203 | 0.504610 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.62687 | 0.673493 | 0.336746 | − | 0.941595i | \(-0.390674\pi\) | ||||
0.336746 | + | 0.941595i | \(0.390674\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.20008 | 1.11357 | 0.556783 | − | 0.830658i | \(-0.312035\pi\) | ||||
0.556783 | + | 0.830658i | \(0.312035\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.356246 | 0.0620145 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.74674 | −0.633315 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.71962 | 1.59790 | 0.798948 | − | 0.601400i | \(-0.205390\pi\) | ||||
0.798948 | + | 0.601400i | \(0.205390\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.62252 | −0.419940 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.892103 | −0.139323 | −0.0696615 | − | 0.997571i | \(-0.522192\pi\) | ||||
−0.0696615 | + | 0.997571i | \(0.522192\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.80229 | 0.884840 | 0.442420 | − | 0.896808i | \(-0.354120\pi\) | ||||
0.442420 | + | 0.896808i | \(0.354120\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.34012 | −0.796058 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.65849 | −0.533646 | −0.266823 | − | 0.963746i | \(-0.585974\pi\) | ||||
−0.266823 | + | 0.963746i | \(0.585974\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.15353 | −0.450505 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.41727 | 0.198457 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.6489 | 1.73746 | 0.868729 | − | 0.495288i | \(-0.164938\pi\) | ||||
0.868729 | + | 0.495288i | \(0.164938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50422 | −0.202829 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.09786 | 0.277869 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.08621 | −0.792357 | −0.396178 | − | 0.918174i | \(-0.629664\pi\) | ||||
−0.396178 | + | 0.918174i | \(0.629664\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.47835 | 0.829467 | 0.414734 | − | 0.909943i | \(-0.363875\pi\) | ||||
0.414734 | + | 0.909943i | \(0.363875\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.48225 | 0.690699 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.0734 | 1.37348 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.94464 | 1.09276 | 0.546381 | − | 0.837537i | \(-0.316005\pi\) | ||||
0.546381 | + | 0.837537i | \(0.316005\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.13679 | 0.136853 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.14955 | −0.848496 | −0.424248 | − | 0.905546i | \(-0.639461\pi\) | ||||
−0.424248 | + | 0.905546i | \(0.639461\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3319 | −1.32629 | −0.663147 | − | 0.748489i | \(-0.730780\pi\) | ||||
−0.663147 | + | 0.748489i | \(0.730780\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.610974 | 0.0705492 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.54426 | 0.175984 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.9354 | 1.34283 | 0.671416 | − | 0.741080i | \(-0.265686\pi\) | ||||
0.671416 | + | 0.741080i | \(0.265686\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.19957 | 0.799953 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.55162 | −0.499606 | −0.249803 | − | 0.968297i | \(-0.580366\pi\) | ||||
−0.249803 | + | 0.968297i | \(0.580366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.98429 | −0.649087 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.64095 | −0.175928 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.55704 | 0.165046 | 0.0825228 | − | 0.996589i | \(-0.473702\pi\) | ||||
0.0825228 | + | 0.996589i | \(0.473702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3681 | −1.19170 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.80517 | −0.290883 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.85805 | −0.908816 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.55502 | 0.564027 | 0.282013 | − | 0.959410i | \(-0.408998\pi\) | ||||
0.282013 | + | 0.959410i | \(0.408998\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.20098 | 0.221207 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.50744 | 0.249500 | 0.124750 | − | 0.992188i | \(-0.460187\pi\) | ||||
0.124750 | + | 0.992188i | \(0.460187\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.7471 | 1.55161 | 0.775805 | − | 0.630973i | \(-0.217344\pi\) | ||||
0.775805 | + | 0.630973i | \(0.217344\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.69518 | 0.165433 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.5671 | 1.40826 | 0.704129 | − | 0.710072i | \(-0.251338\pi\) | ||||
0.704129 | + | 0.710072i | \(0.251338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.2481 | 1.84364 | 0.921818 | − | 0.387623i | \(-0.126704\pi\) | ||||
0.921818 | + | 0.387623i | \(0.126704\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.39756 | −0.417398 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.5531 | 1.46311 | 0.731555 | − | 0.681782i | \(-0.238795\pi\) | ||||
0.731555 | + | 0.681782i | \(0.238795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.79999 | −0.447601 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.2026 | −1.49793 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.14356 | 0.563179 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3800 | −0.943638 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.403624 | 0.0363936 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1318 | −1.08510 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.29660 | −0.203790 | −0.101895 | − | 0.994795i | \(-0.532491\pi\) | ||||
−0.101895 | + | 0.994795i | \(0.532491\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.62519 | −0.231135 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3850 | 0.994711 | 0.497355 | − | 0.867547i | \(-0.334305\pi\) | ||||
0.497355 | + | 0.867547i | \(0.334305\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.09381 | 0.788533 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.00912 | 0.431116 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.6460 | −1.76390 | −0.881951 | − | 0.471340i | \(-0.843770\pi\) | ||||
