Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, 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("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 93x^{6} - 119x^{5} - 174x^{4} + 107x^{3} + 51x^{2} - 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.0962745\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.0962745 | 0.0555841 | 0.0277920 | − | 0.999614i | \(-0.491152\pi\) | ||||
0.0277920 | + | 0.999614i | \(0.491152\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.48698 | −0.664998 | −0.332499 | − | 0.943104i | \(-0.607892\pi\) | ||||
−0.332499 | + | 0.943104i | \(0.607892\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99073 | −0.996910 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.143158 | −0.0369633 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.53478 | −1.82745 | −0.913726 | − | 0.406331i | \(-0.866808\pi\) | ||||
−0.913726 | + | 0.406331i | \(0.866808\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.59969 | 1.74349 | 0.871744 | − | 0.489961i | \(-0.162989\pi\) | ||||
0.871744 | + | 0.489961i | \(0.162989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0962745 | −0.0210088 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.71789 | −0.775233 | −0.387616 | − | 0.921821i | \(-0.626701\pi\) | ||||
−0.387616 | + | 0.921821i | \(0.626701\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.78889 | −0.557778 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.576755 | −0.110996 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.29580 | −1.72619 | −0.863093 | − | 0.505044i | \(-0.831476\pi\) | ||||
−0.863093 | + | 0.505044i | \(0.831476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.27772 | 1.12751 | 0.563756 | − | 0.825941i | \(-0.309356\pi\) | ||||
0.563756 | + | 0.825941i | \(0.309356\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0962745 | −0.0167592 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.48698 | 0.251345 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.976345 | 0.160510 | 0.0802551 | − | 0.996774i | \(-0.474427\pi\) | ||||
0.0802551 | + | 0.996774i | \(0.474427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0962745 | −0.0154163 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24087 | 0.662312 | 0.331156 | − | 0.943576i | \(-0.392561\pi\) | ||||
0.331156 | + | 0.943576i | \(0.392561\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.8980 | 1.81443 | 0.907217 | − | 0.420663i | \(-0.138202\pi\) | ||||
0.907217 | + | 0.420663i | \(0.138202\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.44716 | 0.662943 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.9010 | 1.88180 | 0.940901 | − | 0.338681i | \(-0.109981\pi\) | ||||
0.940901 | + | 0.338681i | \(0.109981\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.725407 | −0.101577 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.71919 | −0.648231 | −0.324116 | − | 0.946017i | \(-0.605067\pi\) | ||||
−0.324116 | + | 0.946017i | \(0.605067\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.48698 | 0.200504 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.731656 | 0.0969102 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.01808 | −0.653298 | −0.326649 | − | 0.945146i | \(-0.605919\pi\) | ||||
−0.326649 | + | 0.945146i | \(0.605919\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.65793 | −0.468350 | −0.234175 | − | 0.972194i | \(-0.575239\pi\) | ||||
−0.234175 | + | 0.972194i | \(0.575239\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.99073 | 0.376797 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.48698 | 0.184437 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.47832 | 0.669283 | 0.334641 | − | 0.942346i | \(-0.391385\pi\) | ||||
0.334641 | + | 0.942346i | \(0.391385\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.357938 | −0.0430906 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.99423 | −1.18610 | −0.593049 | − | 0.805167i | \(-0.702076\pi\) | ||||
−0.593049 | + | 0.805167i | \(0.702076\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.02335 | 0.939062 | 0.469531 | − | 0.882916i | \(-0.344423\pi\) | ||||
0.469531 | + | 0.882916i | \(0.344423\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.268499 | −0.0310036 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.16743 | 0.243855 | 0.121927 | − | 0.992539i | \(-0.461093\pi\) | ||||
0.121927 | + | 0.992539i | \(0.461093\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.91667 | 0.990741 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0745 | −1.32535 | −0.662673 | − | 0.748909i | \(-0.730578\pi\) | ||||
−0.662673 | + | 0.748909i | \(0.730578\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2041 | 1.21525 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.894948 | −0.0959485 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.1364 | 1.28645 | 0.643226 | − | 0.765676i | \(-0.277596\pi\) | ||||
0.643226 | + | 0.765676i | \(0.277596\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.604385 | 0.0626718 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.3006 | −1.15942 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.20899 | −0.935031 | −0.467515 | − | 0.883985i | \(-0.654851\pi\) | ||||
−0.467515 | + | 0.883985i | \(0.654851\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.99073 | 0.300580 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.95809 | 0.493348 | 0.246674 | − | 0.969098i | \(-0.420662\pi\) | ||||
0.246674 | + | 0.969098i | \(0.420662\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.232419 | −0.0229009 | −0.0114504 | − | 0.999934i | \(-0.503645\pi\) | ||||
−0.0114504 | + | 0.999934i | \(0.503645\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.143158 | 0.0139708 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.52905 | 0.244492 | 0.122246 | − | 0.992500i | \(-0.460990\pi\) | ||||
0.122246 | + | 0.992500i | \(0.460990\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.23676 | 0.118460 | 0.0592301 | − | 0.998244i | \(-0.481135\pi\) | ||||
0.0592301 | + | 0.998244i | \(0.481135\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0939972 | 0.00892181 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.71296 | −0.443358 | −0.221679 | − | 0.975120i | \(-0.571154\pi\) | ||||
