Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 19 x^{9} + 33 x^{8} + 120 x^{7} - 178 x^{6} - 296 x^{5} + 380 x^{4} + 280 x^{3} - 295 x^{2} - 87 x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.48564\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | −1.48564 | −0.857736 | −0.428868 | − | 0.903367i | \(-0.641087\pi\) | ||||
−0.428868 | + | 0.903367i | \(0.641087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.395242 | −0.176758 | −0.0883788 | − | 0.996087i | \(-0.528169\pi\) | ||||
−0.0883788 | + | 0.996087i | \(0.528169\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.792869 | −0.264290 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.587188 | 0.151611 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.74936 | −0.666819 | −0.333409 | − | 0.942782i | \(-0.608199\pi\) | ||||
−0.333409 | + | 0.942782i | \(0.608199\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.24077 | 1.20232 | 0.601158 | − | 0.799130i | \(-0.294706\pi\) | ||||
0.601158 | + | 0.799130i | \(0.294706\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.48564 | 0.324194 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.01585 | −0.420334 | −0.210167 | − | 0.977666i | \(-0.567401\pi\) | ||||
−0.210167 | + | 0.977666i | \(0.567401\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.84378 | −0.968757 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.63484 | 1.08443 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.19717 | 0.965090 | 0.482545 | − | 0.875871i | \(-0.339713\pi\) | ||||
0.482545 | + | 0.875871i | \(0.339713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.17745 | −1.46871 | −0.734357 | − | 0.678764i | \(-0.762516\pi\) | ||||
−0.734357 | + | 0.678764i | \(0.762516\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.48564 | −0.258617 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.395242 | 0.0668081 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.28617 | 0.540244 | 0.270122 | − | 0.962826i | \(-0.412936\pi\) | ||||
0.270122 | + | 0.962826i | \(0.412936\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.48564 | 0.237893 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.42704 | 1.47226 | 0.736128 | − | 0.676842i | \(-0.236652\pi\) | ||||
0.736128 | + | 0.676842i | \(0.236652\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.55917 | 1.00026 | 0.500132 | − | 0.865949i | \(-0.333285\pi\) | ||||
0.500132 | + | 0.865949i | \(0.333285\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.313375 | 0.0467152 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.01585 | −0.294042 | −0.147021 | − | 0.989133i | \(-0.546968\pi\) | ||||
−0.147021 | + | 0.989133i | \(0.546968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.08457 | 0.571954 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.08665 | −0.561344 | −0.280672 | − | 0.959804i | \(-0.590557\pi\) | ||||
−0.280672 | + | 0.959804i | \(0.590557\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.395242 | −0.0532944 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.78591 | −1.03127 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.11865 | 1.18715 | 0.593573 | − | 0.804780i | \(-0.297717\pi\) | ||||
0.593573 | + | 0.804780i | \(0.297717\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.32901 | 1.19446 | 0.597229 | − | 0.802071i | \(-0.296268\pi\) | ||||
0.597229 | + | 0.802071i | \(0.296268\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.792869 | 0.0998921 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.395242 | 0.0490237 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.16464 | −0.997470 | −0.498735 | − | 0.866754i | \(-0.666202\pi\) | ||||
−0.498735 | + | 0.866754i | \(0.666202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.99483 | 0.360535 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.19413 | −0.260395 | −0.130198 | − | 0.991488i | \(-0.541561\pi\) | ||||
−0.130198 | + | 0.991488i | \(0.541561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.40454 | −1.10072 | −0.550359 | − | 0.834928i | \(-0.685509\pi\) | ||||
−0.550359 | + | 0.834928i | \(0.685509\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.19613 | 0.830937 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.94436 | 0.668793 | 0.334396 | − | 0.942433i | \(-0.391468\pi\) | ||||
0.334396 | + | 0.942433i | \(0.391468\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.99275 | −0.665861 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.9777 | −1.42449 | −0.712246 | − | 0.701930i | \(-0.752322\pi\) | ||||
−0.712246 | + | 0.701930i | \(0.752322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.08666 | 0.117865 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.72113 | −0.827792 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.69667 | 0.285847 | 0.142923 | − | 0.989734i | \(-0.454350\pi\) | ||||
0.142923 | + | 0.989734i | \(0.454350\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.1488 | 1.25977 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.07137 | −0.212518 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.44684 | −0.959181 | −0.479591 | − | 0.877492i | \(-0.659215\pi\) | ||||
−0.479591 | + | 0.877492i | \(0.659215\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.792869 | −0.0796864 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.33953 | 0.431800 | 0.215900 | − | 0.976416i | \(-0.430732\pi\) | ||||
0.215900 | + | 0.976416i | \(0.430732\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.30468 | −0.719751 | −0.359876 | − | 0.933000i | \(-0.617181\pi\) | ||||
−0.359876 | + | 0.933000i | \(0.617181\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.587188 | −0.0573037 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.5263 | −1.21096 | −0.605481 | − | 0.795860i | \(-0.707019\pi\) | ||||
−0.605481 | + | 0.795860i | \(0.707019\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.8768 | 1.71229 | 0.856144 | − | 0.516737i | \(-0.172853\pi\) | ||||
0.856144 | + | 0.516737i | \(0.172853\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.88208 | −0.463386 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.36174 | −0.316246 | −0.158123 | − | 0.987419i | \(-0.550544\pi\) | ||||
