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 | 1.7 | ||
Root | \(-0.812118\) 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 | ||||||||
\(5\) | −0.812118 | −0.363190 | −0.181595 | − | 0.983373i | \(-0.558126\pi\) | ||||
−0.181595 | + | 0.983373i | \(0.558126\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.94593 | −1.86939 | −0.934693 | − | 0.355456i | \(-0.884325\pi\) | ||||
−0.934693 | + | 0.355456i | \(0.884325\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.85682 | 0.559852 | 0.279926 | − | 0.960022i | \(-0.409690\pi\) | ||||
0.279926 | + | 0.960022i | \(0.409690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.88102 | −1.90845 | −0.954226 | − | 0.299088i | \(-0.903318\pi\) | ||||
−0.954226 | + | 0.299088i | \(0.903318\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.812118 | −0.209688 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.62412 | −1.84912 | −0.924560 | − | 0.381037i | \(-0.875567\pi\) | ||||
−0.924560 | + | 0.381037i | \(0.875567\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.765989 | 0.175730 | 0.0878650 | − | 0.996132i | \(-0.471996\pi\) | ||||
0.0878650 | + | 0.996132i | \(0.471996\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.94593 | −1.07929 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.34046 | −0.868093 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.16139 | −1.28622 | −0.643112 | − | 0.765773i | \(-0.722357\pi\) | ||||
−0.643112 | + | 0.765773i | \(0.722357\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.85682 | 0.323231 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.01668 | 0.678942 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.94133 | −1.14115 | −0.570574 | − | 0.821246i | \(-0.693279\pi\) | ||||
−0.570574 | + | 0.821246i | \(0.693279\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.88102 | −1.10184 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.06531 | −0.322548 | −0.161274 | − | 0.986910i | \(-0.551560\pi\) | ||||
−0.161274 | + | 0.986910i | \(0.551560\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.9781 | 1.97914 | 0.989570 | − | 0.144051i | \(-0.0460130\pi\) | ||||
0.989570 | + | 0.144051i | \(0.0460130\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.812118 | −0.121063 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.03906 | −0.443292 | −0.221646 | − | 0.975127i | \(-0.571143\pi\) | ||||
−0.221646 | + | 0.975127i | \(0.571143\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.4622 | 2.49460 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.62412 | −1.06759 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.0836 | 1.79717 | 0.898586 | − | 0.438798i | \(-0.144596\pi\) | ||||
0.898586 | + | 0.438798i | \(0.144596\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50796 | −0.203333 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.765989 | 0.101458 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.09500 | 0.793501 | 0.396750 | − | 0.917927i | \(-0.370138\pi\) | ||||
0.396750 | + | 0.917927i | \(0.370138\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.49906 | −0.448009 | −0.224005 | − | 0.974588i | \(-0.571913\pi\) | ||||
−0.224005 | + | 0.974588i | \(0.571913\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.94593 | −0.623129 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.58820 | 0.693130 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.90455 | −1.21003 | −0.605016 | − | 0.796213i | \(-0.706833\pi\) | ||||
−0.605016 | + | 0.796213i | \(0.706833\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9449 | 1.65495 | 0.827477 | − | 0.561500i | \(-0.189775\pi\) | ||||
0.827477 | + | 0.561500i | \(0.189775\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.62415 | −0.424175 | −0.212088 | − | 0.977251i | \(-0.568026\pi\) | ||||
−0.212088 | + | 0.977251i | \(0.568026\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.34046 | −0.501194 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.18370 | −1.04658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.4261 | 1.73557 | 0.867783 | − | 0.496943i | \(-0.165544\pi\) | ||||
0.867783 | + | 0.496943i | \(0.165544\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.720700 | 0.0791071 | 0.0395535 | − | 0.999217i | \(-0.487406\pi\) | ||||
0.0395535 | + | 0.999217i | \(0.487406\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.19168 | 0.671582 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.99841 | 0.529830 | 0.264915 | − | 0.964272i | \(-0.414656\pi\) | ||||
0.264915 | + | 0.964272i | \(0.414656\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 34.0330 | 3.56763 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.16139 | −0.742601 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.622073 | −0.0638234 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.22122 | −0.530134 | −0.265067 | − | 0.964230i | \(-0.585394\pi\) | ||||
−0.265067 | + | 0.964230i | \(0.585394\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.85682 | 0.186617 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5973 | 1.75100 | 0.875499 | − | 0.483220i | \(-0.160533\pi\) | ||||
0.875499 | + | 0.483220i | \(0.160533\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.42864 | −0.929031 | −0.464516 | − | 0.885565i | \(-0.653772\pi\) | ||||
−0.464516 | + | 0.885565i | \(0.653772\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.01668 | 0.391988 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.07940 | 0.587717 | 0.293859 | − | 0.955849i | \(-0.405060\pi\) | ||||
0.293859 | + | 0.955849i | \(0.405060\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.4110 | −1.66767 | −0.833834 | − | 0.552015i | \(-0.813859\pi\) | ||||
−0.833834 | + | 0.552015i | \(0.813859\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.94133 | −0.658842 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.07795 | 0.195477 | 0.0977386 | − | 0.995212i | \(-0.468839\pi\) | ||||
0.0977386 | + | 0.995212i | \(0.468839\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.812118 | −0.0757304 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.88102 | −0.636150 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 37.7083 | 3.45672 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.55222 | −0.686566 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.06531 | −0.186223 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.58556 | 0.678473 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.91116 | 0.879473 | 0.439737 | − | 0.898127i | \(-0.355072\pi\) | ||||