−0.221679 | + | 0.975120i | \(0.571154\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.52842 | 0.515528 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.99073 | 0.276493 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.53478 | 0.690712 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.408287 | 0.0368140 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5819 | 1.03592 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.6384 | 1.83137 | 0.915683 | − | 0.401902i | \(-0.131651\pi\) | ||||
0.915683 | + | 0.401902i | \(0.131651\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.14548 | 0.100854 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.43721 | −0.125570 | −0.0627850 | − | 0.998027i | \(-0.519998\pi\) | ||||
−0.0627850 | + | 0.998027i | \(0.519998\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.59969 | −0.658977 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.857622 | 0.0738124 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.9061 | 1.87156 | 0.935782 | − | 0.352580i | \(-0.114695\pi\) | ||||
0.935782 | + | 0.352580i | \(0.114695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.33207 | −0.367441 | −0.183721 | − | 0.982978i | \(-0.558814\pi\) | ||||
−0.183721 | + | 0.982978i | \(0.558814\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.24204 | 0.104598 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.8227 | 1.14791 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.0962745 | 0.00794059 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4447 | 1.01951 | 0.509755 | − | 0.860320i | \(-0.329736\pi\) | ||||
0.509755 | + | 0.860320i | \(0.329736\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1067 | 1.63626 | 0.818132 | − | 0.575031i | \(-0.195010\pi\) | ||||
0.818132 | + | 0.575031i | \(0.195010\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.5345 | 1.82181 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.33485 | −0.749793 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.44888 | 0.434868 | 0.217434 | − | 0.976075i | \(-0.430231\pi\) | ||||
0.217434 | + | 0.976075i | \(0.430231\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.454338 | −0.0360313 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.71789 | 0.293011 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.33546 | −0.261253 | −0.130627 | − | 0.991432i | \(-0.541699\pi\) | ||||
−0.130627 | + | 0.991432i | \(0.541699\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.143158 | 0.0111449 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.6360 | −1.36471 | −0.682356 | − | 0.731020i | \(-0.739045\pi\) | ||||
−0.682356 | + | 0.731020i | \(0.739045\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.7286 | −1.73810 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.9723 | −1.36641 | −0.683204 | − | 0.730227i | \(-0.739414\pi\) | ||||
−0.683204 | + | 0.730227i | \(0.739414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.78889 | 0.210820 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.483113 | −0.0363130 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.5233 | 0.786547 | 0.393273 | − | 0.919422i | \(-0.371343\pi\) | ||||
0.393273 | + | 0.919422i | \(0.371343\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.25277 | −0.390436 | −0.195218 | − | 0.980760i | \(-0.562541\pi\) | ||||
−0.195218 | + | 0.980760i | \(0.562541\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.352165 | −0.0260328 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.45181 | −0.106739 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.53478 | 0.550997 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.576755 | 0.0419527 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5412 | 0.835091 | 0.417545 | − | 0.908656i | \(-0.362890\pi\) | ||||
0.417545 | + | 0.908656i | \(0.362890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.170184 | 0.0122501 | 0.00612505 | − | 0.999981i | \(-0.498050\pi\) | ||||
0.00612505 | + | 0.999981i | \(0.498050\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.143158 | 0.0102518 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.4451 | −1.95538 | −0.977691 | − | 0.210047i | \(-0.932638\pi\) | ||||
−0.977691 | + | 0.210047i | \(0.932638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2838 | −0.941664 | −0.470832 | − | 0.882223i | \(-0.656046\pi\) | ||||
−0.470832 | + | 0.882223i | \(0.656046\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.527422 | 0.0372015 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.29580 | 0.652437 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.30609 | −0.440436 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.1192 | 0.772838 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.59969 | −0.525682 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.47275 | 0.307917 | 0.153958 | − | 0.988077i | \(-0.450798\pi\) | ||||
0.153958 | + | 0.988077i | \(0.450798\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.962190 | −0.0659281 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.6921 | −1.20659 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.27772 | −0.426160 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.772444 | 0.0521969 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.53478 | 0.506844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.6613 | −1.11573 | −0.557863 | − | 0.829933i | \(-0.688378\pi\) | ||||
−0.557863 | + | 0.829933i | \(0.688378\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.34082 | 0.556055 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.9568 | 1.85556 | 0.927779 | − | 0.373130i | \(-0.121716\pi\) | ||||
0.927779 | + | 0.373130i | \(0.121716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.91041 | 0.654898 | 0.327449 | − | 0.944869i | \(-0.393811\pi\) | ||||
0.327449 | + | 0.944869i | \(0.393811\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0962745 | 0.00633440 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.0561 | −0.855334 | −0.427667 | − | 0.903936i | \(-0.640664\pi\) | ||||
−0.427667 | + | 0.903936i | \(0.640664\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.1835 | −1.25139 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.208668 | 0.0135544 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8509 | 0.960623 | 0.480311 | − | 0.877098i | \(-0.340524\pi\) | ||||
