Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 49 x^{14} + 130 x^{13} + 932 x^{12} - 2028 x^{11} - 8965 x^{10} + 14400 x^{9} + \cdots + 3888 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.34509\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(5\) | −2.34509 | −1.04876 | −0.524379 | − | 0.851485i | \(-0.675702\pi\) | ||||
−0.524379 | + | 0.851485i | \(0.675702\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.25807 | −0.475507 | −0.237754 | − | 0.971326i | \(-0.576411\pi\) | ||||
−0.237754 | + | 0.971326i | \(0.576411\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.44999 | −1.94475 | −0.972373 | − | 0.233434i | \(-0.925004\pi\) | ||||
−0.972373 | + | 0.233434i | \(0.925004\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.34717 | 0.373639 | 0.186819 | − | 0.982394i | \(-0.440182\pi\) | ||||
0.186819 | + | 0.982394i | \(0.440182\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.34509 | −0.605501 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.39461 | −1.79346 | −0.896728 | − | 0.442582i | \(-0.854063\pi\) | ||||
−0.896728 | + | 0.442582i | \(0.854063\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.27627 | −0.981043 | −0.490521 | − | 0.871429i | \(-0.663194\pi\) | ||||
−0.490521 | + | 0.871429i | \(0.663194\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.25807 | −0.274534 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.499463 | 0.0998926 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1300 | 1.81941 | 0.909704 | − | 0.415256i | \(-0.136308\pi\) | ||||
0.909704 | + | 0.415256i | \(0.136308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.44999 | −1.12280 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.95030 | 0.498692 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.20798 | −0.856187 | −0.428093 | − | 0.903735i | \(-0.640815\pi\) | ||||
−0.428093 | + | 0.903735i | \(0.640815\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.34717 | 0.215720 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.6226 | −1.65898 | −0.829489 | − | 0.558523i | \(-0.811368\pi\) | ||||
−0.829489 | + | 0.558523i | \(0.811368\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.118668 | 0.0180967 | 0.00904836 | − | 0.999959i | \(-0.497120\pi\) | ||||
0.00904836 | + | 0.999959i | \(0.497120\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.34509 | −0.349586 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.08470 | 1.32514 | 0.662570 | − | 0.749000i | \(-0.269466\pi\) | ||||
0.662570 | + | 0.749000i | \(0.269466\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.41725 | −0.773893 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.39461 | −1.03545 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4167 | 1.43085 | 0.715423 | − | 0.698691i | \(-0.246234\pi\) | ||||
0.715423 | + | 0.698691i | \(0.246234\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.1258 | 2.03957 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.27627 | −0.566405 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.39629 | −0.442159 | −0.221080 | − | 0.975256i | \(-0.570958\pi\) | ||||
−0.221080 | + | 0.975256i | \(0.570958\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.23961 | −0.286753 | −0.143377 | − | 0.989668i | \(-0.545796\pi\) | ||||
−0.143377 | + | 0.989668i | \(0.545796\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.25807 | −0.158502 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.15925 | −0.391857 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.85081 | 0.959130 | 0.479565 | − | 0.877506i | \(-0.340795\pi\) | ||||
0.479565 | + | 0.877506i | \(0.340795\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7923 | −1.28081 | −0.640404 | − | 0.768038i | \(-0.721233\pi\) | ||||
−0.640404 | + | 0.768038i | \(0.721233\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.17561 | 0.839842 | 0.419921 | − | 0.907561i | \(-0.362058\pi\) | ||||
0.419921 | + | 0.907561i | \(0.362058\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.499463 | 0.0576730 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.11456 | 0.924740 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.24131 | −0.477185 | −0.238592 | − | 0.971120i | \(-0.576686\pi\) | ||||
−0.238592 | + | 0.971120i | \(0.576686\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.91341 | −0.868609 | −0.434305 | − | 0.900766i | \(-0.643006\pi\) | ||||
−0.434305 | + | 0.900766i | \(0.643006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.3410 | 1.88090 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.52488 | −0.479636 | −0.239818 | − | 0.970818i | \(-0.577088\pi\) | ||||
−0.239818 | + | 0.970818i | \(0.577088\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.69484 | −0.177668 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.1300 | 1.05044 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.0282 | 1.02888 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.279080 | −0.0283363 | −0.0141681 | − | 0.999900i | \(-0.504510\pi\) | ||||
−0.0141681 | + | 0.999900i | \(0.504510\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.44999 | −0.648248 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.46268 | 0.145542 | 0.0727709 | − | 0.997349i | \(-0.476816\pi\) | ||||
0.0727709 | + | 0.997349i | \(0.476816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.7654 | 1.65194 | 0.825970 | − | 0.563714i | \(-0.190628\pi\) | ||||
0.825970 | + | 0.563714i | \(0.190628\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.95030 | 0.287920 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.86261 | 0.470087 | 0.235043 | − | 0.971985i | \(-0.424477\pi\) | ||||
0.235043 | + | 0.971985i | \(0.424477\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.10927 | −0.297814 | −0.148907 | − | 0.988851i | \(-0.547575\pi\) | ||||
−0.148907 | + | 0.988851i | \(0.547575\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.20798 | −0.494320 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.8302 | −1.11290 | −0.556448 | − | 0.830883i | \(-0.687836\pi\) | ||||