−0.881951 | + | 0.471340i | \(0.843770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.4827 | −1.56769 | −0.783843 | − | 0.620959i | \(-0.786743\pi\) | ||||
−0.783843 | + | 0.620959i | \(0.786743\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.65525 | 0.139398 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.56400 | −0.381661 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.92875 | 0.575401 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.42679 | 0.117680 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.25249 | 0.430301 | 0.215150 | − | 0.976581i | \(-0.430976\pi\) | ||||
0.215150 | + | 0.976581i | \(0.430976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.5014 | −1.91252 | −0.956258 | − | 0.292525i | \(-0.905504\pi\) | ||||
−0.956258 | + | 0.292525i | \(0.905504\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.75623 | 0.707899 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.8446 | 0.951381 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0874349 | −0.00697807 | −0.00348903 | − | 0.999994i | \(-0.501111\pi\) | ||||
−0.00348903 | + | 0.999994i | \(0.501111\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.72288 | −0.453854 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.92774 | 0.388361 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.1980 | 1.50371 | 0.751853 | − | 0.659331i | \(-0.229160\pi\) | ||||
0.751853 | + | 0.659331i | \(0.229160\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.680571 | 0.0529824 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.82664 | −0.141349 | −0.0706747 | − | 0.997499i | \(-0.522515\pi\) | ||||
−0.0706747 | + | 0.997499i | \(0.522515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.5981 | 1.58447 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.9611 | 0.991162 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.4790 | 1.63302 | 0.816509 | − | 0.577333i | \(-0.195906\pi\) | ||||
0.816509 | + | 0.577333i | \(0.195906\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.64845 | 0.200204 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.75365 | 0.206977 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.53705 | −0.563346 | −0.281673 | − | 0.959510i | \(-0.590889\pi\) | ||||
−0.281673 | + | 0.959510i | \(0.590889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.63731 | 0.196029 | 0.0980147 | − | 0.995185i | \(-0.468751\pi\) | ||||
0.0980147 | + | 0.995185i | \(0.468751\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.93107 | −0.216671 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.5683 | 1.36517 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.46648 | 0.180367 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.14244 | −0.374057 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.11657 | 0.370222 | 0.185111 | − | 0.982718i | \(-0.440736\pi\) | ||||
0.185111 | + | 0.982718i | \(0.440736\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.28124 | −0.0922257 | −0.0461128 | − | 0.998936i | \(-0.514683\pi\) | ||||
−0.0461128 | + | 0.998936i | \(0.514683\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.01006 | −0.358778 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.8801 | 0.917667 | 0.458833 | − | 0.888522i | \(-0.348267\pi\) | ||||
0.458833 | + | 0.888522i | \(0.348267\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0559 | 1.70528 | 0.852638 | − | 0.522503i | \(-0.175001\pi\) | ||||
0.852638 | + | 0.522503i | \(0.175001\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.04693 | −0.285448 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.11316 | −0.499246 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.70427 | −0.119031 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.02336 | 0.488157 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.65093 | 0.252540 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.7763 | 0.741874 | 0.370937 | − | 0.928658i | \(-0.379037\pi\) | ||||
0.370937 | + | 0.928658i | \(0.379037\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.23475 | 0.221642 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.0847 | 0.755967 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.1598 | −0.825464 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.12700 | 0.346451 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.1571 | −1.22138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.8073 | −1.05854 | −0.529268 | − | 0.848455i | \(-0.677534\pi\) | ||||
−0.529268 | + | 0.848455i | \(0.677534\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.77475 | 0.251650 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.8386 | −1.18399 | −0.591995 | − | 0.805942i | \(-0.701659\pi\) | ||||
−0.591995 | + | 0.805942i | \(0.701659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.0567 | −1.58971 | −0.794856 | − | 0.606798i | \(-0.792454\pi\) | ||||
−0.794856 | + | 0.606798i | \(0.792454\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.698685 | −0.0459701 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.4663 | 1.01323 | 0.506616 | − | 0.862172i | \(-0.330896\pi\) | ||||
0.506616 | + | 0.862172i | \(0.330896\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.98917 | −0.455923 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.40005 | −0.350771 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.57069 | −0.295653 | −0.147827 | − | 0.989013i | \(-0.547228\pi\) | ||||
−0.147827 | + | 0.989013i | \(0.547228\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.9646 | 1.02837 | 0.514185 | − | 0.857679i | \(-0.328095\pi\) | ||||
0.514185 | + | 0.857679i | \(0.328095\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.1235 | −0.713572 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.02449 | −0.384891 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.8765 | −1.71011 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.05934 | 0.130506 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.97836 | 0.124378 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.70754 | 0.169553 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.72312 | −0.544133 | −0.272067 | − | 0.962278i | \(-0.587707\pi\) | ||||