−0.158123 | + | 0.987419i | \(0.550544\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.796748 | 0.0742971 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.792869 | 0.0733008 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.74936 | 0.252034 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.0052 | −1.26281 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.89068 | 0.347993 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3023 | 1.26913 | 0.634563 | − | 0.772871i | \(-0.281180\pi\) | ||||
0.634563 | + | 0.772871i | \(0.281180\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.74457 | −0.857961 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.3233 | 1.25143 | 0.625715 | − | 0.780051i | \(-0.284807\pi\) | ||||
0.625715 | + | 0.780051i | \(0.284807\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.24077 | −0.454432 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.22713 | −0.191681 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.01281 | 0.428273 | 0.214137 | − | 0.976804i | \(-0.431306\pi\) | ||||
0.214137 | + | 0.976804i | \(0.431306\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.11317 | 0.518513 | 0.259256 | − | 0.965809i | \(-0.416523\pi\) | ||||
0.259256 | + | 0.965809i | \(0.416523\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.99483 | 0.252210 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.05414 | −0.170587 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.48564 | −0.122534 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.57652 | −0.293000 | −0.146500 | − | 0.989211i | \(-0.546801\pi\) | ||||
−0.146500 | + | 0.989211i | \(0.546801\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.966800 | 0.0786771 | 0.0393385 | − | 0.999226i | \(-0.487475\pi\) | ||||
0.0393385 | + | 0.999226i | \(0.487475\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.17989 | 0.176233 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.23207 | 0.259606 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.48916 | −0.677509 | −0.338754 | − | 0.940875i | \(-0.610006\pi\) | ||||
−0.338754 | + | 0.940875i | \(0.610006\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.07129 | 0.481485 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.01585 | 0.158871 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.3150 | −1.12124 | −0.560620 | − | 0.828073i | \(-0.689437\pi\) | ||||
−0.560620 | + | 0.828073i | \(0.689437\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.587188 | 0.0457125 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.8926 | 0.842892 | 0.421446 | − | 0.906854i | \(-0.361523\pi\) | ||||
0.421446 | + | 0.906854i | \(0.361523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.15525 | −0.317760 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.8125 | 1.58234 | 0.791172 | − | 0.611594i | \(-0.209471\pi\) | ||||
0.791172 | + | 0.611594i | \(0.209471\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.84378 | 0.366156 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.5470 | −1.01826 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.2990 | −1.74145 | −0.870726 | − | 0.491769i | \(-0.836350\pi\) | ||||
−0.870726 | + | 0.491769i | \(0.836350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.77497 | −0.280591 | −0.140296 | − | 0.990110i | \(-0.544805\pi\) | ||||
−0.140296 | + | 0.990110i | \(0.544805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.8596 | −1.02453 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.29883 | −0.0954922 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.74936 | −0.201053 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.63484 | −0.409875 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.41627 | 0.608980 | 0.304490 | − | 0.952515i | \(-0.401514\pi\) | ||||
0.304490 | + | 0.952515i | \(0.401514\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.7515 | 1.34976 | 0.674880 | − | 0.737928i | \(-0.264196\pi\) | ||||
0.674880 | + | 0.737928i | \(0.264196\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.587188 | −0.0420494 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.89963 | −0.349084 | −0.174542 | − | 0.984650i | \(-0.555845\pi\) | ||||
−0.174542 | + | 0.984650i | \(0.555845\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.8729 | −1.47964 | −0.739822 | − | 0.672803i | \(-0.765090\pi\) | ||||
−0.739822 | + | 0.672803i | \(0.765090\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.1297 | 0.855566 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.19717 | −0.364770 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.72596 | −0.260232 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.59831 | 0.111090 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.24077 | 0.362512 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0853 | −1.72694 | −0.863470 | − | 0.504400i | \(-0.831714\pi\) | ||||
−0.863470 | + | 0.504400i | \(0.831714\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.25969 | 0.223350 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.59246 | −0.176804 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.17745 | 0.555122 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.9718 | 0.944125 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.74936 | 0.184942 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.0089 | −1.27293 | −0.636464 | − | 0.771307i | \(-0.719604\pi\) | ||||
−0.636464 | + | 0.771307i | \(0.719604\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.84049 | 0.256033 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.05764 | −0.402060 | −0.201030 | − | 0.979585i | \(-0.564429\pi\) | ||||
−0.201030 | + | 0.979585i | \(0.564429\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.9295 | 1.11874 | 0.559368 | − | 0.828920i | \(-0.311044\pi\) | ||||
0.559368 | + | 0.828920i | \(0.311044\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.48564 | 0.0977480 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.52201 | −0.0997099 | −0.0498550 | − | 0.998756i | \(-0.515876\pi\) | ||||
−0.0498550 | + | 0.998756i | \(0.515876\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.796748 | 0.0519741 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.83118 | −0.573647 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.0413 | −1.10231 | −0.551156 | − | 0.834402i | \(-0.685813\pi\) | ||||