0.480311 | + | 0.877098i | \(0.340524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.60632 | 0.361135 | 0.180567 | − | 0.983563i | \(-0.442207\pi\) | ||||
0.180567 | + | 0.983563i | \(0.442207\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.58871 | 0.166066 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.48698 | −0.0949997 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.59969 | −0.483557 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.16246 | −0.0736682 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.74971 | 0.426038 | 0.213019 | − | 0.977048i | \(-0.431670\pi\) | ||||
0.213019 | + | 0.977048i | \(0.431670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.71789 | 0.233742 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.07867 | 0.0675486 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.1654 | −0.945992 | −0.472996 | − | 0.881065i | \(-0.656828\pi\) | ||||
−0.472996 | + | 0.881065i | \(0.656828\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.976345 | −0.0606672 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.8012 | 1.72085 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.9930 | 1.17116 | 0.585578 | − | 0.810616i | \(-0.300867\pi\) | ||||
0.585578 | + | 0.810616i | \(0.300867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.01735 | 0.431072 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.16842 | 0.0715063 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.4136 | 1.61046 | 0.805231 | − | 0.592961i | \(-0.202041\pi\) | ||||
0.805231 | + | 0.592961i | \(0.202041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.3654 | −0.811888 | −0.405944 | − | 0.913898i | \(-0.633057\pi\) | ||||
−0.405944 | + | 0.913898i | \(0.633057\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0962745 | 0.00582680 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.78889 | 0.168176 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.7062 | 1.90504 | 0.952521 | − | 0.304473i | \(-0.0984802\pi\) | ||||
0.952521 | + | 0.304473i | \(0.0984802\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.7750 | −1.12403 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.7863 | −0.882074 | −0.441037 | − | 0.897489i | \(-0.645389\pi\) | ||||
−0.441037 | + | 0.897489i | \(0.645389\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.6881 | −1.64589 | −0.822943 | − | 0.568124i | \(-0.807669\pi\) | ||||
−0.822943 | + | 0.568124i | \(0.807669\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.08796 | −0.0644451 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.24087 | −0.250331 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 39.7729 | 2.33958 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.886590 | −0.0519728 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.36339 | 0.138071 | 0.0690355 | − | 0.997614i | \(-0.478008\pi\) | ||||
0.0690355 | + | 0.997614i | \(0.478008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.46178 | 0.434442 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.576755 | 0.0334667 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.71789 | 0.215011 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.8980 | −0.685792 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.477337 | 0.0274223 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.43927 | 0.311452 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.1239 | 0.634875 | 0.317438 | − | 0.948279i | \(-0.397178\pi\) | ||||
0.317438 | + | 0.948279i | \(0.397178\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0223760 | −0.00127293 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.39075 | 0.419091 | 0.209546 | − | 0.977799i | \(-0.432802\pi\) | ||||
0.209546 | + | 0.977799i | \(0.432802\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.1279 | 1.02465 | 0.512325 | − | 0.858792i | \(-0.328784\pi\) | ||||
0.512325 | + | 0.858792i | \(0.328784\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.44716 | −0.250569 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.9342 | 0.670293 | 0.335147 | − | 0.942166i | \(-0.391214\pi\) | ||||
0.335147 | + | 0.942166i | \(0.391214\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.29580 | 0.520465 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.243483 | 0.0135899 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −57.2620 | −3.18614 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.78889 | 0.154700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.119068 | 0.00658450 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.9010 | −0.711254 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.7216 | −1.52372 | −0.761858 | − | 0.647744i | \(-0.775713\pi\) | ||||
−0.761858 | + | 0.647744i | \(0.775713\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.91999 | −0.160014 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.14614 | −0.445071 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.3079 | −0.779400 | −0.389700 | − | 0.920942i | \(-0.627421\pi\) | ||||
−0.389700 | + | 0.920942i | \(0.627421\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.453738 | −0.0246437 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.27772 | −0.339958 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.532246 | 0.0286552 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.2795 | 1.03498 | 0.517489 | − | 0.855690i | \(-0.326867\pi\) | ||||
0.517489 | + | 0.855690i | \(0.326867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.55297 | −0.511359 | −0.255679 | − | 0.966762i | \(-0.582299\pi\) | ||||
−0.255679 | + | 0.966762i | \(0.582299\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.576755 | 0.0307849 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.4085 | 0.713664 | 0.356832 | − | 0.934169i | \(-0.383857\pi\) | ||||
0.356832 | + | 0.934169i | \(0.383857\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.8612 | 0.788752 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.725407 | 0.0383926 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.0564 | 1.58632 | 0.793159 | − | 0.609014i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609014i | \(0.208435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.7553 | 2.03975 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0962745 | 0.00505310 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.9306 | −0.624474 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.13021 | −0.0589963 | −0.0294982 | − | 0.999565i | \(-0.509391\pi\) | ||||