0.439737 | + | 0.898127i | \(0.355072\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.9781 | 1.14266 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.89560 | −0.864583 | −0.432291 | − | 0.901734i | \(-0.642295\pi\) | ||||
−0.432291 | + | 0.901734i | \(0.642295\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.78853 | −0.328507 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.812118 | −0.0698960 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.4914 | 1.06721 | 0.533607 | − | 0.845733i | \(-0.320836\pi\) | ||||
0.533607 | + | 0.845733i | \(0.320836\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0653 | 1.10819 | 0.554093 | − | 0.832455i | \(-0.313065\pi\) | ||||
0.554093 | + | 0.832455i | \(0.313065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.03906 | −0.255935 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.7768 | −1.06845 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.812118 | 0.0674427 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.4622 | 1.44026 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.9919 | −1.88357 | −0.941786 | − | 0.336214i | \(-0.890854\pi\) | ||||
−0.941786 | + | 0.336214i | \(0.890854\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.78139 | −0.633240 | −0.316620 | − | 0.948552i | \(-0.602548\pi\) | ||||
−0.316620 | + | 0.948552i | \(0.602548\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.62412 | −0.616373 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.81589 | 0.467143 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.12748 | −0.329409 | −0.164704 | − | 0.986343i | \(-0.552667\pi\) | ||||
−0.164704 | + | 0.986343i | \(0.552667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.0836 | 1.03760 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.94593 | −0.389794 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.4265 | −1.20829 | −0.604147 | − | 0.796873i | \(-0.706486\pi\) | ||||
−0.604147 | + | 0.796873i | \(0.706486\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.50796 | −0.117394 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.47945 | −0.733542 | −0.366771 | − | 0.930311i | \(-0.619537\pi\) | ||||
−0.366771 | + | 0.930311i | \(0.619537\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.3484 | 2.64219 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.765989 | 0.0585767 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.7240 | −0.967385 | −0.483692 | − | 0.875238i | \(-0.660705\pi\) | ||||
−0.483692 | + | 0.875238i | \(0.660705\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.4676 | 1.62280 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.09500 | 0.458128 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.5450 | 1.01240 | 0.506200 | − | 0.862416i | \(-0.331050\pi\) | ||||
0.506200 | + | 0.862416i | \(0.331050\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.9936 | −1.41178 | −0.705891 | − | 0.708320i | \(-0.749453\pi\) | ||||
−0.705891 | + | 0.708320i | \(0.749453\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.49906 | −0.258658 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.63718 | 0.414454 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.1566 | −1.03523 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.94593 | −0.359763 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0249716 | −0.00180688 | −0.000903439 | − | 1.00000i | \(-0.500288\pi\) | ||||
−0.000903439 | 1.00000i | \(0.500288\pi\) | ||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.83124 | 0.707668 | 0.353834 | − | 0.935308i | \(-0.384878\pi\) | ||||
0.353834 | + | 0.935308i | \(0.384878\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.58820 | 0.400179 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.42935 | 0.315578 | 0.157789 | − | 0.987473i | \(-0.449563\pi\) | ||||
0.157789 | + | 0.987473i | \(0.449563\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.93109 | −0.136891 | −0.0684455 | − | 0.997655i | \(-0.521804\pi\) | ||||
−0.0684455 | + | 0.997655i | \(0.521804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.90455 | −0.698613 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.94593 | 0.347136 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.67728 | 0.117146 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.42230 | 0.0983828 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.35328 | 0.643907 | 0.321953 | − | 0.946756i | \(-0.395661\pi\) | ||||
0.321953 | + | 0.946756i | \(0.395661\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.9449 | 0.955488 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.5397 | −0.718804 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.4197 | 2.40445 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.62415 | −0.244898 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 52.4617 | 3.52895 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.62611 | −0.108892 | −0.0544462 | − | 0.998517i | \(-0.517339\pi\) | ||||
−0.0544462 | + | 0.998517i | \(0.517339\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.34046 | −0.289364 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0590 | −0.933126 | −0.466563 | − | 0.884488i | \(-0.654508\pi\) | ||||
−0.466563 | + | 0.884488i | \(0.654508\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.113933 | 0.00752890 | 0.00376445 | − | 0.999993i | \(-0.498802\pi\) | ||||
0.00376445 | + | 0.999993i | \(0.498802\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.18370 | −0.604243 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.05724 | −0.331311 | −0.165655 | − | 0.986184i | \(-0.552974\pi\) | ||||
−0.165655 | + | 0.986184i | \(0.552974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.46807 | 0.160999 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.4261 | 1.00203 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.38121 | −0.606820 | −0.303410 | − | 0.952860i | \(-0.598125\pi\) | ||||