−0.272067 | + | 0.962278i | \(0.587707\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.0625 | −1.18449 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.1382 | −0.627537 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.8788 | 1.47243 | 0.736214 | − | 0.676749i | \(-0.236612\pi\) | ||||
0.736214 | + | 0.676749i | \(0.236612\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.1643 | 1.48440 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.704468 | −0.0431127 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4422 | 0.819587 | 0.409794 | − | 0.912178i | \(-0.365601\pi\) | ||||
0.409794 | + | 0.912178i | \(0.365601\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5155 | 0.699518 | 0.349759 | − | 0.936840i | \(-0.386263\pi\) | ||||
0.349759 | + | 0.936840i | \(0.386263\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.14340 | 0.311293 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.06328 | 0.0641183 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.37275 | −0.442986 | −0.221493 | − | 0.975162i | \(-0.571093\pi\) | ||||
−0.221493 | + | 0.975162i | \(0.571093\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.3311 | −1.03758 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.9735 | −1.19152 | −0.595758 | − | 0.803164i | \(-0.703148\pi\) | ||||
−0.595758 | + | 0.803164i | \(0.703148\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.0411 | 1.66687 | 0.833434 | − | 0.552619i | \(-0.186371\pi\) | ||||
0.833434 | + | 0.552619i | \(0.186371\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00775 | 0.237398 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.74963 | 0.103277 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.18753 | −0.422796 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.51332 | −0.147333 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.2201 | −1.41496 | −0.707478 | − | 0.706735i | \(-0.750167\pi\) | ||||
−0.707478 | + | 0.706735i | \(0.750167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.6271 | −0.676954 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.06455 | −0.119798 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.5638 | −0.842246 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.3797 | −0.655914 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.13447 | −0.0651737 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.3762 | 0.708659 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.9324 | −0.852236 | −0.426118 | − | 0.904667i | \(-0.640119\pi\) | ||||
−0.426118 | + | 0.904667i | \(0.640119\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.12464 | −0.405307 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.2949 | 1.49105 | 0.745524 | − | 0.666479i | \(-0.232199\pi\) | ||||
0.745524 | + | 0.666479i | \(0.232199\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.51404 | −0.198625 | −0.0993127 | − | 0.995056i | \(-0.531664\pi\) | ||||
−0.0993127 | + | 0.995056i | \(0.531664\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.4733 | 0.590101 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.1169 | −0.849047 | −0.424524 | − | 0.905417i | \(-0.639558\pi\) | ||||
−0.424524 | + | 0.905417i | \(0.639558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.85575 | −0.159891 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.59077 | −0.367861 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.5246 | 0.808170 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.82740 | −0.434186 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.70865 | −0.481589 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.17519 | 0.395581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.0881 | 1.87365 | 0.936825 | − | 0.349799i | \(-0.113750\pi\) | ||||
0.936825 | + | 0.349799i | \(0.113750\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.1692 | −1.48886 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.0878 | 0.933606 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.67369 | −0.145645 | −0.0728227 | − | 0.997345i | \(-0.523201\pi\) | ||||
−0.0728227 | + | 0.997345i | \(0.523201\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.03686 | −0.382190 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.88186 | −0.264368 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9135 | 1.07523 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.17171 | 0.116921 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.8044 | 1.33157 | 0.665786 | − | 0.746143i | \(-0.268096\pi\) | ||||
0.665786 | + | 0.746143i | \(0.268096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.31555 | −0.0704198 | −0.0352099 | − | 0.999380i | \(-0.511210\pi\) | ||||
−0.0352099 | + | 0.999380i | \(0.511210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.1983 | 0.811226 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.7470 | −0.944576 | −0.472288 | − | 0.881444i | \(-0.656572\pi\) | ||||
−0.472288 | + | 0.881444i | \(0.656572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.6585 | −0.724916 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.77960 | −0.147112 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.9012 | 0.786457 | 0.393228 | − | 0.919441i | \(-0.371358\pi\) | ||||
0.393228 | + | 0.919441i | \(0.371358\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.49957 | 0.131556 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.69635 | 0.246494 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.6483 | −1.13313 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.1918 | 1.36720 | 0.683600 | − | 0.729857i | \(-0.260413\pi\) | ||||
0.683600 | + | 0.729857i | \(0.260413\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.49369 | 0.129816 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.8075 | −1.28794 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.81955 | −0.0942130 | −0.0471065 | − | 0.998890i | \(-0.515000\pi\) | ||||
−0.0471065 | + | 0.998890i | \(0.515000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.48891 | 0.283446 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.0227 | 1.08273 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.39119 | −0.0714607 | −0.0357304 | − | 0.999361i | \(-0.511376\pi\) | ||||
