Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9122617778\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 31 x^{10} + 80 x^{9} + 347 x^{8} - 697 x^{7} - 1714 x^{6} + 2146 x^{5} + 3304 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-2.48147\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.48147 | 1.10975 | 0.554874 | − | 0.831934i | \(-0.312766\pi\) | ||||
0.554874 | + | 0.831934i | \(0.312766\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0448560 | −0.0169540 | −0.00847699 | − | 0.999964i | \(-0.502698\pi\) | ||||
−0.00847699 | + | 0.999964i | \(0.502698\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.683409 | −0.206056 | −0.103028 | − | 0.994678i | \(-0.532853\pi\) | ||||
−0.103028 | + | 0.994678i | \(0.532853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.72642 | −1.86557 | −0.932787 | − | 0.360429i | \(-0.882630\pi\) | ||||
−0.932787 | + | 0.360429i | \(0.882630\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.48147 | −0.640713 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.19277 | −0.289289 | −0.144645 | − | 0.989484i | \(-0.546204\pi\) | ||||
−0.144645 | + | 0.989484i | \(0.546204\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.53130 | 0.351305 | 0.175653 | − | 0.984452i | \(-0.443796\pi\) | ||||
0.175653 | + | 0.984452i | \(0.443796\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0448560 | 0.00978839 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.15770 | 0.231541 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.40385 | 0.252139 | 0.126069 | − | 0.992021i | \(-0.459764\pi\) | ||||
0.126069 | + | 0.992021i | \(0.459764\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.683409 | 0.118966 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.111309 | −0.0188147 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.68984 | 1.42860 | 0.714301 | − | 0.699839i | \(-0.246745\pi\) | ||||
0.714301 | + | 0.699839i | \(0.246745\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.72642 | 1.07709 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.5300 | 1.80069 | 0.900345 | − | 0.435178i | \(-0.143314\pi\) | ||||
0.900345 | + | 0.435178i | \(0.143314\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.28573 | −0.958565 | −0.479283 | − | 0.877661i | \(-0.659103\pi\) | ||||
−0.479283 | + | 0.877661i | \(0.659103\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.48147 | 0.369916 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.00128 | 0.729512 | 0.364756 | − | 0.931103i | \(-0.381152\pi\) | ||||
0.364756 | + | 0.931103i | \(0.381152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99799 | −0.999713 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.19277 | 0.167021 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.85106 | −0.254263 | −0.127131 | − | 0.991886i | \(-0.540577\pi\) | ||||
−0.127131 | + | 0.991886i | \(0.540577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.69586 | −0.228670 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.53130 | −0.202826 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.14821 | −0.279673 | −0.139837 | − | 0.990175i | \(-0.544658\pi\) | ||||
−0.139837 | + | 0.990175i | \(0.544658\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.75349 | −0.352548 | −0.176274 | − | 0.984341i | \(-0.556404\pi\) | ||||
−0.176274 | + | 0.984341i | \(0.556404\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0448560 | −0.00565133 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.6914 | −2.07032 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0568657 | −0.00694725 | −0.00347362 | − | 0.999994i | \(-0.501106\pi\) | ||||
−0.00347362 | + | 0.999994i | \(0.501106\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.36240 | −0.161687 | −0.0808436 | − | 0.996727i | \(-0.525761\pi\) | ||||
−0.0808436 | + | 0.996727i | \(0.525761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.19218 | −0.139534 | −0.0697672 | − | 0.997563i | \(-0.522226\pi\) | ||||
−0.0697672 | + | 0.997563i | \(0.522226\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.15770 | −0.133680 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0306550 | 0.00349346 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0825347 | 0.00928587 | 0.00464294 | − | 0.999989i | \(-0.498522\pi\) | ||||
0.00464294 | + | 0.999989i | \(0.498522\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.83176 | 0.859647 | 0.429824 | − | 0.902913i | \(-0.358576\pi\) | ||||
0.429824 | + | 0.902913i | \(0.358576\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.95982 | −0.321038 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.473510 | −0.0501920 | −0.0250960 | − | 0.999685i | \(-0.507989\pi\) | ||||
−0.0250960 | + | 0.999685i | \(0.507989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.301720 | 0.0316289 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.40385 | −0.145572 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.79989 | 0.389860 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.20158 | −0.528141 | −0.264070 | − | 0.964503i | \(-0.585065\pi\) | ||||
−0.264070 | + | 0.964503i | \(0.585065\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.683409 | −0.0686852 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4401 | −1.33734 | −0.668669 | − | 0.743560i | \(-0.733136\pi\) | ||||
−0.668669 | + | 0.743560i | \(0.733136\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.12497 | 0.307912 | 0.153956 | − | 0.988078i | \(-0.450799\pi\) | ||||
0.153956 | + | 0.988078i | \(0.450799\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.111309 | 0.0108626 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.76781 | 0.267574 | 0.133787 | − | 0.991010i | \(-0.457286\pi\) | ||||
0.133787 | + | 0.991010i | \(0.457286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.7736 | −1.98975 | −0.994877 | − | 0.101095i | \(-0.967766\pi\) | ||||
−0.994877 | + | 0.101095i | \(0.967766\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.68984 | −0.824803 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.18272 | −0.769765 | −0.384883 | − | 0.922965i | \(-0.625758\pi\) | ||||