−0.556448 | + | 0.830883i | \(0.687836\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.34509 | −0.218681 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.34717 | 0.124546 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.30296 | 0.852801 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.6024 | 2.78203 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.6226 | −0.957812 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.5542 | 0.943995 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0935 | 0.984392 | 0.492196 | − | 0.870484i | \(-0.336194\pi\) | ||||
0.492196 | + | 0.870484i | \(0.336194\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.118668 | 0.0104482 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.1623 | 1.41211 | 0.706055 | − | 0.708157i | \(-0.250473\pi\) | ||||
0.706055 | + | 0.708157i | \(0.250473\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.37986 | 0.466493 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.34509 | −0.201834 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.08719 | 0.349192 | 0.174596 | − | 0.984640i | \(-0.444138\pi\) | ||||
0.174596 | + | 0.984640i | \(0.444138\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.11732 | 0.688503 | 0.344251 | − | 0.938878i | \(-0.388133\pi\) | ||||
0.344251 | + | 0.938878i | \(0.388133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.08470 | 0.765069 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.68926 | −0.726632 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.34509 | 0.194749 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.41725 | −0.446807 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.82849 | 0.641335 | 0.320667 | − | 0.947192i | \(-0.396093\pi\) | ||||
0.320667 | + | 0.947192i | \(0.396093\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.0112 | −1.54711 | −0.773554 | − | 0.633730i | \(-0.781523\pi\) | ||||
−0.773554 | + | 0.633730i | \(0.781523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.39461 | −0.597819 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.7559 | −1.90812 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.2471 | 1.05723 | 0.528615 | − | 0.848862i | \(-0.322712\pi\) | ||||
0.528615 | + | 0.848862i | \(0.322712\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.4167 | 0.826100 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.25807 | −0.0991501 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.77321 | −0.138889 | −0.0694443 | − | 0.997586i | \(-0.522123\pi\) | ||||
−0.0694443 | + | 0.997586i | \(0.522123\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.1258 | 1.17754 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.42037 | 0.109911 | 0.0549557 | − | 0.998489i | \(-0.482498\pi\) | ||||
0.0549557 | + | 0.998489i | \(0.482498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1851 | −0.860394 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.27627 | −0.327014 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.6543 | 1.03812 | 0.519058 | − | 0.854739i | \(-0.326283\pi\) | ||||
0.519058 | + | 0.854739i | \(0.326283\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.628361 | −0.0474996 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.39629 | −0.255281 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.98920 | −0.746628 | −0.373314 | − | 0.927705i | \(-0.621779\pi\) | ||||
−0.373314 | + | 0.927705i | \(0.621779\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.29509 | 0.393581 | 0.196790 | − | 0.980446i | \(-0.436948\pi\) | ||||
0.196790 | + | 0.980446i | \(0.436948\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.23961 | −0.165557 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.2132 | 0.897932 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 47.6952 | 3.48782 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.25807 | −0.0915114 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3030 | −0.817856 | −0.408928 | − | 0.912567i | \(-0.634097\pi\) | ||||
−0.408928 | + | 0.912567i | \(0.634097\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.2983 | 1.74903 | 0.874514 | − | 0.485001i | \(-0.161181\pi\) | ||||
0.874514 | + | 0.485001i | \(0.161181\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.15925 | −0.226238 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.204036 | −0.0145370 | −0.00726848 | − | 0.999974i | \(-0.502314\pi\) | ||||
−0.00726848 | + | 0.999974i | \(0.502314\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.69588 | −0.261994 | −0.130997 | − | 0.991383i | \(-0.541818\pi\) | ||||
−0.130997 | + | 0.991383i | \(0.541818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.85081 | 0.553754 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.25807 | 0.0882994 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.9111 | 1.73987 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.5819 | 1.90788 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3858 | −0.714989 | −0.357495 | − | 0.933915i | \(-0.616369\pi\) | ||||
−0.357495 | + | 0.933915i | \(0.616369\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.7923 | −0.739475 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.278288 | −0.0189791 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.7443 | −0.865142 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.17561 | 0.484883 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.96183 | −0.670105 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.39453 | 0.160350 | 0.0801749 | − | 0.996781i | \(-0.474452\pi\) | ||||
0.0801749 | + | 0.996781i | \(0.474452\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.499463 | 0.0332975 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.00245 | −0.531141 | −0.265571 | − | 0.964091i | \(-0.585560\pi\) | ||||
−0.265571 | + | 0.964091i | \(0.585560\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.7641 | −0.711312 | −0.355656 | − | 0.934617i | \(-0.615743\pi\) | ||||
−0.355656 | + | 0.934617i | \(0.615743\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.11456 | 0.533899 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.554990 | −0.0363586 | −0.0181793 | − | 0.999835i | \(-0.505787\pi\) | ||||
−0.0181793 | + | 0.999835i | \(0.505787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.3045 | −1.38975 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.24131 | −0.275503 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.4662 | −1.12979 | −0.564897 | − | 0.825162i | \(-0.691084\pi\) | ||||