−0.551156 | + | 0.834402i | \(0.685813\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.41585 | 0.413281 | 0.206641 | − | 0.978417i | \(-0.433747\pi\) | ||||
0.206641 | + | 0.978417i | \(0.433747\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00145 | −0.513294 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.395242 | −0.0252511 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.24077 | −0.333462 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.2803 | 1.22184 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.8571 | −1.50585 | −0.752924 | − | 0.658107i | \(-0.771357\pi\) | ||||
−0.752924 | + | 0.658107i | \(0.771357\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.01585 | −0.126735 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.61439 | −0.101097 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.2849 | 0.953447 | 0.476724 | − | 0.879053i | \(-0.341824\pi\) | ||||
0.476724 | + | 0.879053i | \(0.341824\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.28617 | −0.204193 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.12067 | −0.255063 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.5748 | −1.57701 | −0.788504 | − | 0.615029i | \(-0.789144\pi\) | ||||
−0.788504 | + | 0.615029i | \(0.789144\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.61521 | 0.0992218 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.00629 | −0.245181 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.9514 | −0.728690 | −0.364345 | − | 0.931264i | \(-0.618707\pi\) | ||||
−0.364345 | + | 0.931264i | \(0.618707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.0837 | −1.22000 | −0.610000 | − | 0.792401i | \(-0.708831\pi\) | ||||
−0.610000 | + | 0.792401i | \(0.708831\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.48564 | −0.0899151 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.84378 | −0.292091 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8713 | −0.713279 | −0.356640 | − | 0.934242i | \(-0.616078\pi\) | ||||
−0.356640 | + | 0.934242i | \(0.616078\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.48365 | 0.388166 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.9066 | −0.769943 | −0.384971 | − | 0.922928i | \(-0.625789\pi\) | ||||
−0.384971 | + | 0.922928i | \(0.625789\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.52500 | 0.328427 | 0.164214 | − | 0.986425i | \(-0.447491\pi\) | ||||
0.164214 | + | 0.986425i | \(0.447491\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.07732 | 0.182284 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.42704 | −0.556461 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.44099 | −0.555353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0346 | 0.822724 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.09243 | 0.297503 | 0.148751 | − | 0.988875i | \(-0.452475\pi\) | ||||
0.148751 | + | 0.988875i | \(0.452475\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.60407 | −0.209837 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.63484 | 0.326967 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.01585 | 0.116580 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.55917 | −0.378064 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.44699 | −0.370370 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.68722 | −0.211129 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.9067 | 1.70686 | 0.853431 | − | 0.521205i | \(-0.174517\pi\) | ||||
0.853431 | + | 0.521205i | \(0.174517\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8521 | 0.617356 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.2096 | 0.805755 | 0.402877 | − | 0.915254i | \(-0.368010\pi\) | ||||
0.402877 | + | 0.915254i | \(0.368010\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.7745 | −1.45686 | −0.728430 | − | 0.685120i | \(-0.759750\pi\) | ||||
−0.728430 | + | 0.685120i | \(0.759750\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.313375 | −0.0176567 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.9921 | −1.06670 | −0.533352 | − | 0.845893i | \(-0.679068\pi\) | ||||
−0.533352 | + | 0.845893i | \(0.679068\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.19717 | 0.290985 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.6096 | 1.03869 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.4088 | −0.801727 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.84378 | 0.268685 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.5585 | −1.46869 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.01585 | 0.111137 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.1626 | −1.27313 | −0.636565 | − | 0.771223i | \(-0.719645\pi\) | ||||
−0.636565 | + | 0.771223i | \(0.719645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.60551 | −0.142781 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.22701 | 0.176310 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.46696 | 0.188857 | 0.0944287 | − | 0.995532i | \(-0.469898\pi\) | ||||
0.0944287 | + | 0.995532i | \(0.469898\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.99435 | 0.271256 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.17745 | −0.442834 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.18368 | −0.0637273 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.5966 | −0.890954 | −0.445477 | − | 0.895293i | \(-0.646966\pi\) | ||||
−0.445477 | + | 0.895293i | \(0.646966\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.3800 | 1.30503 | 0.652515 | − | 0.757776i | \(-0.273714\pi\) | ||||
0.652515 | + | 0.757776i | \(0.273714\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.63484 | −0.300766 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.00125 | 0.106516 | 0.0532578 | − | 0.998581i | \(-0.483039\pi\) | ||||
0.0532578 | + | 0.998581i | \(0.483039\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.867212 | 0.0460268 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.08457 | −0.216178 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.62284 | 0.455096 | 0.227548 | − | 0.973767i | \(-0.426929\pi\) | ||||
0.227548 | + | 0.973767i | \(0.426929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.46568 | 0.445562 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.48564 | −0.0779760 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.71707 | 0.194560 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.63360 | −0.241872 | −0.120936 | − | 0.992660i | \(-0.538590\pi\) | ||||