−0.0294982 | + | 0.999565i | \(0.509391\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.6833 | −0.660266 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.71919 | 0.245008 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.2307 | −1.25462 | −0.627309 | − | 0.778770i | \(-0.715844\pi\) | ||||
−0.627309 | + | 0.778770i | \(0.715844\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.11504 | 0.0575806 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.29580 | 0.478758 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5563 | −0.747705 | −0.373852 | − | 0.927488i | \(-0.621963\pi\) | ||||
−0.373852 | + | 0.927488i | \(0.621963\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.98696 | 0.101795 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.1806 | 0.520202 | 0.260101 | − | 0.965581i | \(-0.416244\pi\) | ||||
0.260101 | + | 0.965581i | \(0.416244\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.48698 | −0.0757835 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −35.5838 | −1.80883 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.101396 | 0.00514100 | 0.00257050 | − | 0.999997i | \(-0.499182\pi\) | ||||
0.00257050 | + | 0.999997i | \(0.499182\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.0134 | 1.41670 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.138367 | −0.00697970 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.22292 | −0.162163 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.8536 | −1.64888 | −0.824438 | − | 0.565953i | \(-0.808508\pi\) | ||||
−0.824438 | + | 0.565953i | \(0.808508\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.731656 | −0.0366286 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.2263 | −1.10993 | −0.554964 | − | 0.831874i | \(-0.687268\pi\) | ||||
−0.554964 | + | 0.831874i | \(0.687268\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.27772 | −0.312716 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.2589 | −0.658840 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.976345 | −0.0483956 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.74445 | 0.382939 | 0.191469 | − | 0.981499i | \(-0.438675\pi\) | ||||
0.191469 | + | 0.981499i | \(0.438675\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.10900 | 0.104029 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.01808 | 0.246923 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.9545 | 0.881352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.417068 | −0.0204239 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.4417 | 1.58488 | 0.792440 | − | 0.609950i | \(-0.208811\pi\) | ||||
0.792440 | + | 0.609950i | \(0.208811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.2537 | −1.32827 | −0.664133 | − | 0.747614i | \(-0.731199\pi\) | ||||
−0.664133 | + | 0.747614i | \(0.731199\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −38.5834 | −1.87599 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.0137 | 1.01931 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.65793 | 0.177020 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0962745 | 0.00464818 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.3245 | 1.02716 | 0.513582 | − | 0.858040i | \(-0.328318\pi\) | ||||
0.513582 | + | 0.858040i | \(0.328318\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.57252 | −0.0755706 | −0.0377853 | − | 0.999286i | \(-0.512030\pi\) | ||||
−0.0377853 | + | 0.999286i | \(0.512030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.33077 | 0.0638055 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.2548 | −1.35161 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4666 | −1.21546 | −0.607728 | − | 0.794145i | \(-0.707919\pi\) | ||||
−0.607728 | + | 0.794145i | \(0.707919\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.99073 | −0.142416 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.9443 | 1.66025 | 0.830126 | − | 0.557576i | \(-0.188268\pi\) | ||||
0.830126 | + | 0.557576i | \(0.188268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0465 | −0.855488 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.19811 | 0.0566685 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.6772 | 1.02301 | 0.511505 | − | 0.859281i | \(-0.329088\pi\) | ||||
0.511505 | + | 0.859281i | \(0.329088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.24087 | −0.199695 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.93577 | 0.0909502 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.48698 | −0.0697107 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.2417 | −0.619418 | −0.309709 | − | 0.950831i | \(-0.600232\pi\) | ||||
−0.309709 | + | 0.950831i | \(0.600232\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.34572 | 0.202841 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.1588 | 1.73066 | 0.865328 | − | 0.501206i | \(-0.167110\pi\) | ||||
0.865328 | + | 0.501206i | \(0.167110\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.624236 | −0.0290107 | −0.0145054 | − | 0.999895i | \(-0.504617\pi\) | ||||
−0.0145054 | + | 0.999895i | \(0.504617\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.898708 | −0.0416766 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.53216 | −0.209723 | −0.104862 | − | 0.994487i | \(-0.533440\pi\) | ||||
−0.104862 | + | 0.994487i | \(0.533440\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.47832 | −0.252965 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.524588 | 0.0241717 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.8980 | −0.547072 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.1947 | −0.972480 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.1138 | 0.646228 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.2480 | −1.01654 | −0.508269 | − | 0.861199i | \(-0.669714\pi\) | ||||
−0.508269 | + | 0.861199i | \(0.669714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.976345 | −0.0445175 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.357938 | 0.0162867 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.6936 | 0.621793 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.46077 | −0.428709 | −0.214354 | − | 0.976756i | \(-0.568765\pi\) | ||||