−0.303410 | + | 0.952860i | \(0.598125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7142 | −1.26990 | −0.634952 | − | 0.772551i | \(-0.718980\pi\) | ||||
−0.634952 | + | 0.772551i | \(0.718980\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.1814 | −0.906015 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.27079 | −0.335372 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.720700 | 0.0456725 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.4703 | −1.29208 | −0.646038 | − | 0.763305i | \(-0.723575\pi\) | ||||
−0.646038 | + | 0.763305i | \(0.723575\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.85682 | 0.116737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.19168 | 0.387738 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.14767 | 0.383481 | 0.191740 | − | 0.981446i | \(-0.438587\pi\) | ||||
0.191740 | + | 0.981446i | \(0.438587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 34.3313 | 2.13325 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.0386 | −0.619005 | −0.309503 | − | 0.950899i | \(-0.600163\pi\) | ||||
−0.309503 | + | 0.950899i | \(0.600163\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.6254 | −0.652715 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.99841 | 0.305898 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.5233 | 1.73910 | 0.869549 | − | 0.493847i | \(-0.164410\pi\) | ||||
0.869549 | + | 0.493847i | \(0.164410\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.35548 | 0.568305 | 0.284152 | − | 0.958779i | \(-0.408288\pi\) | ||||
0.284152 | + | 0.958779i | \(0.408288\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 34.0330 | 2.05977 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.05946 | −0.486004 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.246488 | 0.0148100 | 0.00740502 | − | 0.999973i | \(-0.497643\pi\) | ||||
0.00740502 | + | 0.999973i | \(0.497643\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.16139 | −0.428741 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.4451 | 1.57758 | 0.788791 | − | 0.614662i | \(-0.210708\pi\) | ||||
0.788791 | + | 0.614662i | \(0.210708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.59503 | 0.392034 | 0.196017 | − | 0.980601i | \(-0.437199\pi\) | ||||
0.196017 | + | 0.980601i | \(0.437199\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.622073 | −0.0368485 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.2149 | 0.602966 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.1272 | 2.41924 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.22122 | −0.306073 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.3626 | 0.955912 | 0.477956 | − | 0.878384i | \(-0.341378\pi\) | ||||
0.477956 | + | 0.878384i | \(0.341378\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.94985 | −0.288192 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.85682 | 0.107744 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.88102 | −0.397940 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −64.1887 | −3.69978 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.5973 | 1.01094 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.84165 | 0.162712 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5073 | −0.999197 | −0.499599 | − | 0.866257i | \(-0.666519\pi\) | ||||
−0.499599 | + | 0.866257i | \(0.666519\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.42864 | −0.536377 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.0872 | −0.571993 | −0.285997 | − | 0.958231i | \(-0.592325\pi\) | ||||
−0.285997 | + | 0.958231i | \(0.592325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.6111 | 1.22153 | 0.610765 | − | 0.791812i | \(-0.290862\pi\) | ||||
0.610765 | + | 0.791812i | \(0.290862\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.01668 | 0.226314 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.6316 | −0.990288 | −0.495144 | − | 0.868811i | \(-0.664885\pi\) | ||||
−0.495144 | + | 0.868811i | \(0.664885\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.85682 | −0.103962 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.07940 | 0.339319 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.83999 | −0.324946 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.8668 | 1.65671 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.4110 | −0.962829 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0310 | 0.828684 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.2302 | 1.00202 | 0.501012 | − | 0.865440i | \(-0.332961\pi\) | ||||
0.501012 | + | 0.865440i | \(0.332961\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.94133 | −0.380383 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.04366 | 0.439472 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.5663 | 0.902423 | 0.451211 | − | 0.892417i | \(-0.350992\pi\) | ||||
0.451211 | + | 0.892417i | \(0.350992\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.07795 | 0.112859 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.2974 | −0.720094 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −51.7454 | −2.79399 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.812118 | −0.0437229 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.993493 | −0.0533335 | −0.0266668 | − | 0.999644i | \(-0.508489\pi\) | ||||
−0.0266668 | + | 0.999644i | \(0.508489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.2438 | −0.815981 | −0.407991 | − | 0.912986i | \(-0.633770\pi\) | ||||
−0.407991 | + | 0.912986i | \(0.633770\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.88102 | −0.367282 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.35780 | 0.231942 | 0.115971 | − | 0.993253i | \(-0.463002\pi\) | ||||
0.115971 | + | 0.993253i | \(0.463002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.3249 | −0.601063 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 37.7083 | 1.99574 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0026 | −0.791808 | −0.395904 | − | 0.918292i | \(-0.629569\pi\) | ||||
−0.395904 | + | 0.918292i | \(0.629569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4133 | −0.969119 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.55222 | −0.396389 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.94324 | 0.154056 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.7494 | 1.55291 | 0.776454 | − | 0.630174i | \(-0.217016\pi\) | ||||