−0.384883 | + | 0.922965i | \(0.625758\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.48147 | 0.231398 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.72642 | −0.621858 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0535029 | 0.00490460 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5330 | −0.957541 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.5300 | −1.03963 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.53455 | −0.852796 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.44035 | −0.660225 | −0.330112 | − | 0.943942i | \(-0.607087\pi\) | ||||
−0.330112 | + | 0.943942i | \(0.607087\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.28573 | 0.553428 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.7398 | −1.54993 | −0.774965 | − | 0.632004i | \(-0.782233\pi\) | ||||
−0.774965 | + | 0.632004i | \(0.782233\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0686882 | −0.00595603 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.48147 | −0.213571 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.55498 | 0.132851 | 0.0664255 | − | 0.997791i | \(-0.478841\pi\) | ||||
0.0664255 | + | 0.997791i | \(0.478841\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.65605 | 0.394921 | 0.197461 | − | 0.980311i | \(-0.436731\pi\) | ||||
0.197461 | + | 0.980311i | \(0.436731\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.00128 | −0.421184 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.59690 | 0.384412 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.48147 | −0.206075 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.99799 | 0.577184 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.44818 | 0.692102 | 0.346051 | − | 0.938216i | \(-0.387522\pi\) | ||||
0.346051 | + | 0.938216i | \(0.387522\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.0547 | −1.55065 | −0.775325 | − | 0.631562i | \(-0.782414\pi\) | ||||
−0.775325 | + | 0.631562i | \(0.782414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.19277 | −0.0964297 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.48361 | 0.279810 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.91226 | −0.232423 | −0.116212 | − | 0.993224i | \(-0.537075\pi\) | ||||
−0.116212 | + | 0.993224i | \(0.537075\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.85106 | 0.146799 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0448560 | −0.00353515 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.1417 | −1.02934 | −0.514670 | − | 0.857389i | \(-0.672085\pi\) | ||||
−0.514670 | + | 0.857389i | \(0.672085\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.69586 | 0.132023 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0649 | −1.24314 | −0.621570 | − | 0.783359i | \(-0.713505\pi\) | ||||
−0.621570 | + | 0.783359i | \(0.713505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.2447 | 2.48036 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.53130 | 0.117102 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.3946 | −0.790286 | −0.395143 | − | 0.918620i | \(-0.629305\pi\) | ||||
−0.395143 | + | 0.918620i | \(0.629305\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0519300 | −0.00392554 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.14821 | 0.161469 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.127749 | 0.00954841 | 0.00477421 | − | 0.999989i | \(-0.498480\pi\) | ||||
0.00477421 | + | 0.999989i | \(0.498480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.28371 | −0.541394 | −0.270697 | − | 0.962665i | \(-0.587254\pi\) | ||||
−0.270697 | + | 0.962665i | \(0.587254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.75349 | 0.203544 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.5636 | 1.58539 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.815150 | 0.0596097 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.0448560 | 0.00326280 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.58690 | 0.114824 | 0.0574119 | − | 0.998351i | \(-0.481715\pi\) | ||||
0.0574119 | + | 0.998351i | \(0.481715\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.87850 | 0.567107 | 0.283553 | − | 0.958956i | \(-0.408487\pi\) | ||||
0.283553 | + | 0.958956i | \(0.408487\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.6914 | 1.19530 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.56121 | 0.681208 | 0.340604 | − | 0.940207i | \(-0.389368\pi\) | ||||
0.340604 | + | 0.940207i | \(0.389368\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9842 | −0.778647 | −0.389323 | − | 0.921101i | \(-0.627291\pi\) | ||||
−0.389323 | + | 0.921101i | \(0.627291\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.0568657 | 0.00401100 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0448560 | 0.00314828 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.6115 | 1.99831 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.04651 | −0.0723885 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.04284 | −0.553692 | −0.276846 | − | 0.960914i | \(-0.589289\pi\) | ||||
−0.276846 | + | 0.960914i | \(0.589289\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.36240 | 0.0933501 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.5979 | −1.06377 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0629711 | −0.00427476 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.19218 | 0.0805602 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.02307 | 0.539690 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.7333 | 1.79019 | 0.895097 | − | 0.445871i | \(-0.147106\pi\) | ||||
0.895097 | + | 0.445871i | \(0.147106\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.15770 | 0.0771802 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.0072 | 1.59342 | 0.796708 | − | 0.604365i | \(-0.206573\pi\) | ||||
0.796708 | + | 0.604365i | \(0.206573\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.2022 | −1.40108 | −0.700539 | − | 0.713614i | \(-0.747057\pi\) | ||||
−0.700539 | + | 0.713614i | \(0.747057\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0306550 | −0.00201695 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.50352 | −0.360548 | −0.180274 | − | 0.983616i | \(-0.557698\pi\) | ||||
−0.180274 | + | 0.983616i | \(0.557698\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.4105 | 0.809575 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.0825347 | −0.00536120 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.0700 | 1.68633 | 0.843163 | − | 0.537658i | \(-0.180691\pi\) | ||||