−0.120936 | + | 0.992660i | \(0.538590\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.47441 | −0.389102 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.08665 | 0.212168 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.9380 | −1.44657 | −0.723287 | − | 0.690547i | \(-0.757370\pi\) | ||||
−0.723287 | + | 0.690547i | \(0.757370\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.78015 | −0.298486 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.19717 | −0.267668 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.7993 | 0.657454 | 0.328727 | − | 0.944425i | \(-0.393380\pi\) | ||||
0.328727 | + | 0.944425i | \(0.393380\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.2481 | −1.08857 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.8587 | 1.16803 | 0.584013 | − | 0.811744i | \(-0.301482\pi\) | ||||
0.584013 | + | 0.811744i | \(0.301482\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.395242 | 0.0201434 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.20056 | −0.264359 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.1779 | 0.566744 | 0.283372 | − | 0.959010i | \(-0.408547\pi\) | ||||
0.283372 | + | 0.959010i | \(0.408547\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.54231 | 0.280286 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.2793 | −1.07340 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.34946 | −0.118214 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.76780 | −0.339666 | −0.169833 | − | 0.985473i | \(-0.554323\pi\) | ||||
−0.169833 | + | 0.985473i | \(0.554323\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.78591 | 0.389783 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.1959 | −1.65772 | −0.828862 | − | 0.559453i | \(-0.811011\pi\) | ||||
−0.828862 | + | 0.559453i | \(0.811011\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.17745 | 0.407348 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.36859 | 0.117696 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.28617 | 0.162890 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.0191 | 1.87992 | 0.939961 | − | 0.341282i | \(-0.110861\pi\) | ||||
0.939961 | + | 0.341282i | \(0.110861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.44724 | −0.367345 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.11865 | −0.448699 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.12935 | 0.251790 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.08199 | −0.444747 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.0207 | −1.66202 | −0.831011 | − | 0.556256i | \(-0.812237\pi\) | ||||
−0.831011 | + | 0.556256i | \(0.812237\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.64631 | 0.372658 | 0.186329 | − | 0.982487i | \(-0.440341\pi\) | ||||
0.186329 | + | 0.982487i | \(0.440341\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.59831 | 0.0777123 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.3173 | 0.645985 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.32901 | −0.451462 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.48564 | 0.0717274 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.67146 | 0.369521 | 0.184761 | − | 0.982784i | \(-0.440849\pi\) | ||||
0.184761 | + | 0.982784i | \(0.440849\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.5490 | 1.80449 | 0.902245 | − | 0.431225i | \(-0.141918\pi\) | ||||
0.902245 | + | 0.431225i | \(0.141918\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.05171 | 0.146318 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.5646 | −0.505374 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.4285 | −1.59546 | −0.797728 | − | 0.603017i | \(-0.793965\pi\) | ||||
−0.797728 | + | 0.603017i | \(0.793965\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.792869 | −0.0377557 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.2249 | 1.00842 | 0.504212 | − | 0.863580i | \(-0.331783\pi\) | ||||
0.504212 | + | 0.863580i | \(0.331783\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.06584 | −0.0505256 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.31343 | 0.251317 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.47085 | 0.163799 | 0.0818997 | − | 0.996641i | \(-0.473901\pi\) | ||||
0.0818997 | + | 0.996641i | \(0.473901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.42704 | 0.443902 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.43632 | −0.0674841 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.395242 | −0.0185292 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.73156 | −0.174555 | −0.0872774 | − | 0.996184i | \(-0.527817\pi\) | ||||
−0.0872774 | + | 0.996184i | \(0.527817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.4922 | −0.723116 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.7886 | −1.15452 | −0.577261 | − | 0.816560i | \(-0.695879\pi\) | ||||
−0.577261 | + | 0.816560i | \(0.695879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.9542 | 1.48504 | 0.742519 | − | 0.669825i | \(-0.233631\pi\) | ||||
0.742519 | + | 0.669825i | \(0.233631\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.80170 | −0.222673 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.7660 | −0.498191 | −0.249096 | − | 0.968479i | \(-0.580133\pi\) | ||||
−0.249096 | + | 0.968479i | \(0.580133\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.16464 | 0.377008 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6118 | 0.581123 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.55917 | 0.301591 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.3852 | −1.16475 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.24018 | 0.148357 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.4816 | −1.75827 | −0.879135 | − | 0.476573i | \(-0.841879\pi\) | ||||
−0.879135 | + | 0.476573i | \(0.841879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.28617 | −0.149837 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.99483 | −0.136269 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.73379 | 0.169543 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.40359 | 0.426117 | 0.213059 | − | 0.977039i | \(-0.431657\pi\) | ||||