0.776454 | + | 0.630174i | \(0.217016\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.06531 | −0.107516 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −64.7106 | −3.35961 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.3697 | 0.744036 | 0.372018 | − | 0.928226i | \(-0.378666\pi\) | ||||
0.372018 | + | 0.928226i | \(0.378666\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.58556 | 0.391716 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.88102 | 0.354390 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5341 | −1.15750 | −0.578749 | − | 0.815506i | \(-0.696459\pi\) | ||||
−0.578749 | + | 0.815506i | \(0.696459\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.91116 | 0.507764 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.3663 | 0.836278 | 0.418139 | − | 0.908383i | \(-0.362682\pi\) | ||||
0.418139 | + | 0.908383i | \(0.362682\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.45824 | 0.380107 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.9781 | 0.659713 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.6023 | 0.892470 | 0.446235 | − | 0.894916i | \(-0.352764\pi\) | ||||
0.446235 | + | 0.894916i | \(0.352764\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.62412 | −0.385568 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.89560 | −0.499167 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.5278 | −0.630340 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.5933 | 1.18411 | 0.592056 | − | 0.805897i | \(-0.298316\pi\) | ||||
0.592056 | + | 0.805897i | \(0.298316\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.78853 | −0.189664 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.5098 | −0.874400 | −0.437200 | − | 0.899364i | \(-0.644030\pi\) | ||||
−0.437200 | + | 0.899364i | \(0.644030\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 49.2776 | 2.45469 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.812118 | −0.0403544 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.8888 | −0.638874 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.91708 | 0.342027 | 0.171014 | − | 0.985269i | \(-0.445296\pi\) | ||||
0.171014 | + | 0.985269i | \(0.445296\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.4914 | 0.616156 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −30.1454 | −1.48336 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.585293 | −0.0287309 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.0653 | 0.639812 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.1660 | 1.76683 | 0.883413 | − | 0.468595i | \(-0.155240\pi\) | ||||
0.883413 | + | 0.468595i | \(0.155240\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.14718 | −0.250858 | −0.125429 | − | 0.992103i | \(-0.540031\pi\) | ||||
−0.125429 | + | 0.992103i | \(0.540031\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.03906 | −0.147764 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 33.0922 | 1.60521 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.3061 | 0.837502 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.7768 | −0.616870 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.24355 | −0.252573 | −0.126286 | − | 0.991994i | \(-0.540306\pi\) | ||||
−0.126286 | + | 0.991994i | \(0.540306\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.0784 | 1.20519 | 0.602595 | − | 0.798047i | \(-0.294133\pi\) | ||||
0.602595 | + | 0.798047i | \(0.294133\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.812118 | 0.0389381 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.765989 | 0.0366422 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.1658 | 0.532915 | 0.266457 | − | 0.963847i | \(-0.414147\pi\) | ||||
0.266457 | + | 0.963847i | \(0.414147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.4622 | 0.831534 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.99870 | −0.332518 | −0.166259 | − | 0.986082i | \(-0.553169\pi\) | ||||
−0.166259 | + | 0.986082i | \(0.553169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.05930 | −0.192429 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.9919 | −1.08748 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.6458 | 1.68223 | 0.841114 | − | 0.540857i | \(-0.181900\pi\) | ||||
0.841114 | + | 0.540857i | \(0.181900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.83491 | −0.180579 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.78139 | −0.365602 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.6388 | −1.29573 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.92721 | −0.136929 | −0.0684647 | − | 0.997654i | \(-0.521810\pi\) | ||||
−0.0684647 | + | 0.997654i | \(0.521810\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.62412 | −0.355863 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.11556 | −0.377979 | −0.188990 | − | 0.981979i | \(-0.560521\pi\) | ||||
−0.188990 | + | 0.981979i | \(0.560521\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.8955 | 0.552830 | 0.276415 | − | 0.961038i | \(-0.410854\pi\) | ||||
0.276415 | + | 0.961038i | \(0.410854\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.81589 | 0.269705 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.3979 | −1.26782 | −0.633912 | − | 0.773405i | \(-0.718552\pi\) | ||||
−0.633912 | + | 0.773405i | \(0.718552\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.9872 | 2.26202 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.12748 | −0.190184 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.0980 | 1.10803 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.32475 | −0.152550 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.0836 | 0.599057 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.2273 | 0.832827 | 0.416413 | − | 0.909175i | \(-0.363287\pi\) | ||||
0.416413 | + | 0.909175i | \(0.363287\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 47.7634 | 2.17782 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.94593 | −0.225048 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.24024 | 0.192539 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.2112 | 0.553344 | 0.276672 | − | 0.960964i | \(-0.410769\pi\) | ||||