0.843163 | + | 0.537658i | \(0.180691\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.5744 | −1.51856 | −0.759279 | − | 0.650765i | \(-0.774448\pi\) | ||||
−0.759279 | + | 0.650765i | \(0.774448\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.3653 | −1.10943 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.3002 | −0.655386 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.83176 | −0.496318 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.8586 | −0.937869 | −0.468934 | − | 0.883233i | \(-0.655362\pi\) | ||||
−0.468934 | + | 0.883233i | \(0.655362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.683409 | −0.0429656 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.95982 | 0.185351 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.87765 | −0.429016 | −0.214508 | − | 0.976722i | \(-0.568815\pi\) | ||||
−0.214508 | + | 0.976722i | \(0.568815\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.389792 | −0.0242205 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.3741 | 1.31798 | 0.658992 | − | 0.752150i | \(-0.270983\pi\) | ||||
0.658992 | + | 0.752150i | \(0.270983\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.59335 | −0.282167 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.473510 | 0.0289784 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.5934 | −0.767836 | −0.383918 | − | 0.923367i | \(-0.625425\pi\) | ||||
−0.383918 | + | 0.923367i | \(0.625425\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.59472 | 0.279109 | 0.139555 | − | 0.990214i | \(-0.455433\pi\) | ||||
0.139555 | + | 0.990214i | \(0.455433\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.301720 | −0.0182610 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.791185 | −0.0477103 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.28953 | −0.137565 | −0.0687823 | − | 0.997632i | \(-0.521911\pi\) | ||||
−0.0687823 | + | 0.997632i | \(0.521911\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.40385 | 0.0840462 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.3041 | −1.21124 | −0.605620 | − | 0.795754i | \(-0.707075\pi\) | ||||
−0.605620 | + | 0.795754i | \(0.707075\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.01310 | −0.119666 | −0.0598332 | − | 0.998208i | \(-0.519057\pi\) | ||||
−0.0598332 | + | 0.998208i | \(0.519057\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.79989 | −0.225086 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.517192 | −0.0305289 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5773 | −0.916312 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.20158 | 0.304922 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.6955 | 0.858518 | 0.429259 | − | 0.903181i | \(-0.358775\pi\) | ||||
0.429259 | + | 0.903181i | \(0.358775\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.33072 | −0.310367 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.683409 | 0.0396554 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.72642 | −0.388999 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.281953 | 0.0162515 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.4401 | 0.772112 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.83271 | −0.391240 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.8416 | −1.41779 | −0.708893 | − | 0.705316i | \(-0.750805\pi\) | ||||
−0.708893 | + | 0.705316i | \(0.750805\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.12497 | −0.177773 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.957541 | −0.0542972 | −0.0271486 | − | 0.999631i | \(-0.508643\pi\) | ||||
−0.0271486 | + | 0.999631i | \(0.508643\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.6885 | 0.999813 | 0.499907 | − | 0.866079i | \(-0.333368\pi\) | ||||
0.499907 | + | 0.866079i | \(0.333368\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.111309 | −0.00627155 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.3391 | −1.70401 | −0.852006 | − | 0.523533i | \(-0.824614\pi\) | ||||
−0.852006 | + | 0.523533i | \(0.824614\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.683409 | 0.0382636 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.76781 | −0.154484 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.82649 | −0.101629 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.78720 | −0.431956 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.7736 | 1.14878 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.224338 | −0.0123681 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.8890 | 0.818371 | 0.409186 | − | 0.912451i | \(-0.365813\pi\) | ||||
0.409186 | + | 0.912451i | \(0.365813\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.68984 | 0.476200 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.141111 | −0.00770970 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.4693 | 1.00608 | 0.503042 | − | 0.864262i | \(-0.332214\pi\) | ||||
0.503042 | + | 0.864262i | \(0.332214\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.18272 | 0.444424 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.959404 | −0.0519546 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.627894 | 0.0339031 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.48147 | −0.133598 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 36.2946 | 1.94840 | 0.974198 | − | 0.225697i | \(-0.0724658\pi\) | ||||
0.974198 | + | 0.225697i | \(0.0724658\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.14729 | 0.275528 | 0.137764 | − | 0.990465i | \(-0.456008\pi\) | ||||
0.137764 | + | 0.990465i | \(0.456008\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.72642 | 0.359030 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.6393 | −1.25819 | −0.629096 | − | 0.777327i | \(-0.716575\pi\) | ||||
−0.629096 | + | 0.777327i | \(0.716575\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.38076 | −0.179432 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0535029 | −0.00283167 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.7411 | 1.30578 | 0.652891 | − | 0.757451i | \(-0.273556\pi\) | ||||
0.652891 | + | 0.757451i | \(0.273556\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6551 | −0.876585 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.5330 | 0.552837 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.95837 | −0.154848 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.6328 | −0.659426 | −0.329713 | − | 0.944081i | \(-0.606952\pi\) | ||||