−0.0357304 | + | 0.999361i | \(0.511376\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.03908 | 0.0532335 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.65910 | −0.289167 | −0.144583 | − | 0.989493i | \(-0.546184\pi\) | ||||
−0.144583 | + | 0.989493i | \(0.546184\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.95014 | 0.150353 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.2191 | −0.824464 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.3761 | 1.69224 | 0.846118 | − | 0.532996i | \(-0.178934\pi\) | ||||
0.846118 | + | 0.532996i | \(0.178934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.87057 | 0.398032 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.15104 | −0.259835 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.8012 | 1.14726 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.80826 | 0.140943 | 0.0704713 | − | 0.997514i | \(-0.477550\pi\) | ||||
0.0704713 | + | 0.997514i | \(0.477550\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.11442 | −0.205978 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.0554 | 1.00152 | 0.500759 | − | 0.865587i | \(-0.333054\pi\) | ||||
0.500759 | + | 0.865587i | \(0.333054\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.9380 | 1.79020 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.7540 | 0.683443 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.65310 | −0.379350 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.60055 | 0.276929 | 0.138465 | − | 0.990367i | \(-0.455783\pi\) | ||||
0.138465 | + | 0.990367i | \(0.455783\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.34108 | 0.460762 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.9365 | 0.587358 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.69540 | −0.426840 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.36236 | 0.409506 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.6046 | −0.566922 | −0.283461 | − | 0.958984i | \(-0.591483\pi\) | ||||
−0.283461 | + | 0.958984i | \(0.591483\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.0502 | −1.56203 | −0.781014 | − | 0.624513i | \(-0.785298\pi\) | ||||
−0.781014 | + | 0.624513i | \(0.785298\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.2266 | 0.497233 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.23009 | 0.205189 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.7056 | −0.614867 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.06494 | 0.0996963 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.0806 | 1.59344 | 0.796719 | − | 0.604349i | \(-0.206567\pi\) | ||||
0.796719 | + | 0.604349i | \(0.206567\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.51349 | 0.361075 | 0.180538 | − | 0.983568i | \(-0.442216\pi\) | ||||
0.180538 | + | 0.983568i | \(0.442216\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.13485 | −0.150305 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.6502 | 0.557303 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.95743 | 0.0934231 | 0.0467116 | − | 0.998908i | \(-0.485126\pi\) | ||||
0.0467116 | + | 0.998908i | \(0.485126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.81506 | 0.419765 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.880392 | −0.0418287 | −0.0209143 | − | 0.999781i | \(-0.506658\pi\) | ||||
−0.0209143 | + | 0.999781i | \(0.506658\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.97456 | 0.141007 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.37644 | −0.112402 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.1514 | −1.56451 | −0.782255 | − | 0.622958i | \(-0.785931\pi\) | ||||
−0.782255 | + | 0.622958i | \(0.785931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.702430 | 0.0330761 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.6330 | 0.499582 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.7176 | −1.01814 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.5917 | 1.57136 | 0.785678 | − | 0.618636i | \(-0.212314\pi\) | ||||
0.785678 | + | 0.618636i | \(0.212314\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.21348 | −0.383372 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.2767 | −0.664930 | −0.332465 | − | 0.943116i | \(-0.607880\pi\) | ||||
−0.332465 | + | 0.943116i | \(0.607880\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.99819 | 0.0928636 | 0.0464318 | − | 0.998921i | \(-0.485215\pi\) | ||||
0.0464318 | + | 0.998921i | \(0.485215\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.35898 | −0.248517 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.7336 | 1.05199 | 0.525993 | − | 0.850489i | \(-0.323694\pi\) | ||||
0.525993 | + | 0.850489i | \(0.323694\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.5426 | −0.810042 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0395592 | 0.00182279 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.56864 | −0.210066 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.26145 | 0.287295 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.3574 | −1.61890 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.15942 | 0.372813 | 0.186407 | − | 0.982473i | \(-0.440316\pi\) | ||||
0.186407 | + | 0.982473i | \(0.440316\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.3387 | 2.56882 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.22951 | −0.101446 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.6123 | 0.481879 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.44996 | −0.111019 | −0.0555093 | − | 0.998458i | \(-0.517678\pi\) | ||||
−0.0555093 | + | 0.998458i | \(0.517678\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.68599 | −0.392794 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.7893 | −0.577171 | −0.288586 | − | 0.957454i | \(-0.593185\pi\) | ||||
−0.288586 | + | 0.957454i | \(0.593185\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.3611 | −0.511679 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.20474 | 0.188989 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.0220 | 0.628972 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.938315 | 0.0420048 | 0.0210024 | − | 0.999779i | \(-0.493314\pi\) | ||||
0.0210024 | + | 0.999779i | \(0.493314\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.826446 | 0.0369229 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.2146 | −1.30262 | −0.651308 | − | 0.758814i | \(-0.725779\pi\) | ||||