−0.564897 | + | 0.825162i | \(0.691084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5598 | 1.06671 | 0.533354 | − | 0.845892i | \(-0.320931\pi\) | ||||
0.533354 | + | 0.845892i | \(0.320931\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.7040 | 0.811626 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.76087 | −0.366556 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.91341 | −0.501492 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.55045 | 0.287222 | 0.143611 | − | 0.989634i | \(-0.454129\pi\) | ||||
0.143611 | + | 0.989634i | \(0.454129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.44999 | −0.405507 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.3410 | 1.08594 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.8900 | −1.17833 | −0.589163 | − | 0.808014i | \(-0.700543\pi\) | ||||
−0.589163 | + | 0.808014i | \(0.700543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.55202 | 0.407123 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.490569 | −0.0302498 | −0.0151249 | − | 0.999886i | \(-0.504815\pi\) | ||||
−0.0151249 | + | 0.999886i | \(0.504815\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.4282 | −1.50061 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.52488 | −0.276918 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.1733 | 1.16902 | 0.584508 | − | 0.811388i | \(-0.301288\pi\) | ||||
0.584508 | + | 0.811388i | \(0.301288\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.7636 | −1.74726 | −0.873631 | − | 0.486588i | \(-0.838241\pi\) | ||||
−0.873631 | + | 0.486588i | \(0.838241\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.69484 | −0.102577 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.22153 | −0.194266 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.2754 | −1.45857 | −0.729283 | − | 0.684212i | \(-0.760146\pi\) | ||||
−0.729283 | + | 0.684212i | \(0.760146\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.1300 | 0.606470 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.36539 | −0.141107 | −0.0705537 | − | 0.997508i | \(-0.522477\pi\) | ||||
−0.0705537 | + | 0.997508i | \(0.522477\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.24568 | −0.133492 | −0.0667459 | − | 0.997770i | \(-0.521262\pi\) | ||||
−0.0667459 | + | 0.997770i | \(0.521262\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.0282 | 0.594022 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.3641 | 0.788856 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.6803 | 2.21649 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.279080 | −0.0163599 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.7523 | 1.62131 | 0.810655 | − | 0.585525i | \(-0.199111\pi\) | ||||
0.810655 | + | 0.585525i | \(0.199111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.96461 | 0.463718 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.44999 | −0.374266 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.34717 | 0.0779091 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.149293 | −0.00860512 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.46268 | 0.0840286 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.25210 | 0.300735 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.01961 | −0.229411 | −0.114706 | − | 0.993400i | \(-0.536592\pi\) | ||||
−0.114706 | + | 0.993400i | \(0.536592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.7654 | 0.953748 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.4335 | −1.38550 | −0.692748 | − | 0.721180i | \(-0.743600\pi\) | ||||
−0.692748 | + | 0.721180i | \(0.743600\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.4118 | −0.927648 | −0.463824 | − | 0.885927i | \(-0.653523\pi\) | ||||
−0.463824 | + | 0.885927i | \(0.653523\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.95030 | 0.166231 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.1766 | 1.18939 | 0.594697 | − | 0.803950i | \(-0.297272\pi\) | ||||
0.594697 | + | 0.803950i | \(0.297272\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.44999 | 0.361130 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.86261 | 0.271405 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.6213 | 1.75946 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.672863 | 0.0373237 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.10927 | −0.171943 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.4292 | −0.630113 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9757 | −0.603278 | −0.301639 | − | 0.953422i | \(-0.597534\pi\) | ||||
−0.301639 | + | 0.953422i | \(0.597534\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.20798 | −0.285396 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.4109 | −1.00589 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0132 | 1.09019 | 0.545094 | − | 0.838375i | \(-0.316494\pi\) | ||||
0.545094 | + | 0.838375i | \(0.316494\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.8302 | −0.642531 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −65.3387 | −3.53829 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.6218 | 0.843499 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.34509 | −0.126256 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.3958 | 0.880171 | 0.440085 | − | 0.897956i | \(-0.354948\pi\) | ||||
0.440085 | + | 0.897956i | \(0.354948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.00885 | −0.268117 | −0.134059 | − | 0.990973i | \(-0.542801\pi\) | ||||
−0.134059 | + | 0.990973i | \(0.542801\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.34717 | 0.0719068 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.40928 | −0.234682 | −0.117341 | − | 0.993092i | \(-0.537437\pi\) | ||||
−0.117341 | + | 0.993092i | \(0.537437\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.3089 | 1.34326 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.30296 | 0.492365 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.94966 | 0.102899 | 0.0514495 | − | 0.998676i | \(-0.483616\pi\) | ||||
0.0514495 | + | 0.998676i | \(0.483616\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.713549 | −0.0375552 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 30.6024 | 1.60621 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.8275 | −0.880791 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.5834 | 0.656847 | 0.328424 | − | 0.944531i | \(-0.393483\pi\) | ||||