−0.329713 | + | 0.944081i | \(0.606952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.5300 | 0.600230 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0830312 | 0.00431076 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.6850 | −0.605024 | −0.302512 | − | 0.953146i | \(-0.597825\pi\) | ||||
−0.302512 | + | 0.953146i | \(0.597825\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.53455 | 0.492362 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.72642 | 0.346428 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8719 | 0.969384 | 0.484692 | − | 0.874685i | \(-0.338932\pi\) | ||||
0.484692 | + | 0.874685i | \(0.338932\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.44035 | 0.381181 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.17604 | 0.366678 | 0.183339 | − | 0.983050i | \(-0.441309\pi\) | ||||
0.183339 | + | 0.983050i | \(0.441309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0760696 | 0.00387687 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.28573 | −0.319522 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.5320 | −1.19312 | −0.596560 | − | 0.802568i | \(-0.703466\pi\) | ||||
−0.596560 | + | 0.802568i | \(0.703466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.19277 | −0.0603210 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.7398 | 0.894853 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.204807 | 0.0103050 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.90830 | −0.296529 | −0.148264 | − | 0.988948i | \(-0.547369\pi\) | ||||
−0.148264 | + | 0.988948i | \(0.547369\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0686882 | 0.00343871 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.3654 | −1.66619 | −0.833095 | − | 0.553130i | \(-0.813433\pi\) | ||||
−0.833095 | + | 0.553130i | \(0.813433\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.44288 | −0.470383 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.48147 | 0.123305 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.93872 | −0.294371 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.6673 | 0.824143 | 0.412071 | − | 0.911152i | \(-0.364805\pi\) | ||||
0.412071 | + | 0.911152i | \(0.364805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.55498 | −0.0767016 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.0963602 | 0.00474157 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.4343 | 0.953992 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.65605 | −0.228008 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.9304 | −1.51105 | −0.755523 | − | 0.655122i | \(-0.772617\pi\) | ||||
−0.755523 | + | 0.655122i | \(0.772617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.5383 | 1.39087 | 0.695435 | − | 0.718589i | \(-0.255212\pi\) | ||||
0.695435 | + | 0.718589i | \(0.255212\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.00128 | 0.243171 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.38087 | −0.0669822 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.123511 | 0.00597710 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.59690 | −0.221940 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.6926 | −1.47841 | −0.739206 | − | 0.673480i | \(-0.764799\pi\) | ||||
−0.739206 | + | 0.673480i | \(0.764799\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.3757 | −0.883078 | −0.441539 | − | 0.897242i | \(-0.645567\pi\) | ||||
−0.441539 | + | 0.897242i | \(0.645567\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.48147 | 0.118977 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.53130 | 0.0732522 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.5696 | 1.88855 | 0.944277 | − | 0.329151i | \(-0.106762\pi\) | ||||
0.944277 | + | 0.329151i | \(0.106762\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.99799 | −0.333238 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.7869 | −1.46273 | −0.731365 | − | 0.681986i | \(-0.761116\pi\) | ||||
−0.731365 | + | 0.681986i | \(0.761116\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.17500 | −0.0557005 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.44818 | −0.399585 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.8707 | −0.748986 | −0.374493 | − | 0.927230i | \(-0.622183\pi\) | ||||
−0.374493 | + | 0.927230i | \(0.622183\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.87973 | −0.371042 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.0547 | 0.895269 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.748711 | 0.0351001 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.4522 | 0.535710 | 0.267855 | − | 0.963459i | \(-0.413685\pi\) | ||||
0.267855 | + | 0.963459i | \(0.413685\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.19277 | 0.0556737 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.768140 | −0.0357759 | −0.0178879 | − | 0.999840i | \(-0.505694\pi\) | ||||
−0.0178879 | + | 0.999840i | \(0.505694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.41811 | 0.205327 | 0.102663 | − | 0.994716i | \(-0.467264\pi\) | ||||
0.102663 | + | 0.994716i | \(0.467264\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.48361 | −0.161549 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.1128 | −0.653060 | −0.326530 | − | 0.945187i | \(-0.605879\pi\) | ||||
−0.326530 | + | 0.945187i | \(0.605879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.00255077 | 0.000117784 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.91226 | 0.134190 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.29573 | 0.197518 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.77280 | 0.0813415 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.85106 | −0.0847542 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.8727 | −0.542480 | −0.271240 | − | 0.962512i | \(-0.587434\pi\) | ||||
−0.271240 | + | 0.962512i | \(0.587434\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −58.4515 | −2.66516 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0448560 | 0.00204102 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.9076 | −0.586103 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7138 | 0.802687 | 0.401343 | − | 0.915928i | \(-0.368543\pi\) | ||||