0.213059 | + | 0.977039i | \(0.431657\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.2670 | 0.961727 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.6492 | −0.841626 | −0.420813 | − | 0.907147i | \(-0.638255\pi\) | ||||
−0.420813 | + | 0.907147i | \(0.638255\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.2889 | −0.643540 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.313375 | 0.0140852 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.19413 | 0.0984202 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.6231 | −0.699387 | −0.349694 | − | 0.936864i | \(-0.613714\pi\) | ||||
−0.349694 | + | 0.936864i | \(0.613714\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.1824 | −0.722978 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.6033 | −1.27536 | −0.637679 | − | 0.770302i | \(-0.720105\pi\) | ||||
−0.637679 | + | 0.770302i | \(0.720105\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.71516 | −0.0763238 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.48564 | −0.0659797 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.0076 | −0.753848 | −0.376924 | − | 0.926244i | \(-0.623018\pi\) | ||||
−0.376924 | + | 0.926244i | \(0.623018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.40454 | 0.416033 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29.5309 | 1.30382 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.88711 | 0.127221 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.01585 | −0.0886570 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.9199 | −1.35723 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.09237 | 0.266911 | 0.133456 | − | 0.991055i | \(-0.457393\pi\) | ||||
0.133456 | + | 0.991055i | \(0.457393\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.1123 | 1.01063 | 0.505315 | − | 0.862935i | \(-0.331376\pi\) | ||||
0.505315 | + | 0.862935i | \(0.331376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.19613 | −0.314065 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.4828 | 0.979366 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.9364 | −0.823320 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.22989 | −0.313751 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.42704 | −0.408331 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.95091 | 0.214047 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.6140 | 1.49370 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.73491 | 0.332550 | 0.166275 | − | 0.986079i | \(-0.446826\pi\) | ||||
0.166275 | + | 0.986079i | \(0.446826\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.60825 | 0.240673 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.06567 | −0.302660 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.85752 | 0.421477 | 0.210739 | − | 0.977542i | \(-0.432413\pi\) | ||||
0.210739 | + | 0.977542i | \(0.432413\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.39669 | −0.315683 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.2372 | 1.16034 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.94436 | −0.252780 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.92960 | 0.0819070 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.8727 | −1.09626 | −0.548130 | − | 0.836393i | \(-0.684660\pi\) | ||||
−0.548130 | + | 0.836393i | \(0.684660\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.55917 | −0.277423 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.08457 | 0.172451 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.556102 | 0.0234369 | 0.0117185 | − | 0.999931i | \(-0.496270\pi\) | ||||
0.0117185 | + | 0.999931i | \(0.496270\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.32870 | 0.0558989 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.99275 | 0.251672 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.1810 | −1.26525 | −0.632626 | − | 0.774458i | \(-0.718023\pi\) | ||||
−0.632626 | + | 0.774458i | \(0.718023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.8821 | −1.58531 | −0.792657 | − | 0.609667i | \(-0.791303\pi\) | ||||
−0.792657 | + | 0.609667i | \(0.791303\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.5036 | −0.522344 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.76434 | 0.407201 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.2960 | −1.59428 | −0.797142 | − | 0.603792i | \(-0.793656\pi\) | ||||
−0.797142 | + | 0.603792i | \(0.793656\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.8579 | −1.15774 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.9777 | 0.538408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.08665 | −0.169252 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.313375 | −0.0129565 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.59160 | −0.354613 | −0.177307 | − | 0.984156i | \(-0.556738\pi\) | ||||
−0.177307 | + | 0.984156i | \(0.556738\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.8562 | −1.76586 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.27910 | 0.299422 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.8725 | 1.30885 | 0.654424 | − | 0.756128i | \(-0.272911\pi\) | ||||
0.654424 | + | 0.756128i | \(0.272911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.08666 | −0.0445489 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.0097 | 1.26914 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.482125 | −0.0196991 | −0.00984955 | − | 0.999951i | \(-0.503135\pi\) | ||||
−0.00984955 | + | 0.999951i | \(0.503135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.1899 | −1.35384 | −0.676922 | − | 0.736055i | \(-0.736687\pi\) | ||||
−0.676922 | + | 0.736055i | \(0.736687\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.47350 | 0.263621 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.395242 | −0.0160689 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.4892 | −0.791040 | −0.395520 | − | 0.918457i | \(-0.629436\pi\) | ||||
−0.395520 | + | 0.918457i | \(0.629436\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.72113 | 0.312876 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.01585 | 0.0815525 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.00058 | −0.161582 | −0.0807910 | − | 0.996731i | \(-0.525745\pi\) | ||||
−0.0807910 | + | 0.996731i | \(0.525745\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.53544 | 0.223211 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.3626 | −1.46390 | −0.731951 | − | 0.681357i | \(-0.761390\pi\) | ||||