0.328424 | + | 0.944531i | \(0.393483\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.6226 | −0.552993 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.1050 | −0.680378 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.3078 | −0.947941 | −0.473970 | − | 0.880541i | \(-0.657180\pi\) | ||||
−0.473970 | + | 0.880541i | \(0.657180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.5542 | 0.545016 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.34717 | −0.0693830 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.2890 | 1.35038 | 0.675188 | − | 0.737646i | \(-0.264063\pi\) | ||||
0.675188 | + | 0.737646i | \(0.264063\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.0935 | 0.568339 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.06675 | −0.412192 | −0.206096 | − | 0.978532i | \(-0.566076\pi\) | ||||
−0.206096 | + | 0.978532i | \(0.566076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.0294 | −0.969828 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.118668 | 0.00603224 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.4242 | 1.74538 | 0.872688 | − | 0.488279i | \(-0.162375\pi\) | ||||
0.872688 | + | 0.488279i | \(0.162375\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.39461 | −0.373961 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.1623 | 0.815283 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.94627 | 0.500451 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.7751 | −1.24343 | −0.621714 | − | 0.783244i | \(-0.713563\pi\) | ||||
−0.621714 | + | 0.783244i | \(0.713563\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.37986 | 0.269330 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.97629 | 0.248504 | 0.124252 | − | 0.992251i | \(-0.460347\pi\) | ||||
0.124252 | + | 0.992251i | \(0.460347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.6469 | 0.679802 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.34509 | −0.116529 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.5914 | 1.66507 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.3193 | −1.05417 | −0.527087 | − | 0.849811i | \(-0.676716\pi\) | ||||
−0.527087 | + | 0.849811i | \(0.676716\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.08719 | 0.201606 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.27278 | 0.210250 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.5577 | 0.910961 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.11732 | 0.397507 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.4117 | 1.68112 | 0.840561 | − | 0.541717i | \(-0.182226\pi\) | ||||
0.840561 | + | 0.541717i | \(0.182226\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.3508 | −0.650680 | −0.325340 | − | 0.945597i | \(-0.605479\pi\) | ||||
−0.325340 | + | 0.945597i | \(0.605479\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.08470 | 0.441713 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.69333 | −0.179153 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.81760 | 0.136353 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.68926 | −0.419521 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.0934 | −1.83490 | −0.917448 | − | 0.397856i | \(-0.869754\pi\) | ||||
−0.917448 | + | 0.397856i | \(0.869754\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.6448 | 1.08824 | 0.544120 | − | 0.839008i | \(-0.316864\pi\) | ||||
0.544120 | + | 0.839008i | \(0.316864\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.34509 | 0.112439 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.27627 | −0.204562 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.9826 | 1.43099 | 0.715495 | − | 0.698618i | \(-0.246201\pi\) | ||||
0.715495 | + | 0.698618i | \(0.246201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.41725 | −0.257964 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.1631 | −0.672910 | −0.336455 | − | 0.941699i | \(-0.609228\pi\) | ||||
−0.336455 | + | 0.941699i | \(0.609228\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.6113 | 0.503022 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.82849 | 0.370275 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.1865 | 1.56617 | 0.783084 | − | 0.621915i | \(-0.213645\pi\) | ||||
0.783084 | + | 0.621915i | \(0.213645\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 68.5160 | 3.22629 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.0112 | −0.893223 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.97457 | 0.186331 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.41745 | −0.206640 | −0.103320 | − | 0.994648i | \(-0.532947\pi\) | ||||
−0.103320 | + | 0.994648i | \(0.532947\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.39461 | −0.345151 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.2457 | 1.82785 | 0.913927 | − | 0.405878i | \(-0.133034\pi\) | ||||
0.913927 | + | 0.405878i | \(0.133034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.2262 | 1.21883 | 0.609416 | − | 0.792850i | \(-0.291404\pi\) | ||||
0.609416 | + | 0.792850i | \(0.291404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −23.7559 | −1.10165 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.1356 | 0.561571 | 0.280785 | − | 0.959771i | \(-0.409405\pi\) | ||||
0.280785 | + | 0.959771i | \(0.409405\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.87690 | −0.456073 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.2471 | 0.610392 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.765409 | −0.0351935 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.13584 | −0.0979989 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.4167 | 0.476949 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.9110 | 0.544229 | 0.272115 | − | 0.962265i | \(-0.412277\pi\) | ||||
0.272115 | + | 0.962265i | \(0.412277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.01606 | −0.319905 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.25807 | −0.0572443 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.654468 | 0.0297179 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.9032 | 0.901899 | 0.450950 | − | 0.892549i | \(-0.351085\pi\) | ||||