0.401343 | + | 0.915928i | \(0.368543\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.1417 | 0.594289 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.0560 | 1.76257 | 0.881287 | − | 0.472581i | \(-0.156678\pi\) | ||||
0.881287 | + | 0.472581i | \(0.156678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.19277 | 0.0537196 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.69586 | −0.0762233 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0611119 | 0.00274124 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.9240 | −1.60818 | −0.804091 | − | 0.594507i | \(-0.797347\pi\) | ||||
−0.804091 | + | 0.594507i | \(0.797347\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.0649 | 0.717727 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.3600 | 1.48745 | 0.743724 | − | 0.668487i | \(-0.233058\pi\) | ||||
0.743724 | + | 0.668487i | \(0.233058\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.3512 | −1.48411 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.2447 | −1.43204 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.7899 | −0.921497 | −0.460748 | − | 0.887531i | \(-0.652419\pi\) | ||||
−0.460748 | + | 0.887531i | \(0.652419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0534766 | 0.00236566 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.53130 | −0.0676087 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.75452 | 0.341705 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.41792 | −0.150320 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.3946 | 0.456272 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.7417 | −1.21539 | −0.607693 | − | 0.794172i | \(-0.707905\pi\) | ||||
−0.607693 | + | 0.794172i | \(0.707905\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.1577 | 1.05634 | 0.528170 | − | 0.849139i | \(-0.322878\pi\) | ||||
0.528170 | + | 0.849139i | \(0.322878\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0519300 | 0.00226641 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.67447 | −0.0729410 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.14821 | −0.0932244 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −77.5559 | −3.35932 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.86823 | 0.296940 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.127749 | −0.00551278 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.78249 | 0.205996 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.5006 | −1.18234 | −0.591171 | − | 0.806546i | \(-0.701334\pi\) | ||||
−0.591171 | + | 0.806546i | \(0.701334\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.28371 | 0.312574 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −51.5492 | −2.20813 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.6516 | 1.26781 | 0.633905 | − | 0.773411i | \(-0.281451\pi\) | ||||
0.633905 | + | 0.773411i | \(0.281451\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.75349 | −0.117516 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.53130 | −0.0652358 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.00370218 | −0.000157433 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.5636 | −0.915324 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8913 | 0.630965 | 0.315483 | − | 0.948931i | \(-0.397834\pi\) | ||||
0.315483 | + | 0.948931i | \(0.397834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.2805 | 1.78827 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.815150 | −0.0344157 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.4014 | −1.40770 | −0.703850 | − | 0.710348i | \(-0.748537\pi\) | ||||
−0.703850 | + | 0.710348i | \(0.748537\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.3052 | −0.854246 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.0448560 | −0.00188378 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.3289 | −1.39722 | −0.698611 | − | 0.715502i | \(-0.746198\pi\) | ||||
−0.698611 | + | 0.715502i | \(0.746198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.86311 | −0.119818 | −0.0599088 | − | 0.998204i | \(-0.519081\pi\) | ||||
−0.0599088 | + | 0.998204i | \(0.519081\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.58690 | −0.0662936 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.15770 | 0.0482796 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.6396 | 1.48370 | 0.741848 | − | 0.670568i | \(-0.233949\pi\) | ||||
0.741848 | + | 0.670568i | \(0.233949\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.87850 | −0.327419 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.351302 | −0.0145744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.26503 | 0.0523922 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.6914 | −0.690105 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.66341 | 0.275029 | 0.137514 | − | 0.990500i | \(-0.456089\pi\) | ||||
0.137514 | + | 0.990500i | \(0.456089\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.14972 | 0.0885777 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.56121 | −0.393296 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.6118 | −1.46240 | −0.731201 | − | 0.682162i | \(-0.761040\pi\) | ||||
−0.731201 | + | 0.682162i | \(0.761040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.132766 | 0.00544287 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.9842 | 0.449552 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.38122 | −0.383306 | −0.191653 | − | 0.981463i | \(-0.561385\pi\) | ||||
−0.191653 | + | 0.981463i | \(0.561385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.4516 | 1.36452 | 0.682259 | − | 0.731111i | \(-0.260998\pi\) | ||||
0.682259 | + | 0.731111i | \(0.260998\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0568657 | −0.00231575 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.1372 | −1.06263 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.7731 | −0.640208 | −0.320104 | − | 0.947382i | \(-0.603718\pi\) | ||||
−0.320104 | + | 0.947382i | \(0.603718\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0448560 | −0.00181766 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.6407 | −1.36096 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.26903 | −0.172424 | −0.0862122 | − | 0.996277i | \(-0.527476\pi\) | ||||