0.276672 | + | 0.960964i | \(0.410769\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.4265 | −0.697608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.7324 | 1.11616 | 0.558079 | − | 0.829788i | \(-0.311539\pi\) | ||||
0.558079 | + | 0.829788i | \(0.311539\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.62412 | 0.343373 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.50796 | −0.0677776 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −68.9704 | −3.09375 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.7864 | 1.87062 | 0.935309 | − | 0.353832i | \(-0.115121\pi\) | ||||
0.935309 | + | 0.353832i | \(0.115121\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.47945 | −0.423511 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.4959 | −1.18139 | −0.590697 | − | 0.806894i | \(-0.701147\pi\) | ||||
−0.590697 | + | 0.806894i | \(0.701147\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.2911 | −0.635945 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 34.3484 | 1.52547 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.6337 | −1.31349 | −0.656746 | − | 0.754112i | \(-0.728068\pi\) | ||||
−0.656746 | + | 0.754112i | \(0.728068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.9248 | 0.792947 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.765989 | 0.0338193 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.65716 | 0.337415 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.64298 | −0.248178 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.7240 | −0.558520 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.07091 | 0.222160 | 0.111080 | − | 0.993811i | \(-0.464569\pi\) | ||||
0.111080 | + | 0.993811i | \(0.464569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.70485 | −0.162002 | −0.0810008 | − | 0.996714i | \(-0.525812\pi\) | ||||
−0.0810008 | + | 0.996714i | \(0.525812\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.4676 | 0.936924 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 54.5993 | 2.37838 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.09500 | 0.264500 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.2114 | 0.615566 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.93719 | −0.213453 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.5450 | 0.584509 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.4242 | 1.39661 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.15109 | 0.178469 | 0.0892347 | − | 0.996011i | \(-0.471558\pi\) | ||||
0.0892347 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.9936 | −0.815093 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.1398 | 0.605681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.2304 | −0.565691 | −0.282846 | − | 0.959165i | \(-0.591278\pi\) | ||||
−0.282846 | + | 0.959165i | \(0.591278\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.49906 | −0.149336 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.765989 | −0.0326322 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −76.2962 | −3.24444 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.63718 | 0.239285 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.6588 | −1.55328 | −0.776641 | − | 0.629943i | \(-0.783078\pi\) | ||||
−0.776641 | + | 0.629943i | \(0.783078\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −89.3025 | −3.77709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.1566 | −0.597692 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0766 | −0.803982 | −0.401991 | − | 0.915644i | \(-0.631682\pi\) | ||||
−0.401991 | + | 0.915644i | \(0.631682\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.68754 | −0.0709953 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.94593 | −0.207710 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.3700 | −1.77624 | −0.888121 | − | 0.459610i | \(-0.847989\pi\) | ||||
−0.888121 | + | 0.459610i | \(0.847989\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.63564 | 0.110298 | 0.0551490 | − | 0.998478i | \(-0.482437\pi\) | ||||
0.0551490 | + | 0.998478i | \(0.482437\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.0249716 | −0.00104320 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.34046 | −0.181010 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.740812 | 0.0308404 | 0.0154202 | − | 0.999881i | \(-0.495091\pi\) | ||||
0.0154202 | + | 0.999881i | \(0.495091\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.83124 | 0.408573 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.56453 | −0.147882 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.2939 | 1.00615 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.58820 | 0.231043 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.89109 | −0.284426 | −0.142213 | − | 0.989836i | \(-0.545422\pi\) | ||||
−0.142213 | + | 0.989836i | \(0.545422\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.48555 | −0.226028 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.42935 | 0.182199 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −44.3354 | −1.82064 | −0.910319 | − | 0.413907i | \(-0.864164\pi\) | ||||
−0.910319 | + | 0.413907i | \(0.864164\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.6236 | −1.25545 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.93109 | −0.0790341 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.2406 | −1.11302 | −0.556509 | − | 0.830841i | \(-0.687860\pi\) | ||||
−0.556509 | + | 0.830841i | \(0.687860\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.15062 | −0.332471 | −0.166235 | − | 0.986086i | \(-0.553161\pi\) | ||||
−0.166235 | + | 0.986086i | \(0.553161\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.90455 | −0.403344 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.13329 | 0.249354 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.6056 | 1.07989 | 0.539944 | − | 0.841701i | \(-0.318446\pi\) | ||||
0.539944 | + | 0.841701i | \(0.318446\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.94593 | 0.200419 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.9118 | 0.846001 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.44054 | −0.381300 | −0.190650 | − | 0.981658i | \(-0.561059\pi\) | ||||