−0.651308 | + | 0.758814i | \(0.725779\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.79021 | 0.213161 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.31942 | −0.413890 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.9310 | 1.81423 | 0.907117 | − | 0.420879i | \(-0.138278\pi\) | ||||
0.907117 | + | 0.420879i | \(0.138278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.2245 | 0.983154 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.1577 | −0.536777 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.0832 | 1.32562 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.88065 | 0.126691 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.71799 | −0.426572 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.9804 | 1.31347 | 0.656733 | − | 0.754123i | \(-0.271938\pi\) | ||||
0.656733 | + | 0.754123i | \(0.271938\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.2955 | 1.14982 | 0.574911 | − | 0.818216i | \(-0.305037\pi\) | ||||
0.574911 | + | 0.818216i | \(0.305037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.19827 | −0.0522966 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.4217 | −0.846021 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6870 | −0.725523 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.0128 | 0.738291 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.17097 | −0.223980 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.8290 | 1.20315 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.41008 | 0.147156 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.48305 | 0.106953 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9843 | −0.988171 | −0.494085 | − | 0.869413i | \(-0.664497\pi\) | ||||
−0.494085 | + | 0.869413i | \(0.664497\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.19323 | −0.0512063 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36.7715 | 1.57512 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.79728 | −0.333387 | −0.166694 | − | 0.986009i | \(-0.553309\pi\) | ||||
−0.166694 | + | 0.986009i | \(0.553309\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.1089 | −0.772869 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.8169 | −0.716425 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.4081 | −0.995414 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.40107 | −0.356606 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.6843 | −1.13065 | −0.565325 | − | 0.824868i | \(-0.691249\pi\) | ||||
−0.565325 | + | 0.824868i | \(0.691249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.6323 | 1.42249 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.11594 | −0.0471149 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.3602 | −0.647357 | −0.323679 | − | 0.946167i | \(-0.604920\pi\) | ||||
−0.323679 | + | 0.946167i | \(0.604920\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.7125 | 1.25001 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.1201 | −0.592988 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.53660 | 0.106340 | 0.0531700 | − | 0.998585i | \(-0.483067\pi\) | ||||
0.0531700 | + | 0.998585i | \(0.483067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.5090 | −1.02567 | −0.512836 | − | 0.858487i | \(-0.671405\pi\) | ||||
−0.512836 | + | 0.858487i | \(0.671405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.31495 | −0.0967083 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.39295 | 0.141496 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.4112 | −1.55745 | −0.778725 | − | 0.627366i | \(-0.784133\pi\) | ||||
−0.778725 | + | 0.627366i | \(0.784133\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.579686 | 0.0240909 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.92683 | 0.370347 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.95956 | −0.412483 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −30.9534 | −1.27977 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.3390 | −1.33477 | −0.667387 | − | 0.744711i | \(-0.732587\pi\) | ||||
−0.667387 | + | 0.744711i | \(0.732587\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.7483 | −1.18455 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.82748 | −0.239710 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.8932 | −0.734785 | −0.367392 | − | 0.930066i | \(-0.619749\pi\) | ||||
−0.367392 | + | 0.930066i | \(0.619749\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.7366 | 0.481155 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.8839 | −0.445447 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.3881 | −0.792175 | −0.396088 | − | 0.918213i | \(-0.629632\pi\) | ||||
−0.396088 | + | 0.918213i | \(0.629632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0687 | −0.451503 | −0.225751 | − | 0.974185i | \(-0.572484\pi\) | ||||
−0.225751 | + | 0.974185i | \(0.572484\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.0029 | −1.01820 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.8299 | −0.806202 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.8771 | 1.25326 | 0.626632 | − | 0.779316i | \(-0.284433\pi\) | ||||
0.626632 | + | 0.779316i | \(0.284433\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.21829 | 0.130412 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.2060 | −0.857905 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.94691 | 0.401752 | 0.200876 | − | 0.979617i | \(-0.435621\pi\) | ||||
0.200876 | + | 0.979617i | \(0.435621\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.771081 | 0.0310930 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.8807 | −1.16269 | −0.581346 | − | 0.813656i | \(-0.697474\pi\) | ||||
−0.581346 | + | 0.813656i | \(0.697474\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.25598 | −0.372029 | −0.186015 | − | 0.982547i | \(-0.559557\pi\) | ||||
−0.186015 | + | 0.982547i | \(0.559557\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.58802 | −0.264368 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.05373 | −0.122345 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.4245 | −0.656979 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.65183 | −0.0659678 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.4466 | −1.21398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.76256 | 0.309023 | 0.154511 | − | 0.987991i | \(-0.450620\pi\) | ||||