−0.0862122 | + | 0.996277i | \(0.527476\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −28.6115 | −1.15373 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.0080 | 0.966527 | 0.483263 | − | 0.875475i | \(-0.339451\pi\) | ||||
0.483263 | + | 0.875475i | \(0.339451\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.9394 | −1.24356 | −0.621780 | − | 0.783192i | \(-0.713590\pi\) | ||||
−0.621780 | + | 0.783192i | \(0.713590\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.0212398 | 0.000850954 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.4482 | −1.17793 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.04651 | 0.0417935 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.3650 | −0.413279 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.3669 | −0.930222 | −0.465111 | − | 0.885252i | \(-0.653986\pi\) | ||||
−0.465111 | + | 0.885252i | \(0.653986\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.04284 | 0.319674 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.4630 | −0.732683 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 47.0714 | 1.86504 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.36240 | −0.0538957 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.1059 | −0.675641 | −0.337820 | − | 0.941211i | \(-0.609690\pi\) | ||||
−0.337820 | + | 0.941211i | \(0.609690\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0493 | −0.475179 | −0.237589 | − | 0.971366i | \(-0.576357\pi\) | ||||
−0.237589 | + | 0.971366i | \(0.576357\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.5979 | 0.614166 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.7704 | 0.737940 | 0.368970 | − | 0.929441i | \(-0.379711\pi\) | ||||
0.368970 | + | 0.929441i | \(0.379711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.46811 | 0.0576282 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0629711 | 0.00246803 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.6034 | −0.610607 | −0.305303 | − | 0.952255i | \(-0.598758\pi\) | ||||
−0.305303 | + | 0.952255i | \(0.598758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −44.0207 | −1.72003 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.19218 | −0.0465115 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.8795 | 0.579623 | 0.289812 | − | 0.957084i | \(-0.406407\pi\) | ||||
0.289812 | + | 0.957084i | \(0.406407\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.34822 | −0.169126 | −0.0845630 | − | 0.996418i | \(-0.526949\pi\) | ||||
−0.0845630 | + | 0.996418i | \(0.526949\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.02307 | −0.311590 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.170448 | −0.00660969 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.7333 | −1.03357 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.88176 | 0.0726445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.5468 | 0.830567 | 0.415284 | − | 0.909692i | \(-0.363682\pi\) | ||||
0.415284 | + | 0.909692i | \(0.363682\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.15770 | −0.0445600 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.0704 | 1.23257 | 0.616283 | − | 0.787525i | \(-0.288638\pi\) | ||||
0.616283 | + | 0.787525i | \(0.288638\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.233322 | 0.00895409 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.0072 | −0.919959 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.8385 | 0.720836 | 0.360418 | − | 0.932791i | \(-0.382634\pi\) | ||||
0.360418 | + | 0.932791i | \(0.382634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.85864 | 0.147431 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.2022 | 0.808913 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.4510 | 0.474345 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.6594 | −0.443544 | −0.221772 | − | 0.975099i | \(-0.571184\pi\) | ||||
−0.221772 | + | 0.975099i | \(0.571184\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0306550 | 0.00116449 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.5539 | 0.438263 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.7527 | −0.520920 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.50352 | 0.208162 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.2820 | 1.10597 | 0.552983 | − | 0.833192i | \(-0.313489\pi\) | ||||
0.552983 | + | 0.833192i | \(0.313489\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.3068 | 0.501875 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.4105 | −0.467408 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.602869 | 0.0226732 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.8523 | −1.83469 | −0.917343 | − | 0.398097i | \(-0.869671\pi\) | ||||
−0.917343 | + | 0.398097i | \(0.869671\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0825347 | 0.00309529 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.40385 | 0.0525746 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.4071 | 0.426600 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.0700 | −0.973601 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.3601 | −0.796597 | −0.398299 | − | 0.917256i | \(-0.630399\pi\) | ||||
−0.398299 | + | 0.917256i | \(0.630399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.140174 | −0.00522034 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.5744 | 0.876740 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.15770 | −0.0429960 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.2219 | 0.675814 | 0.337907 | − | 0.941180i | \(-0.390281\pi\) | ||||
0.337907 | + | 0.941180i | \(0.390281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.49743 | 0.277303 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.7818 | −0.435169 | −0.217584 | − | 0.976042i | \(-0.569818\pi\) | ||||
−0.217584 | + | 0.976042i | \(0.569818\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.3653 | 0.640529 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.0388625 | 0.00143152 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.3717 | 0.822958 | 0.411479 | − | 0.911419i | \(-0.365012\pi\) | ||||
0.411479 | + | 0.911419i | \(0.365012\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.3002 | 0.378387 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.4351 | −1.44673 | −0.723367 | − | 0.690464i | \(-0.757407\pi\) | ||||