0.450950 | + | 0.892549i | \(0.351085\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.77321 | −0.0801874 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.2515 | 0.823680 | 0.411840 | − | 0.911256i | \(-0.364886\pi\) | ||||
0.411840 | + | 0.911256i | \(0.364886\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.39461 | 0.333036 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.1258 | 0.679855 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.5775 | 0.609033 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.11958 | −0.229184 | −0.114592 | − | 0.993413i | \(-0.536556\pi\) | ||||
−0.114592 | + | 0.993413i | \(0.536556\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.42037 | 0.0634573 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.4327 | −0.911048 | −0.455524 | − | 0.890224i | \(-0.650548\pi\) | ||||
−0.455524 | + | 0.890224i | \(0.650548\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.43011 | −0.152638 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.1851 | −0.496749 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.82286 | 0.435390 | 0.217695 | − | 0.976017i | \(-0.430146\pi\) | ||||
0.217695 | + | 0.976017i | \(0.430146\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.02745 | −0.399351 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.27627 | −0.188802 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −39.3163 | −1.73248 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −58.5962 | −2.57706 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.6543 | 0.599356 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.3946 | −1.15637 | −0.578184 | − | 0.815906i | \(-0.696238\pi\) | ||||
−0.578184 | + | 0.815906i | \(0.696238\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.4210 | −1.41767 | −0.708835 | − | 0.705375i | \(-0.750779\pi\) | ||||
−0.708835 | + | 0.705375i | \(0.750779\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.628361 | −0.0274239 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −74.9077 | −3.26303 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.39629 | −0.147386 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.3106 | −0.619859 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.4033 | −0.493007 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.98920 | −0.431066 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.9412 | 1.50502 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.1436 | 1.55393 | 0.776967 | − | 0.629541i | \(-0.216757\pi\) | ||||
0.776967 | + | 0.629541i | \(0.216757\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.29509 | 0.227234 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.29152 | 0.312334 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.5761 | 0.494958 | 0.247479 | − | 0.968893i | \(-0.420398\pi\) | ||||
0.247479 | + | 0.968893i | \(0.420398\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.23961 | −0.0955844 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.27627 | 0.182175 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.33588 | 0.226905 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.2132 | 0.518422 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.45992 | −0.0618589 | −0.0309295 | − | 0.999522i | \(-0.509847\pi\) | ||||
−0.0309295 | + | 0.999522i | \(0.509847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.159867 | 0.00676164 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 47.6952 | 2.01369 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.1215 | −1.73307 | −0.866533 | − | 0.499120i | \(-0.833657\pi\) | ||||
−0.866533 | + | 0.499120i | \(0.833657\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.7430 | 1.16716 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.25807 | −0.0528341 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.9105 | −1.79890 | −0.899451 | − | 0.437023i | \(-0.856033\pi\) | ||||
−0.899451 | + | 0.437023i | \(0.856033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.2812 | 0.932439 | 0.466220 | − | 0.884669i | \(-0.345616\pi\) | ||||
0.466220 | + | 0.884669i | \(0.345616\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.3030 | −0.472189 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.499463 | 0.0208290 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.03746 | −0.0431899 | −0.0215950 | − | 0.999767i | \(-0.506874\pi\) | ||||
−0.0215950 | + | 0.999767i | \(0.506874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.2983 | 1.00980 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.95565 | 0.413030 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −67.1878 | −2.78263 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.15925 | −0.130619 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.14391 | 0.171038 | 0.0855188 | − | 0.996337i | \(-0.472745\pi\) | ||||
0.0855188 | + | 0.996337i | \(0.472745\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −43.3187 | −1.78492 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.204036 | −0.00839292 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.4566 | −1.57922 | −0.789612 | − | 0.613607i | \(-0.789718\pi\) | ||||
−0.789612 | + | 0.613607i | \(0.789718\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.8163 | −0.894382 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.69588 | −0.151262 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.86570 | 0.0762303 | 0.0381151 | − | 0.999273i | \(-0.487865\pi\) | ||||
0.0381151 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.4674 | 1.20200 | 0.600999 | − | 0.799250i | \(-0.294769\pi\) | ||||
0.600999 | + | 0.799250i | \(0.294769\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.85081 | 0.319710 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −71.7654 | −2.91768 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.3829 | 0.746141 | 0.373070 | − | 0.927803i | \(-0.378305\pi\) | ||||
0.373070 | + | 0.927803i | \(0.378305\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.25807 | 0.0509797 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.2387 | 0.495123 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0636 | 0.568022 | 0.284011 | − | 0.958821i | \(-0.408335\pi\) | ||||