0.154511 | + | 0.987991i | \(0.450620\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.87566 | −0.193790 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.38741 | −0.174109 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.2791 | −0.724244 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.9851 | 0.790599 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.4109 | −1.55664 | −0.778319 | − | 0.627869i | \(-0.783927\pi\) | ||||
−0.778319 | + | 0.627869i | \(0.783927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.5538 | 1.44154 | 0.720771 | − | 0.693174i | \(-0.243788\pi\) | ||||
0.720771 | + | 0.693174i | \(0.243788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.01516 | −0.197472 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.94030 | 0.351479 | 0.175740 | − | 0.984437i | \(-0.443768\pi\) | ||||
0.175740 | + | 0.984437i | \(0.443768\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.79220 | 0.188110 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.50162 | 0.215625 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.1726 | −0.476352 | −0.238176 | − | 0.971222i | \(-0.576549\pi\) | ||||
−0.238176 | + | 0.971222i | \(0.576549\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.7498 | 0.849835 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.6759 | 1.23580 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.4761 | −1.14823 | −0.574114 | − | 0.818776i | \(-0.694653\pi\) | ||||
−0.574114 | + | 0.818776i | \(0.694653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.5472 | −0.410239 | −0.205120 | − | 0.978737i | \(-0.565758\pi\) | ||||
−0.205120 | + | 0.978737i | \(0.565758\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.21502 | 0.319045 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.3728 | 0.673687 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.11274 | −0.352847 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.15189 | 0.276508 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.10097 | −0.196921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.4861 | −1.09806 | −0.549029 | − | 0.835803i | \(-0.685002\pi\) | ||||
−0.549029 | + | 0.835803i | \(0.685002\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.54077 | −0.136284 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.92813 | 0.150970 | 0.0754851 | − | 0.997147i | \(-0.475949\pi\) | ||||
0.0754851 | + | 0.997147i | \(0.475949\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.8947 | −0.418101 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.07092 | 0.309278 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.9694 | 1.64418 | 0.822089 | − | 0.569359i | \(-0.192808\pi\) | ||||
0.822089 | + | 0.569359i | \(0.192808\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.4419 | −1.50700 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.8843 | 0.415260 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 73.3178 | 2.79318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.4562 | −0.511897 | −0.255949 | − | 0.966690i | \(-0.582388\pi\) | ||||
−0.255949 | + | 0.966690i | \(0.582388\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.31665 | −0.163976 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.3093 | −1.33936 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.79450 | 0.105849 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.99760 | −0.264673 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.9131 | 0.752107 | 0.376054 | − | 0.926598i | \(-0.377281\pi\) | ||||
0.376054 | + | 0.926598i | \(0.377281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.0676 | −1.69976 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.16219 | 0.119095 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.91770 | −0.184949 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.1399 | −0.455924 | −0.227962 | − | 0.973670i | \(-0.573206\pi\) | ||||
−0.227962 | + | 0.973670i | \(0.573206\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.3629 | −1.25121 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.5781 | −0.583404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.71904 | −0.326074 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.06797 | 0.0772297 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.7871 | −1.07358 | −0.536789 | − | 0.843716i | \(-0.680363\pi\) | ||||
−0.536789 | + | 0.843716i | \(0.680363\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.8839 | −1.15018 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.22304 | −0.268628 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.89770 | −0.181896 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.9370 | −1.36992 | −0.684960 | − | 0.728581i | \(-0.740180\pi\) | ||||
−0.684960 | + | 0.728581i | \(0.740180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.5660 | −0.613556 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.1756 | −0.672248 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.7116 | −0.432579 | −0.216289 | − | 0.976329i | \(-0.569395\pi\) | ||||
−0.216289 | + | 0.976329i | \(0.569395\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.72573 | 0.100540 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.04289 | −0.259428 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.6602 | 1.05428 | 0.527141 | − | 0.849778i | \(-0.323264\pi\) | ||||
0.527141 | + | 0.849778i | \(0.323264\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.1600 | 0.446710 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.65811 | −0.354322 | −0.177161 | − | 0.984182i | \(-0.556691\pi\) | ||||
−0.177161 | + | 0.984182i | \(0.556691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0343 | 0.367629 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.7231 | 0.465515 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.5696 | −1.04391 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.1095 | 0.916260 | 0.458130 | − | 0.888885i | \(-0.348519\pi\) | ||||