−0.214354 | + | 0.976756i | \(0.568765\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.321119 | −0.0145215 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.2146 | 1.09279 | 0.546394 | − | 0.837528i | \(-0.316000\pi\) | ||||
0.546394 | + | 0.837528i | \(0.316000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 70.0418 | 3.15452 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.44716 | −0.199885 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.99423 | 0.448303 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.3417 | 1.40305 | 0.701523 | − | 0.712646i | \(-0.252504\pi\) | ||||
0.701523 | + | 0.712646i | \(0.252504\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.69789 | −0.0758563 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.5662 | −1.49664 | −0.748322 | − | 0.663335i | \(-0.769140\pi\) | ||||
−0.748322 | + | 0.663335i | \(0.769140\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.37258 | −0.328075 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.0962745 | 0.00427570 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.5318 | −0.688436 | −0.344218 | − | 0.938890i | \(-0.611856\pi\) | ||||
−0.344218 | + | 0.938890i | \(0.611856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.02335 | −0.354932 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.38316 | −0.193521 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.345602 | 0.0152290 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.9010 | −0.567385 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.73027 | −0.0759506 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.3683 | −1.19903 | −0.599514 | − | 0.800364i | \(-0.704640\pi\) | ||||
−0.599514 | + | 0.800364i | \(0.704640\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.82671 | −0.342238 | −0.171119 | − | 0.985250i | \(-0.554738\pi\) | ||||
−0.171119 | + | 0.985250i | \(0.554738\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.268499 | 0.0117183 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −47.3013 | −2.06047 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.17732 | −0.399014 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.0077 | 0.651280 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.24087 | −0.183692 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.76064 | −0.162587 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.01312 | 0.0437195 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.75618 | −0.290471 | −0.145235 | − | 0.989397i | \(-0.546394\pi\) | ||||
−0.145235 | + | 0.989397i | \(0.546394\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.505708 | −0.0217020 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.83904 | −0.0787757 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.9014 | −1.06471 | −0.532354 | − | 0.846522i | \(-0.678692\pi\) | ||||
−0.532354 | + | 0.846522i | \(0.678692\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.9399 | 0.466903 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −70.6452 | −3.00959 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.16743 | −0.0921684 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.139772 | −0.00593299 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.6165 | 1.29726 | 0.648632 | − | 0.761102i | \(-0.275341\pi\) | ||||
0.648632 | + | 0.761102i | \(0.275341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.8980 | −0.503233 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.725407 | 0.0306267 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.43712 | 0.144857 | 0.0724286 | − | 0.997374i | \(-0.476925\pi\) | ||||
0.0724286 | + | 0.997374i | \(0.476925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.00808 | 0.294832 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.91667 | −0.374465 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.77965 | −0.326140 | −0.163070 | − | 0.986615i | \(-0.552140\pi\) | ||||
−0.163070 | + | 0.986615i | \(0.552140\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.9038 | 1.87916 | 0.939582 | − | 0.342324i | \(-0.111214\pi\) | ||||
0.939582 | + | 0.342324i | \(0.111214\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.11112 | 0.0464178 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.3688 | 0.432408 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.01254 | 0.167044 | 0.0835221 | − | 0.996506i | \(-0.473383\pi\) | ||||
0.0835221 | + | 0.996506i | \(0.473383\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0163844 | 0.000680911 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0745 | 0.500934 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.71919 | 0.195449 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.44716 | −0.183867 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.6248 | 1.55294 | 0.776471 | − | 0.630152i | \(-0.217008\pi\) | ||||
0.776471 | + | 0.630152i | \(0.217008\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 47.7088 | 1.96581 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.64226 | −0.108688 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.3853 | 1.45310 | 0.726551 | − | 0.687113i | \(-0.241122\pi\) | ||||
0.726551 | + | 0.687113i | \(0.241122\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.2041 | −0.459322 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.27889 | −0.0523415 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.7877 | −0.808503 | −0.404252 | − | 0.914648i | \(-0.632468\pi\) | ||||
−0.404252 | + | 0.914648i | \(0.632468\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.93876 | 0.160666 | 0.0803328 | − | 0.996768i | \(-0.474402\pi\) | ||||
0.0803328 | + | 0.996768i | \(0.474402\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.3842 | −0.667215 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.48698 | −0.0604543 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.0332 | 1.86843 | 0.934215 | − | 0.356711i | \(-0.116102\pi\) | ||||
0.934215 | + | 0.356711i | \(0.116102\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.894948 | 0.0362651 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.9010 | −0.521918 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.74471 | −0.191637 | −0.0958186 | − | 0.995399i | \(-0.530547\pi\) | ||||
−0.0958186 | + | 0.995399i | \(0.530547\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.607115 | −0.0244812 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.5014 | −0.503289 | −0.251645 | − | 0.967820i | \(-0.580971\pi\) | ||||