−0.190650 | + | 0.981658i | \(0.561059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.67728 | 0.0676343 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.95593 | 0.400811 | 0.200405 | − | 0.979713i | \(-0.435774\pi\) | ||||
0.200405 | + | 0.979713i | \(0.435774\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.11351 | 0.205529 | 0.102765 | − | 0.994706i | \(-0.467231\pi\) | ||||
0.102765 | + | 0.994706i | \(0.467231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.7218 | −0.990457 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5420 | 0.621678 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.42230 | 0.0568013 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 52.9215 | 2.11012 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.4493 | −1.17236 | −0.586179 | − | 0.810182i | \(-0.699368\pi\) | ||||
−0.586179 | + | 0.810182i | \(0.699368\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.35328 | 0.371760 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.04903 | −0.319416 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −120.158 | −4.76083 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.9449 | 0.551651 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.3757 | 0.607303 | 0.303652 | − | 0.952783i | \(-0.401794\pi\) | ||||
0.303652 | + | 0.952783i | \(0.401794\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.6822 | 1.40717 | 0.703585 | − | 0.710611i | \(-0.251581\pi\) | ||||
0.703585 | + | 0.710611i | \(0.251581\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.5397 | −0.415002 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.9106 | 1.13659 | 0.568297 | − | 0.822824i | \(-0.307603\pi\) | ||||
0.568297 | + | 0.822824i | \(0.307603\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3173 | 0.444243 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 35.4197 | 1.38821 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.58135 | 0.257548 | 0.128774 | − | 0.991674i | \(-0.458896\pi\) | ||||
0.128774 | + | 0.991674i | \(0.458896\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.03639 | 0.314008 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.62415 | −0.141392 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −48.8441 | −1.90270 | −0.951349 | − | 0.308115i | \(-0.900302\pi\) | ||||
−0.951349 | + | 0.308115i | \(0.900302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.9767 | 1.59381 | 0.796904 | − | 0.604106i | \(-0.206470\pi\) | ||||
0.796904 | + | 0.604106i | \(0.206470\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 52.4617 | 2.03744 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.07673 | 0.119311 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.62611 | −0.0628691 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.49713 | −0.250819 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.6389 | 1.64361 | 0.821804 | − | 0.569770i | \(-0.192968\pi\) | ||||
0.821804 | + | 0.569770i | \(0.192968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.34046 | −0.167065 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.8300 | −1.06959 | −0.534796 | − | 0.844981i | \(-0.679612\pi\) | ||||
−0.534796 | + | 0.844981i | \(0.679612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.8238 | 0.991025 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.0590 | −0.538741 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.2516 | 1.42539 | 0.712697 | − | 0.701472i | \(-0.247473\pi\) | ||||
0.712697 | + | 0.701472i | \(0.247473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.1445 | −0.387602 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.113933 | 0.00434681 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −90.0285 | −3.42981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.45465 | −0.359672 | −0.179836 | − | 0.983697i | \(-0.557557\pi\) | ||||
−0.179836 | + | 0.983697i | \(0.557557\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.18370 | −0.348860 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.6106 | −0.402482 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7462 | 0.596429 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.05724 | −0.191282 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.6280 | 1.42119 | 0.710596 | − | 0.703601i | \(-0.248426\pi\) | ||||
0.710596 | + | 0.703601i | \(0.248426\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.31699 | −0.200534 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.46807 | 0.0929530 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −87.0351 | −3.27329 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.0874 | 0.942177 | 0.471088 | − | 0.882086i | \(-0.343861\pi\) | ||||
0.471088 | + | 0.882086i | \(0.343861\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.4261 | 0.578522 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.16139 | −0.268196 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.3763 | 0.388050 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.38121 | −0.350348 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.2087 | −1.31306 | −0.656531 | − | 0.754299i | \(-0.727977\pi\) | ||||
−0.656531 | + | 0.754299i | \(0.727977\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.6334 | 1.73672 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.7142 | −0.733180 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.34046 | 0.161201 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.7656 | −0.695976 | −0.347988 | − | 0.937499i | \(-0.613135\pi\) | ||||
−0.347988 | + | 0.937499i | \(0.613135\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −98.9465 | −3.65967 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.4650 | −1.42074 | −0.710368 | − | 0.703830i | \(-0.751471\pi\) | ||||
−0.710368 | + | 0.703830i | \(0.751471\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.1814 | −0.523088 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.3909 | −0.677439 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.5454 | −0.718988 | −0.359494 | − | 0.933147i | \(-0.617051\pi\) | ||||
−0.359494 | + | 0.933147i | \(0.617051\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.27079 | −0.193627 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.1029 | −0.810878 | −0.405439 | − | 0.914122i | \(-0.632881\pi\) | ||||