0.458130 | + | 0.888885i | \(0.348519\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.452441 | −0.0164879 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44.8969 | −1.63397 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.68729 | 0.206708 | 0.103354 | − | 0.994645i | \(-0.467043\pi\) | ||||
0.103354 | + | 0.994645i | \(0.467043\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.895092 | −0.0324898 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.65366 | 0.349945 | 0.174972 | − | 0.984573i | \(-0.444016\pi\) | ||||
0.174972 | + | 0.984573i | \(0.444016\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −37.7502 | −1.36665 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.7279 | 0.604797 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.2780 | −1.27382 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.79824 | −0.245151 | −0.122575 | − | 0.992459i | \(-0.539115\pi\) | ||||
−0.122575 | + | 0.992459i | \(0.539115\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.94670 | 0.142137 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −51.3076 | −1.84541 | −0.922704 | − | 0.385510i | \(-0.874025\pi\) | ||||
−0.922704 | + | 0.385510i | \(0.874025\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.37254 | −0.300751 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.62467 | 0.309408 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.13647 | 0.148204 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.62947 | 0.201438 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.50976 | 0.339851 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.167035 | −0.00596174 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.4549 | −1.29948 | −0.649738 | − | 0.760158i | \(-0.725121\pi\) | ||||
−0.649738 | + | 0.760158i | \(0.725121\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.8037 | −0.384623 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.5033 | −1.08457 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.5510 | 1.33348 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.9330 | −0.387752 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.1111 | 1.73961 | 0.869803 | − | 0.493399i | \(-0.164246\pi\) | ||||
0.869803 | + | 0.493399i | \(0.164246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.4602 | 0.405432 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.35238 | −0.153784 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.92256 | 0.314870 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.41393 | 0.331798 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.08182 | −0.214090 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.96420 | −0.139374 | −0.0696870 | − | 0.997569i | \(-0.522200\pi\) | ||||
−0.0696870 | + | 0.997569i | \(0.522200\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.6956 | −1.35879 | −0.679393 | − | 0.733774i | \(-0.737757\pi\) | ||||
−0.679393 | + | 0.733774i | \(0.737757\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.21010 | −0.182726 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.6758 | 1.28470 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.9038 | −0.941246 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 31.7772 | 1.11039 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.4011 | −0.642202 | −0.321101 | − | 0.947045i | \(-0.604053\pi\) | ||||
−0.321101 | + | 0.947045i | \(0.604053\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.2854 | −1.36940 | −0.684701 | − | 0.728824i | \(-0.740067\pi\) | ||||
−0.684701 | + | 0.728824i | \(0.740067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.481073 | −0.0167488 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.4883 | −0.851541 | −0.425771 | − | 0.904831i | \(-0.639997\pi\) | ||||
−0.425771 | + | 0.904831i | \(0.639997\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.40002 | 0.118088 | 0.0590438 | − | 0.998255i | \(-0.481195\pi\) | ||||
0.0590438 | + | 0.998255i | \(0.481195\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.33574 | 0.115715 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.87841 | 0.342266 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.48960 | −0.120763 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.2568 | 0.561917 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.8387 | −1.03015 | −0.515074 | − | 0.857146i | \(-0.672235\pi\) | ||||
−0.515074 | + | 0.857146i | \(0.672235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.8458 | −0.546408 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.03681 | 0.311244 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39.3505 | 1.35370 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.3577 | 0.699500 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.6869 | −0.435415 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.4212 | −0.837147 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.73462 | 0.0936315 | 0.0468157 | − | 0.998904i | \(-0.485093\pi\) | ||||
0.0468157 | + | 0.998904i | \(0.485093\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.7609 | 0.846804 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.3691 | −0.559158 | −0.279579 | − | 0.960123i | \(-0.590195\pi\) | ||||
−0.279579 | + | 0.960123i | \(0.590195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.18932 | 0.108818 | 0.0544092 | − | 0.998519i | \(-0.482672\pi\) | ||||
0.0544092 | + | 0.998519i | \(0.482672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.791604 | −0.0269778 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.0992 | 1.43307 | 0.716537 | − | 0.697549i | \(-0.245726\pi\) | ||||
0.716537 | + | 0.697549i | \(0.245726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.0334 | 1.39518 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.25193 | 0.110441 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.39775 | −0.318797 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51.8466 | 1.75675 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.5279 | −0.525541 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.7933 | 0.804360 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.14103 | −0.308671 | −0.154335 | − | 0.988019i | \(-0.549324\pi\) | ||||