−0.251645 | + | 0.967820i | \(0.580971\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.53170 | 0.0615644 | 0.0307822 | − | 0.999526i | \(-0.490200\pi\) | ||||
0.0307822 | + | 0.999526i | \(0.490200\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.14431 | 0.0860481 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.1364 | −0.486233 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.27763 | −0.131105 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.731656 | −0.0292195 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.35655 | −0.293325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.9627 | −0.715083 | −0.357542 | − | 0.933897i | \(-0.616385\pi\) | ||||
−0.357542 | + | 0.933897i | \(0.616385\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.430612 | 0.0171153 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.6890 | −1.21785 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.8901 | 1.18243 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.6689 | −0.895367 | −0.447683 | − | 0.894192i | \(-0.647751\pi\) | ||||
−0.447683 | + | 0.894192i | \(0.647751\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.22386 | −0.363753 | −0.181877 | − | 0.983321i | \(-0.558217\pi\) | ||||
−0.181877 | + | 0.983321i | \(0.558217\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.70330 | −0.0670675 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.0275 | −1.25913 | −0.629566 | − | 0.776947i | \(-0.716767\pi\) | ||||
−0.629566 | + | 0.776947i | \(0.716767\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.01808 | 0.196977 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.604385 | −0.0236877 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.9334 | −0.897452 | −0.448726 | − | 0.893669i | \(-0.648122\pi\) | ||||
−0.448726 | + | 0.893669i | \(0.648122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.13711 | 0.0835037 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.9957 | −0.936161 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.1761 | 1.05863 | 0.529316 | − | 0.848425i | \(-0.322449\pi\) | ||||
0.529316 | + | 0.848425i | \(0.322449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.0555 | 1.16902 | 0.584512 | − | 0.811385i | \(-0.301286\pi\) | ||||
0.584512 | + | 0.811385i | \(0.301286\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.725407 | 0.0281725 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.3006 | 0.438218 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.5607 | 1.33820 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.60406 | −0.0620166 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.65793 | 0.141213 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.1199 | 0.467186 | 0.233593 | − | 0.972334i | \(-0.424952\pi\) | ||||
0.233593 | + | 0.972334i | \(0.424952\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.60851 | 0.0619114 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.61418 | 0.100471 | 0.0502356 | − | 0.998737i | \(-0.484003\pi\) | ||||
0.0502356 | + | 0.998737i | \(0.484003\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.20899 | 0.353408 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.69153 | 0.103140 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.1398 | −1.30632 | −0.653161 | − | 0.757219i | \(-0.726558\pi\) | ||||
−0.653161 | + | 0.757219i | \(0.726558\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.5739 | −1.24459 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.954119 | 0.0364019 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.71919 | 0.179787 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7273 | 1.39717 | 0.698586 | − | 0.715526i | \(-0.253813\pi\) | ||||
0.698586 | + | 0.715526i | \(0.253813\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.99073 | −0.113608 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.44170 | 0.244348 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.9540 | −1.21034 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.25697 | −0.0475429 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.5869 | 1.15525 | 0.577626 | − | 0.816301i | \(-0.303979\pi\) | ||||
0.577626 | + | 0.816301i | \(0.303979\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.41992 | 0.279848 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.84688 | −0.0695576 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.95809 | −0.186468 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.2292 | 0.834836 | 0.417418 | − | 0.908715i | \(-0.362935\pi\) | ||||
0.417418 | + | 0.908715i | \(0.362935\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.48219 | −0.243101 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.3399 | −0.874085 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.48698 | −0.0556099 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.42976 | 0.0533953 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.0582 | −0.859925 | −0.429963 | − | 0.902847i | \(-0.641473\pi\) | ||||
−0.429963 | + | 0.902847i | \(0.641473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.232419 | 0.00865572 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.539745 | 0.0200733 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.9250 | 0.962829 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.1745 | −1.37873 | −0.689364 | − | 0.724415i | \(-0.742110\pi\) | ||||
−0.689364 | + | 0.724415i | \(0.742110\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5008 | −0.981510 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −89.6491 | −3.31579 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.7524 | 0.840380 | 0.420190 | − | 0.907436i | \(-0.361963\pi\) | ||||
0.420190 | + | 0.907436i | \(0.361963\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.143158 | −0.00528047 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.47832 | −0.201796 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.0686 | −0.775020 | −0.387510 | − | 0.921866i | \(-0.626665\pi\) | ||||
−0.387510 | + | 0.921866i | \(0.626665\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.731656 | −0.0268781 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.6490 | −1.52795 | −0.763976 | − | 0.645244i | \(-0.776756\pi\) | ||||