−0.731951 | + | 0.681357i | \(0.761390\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.0793 | −0.847251 | −0.423625 | − | 0.905838i | \(-0.639243\pi\) | ||||
−0.423625 | + | 0.905838i | \(0.639243\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.3590 | −0.455821 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.69667 | −0.108040 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.6812 | 0.907246 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.78591 | −0.310939 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.03489 | −0.360245 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2164 | −0.526135 | −0.263067 | − | 0.964777i | \(-0.584734\pi\) | ||||
−0.263067 | + | 0.964777i | \(0.584734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.2677 | 1.48126 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.65288 | −0.224328 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.73966 | 0.0688198 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.73131 | 0.384364 | 0.192182 | − | 0.981359i | \(-0.438444\pi\) | ||||
0.192182 | + | 0.981359i | \(0.438444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.29861 | 0.248393 | 0.124196 | − | 0.992258i | \(-0.460365\pi\) | ||||
0.124196 | + | 0.992258i | \(0.460365\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.85146 | 0.151651 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.6285 | 0.653735 | 0.326868 | − | 0.945070i | \(-0.394007\pi\) | ||||
0.326868 | + | 0.945070i | \(0.394007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.11865 | 0.357938 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.1488 | −0.476148 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.7298 | −0.576422 | −0.288211 | − | 0.957567i | \(-0.593060\pi\) | ||||
−0.288211 | + | 0.957567i | \(0.593060\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.66116 | −0.221200 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.45657 | 0.290909 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.9289 | −1.78914 | −0.894568 | − | 0.446932i | \(-0.852517\pi\) | ||||
−0.894568 | + | 0.446932i | \(0.852517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.2853 | 1.21686 | 0.608428 | − | 0.793609i | \(-0.291800\pi\) | ||||
0.608428 | + | 0.793609i | \(0.291800\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.08457 | −0.158632 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.07137 | 0.0803244 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.4767 | −0.405660 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.2404 | 1.09184 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.32901 | 0.360142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.9598 | −0.692300 | −0.346150 | − | 0.938179i | \(-0.612511\pi\) | ||||
−0.346150 | + | 0.938179i | \(0.612511\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −27.2940 | −1.05055 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.1779 | 0.468035 | 0.234018 | − | 0.972232i | \(-0.424813\pi\) | ||||
0.234018 | + | 0.972232i | \(0.424813\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.44684 | 0.362536 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.99948 | 0.344861 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.0774 | −1.07435 | −0.537176 | − | 0.843470i | \(-0.680509\pi\) | ||||
−0.537176 | + | 0.843470i | \(0.680509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.98127 | −0.0757005 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.1512 | −0.959579 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.08665 | 0.155689 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.8220 | 0.792106 | 0.396053 | − | 0.918228i | \(-0.370380\pi\) | ||||
0.396053 | + | 0.918228i | \(0.370380\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.792869 | 0.0301186 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.41618 | −0.0916510 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.9184 | −0.981729 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.26115 | 0.0855247 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.6008 | 0.929161 | 0.464581 | − | 0.885531i | \(-0.346205\pi\) | ||||
0.464581 | + | 0.885531i | \(0.346205\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.2221 | 0.649543 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.18368 | −0.0445800 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.33953 | −0.163205 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.4168 | −0.766768 | −0.383384 | − | 0.923589i | \(-0.625241\pi\) | ||||
−0.383384 | + | 0.923589i | \(0.625241\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.71310 | −0.176755 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.4845 | 0.617350 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.395242 | 0.0147812 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.3173 | 0.945493 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.5217 | 1.43662 | 0.718308 | − | 0.695725i | \(-0.244917\pi\) | ||||
0.718308 | + | 0.695725i | \(0.244917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.30468 | 0.272040 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.53166 | −0.354486 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25.1740 | −0.934937 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0033 | 0.593528 | 0.296764 | − | 0.954951i | \(-0.404092\pi\) | ||||
0.296764 | + | 0.954951i | \(0.404092\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8655 | 1.10613 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0335 | −0.666995 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.77633 | 0.287225 | 0.143613 | − | 0.989634i | \(-0.454128\pi\) | ||||
0.143613 | + | 0.989634i | \(0.454128\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.587188 | 0.0216587 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.16464 | −0.300749 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.41142 | 0.272634 | 0.136317 | − | 0.990665i | \(-0.456473\pi\) | ||||
0.136317 | + | 0.990665i | \(0.456473\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.78591 | 0.286022 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.10045 | 0.113745 | 0.0568723 | − | 0.998381i | \(-0.481887\pi\) | ||||