−0.405439 | + | 0.914122i | \(0.632881\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.6721 | 0.684094 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.720700 | 0.0263690 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.0683 | −1.09867 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.6098 | −0.642590 | −0.321295 | − | 0.946979i | \(-0.604118\pi\) | ||||
−0.321295 | + | 0.946979i | \(0.604118\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.4703 | −0.745981 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.31940 | 0.229987 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.3255 | −1.61104 | −0.805519 | − | 0.592570i | \(-0.798113\pi\) | ||||
−0.805519 | + | 0.592570i | \(0.798113\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.85682 | 0.0673983 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.34078 | −0.266103 | −0.133052 | − | 0.991109i | \(-0.542478\pi\) | ||||
−0.133052 | + | 0.991109i | \(0.542478\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 86.1135 | 3.11752 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.19168 | 0.223861 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41.9398 | −1.51436 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.0004 | 0.613050 | 0.306525 | − | 0.951863i | \(-0.400834\pi\) | ||||
0.306525 | + | 0.951863i | \(0.400834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.14767 | 0.221403 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.6061 | −0.381476 | −0.190738 | − | 0.981641i | \(-0.561088\pi\) | ||||
−0.190738 | + | 0.981641i | \(0.561088\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.0837 | 1.11656 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 34.3313 | 1.23163 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.58201 | −0.0566813 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.8931 | 0.926529 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.35200 | 0.119638 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.6736 | −1.02210 | −0.511052 | − | 0.859550i | \(-0.670744\pi\) | ||||
−0.511052 | + | 0.859550i | \(0.670744\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.0386 | −0.357383 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.2774 | −0.365422 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0771 | 0.855003 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.6254 | −0.376845 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.69586 | 0.201758 | 0.100879 | − | 0.994899i | \(-0.467835\pi\) | ||||
0.100879 | + | 0.994899i | \(0.467835\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.1701 | 0.819700 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.99841 | 0.176610 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.72940 | −0.237475 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.01668 | 0.141569 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.5233 | 1.00407 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.2084 | 1.06207 | 0.531035 | − | 0.847350i | \(-0.321803\pi\) | ||||
0.531035 | + | 0.847350i | \(0.321803\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.3134 | 1.06445 | 0.532224 | − | 0.846604i | \(-0.321357\pi\) | ||||
0.532224 | + | 0.846604i | \(0.321357\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.35548 | 0.328111 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.5281 | 0.438840 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.94108 | 0.347794 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34.0330 | 1.18921 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.8099 | 0.865871 | 0.432935 | − | 0.901425i | \(-0.357478\pi\) | ||||
0.432935 | + | 0.901425i | \(0.357478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.77313 | 0.305812 | 0.152906 | − | 0.988241i | \(-0.451137\pi\) | ||||
0.152906 | + | 0.988241i | \(0.451137\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.05946 | −0.280594 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −56.7440 | −1.97318 | −0.986592 | − | 0.163208i | \(-0.947816\pi\) | ||||
−0.986592 | + | 0.163208i | \(0.947816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.30091 | −0.218840 | −0.109420 | − | 0.993996i | \(-0.534899\pi\) | ||||
−0.109420 | + | 0.993996i | \(0.534899\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.246488 | 0.00855058 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −133.134 | −4.61282 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.69843 | 0.266415 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.16139 | −0.247534 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.38808 | −0.0824455 | −0.0412228 | − | 0.999150i | \(-0.513125\pi\) | ||||
−0.0412228 | + | 0.999150i | \(0.513125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.4451 | 0.910817 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −27.8950 | −0.959615 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.3528 | 1.28346 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.59503 | 0.226341 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.94133 | −0.237946 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.6922 | −0.503051 | −0.251526 | − | 0.967851i | \(-0.580932\pi\) | ||||
−0.251526 | + | 0.967851i | \(0.580932\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.622073 | −0.0212745 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.72578 | −0.161430 | −0.0807148 | − | 0.996737i | \(-0.525720\pi\) | ||||
−0.0807148 | + | 0.996737i | \(0.525720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.4858 | −1.27900 | −0.639500 | − | 0.768791i | \(-0.720858\pi\) | ||||
−0.639500 | + | 0.768791i | \(0.720858\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.2149 | 0.348122 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.5637 | −1.10848 | −0.554240 | − | 0.832357i | \(-0.686991\pi\) | ||||
−0.554240 | + | 0.832357i | \(0.686991\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.3334 | 0.351344 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.1272 | 1.39675 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.6434 | 0.971660 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 68.1534 | 2.30929 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.22122 | −0.176711 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −37.5176 | −1.26833 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.0063 | 1.48599 | 0.742994 | − | 0.669298i | \(-0.233405\pi\) | ||||