−0.154335 | + | 0.988019i | \(0.549324\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.9582 | 0.369611 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.14380 | 0.105917 | 0.0529586 | − | 0.998597i | \(-0.483135\pi\) | ||||
0.0529586 | + | 0.998597i | \(0.483135\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.6344 | 1.03093 | 0.515464 | − | 0.856911i | \(-0.327620\pi\) | ||||
0.515464 | + | 0.856911i | \(0.327620\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.26056 | 0.176832 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.3622 | −0.582965 | −0.291483 | − | 0.956576i | \(-0.594149\pi\) | ||||
−0.291483 | + | 0.956576i | \(0.594149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.50418 | 0.151065 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.66885 | −0.189914 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.9636 | 0.567664 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.3987 | −0.481297 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.58926 | 0.220009 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.4869 | 0.749979 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.6224 | −1.32002 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.14864 | 0.171336 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.03830 | 0.167479 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.0635 | −0.433767 | −0.216883 | − | 0.976198i | \(-0.569589\pi\) | ||||
−0.216883 | + | 0.976198i | \(0.569589\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.00905 | −0.232475 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.2857 | −0.771491 | −0.385746 | − | 0.922605i | \(-0.626056\pi\) | ||||
−0.385746 | + | 0.922605i | \(0.626056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.58389 | 0.118609 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.59950 | −0.185114 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.3287 | −0.737358 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.1025 | −1.61974 | −0.809871 | − | 0.586608i | \(-0.800463\pi\) | ||||
−0.809871 | + | 0.586608i | \(0.800463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.75603 | 0.222619 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41.4416 | −1.36407 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.1253 | −0.431557 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −44.0179 | −1.44574 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.9252 | 1.34271 | 0.671356 | − | 0.741135i | \(-0.265712\pi\) | ||||
0.671356 | + | 0.741135i | \(0.265712\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.6222 | 0.479223 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.8969 | −0.389487 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.71195 | 0.154097 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.3581 | 1.41645 | 0.708224 | − | 0.705988i | \(-0.249497\pi\) | ||||
0.708224 | + | 0.705988i | \(0.249497\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.58990 | 0.0518844 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.9586 | 1.17222 | 0.586108 | − | 0.810233i | \(-0.300659\pi\) | ||||
0.586108 | + | 0.810233i | \(0.300659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.24146 | 0.0729921 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.82408 | −0.319577 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.6909 | −1.32228 | −0.661138 | − | 0.750265i | \(-0.729926\pi\) | ||||
−0.661138 | + | 0.750265i | \(0.729926\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −65.6838 | −2.13219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.83949 | 0.221786 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.43322 | 0.0788199 | 0.0394099 | − | 0.999223i | \(-0.487452\pi\) | ||||
0.0394099 | + | 0.999223i | \(0.487452\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.77467 | 0.316301 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.29206 | 0.0417663 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40.4917 | 1.30754 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.44096 | 0.240031 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −40.7194 | −1.31217 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.44767 | −0.0787934 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.8236 | −1.76301 | −0.881504 | − | 0.472177i | \(-0.843468\pi\) | ||||
−0.881504 | + | 0.472177i | \(0.843468\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.57153 | −0.211108 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.42580 | 0.302488 | 0.151244 | − | 0.988496i | \(-0.451672\pi\) | ||||
0.151244 | + | 0.988496i | \(0.451672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.2491 | 1.16209 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.54144 | 0.113417 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.3979 | 0.460630 | 0.230315 | − | 0.973116i | \(-0.426024\pi\) | ||||
0.230315 | + | 0.973116i | \(0.426024\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.22599 | −0.0391828 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −53.8042 | −1.71784 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.7587 | −0.598311 | −0.299156 | − | 0.954204i | \(-0.596705\pi\) | ||||
−0.299156 | + | 0.954204i | \(0.596705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.6060 | 0.784013 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.24635 | −0.103333 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.5786 | −0.463573 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3172 | 0.994824 | 0.497412 | − | 0.867514i | \(-0.334284\pi\) | ||||
0.497412 | + | 0.867514i | \(0.334284\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.4228 | −0.489429 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 45.9562 | 1.45691 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.2848 | 1.24416 | 0.622082 | − | 0.782952i | \(-0.286287\pi\) | ||||
0.622082 | + | 0.782952i | \(0.286287\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25.4852 | 0.806315 |
(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 | 4016.2.a.m.1.10 | 23 | ||
4.3 | odd | 2 | 2008.2.a.d.1.14 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.14 | ✓ | 23 | 4.3 | odd | 2 | ||
4016.2.a.m.1.10 | 23 | 1.1 | even | 1 | trivial |