0.0568723 | + | 0.998381i | \(0.481887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.41359 | 0.0517900 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.2897 | 0.376479 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.5263 | 0.457701 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.8867 | −1.16356 | −0.581780 | − | 0.813346i | \(-0.697644\pi\) | ||||
−0.581780 | + | 0.813346i | \(0.697644\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 35.4431 | 1.29162 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.382120 | −0.0139068 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.97622 | −0.253555 | −0.126777 | − | 0.991931i | \(-0.540463\pi\) | ||||
−0.126777 | + | 0.991931i | \(0.540463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.99483 | 0.108705 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.6791 | −1.40212 | −0.701058 | − | 0.713104i | \(-0.747289\pi\) | ||||
−0.701058 | + | 0.713104i | \(0.747289\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.8768 | −0.647184 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.861583 | −0.0311506 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.11865 | −0.329255 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.1344 | 0.401517 | 0.200759 | − | 0.979641i | \(-0.435659\pi\) | ||||
0.200759 | + | 0.979641i | \(0.435659\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.7079 | −0.817806 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.1746 | −0.689663 | −0.344832 | − | 0.938665i | \(-0.612064\pi\) | ||||
−0.344832 | + | 0.938665i | \(0.612064\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.6098 | 1.42283 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.88208 | 0.175144 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 49.4050 | 1.77012 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.19413 | −0.0785122 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29.2852 | 1.04657 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.35527 | 0.119755 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.33198 | 0.0474799 | 0.0237399 | − | 0.999718i | \(-0.492443\pi\) | ||||
0.0237399 | + | 0.999718i | \(0.492443\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 37.9950 | 1.35266 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.36174 | 0.119530 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.32901 | −0.331283 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.39963 | −0.0851061 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.3605 | −1.53591 | −0.767954 | − | 0.640505i | \(-0.778725\pi\) | ||||
−0.767954 | + | 0.640505i | \(0.778725\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.54231 | 0.196073 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.13811 | −0.0755464 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.40454 | −0.331879 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.796748 | −0.0280817 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.7555 | 0.625024 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.0051 | 0.879134 | 0.439567 | − | 0.898210i | \(-0.355132\pi\) | ||||
0.439567 | + | 0.898210i | \(0.355132\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.9268 | 0.875297 | 0.437648 | − | 0.899146i | \(-0.355811\pi\) | ||||
0.437648 | + | 0.899146i | \(0.355811\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.8372 | 1.04644 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.65790 | 0.198188 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.3751 | 1.20263 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.792869 | −0.0277051 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.5314 | 1.37966 | 0.689828 | − | 0.723973i | \(-0.257686\pi\) | ||||
0.689828 | + | 0.723973i | \(0.257686\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.5703 | −1.86734 | −0.933671 | − | 0.358132i | \(-0.883414\pi\) | ||||
−0.933671 | + | 0.358132i | \(0.883414\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.19613 | 0.250537 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.6925 | −1.76275 | −0.881376 | − | 0.472416i | \(-0.843382\pi\) | ||||
−0.881376 | + | 0.472416i | \(0.843382\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.3434 | 1.43592 | 0.717958 | − | 0.696087i | \(-0.245077\pi\) | ||||
0.717958 | + | 0.696087i | \(0.245077\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.6365 | 0.611805 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.74936 | −0.0952598 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.30520 | −0.148987 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −46.0787 | −1.59271 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.4910 | −1.29433 | −0.647167 | − | 0.762349i | \(-0.724046\pi\) | ||||
−0.647167 | + | 0.762349i | \(0.724046\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.98946 | −0.0686019 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.1746 | 0.660407 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.395242 | −0.0135967 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.20817 | −0.281704 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.62443 | −0.227083 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.9086 | −0.921334 | −0.460667 | − | 0.887573i | \(-0.652390\pi\) | ||||
−0.460667 | + | 0.887573i | \(0.652390\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.64233 | 0.0561664 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.55222 | 0.0871822 | 0.0435911 | − | 0.999049i | \(-0.486120\pi\) | ||||
0.0435911 | + | 0.999049i | \(0.486120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.76793 | −0.196799 | −0.0983996 | − | 0.995147i | \(-0.531372\pi\) | ||||
−0.0983996 | + | 0.995147i | \(0.531372\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.0052 | 0.477296 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.8214 | −1.28745 | −0.643727 | − | 0.765255i | \(-0.722613\pi\) | ||||
−0.643727 | + | 0.765255i | \(0.722613\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.22597 | −0.279691 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.0259 | 0.476346 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.94436 | 0.201649 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.16464 | 0.276648 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.49011 | 0.253502 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.89068 | −0.131529 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.319206 | 0.0107788 | 0.00538941 | − | 0.999985i | \(-0.498284\pi\) | ||||