0.284011 | + | 0.958821i | \(0.408335\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.9111 | 1.00451 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.3676 | 1.66540 | 0.832699 | − | 0.553726i | \(-0.186795\pi\) | ||||
0.832699 | + | 0.553726i | \(0.186795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.9854 | −0.562121 | −0.281060 | − | 0.959690i | \(-0.590686\pi\) | ||||
−0.281060 | + | 0.959690i | \(0.590686\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.69263 | 0.228070 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.2479 | −1.08991 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.5819 | 1.10151 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38.5110 | 1.53553 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.28654 | −0.210454 | −0.105227 | − | 0.994448i | \(-0.533557\pi\) | ||||
−0.105227 | + | 0.994448i | \(0.533557\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.3858 | −0.412799 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.0154 | −1.03239 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.29798 | −0.289156 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.7923 | −0.426936 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.20988 | 0.245276 | 0.122638 | − | 0.992451i | \(-0.460865\pi\) | ||||
0.122638 | + | 0.992451i | \(0.460865\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.7158 | −0.659205 | −0.329603 | − | 0.944120i | \(-0.606915\pi\) | ||||
−0.329603 | + | 0.944120i | \(0.606915\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.278288 | −0.0109576 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.2631 | −1.42565 | −0.712825 | − | 0.701342i | \(-0.752584\pi\) | ||||
−0.712825 | + | 0.701342i | \(0.752584\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.9060 | 0.859887 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.7443 | −0.499490 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.4650 | 0.683458 | 0.341729 | − | 0.939799i | \(-0.388988\pi\) | ||||
0.341729 | + | 0.939799i | \(0.388988\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.9022 | −1.48096 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.17561 | 0.279947 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.1244 | 1.52407 | 0.762034 | − | 0.647536i | \(-0.224201\pi\) | ||||
0.762034 | + | 0.647536i | \(0.224201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.5339 | −1.49879 | −0.749397 | − | 0.662121i | \(-0.769656\pi\) | ||||
−0.749397 | + | 0.662121i | \(0.769656\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.96183 | −0.386885 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.6163 | −0.489238 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.39453 | 0.0925780 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.4455 | 0.557662 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.56580 | 0.0603570 | 0.0301785 | − | 0.999545i | \(-0.490392\pi\) | ||||
0.0301785 | + | 0.999545i | \(0.490392\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.499463 | 0.0192243 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.1966 | 0.584051 | 0.292026 | − | 0.956410i | \(-0.405671\pi\) | ||||
0.292026 | + | 0.956410i | \(0.405671\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.351103 | 0.0134741 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.00245 | −0.306655 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.3797 | −1.00939 | −0.504695 | − | 0.863298i | \(-0.668395\pi\) | ||||
−0.504695 | + | 0.863298i | \(0.668395\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.58485 | −0.366218 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.7641 | −0.410676 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.0331 | 0.534620 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.0803 | −0.573681 | −0.286840 | − | 0.957978i | \(-0.592605\pi\) | ||||
−0.286840 | + | 0.957978i | \(0.592605\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.11456 | 0.308247 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.0359 | −0.722072 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 78.5503 | 2.97531 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.554990 | −0.0209917 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.4316 | −1.33823 | −0.669116 | − | 0.743158i | \(-0.733327\pi\) | ||||
−0.669116 | + | 0.743158i | \(0.733327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.2707 | 0.839956 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.3045 | −0.802372 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.84015 | −0.0692061 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.0617 | −0.715877 | −0.357939 | − | 0.933745i | \(-0.616520\pi\) | ||||
−0.357939 | + | 0.933745i | \(0.616520\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.24131 | −0.159062 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.1300 | 0.379373 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.3771 | 0.762061 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.4662 | −0.652286 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.27886 | −0.234162 | −0.117081 | − | 0.993122i | \(-0.537354\pi\) | ||||
−0.117081 | + | 0.993122i | \(0.537354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.0920 | −0.785509 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.5598 | 0.615864 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.499463 | −0.0185496 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.8619 | −0.551199 | −0.275599 | − | 0.961273i | \(-0.588876\pi\) | ||||
−0.275599 | + | 0.961273i | \(0.588876\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.877505 | −0.0324557 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 52.6052 | 1.94302 | 0.971509 | − | 0.237004i | \(-0.0761653\pi\) | ||||
0.971509 | + | 0.237004i | \(0.0761653\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.7040 | 0.468593 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.6377 | −1.86526 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.794958 | −0.0292430 | −0.0146215 | − | 0.999893i | \(-0.504654\pi\) | ||||
−0.0146215 | + | 0.999893i | \(0.504654\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.76087 | −0.211631 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.73978 | 0.210572 | 0.105286 | − | 0.994442i | \(-0.466424\pi\) | ||||