−0.763976 | + | 0.645244i | \(0.776756\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.5050 | −0.677972 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.1115 | 1.32125 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.52905 | −0.0924093 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.399650 | −0.0145834 | −0.00729171 | − | 0.999973i | \(-0.502321\pi\) | ||||
−0.00729171 | + | 0.999973i | \(0.502321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.649825 | 0.0236809 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.8983 | −1.08811 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.1194 | 1.16740 | 0.583699 | − | 0.811970i | \(-0.301605\pi\) | ||||
0.583699 | + | 0.811970i | \(0.301605\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.357938 | 0.0129923 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.5139 | −1.03363 | −0.516815 | − | 0.856097i | \(-0.672882\pi\) | ||||
−0.516815 | + | 0.856097i | \(0.672882\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.23676 | −0.0447737 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.5083 | −1.21150 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.01808 | 0.181192 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.500827 | 0.0180603 | 0.00903014 | − | 0.999959i | \(-0.497126\pi\) | ||||
0.00903014 | + | 0.999959i | \(0.497126\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.46004 | −0.0525821 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.6976 | −0.924277 | −0.462138 | − | 0.886808i | \(-0.652918\pi\) | ||||
−0.462138 | + | 0.886808i | \(0.652918\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.5079 | −0.628902 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.0939972 | −0.00337213 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.2293 | 1.15473 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.99423 | 0.357622 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.36140 | 0.191601 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.10237 | −0.289186 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.7939 | −0.955100 | −0.477550 | − | 0.878605i | \(-0.658475\pi\) | ||||
−0.477550 | + | 0.878605i | \(0.658475\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.82854 | 0.0650977 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.71296 | 0.167574 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.65793 | 0.129897 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.675591 | 0.0239608 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.6618 | −0.873567 | −0.436784 | − | 0.899567i | \(-0.643882\pi\) | ||||
−0.436784 | + | 0.899567i | \(0.643882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −97.2061 | −3.43890 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36.2966 | −1.28248 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.02335 | −0.283138 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.52842 | −0.194851 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.54295 | 0.0895161 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.7534 | 0.483542 | 0.241771 | − | 0.970333i | \(-0.422272\pi\) | ||||
0.241771 | + | 0.970333i | \(0.422272\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.54296 | −0.264869 | −0.132435 | − | 0.991192i | \(-0.542279\pi\) | ||||
−0.132435 | + | 0.991192i | \(0.542279\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.28674 | −0.0451280 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.95975 | 0.173733 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 90.4214 | 3.16345 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.99073 | −0.104505 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.8612 | −0.937461 | −0.468730 | − | 0.883341i | \(-0.655288\pi\) | ||||
−0.468730 | + | 0.883341i | \(0.655288\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.5461 | −1.72707 | −0.863534 | − | 0.504290i | \(-0.831754\pi\) | ||||
−0.863534 | + | 0.504290i | \(0.831754\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.268499 | 0.00934794 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.0075 | 0.591407 | 0.295704 | − | 0.955280i | \(-0.404446\pi\) | ||||
0.295704 | + | 0.955280i | \(0.404446\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.12070 | −0.143118 | −0.0715589 | − | 0.997436i | \(-0.522797\pi\) | ||||
−0.0715589 | + | 0.997436i | \(0.522797\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.05250 | 0.105890 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.53478 | −0.261065 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.2243 | 0.907530 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.62071 | −0.125150 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.9638 | −0.861846 | −0.430923 | − | 0.902389i | \(-0.641812\pi\) | ||||
−0.430923 | + | 0.902389i | \(0.641812\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.4119 | 1.97972 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.42354 | −0.0490293 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.48698 | −0.0511537 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.66566 | −0.0914851 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.62994 | −0.124433 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.42469 | 0.288456 | 0.144228 | − | 0.989544i | \(-0.453930\pi\) | ||||
0.144228 | + | 0.989544i | \(0.453930\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33.7970 | 1.15583 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.9461 | −1.26205 | −0.631027 | − | 0.775761i | \(-0.717366\pi\) | ||||
−0.631027 | + | 0.775761i | \(0.717366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.5551 | 1.79316 | 0.896579 | − | 0.442884i | \(-0.146045\pi\) | ||||
0.896579 | + | 0.442884i | \(0.146045\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.408287 | −0.0139144 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.4110 | 1.81813 | 0.909066 | − | 0.416653i | \(-0.136797\pi\) | ||||
0.909066 | + | 0.416653i | \(0.136797\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.7244 | 0.908658 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.82911 | 0.130043 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.16743 | −0.0735249 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.47832 | −0.185626 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.5416 | 0.932142 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.5819 | −0.391540 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.8164 | −1.54711 | −0.773556 | − | 0.633728i | \(-0.781524\pi\) | ||||