0.00538941 | + | 0.999985i | \(0.498284\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.56552 | −0.255179 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.06981 | −0.170806 | −0.0854030 | − | 0.996346i | \(-0.527218\pi\) | ||||
−0.0854030 | + | 0.996346i | \(0.527218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.7182 | −1.50489 | −0.752443 | − | 0.658657i | \(-0.771125\pi\) | ||||
−0.752443 | + | 0.658657i | \(0.771125\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.35436 | 0.179985 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 56.8266 | 1.90805 | 0.954026 | − | 0.299725i | \(-0.0968948\pi\) | ||||
0.954026 | + | 0.299725i | \(0.0968948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.3023 | −0.479685 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.99275 | −0.200765 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.5646 | −0.353531 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.20875 | 0.307815 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.99483 | −0.0999944 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −42.4996 | −1.41744 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.2357 | 0.374315 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.74457 | 0.324279 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.49203 | 0.0495966 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.26190 | −0.141514 | −0.0707570 | − | 0.997494i | \(-0.522541\pi\) | ||||
−0.0707570 | + | 0.997494i | \(0.522541\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.44068 | −0.114120 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.90900 | 0.195774 | 0.0978870 | − | 0.995198i | \(-0.468792\pi\) | ||||
0.0978870 | + | 0.995198i | \(0.468792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.9777 | −0.429501 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.47788 | 0.181093 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.3233 | −0.472996 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.4635 | 1.43373 | 0.716864 | − | 0.697213i | \(-0.245577\pi\) | ||||
0.716864 | + | 0.697213i | \(0.245577\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −44.4306 | −1.46404 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.19413 | 0.0722207 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.9175 | −0.523365 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.79165 | 0.190223 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.9863 | −0.819773 | −0.409886 | − | 0.912137i | \(-0.634432\pi\) | ||||
−0.409886 | + | 0.912137i | \(0.634432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.24077 | 0.171759 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.1104 | −0.691124 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.08666 | 0.0355377 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.23303 | −0.138287 | −0.0691436 | − | 0.997607i | \(-0.522027\pi\) | ||||
−0.0691436 | + | 0.997607i | \(0.522027\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.2916 | 1.24960 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.83900 | −0.157747 | −0.0788735 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788735 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.0035 | −0.618839 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.22713 | 0.0724484 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.6261 | 1.12520 | 0.562599 | − | 0.826730i | \(-0.309801\pi\) | ||||
0.562599 | + | 0.826730i | \(0.309801\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.40454 | 0.305284 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.2155 | 0.914951 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.2749 | 0.591982 | 0.295991 | − | 0.955191i | \(-0.404350\pi\) | ||||
0.295991 | + | 0.955191i | \(0.404350\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.32646 | −0.107642 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.72113 | −0.249589 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.01281 | −0.161872 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.8707 | 1.15712 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.93171 | 0.320045 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.41136 | −0.238580 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5705 | −0.436398 | −0.218199 | − | 0.975904i | \(-0.570018\pi\) | ||||
−0.218199 | + | 0.975904i | \(0.570018\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.4063 | 0.687669 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.5052 | 0.946867 | 0.473434 | − | 0.880830i | \(-0.343014\pi\) | ||||
0.473434 | + | 0.880830i | \(0.343014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.11317 | −0.195979 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.19613 | −0.230460 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.1419 | −1.15628 | −0.578142 | − | 0.815936i | \(-0.696222\pi\) | ||||
−0.578142 | + | 0.815936i | \(0.696222\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.69667 | 0.0861860 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.1740 | −0.452540 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.1017 | −0.417879 | −0.208939 | − | 0.977929i | \(-0.567001\pi\) | ||||
−0.208939 | + | 0.977929i | \(0.567001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.93654 | 0.0617033 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.99483 | −0.0953265 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.2223 | −0.420444 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0067 | −0.413171 | −0.206585 | − | 0.978429i | \(-0.566235\pi\) | ||||
−0.206585 | + | 0.978429i | \(0.566235\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.4113 | 1.09201 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.24986 | 0.261538 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.2841 | −1.30748 | −0.653740 | − | 0.756719i | \(-0.726801\pi\) | ||||
−0.653740 | + | 0.756719i | \(0.726801\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.5171 | 0.585855 |
(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 | 8008.2.a.v.1.4 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.v.1.4 | ✓ | 11 | 1.1 | even | 1 | trivial |