0.105286 | + | 0.994442i | \(0.466424\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.3585 | −0.672605 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.91341 | −0.289536 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.11752 | −0.223529 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.7146 | −0.536944 | −0.268472 | − | 0.963287i | \(-0.586519\pi\) | ||||
−0.268472 | + | 0.963287i | \(0.586519\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.55045 | 0.165828 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 44.5830 | 1.62254 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.8286 | 0.938756 | 0.469378 | − | 0.882997i | \(-0.344478\pi\) | ||||
0.469378 | + | 0.882997i | \(0.344478\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.44999 | −0.234120 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.2387 | 0.733651 | 0.366826 | − | 0.930290i | \(-0.380445\pi\) | ||||
0.366826 | + | 0.930290i | \(0.380445\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.91169 | 0.141613 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.3410 | 0.626967 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.57539 | −0.165208 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.6534 | −1.75449 | −0.877244 | − | 0.480045i | \(-0.840620\pi\) | ||||
−0.877244 | + | 0.480045i | \(0.840620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.8900 | −0.680307 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.0404 | 0.828707 | 0.414353 | − | 0.910116i | \(-0.364008\pi\) | ||||
0.414353 | + | 0.910116i | \(0.364008\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.05958 | 0.181745 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.55202 | 0.235052 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 45.4253 | 1.62753 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 69.6101 | 2.49085 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31.0656 | −1.10878 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.48766 | −0.0886756 | −0.0443378 | − | 0.999017i | \(-0.514118\pi\) | ||||
−0.0443378 | + | 0.999017i | \(0.514118\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.490569 | −0.0174647 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.8833 | 0.529190 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.01715 | −0.107142 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.4282 | −0.866378 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −47.1618 | −1.67056 | −0.835278 | − | 0.549828i | \(-0.814693\pi\) | ||||
−0.835278 | + | 0.549828i | \(0.814693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −67.1778 | −2.37658 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.52488 | −0.159879 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −46.2826 | −1.63328 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.95030 | 0.103984 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.1733 | 0.674931 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.7581 | 1.25719 | 0.628593 | − | 0.777734i | \(-0.283631\pi\) | ||||
0.628593 | + | 0.777734i | \(0.283631\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.0722 | −0.739945 | −0.369973 | − | 0.929043i | \(-0.620633\pi\) | ||||
−0.369973 | + | 0.929043i | \(0.620633\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.7636 | −1.00878 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.15835 | 0.145661 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.507457 | −0.0177537 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.69484 | −0.0592226 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.8141 | −1.04052 | −0.520260 | − | 0.854008i | \(-0.674165\pi\) | ||||
−0.520260 | + | 0.854008i | \(0.674165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.3600 | 1.47658 | 0.738289 | − | 0.674485i | \(-0.235634\pi\) | ||||
0.738289 | + | 0.674485i | \(0.235634\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.22153 | −0.112159 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.7101 | −1.06789 | −0.533947 | − | 0.845518i | \(-0.679292\pi\) | ||||
−0.533947 | + | 0.845518i | \(0.679292\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.49418 | −0.0518952 | −0.0259476 | − | 0.999663i | \(-0.508260\pi\) | ||||
−0.0259476 | + | 0.999663i | \(0.508260\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.2754 | −0.842104 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 40.0585 | 1.38794 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.33089 | −0.115270 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.1300 | 0.350145 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.4228 | 0.808643 | 0.404322 | − | 0.914617i | \(-0.367508\pi\) | ||||
0.404322 | + | 0.914617i | \(0.367508\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.36539 | −0.0814685 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.2302 | 0.902345 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.5000 | −1.32288 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.24568 | −0.0770715 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.20798 | −0.178527 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.4457 | 0.802764 | 0.401382 | − | 0.915911i | \(-0.368530\pi\) | ||||
0.401382 | + | 0.915911i | \(0.368530\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.0282 | 0.342959 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.2988 | 1.17163 | 0.585813 | − | 0.810446i | \(-0.300775\pi\) | ||||
0.585813 | + | 0.810446i | \(0.300775\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.9851 | 1.36428 | 0.682138 | − | 0.731224i | \(-0.261051\pi\) | ||||
0.682138 | + | 0.731224i | \(0.261051\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.3641 | 0.455446 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.3589 | 0.556864 | 0.278432 | − | 0.960456i | \(-0.410185\pi\) | ||||
0.278432 | + | 0.960456i | \(0.410185\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.0206 | −1.08873 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37.6803 | 1.27969 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.3564 | 0.928003 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5764 | 0.358368 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.279080 | −0.00944542 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.2779 | −0.448876 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.8906 | 0.739192 | 0.369596 | − | 0.929192i | \(-0.379496\pi\) | ||||