−0.723367 | + | 0.690464i | \(0.757407\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.9639 | 0.768059 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.83176 | 0.286549 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.124153 | −0.00453644 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.4160 | −1.00042 | −0.500211 | − | 0.865903i | \(-0.666744\pi\) | ||||
−0.500211 | + | 0.865903i | \(0.666744\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.8586 | 0.541479 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −47.2837 | −1.72083 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.2228 | −0.807700 | −0.403850 | − | 0.914825i | \(-0.632328\pi\) | ||||
−0.403850 | + | 0.914825i | \(0.632328\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.683409 | 0.0248062 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.5659 | 1.39801 | 0.699006 | − | 0.715116i | \(-0.253626\pi\) | ||||
0.699006 | + | 0.715116i | \(0.253626\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.931823 | 0.0337343 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.95982 | −0.107013 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.4498 | 0.521751 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.9131 | −0.393535 | −0.196768 | − | 0.980450i | \(-0.563044\pi\) | ||||
−0.196768 | + | 0.980450i | \(0.563044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.87765 | 0.247692 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.0493 | −0.397416 | −0.198708 | − | 0.980059i | \(-0.563675\pi\) | ||||
−0.198708 | + | 0.980059i | \(0.563675\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.62524 | 0.0583804 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.389792 | 0.0139837 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.6560 | 0.632592 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.931077 | 0.0333166 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.22668 | −0.257931 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.2832 | 1.54288 | 0.771440 | − | 0.636301i | \(-0.219537\pi\) | ||||
0.771440 | + | 0.636301i | \(0.219537\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.3741 | −0.760939 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.367044 | 0.0130506 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.5211 | 0.657704 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.59335 | 0.162909 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.8858 | −0.456437 | −0.228218 | − | 0.973610i | \(-0.573290\pi\) | ||||
−0.228218 | + | 0.973610i | \(0.573290\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.96538 | −0.211040 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.473510 | −0.0167307 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.814748 | 0.0287518 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.111309 | −0.00392313 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.5934 | 0.443310 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.36974 | −0.118474 | −0.0592368 | − | 0.998244i | \(-0.518867\pi\) | ||||
−0.0592368 | + | 0.998244i | \(0.518867\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.5650 | −0.441218 | −0.220609 | − | 0.975362i | \(-0.570805\pi\) | ||||
−0.220609 | + | 0.975362i | \(0.570805\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.59472 | −0.161144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.6108 | −1.14231 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.62537 | −0.336749 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.301720 | 0.0105430 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.1970 | 1.26328 | 0.631642 | − | 0.775261i | \(-0.282381\pi\) | ||||
0.631642 | + | 0.775261i | \(0.282381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.1322 | 0.422903 | 0.211452 | − | 0.977388i | \(-0.432181\pi\) | ||||
0.211452 | + | 0.977388i | \(0.432181\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.791185 | 0.0275455 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.718101 | −0.0249708 | −0.0124854 | − | 0.999922i | \(-0.503974\pi\) | ||||
−0.0124854 | + | 0.999922i | \(0.503974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.3297 | 0.428230 | 0.214115 | − | 0.976808i | \(-0.431313\pi\) | ||||
0.214115 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.28953 | 0.0794230 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.34699 | 0.289206 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.8646 | −1.37957 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.40385 | −0.0485241 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.8107 | 1.02918 | 0.514590 | − | 0.857437i | \(-0.327944\pi\) | ||||
0.514590 | + | 0.857437i | \(0.327944\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.3041 | 0.699310 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 80.0144 | 2.75258 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.472466 | 0.0162341 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.01310 | 0.0690894 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.68984 | 0.297884 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.8950 | 0.578474 | 0.289237 | − | 0.957258i | \(-0.406598\pi\) | ||||
0.289237 | + | 0.957258i | \(0.406598\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.79989 | 0.129953 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.3776 | 0.456970 | 0.228485 | − | 0.973547i | \(-0.426623\pi\) | ||||
0.228485 | + | 0.973547i | \(0.426623\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.9155 | 1.02070 | 0.510352 | − | 0.859966i | \(-0.329515\pi\) | ||||
0.510352 | + | 0.859966i | \(0.329515\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.517192 | 0.0176258 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.9042 | −0.813709 | −0.406854 | − | 0.913493i | \(-0.633374\pi\) | ||||
−0.406854 | + | 0.913493i | \(0.633374\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.7939 | −0.877018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.5773 | 0.529033 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.0564050 | −0.00191341 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.382502 | 0.0129606 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.20158 | −0.176047 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.427682 | 0.0144583 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.7542 | 0.768356 | 0.384178 | − | 0.923259i | \(-0.374485\pi\) | ||||