−0.773556 | + | 0.633728i | \(0.781524\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.227535 | 0.00767455 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.1659 | −1.52168 | −0.760839 | − | 0.648941i | \(-0.775212\pi\) | ||||
−0.760839 | + | 0.648941i | \(0.775212\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.93907 | −0.166213 | −0.0831064 | − | 0.996541i | \(-0.526484\pi\) | ||||
−0.0831064 | + | 0.996541i | \(0.526484\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.718379 | 0.0241480 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 56.1806 | 1.88636 | 0.943179 | − | 0.332284i | \(-0.107819\pi\) | ||||
0.943179 | + | 0.332284i | \(0.107819\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.6384 | −0.692191 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.91667 | −0.298720 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 98.0435 | 3.28090 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.6479 | −0.523052 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.357938 | 0.0119512 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −58.3565 | −1.94630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.5581 | 1.18461 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.14548 | −0.0381191 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.81077 | 0.259639 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.175012 | −0.00581117 | −0.00290559 | − | 0.999996i | \(-0.500925\pi\) | ||||
−0.00290559 | + | 0.999996i | \(0.500925\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.8283 | −0.491824 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.3521 | −0.939348 | −0.469674 | − | 0.882840i | \(-0.655628\pi\) | ||||
−0.469674 | + | 0.882840i | \(0.655628\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0745 | 0.399607 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.523663 | 0.0173118 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.43721 | 0.0474610 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.6918 | −0.385676 | −0.192838 | − | 0.981231i | \(-0.561769\pi\) | ||||
−0.192838 | + | 0.981231i | \(0.561769\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.07095 | 0.0352890 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.99423 | 0.328964 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.72292 | −0.0895291 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.695102 | 0.0228301 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.3318 | 0.568639 | 0.284320 | − | 0.958730i | \(-0.408232\pi\) | ||||
0.284320 | + | 0.958730i | \(0.408232\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.59969 | 0.249070 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.711541 | 0.0232948 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.2041 | −0.366412 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.4827 | 1.02849 | 0.514247 | − | 0.857642i | \(-0.328072\pi\) | ||||
0.514247 | + | 0.857642i | \(0.328072\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.74526 | 0.0569543 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.6213 | −1.09602 | −0.548011 | − | 0.836471i | \(-0.684615\pi\) | ||||
−0.548011 | + | 0.836471i | \(0.684615\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.7671 | −0.513446 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.857622 | −0.0278985 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.1792 | 0.785720 | 0.392860 | − | 0.919598i | \(-0.371486\pi\) | ||||
0.392860 | + | 0.919598i | \(0.371486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.02335 | −0.260449 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.14896 | 0.0372576 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.3155 | −0.593297 | −0.296649 | − | 0.954987i | \(-0.595869\pi\) | ||||
−0.296649 | + | 0.954987i | \(0.595869\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.1615 | −0.555333 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.894948 | 0.0289296 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21.9061 | −0.707385 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.40982 | 0.271284 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.56370 | −0.243737 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.253060 | −0.00814629 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.0244 | 0.804731 | 0.402365 | − | 0.915479i | \(-0.368188\pi\) | ||||
0.402365 | + | 0.915479i | \(0.368188\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.51287 | −0.177099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.74207 | 0.280547 | 0.140273 | − | 0.990113i | \(-0.455202\pi\) | ||||
0.140273 | + | 0.990113i | \(0.455202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.33207 | 0.138880 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.268499 | 0.00859885 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.82118 | −0.154243 | −0.0771216 | − | 0.997022i | \(-0.524573\pi\) | ||||
−0.0771216 | + | 0.997022i | \(0.524573\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.1364 | −0.387880 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.69882 | −0.118094 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.55814 | 0.0496968 | 0.0248484 | − | 0.999691i | \(-0.492090\pi\) | ||||
0.0248484 | + | 0.999691i | \(0.492090\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.8103 | 1.30032 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.24204 | −0.0395344 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.2356 | −1.40661 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5716 | 0.748776 | 0.374388 | − | 0.927272i | \(-0.377853\pi\) | ||||
0.374388 | + | 0.927272i | \(0.377853\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.66888 | −0.0846944 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.7527 | 0.626204 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.9566 | 1.23377 | 0.616884 | − | 0.787054i | \(-0.288395\pi\) | ||||
0.616884 | + | 0.787054i | \(0.288395\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.563112 | −0.0178161 |
(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 | 4004.2.a.j.1.6 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.j.1.6 | ✓ | 10 | 1.1 | even | 1 | trivial |