0.369596 | + | 0.929192i | \(0.379496\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.7523 | 0.936063 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.5595 | 0.355759 | 0.177880 | − | 0.984052i | \(-0.443076\pi\) | ||||
0.177880 | + | 0.984052i | \(0.443076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8359 | 0.633879 | 0.316939 | − | 0.948446i | \(-0.397345\pi\) | ||||
0.316939 | + | 0.948446i | \(0.397345\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.96461 | 0.267728 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.7738 | 1.20117 | 0.600584 | − | 0.799562i | \(-0.294935\pi\) | ||||
0.600584 | + | 0.799562i | \(0.294935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.9565 | −0.468086 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.44999 | −0.216083 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.8486 | −1.30002 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.4256 | 0.783032 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.34717 | 0.0449808 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.1300 | −0.337856 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −77.0276 | −2.56616 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.149293 | −0.00496817 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.4175 | −0.412771 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.6997 | 1.11898 | 0.559491 | − | 0.828837i | \(-0.310997\pi\) | ||||
0.559491 | + | 0.828837i | \(0.310997\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.46268 | 0.0485139 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.7400 | −0.819672 | −0.409836 | − | 0.912159i | \(-0.634414\pi\) | ||||
−0.409836 | + | 0.912159i | \(0.634414\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.0414 | 1.68922 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.25210 | 0.173629 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.3334 | −0.671469 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.1870 | −1.62253 | −0.811264 | − | 0.584680i | \(-0.801220\pi\) | ||||
−0.811264 | + | 0.584680i | \(0.801220\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.01961 | −0.132451 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.5391 | −0.478560 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.60119 | −0.0855267 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.7654 | 0.550646 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.2541 | −1.05822 | −0.529112 | − | 0.848552i | \(-0.677475\pi\) | ||||
−0.529112 | + | 0.848552i | \(0.677475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.1656 | 0.759222 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.4335 | −0.799916 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −111.850 | −3.65787 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.64033 | 0.118924 | 0.0594622 | − | 0.998231i | \(-0.481061\pi\) | ||||
0.0594622 | + | 0.998231i | \(0.481061\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.4118 | −0.535578 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.7029 | −1.42467 | −0.712336 | − | 0.701838i | \(-0.752363\pi\) | ||||
−0.712336 | + | 0.701838i | \(0.752363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.6226 | −0.345921 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.95030 | 0.0959732 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.2115 | −0.559297 | −0.279649 | − | 0.960102i | \(-0.590218\pi\) | ||||
−0.279649 | + | 0.960102i | \(0.590218\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.66680 | 0.313798 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.1766 | 0.686697 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.0372 | −1.42651 | −0.713253 | − | 0.700907i | \(-0.752779\pi\) | ||||
−0.713253 | + | 0.700907i | \(0.752779\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.5066 | 0.857733 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.44999 | 0.208499 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.14199 | −0.166043 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.6177 | 2.31025 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.86261 | 0.156696 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −56.9817 | −1.83431 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.47069 | −0.272399 | −0.136200 | − | 0.990681i | \(-0.543489\pi\) | ||||
−0.136200 | + | 0.990681i | \(0.543489\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.6213 | 1.01582 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.8562 | 1.66414 | 0.832072 | − | 0.554667i | \(-0.187154\pi\) | ||||
0.832072 | + | 0.554667i | \(0.187154\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.2122 | −0.327388 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.672863 | 0.0215489 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.2841 | −1.12884 | −0.564420 | − | 0.825488i | \(-0.690900\pi\) | ||||
−0.564420 | + | 0.825488i | \(0.690900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.1854 | 0.932770 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.10927 | −0.0992712 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.4820 | −0.780854 | −0.390427 | − | 0.920634i | \(-0.627673\pi\) | ||||
−0.390427 | + | 0.920634i | \(0.627673\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.478484 | 0.0152458 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.4292 | −0.363796 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.118668 | 0.00377343 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.8045 | −0.978538 | −0.489269 | − | 0.872133i | \(-0.662736\pi\) | ||||
−0.489269 | + | 0.872133i | \(0.662736\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.9757 | −0.348303 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.66719 | 0.274768 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.1338 | −0.922676 | −0.461338 | − | 0.887224i | \(-0.652631\pi\) | ||||
−0.461338 | + | 0.887224i | \(0.652631\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.20798 | −0.164773 |
(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 | 8004.2.a.j.1.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.j.1.4 | ✓ | 16 | 1.1 | even | 1 | trivial |