0.384178 | + | 0.923259i | \(0.374485\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.6955 | −0.495666 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.2527 | 1.18769 | 0.593846 | − | 0.804579i | \(-0.297609\pi\) | ||||
0.593846 | + | 0.804579i | \(0.297609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.1303 | 0.677437 | 0.338719 | − | 0.940888i | \(-0.390007\pi\) | ||||
0.338719 | + | 0.940888i | \(0.390007\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.33072 | 0.179190 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.5084 | 0.957219 | 0.478610 | − | 0.878028i | \(-0.341141\pi\) | ||||
0.478610 | + | 0.878028i | \(0.341141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.333745 | 0.0111934 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.683409 | −0.0228951 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.65849 | 0.256282 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.317006 | 0.0105963 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.72642 | 0.224589 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.40385 | −0.0468210 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.20789 | 0.0735554 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.281953 | −0.00938281 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0743 | −0.600811 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.24488 | −0.107744 | −0.0538722 | − | 0.998548i | \(-0.517156\pi\) | ||||
−0.0538722 | + | 0.998548i | \(0.517156\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.4401 | −0.445779 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.9154 | −1.68690 | −0.843451 | − | 0.537207i | \(-0.819479\pi\) | ||||
−0.843451 | + | 0.537207i | \(0.819479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.35230 | −0.177135 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.83271 | 0.225882 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.795735 | 0.0262775 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.6095 | −0.844778 | −0.422389 | − | 0.906415i | \(-0.638808\pi\) | ||||
−0.422389 | + | 0.906415i | \(0.638808\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.8416 | 0.818559 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.16407 | 0.301639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0603 | 0.330779 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.12497 | 0.102637 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.01347 | −0.131678 | −0.0658388 | − | 0.997830i | \(-0.520972\pi\) | ||||
−0.0658388 | + | 0.997830i | \(0.520972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.7161 | −0.351204 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.957541 | 0.0313485 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.02277 | 0.0661517 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.3819 | 1.51523 | 0.757615 | − | 0.652702i | \(-0.226365\pi\) | ||||
0.757615 | + | 0.652702i | \(0.226365\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.6885 | −0.577242 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.1442 | 0.363292 | 0.181646 | − | 0.983364i | \(-0.441858\pi\) | ||||
0.181646 | + | 0.983364i | \(0.441858\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.5300 | 0.375470 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.111309 | 0.00362088 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.6491 | 0.541022 | 0.270511 | − | 0.962717i | \(-0.412807\pi\) | ||||
0.270511 | + | 0.962717i | \(0.412807\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.01912 | 0.260312 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.3391 | 0.983811 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.7628 | −1.54719 | −0.773594 | − | 0.633681i | \(-0.781543\pi\) | ||||
−0.773594 | + | 0.633681i | \(0.781543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.93784 | 0.127426 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.683409 | −0.0220915 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.0697503 | −0.00225235 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0292 | −0.936426 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.76781 | 0.0891913 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.5503 | 0.629345 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.5564 | −1.46499 | −0.732497 | − | 0.680771i | \(-0.761645\pi\) | ||||
−0.732497 | + | 0.680771i | \(0.761645\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.82649 | 0.0586754 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.9958 | −1.34771 | −0.673854 | − | 0.738864i | \(-0.735362\pi\) | ||||
−0.673854 | + | 0.738864i | \(0.735362\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.208852 | −0.00669549 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.78720 | 0.249390 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.1202 | −1.41153 | −0.705765 | − | 0.708446i | \(-0.749397\pi\) | ||||
−0.705765 | + | 0.708446i | \(0.749397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.323601 | 0.0103423 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.7736 | −0.663251 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.0584 | −0.512185 | −0.256092 | − | 0.966652i | \(-0.582435\pi\) | ||||
−0.256092 | + | 0.966652i | \(0.582435\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.7259 | 0.755969 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.224338 | 0.00714075 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.28573 | −0.199875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.4668 | 1.60313 | 0.801565 | − | 0.597907i | \(-0.204001\pi\) | ||||
0.801565 | + | 0.597907i | \(0.204001\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.8890 | −0.472487 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.2569 | −0.864102 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0699 | 0.603950 | 0.301975 | − | 0.953316i | \(-0.402354\pi\) | ||||
0.301975 | + | 0.953316i | \(0.402354\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.68984 | −0.274934 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8004.2.a.g.1.10 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.g.1.10 | ✓ | 12 | 1.1 | even | 1 | trivial |