0.742994 | + | 0.669298i | \(0.233405\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.3626 | 0.551896 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.2383 | 1.08614 | 0.543069 | − | 0.839688i | \(-0.317262\pi\) | ||||
0.543069 | + | 0.839688i | \(0.317262\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.1619 | 0.947724 | 0.473862 | − | 0.880599i | \(-0.342860\pi\) | ||||
0.473862 | + | 0.880599i | \(0.342860\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.94985 | −0.166388 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.6636 | 0.760970 | 0.380485 | − | 0.924787i | \(-0.375757\pi\) | ||||
0.380485 | + | 0.924787i | \(0.375757\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −49.0199 | −1.64408 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.85682 | 0.0622058 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.32789 | −0.0778997 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.0001 | −0.367694 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.88102 | −0.229751 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.16139 | 0.238846 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −99.7510 | −3.32319 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −64.1887 | −2.13607 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.4250 | 0.512745 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.9805 | 0.597033 | 0.298516 | − | 0.954404i | \(-0.403508\pi\) | ||||
0.298516 | + | 0.954404i | \(0.403508\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.5973 | 0.583666 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.4635 | −1.67193 | −0.835965 | − | 0.548783i | \(-0.815091\pi\) | ||||
−0.835965 | + | 0.548783i | \(0.815091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.33821 | 0.0442882 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.84165 | 0.0939421 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 48.9430 | 1.61624 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.9767 | 1.31871 | 0.659355 | − | 0.751832i | \(-0.270830\pi\) | ||||
0.659355 | + | 0.751832i | \(0.270830\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.5073 | −0.576887 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −95.9550 | −3.15840 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.1286 | 0.990622 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.42864 | −0.309677 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.1825 | 0.760593 | 0.380297 | − | 0.924865i | \(-0.375822\pi\) | ||||
0.380297 | + | 0.924865i | \(0.375822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.3759 | 0.438377 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.0872 | −0.330240 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.4968 | 0.375986 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.7331 | −1.03668 | −0.518338 | − | 0.855176i | \(-0.673449\pi\) | ||||
−0.518338 | + | 0.855176i | \(0.673449\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.6111 | 0.705251 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.5878 | 1.94251 | 0.971254 | − | 0.238046i | \(-0.0765069\pi\) | ||||
0.971254 | + | 0.238046i | \(0.0765069\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.06531 | −0.0672558 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.01668 | 0.130663 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.4587 | 1.08726 | 0.543631 | − | 0.839324i | \(-0.317049\pi\) | ||||
0.543631 | + | 0.839324i | \(0.317049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.9379 | 0.809517 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.6316 | −0.571743 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.4240 | 0.499632 | 0.249816 | − | 0.968293i | \(-0.419630\pi\) | ||||
0.249816 | + | 0.968293i | \(0.419630\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0202798 | 0.000656240 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.85682 | −0.0600224 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −61.7817 | −1.99503 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.2855 | 0.654370 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.07940 | 0.195906 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.98413 | −0.257018 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.8301 | −0.573376 | −0.286688 | − | 0.958024i | \(-0.592554\pi\) | ||||
−0.286688 | + | 0.958024i | \(0.592554\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.83999 | −0.187608 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.1093 | 1.60809 | 0.804043 | − | 0.594571i | \(-0.202678\pi\) | ||||
0.804043 | + | 0.594571i | \(0.202678\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −64.6202 | −2.07163 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29.8668 | 0.956504 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.2024 | −1.31818 | −0.659090 | − | 0.752064i | \(-0.729058\pi\) | ||||
−0.659090 | + | 0.752064i | \(0.729058\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.28114 | 0.296626 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.4110 | −0.555890 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.7778 | 1.14113 | 0.570567 | − | 0.821251i | \(-0.306724\pi\) | ||||
0.570567 | + | 0.821251i | \(0.306724\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.59715 | −0.114615 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.0310 | 0.478441 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.9781 | 0.412679 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.3072 | −1.05804 | −0.529019 | − | 0.848610i | \(-0.677440\pi\) | ||||
−0.529019 | + | 0.848610i | \(0.677440\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.2302 | 0.578519 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.56827 | 0.0497175 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.0657 | 0.382123 | 0.191062 | − | 0.981578i | \(-0.438807\pi\) | ||||
0.191062 | + | 0.981578i | \(0.438807\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.94133 | −0.219614 |
(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.1.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.j.1.7 | ✓ | 16 | 1.1 | even | 1 | trivial |