Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9408,2,Mod(1,9408)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9408, 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("9408.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9408.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: | \(75.1232582216\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.523976\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9408.1 |
$q$-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 | ||||||||
\(5\) | −3.20147 | −1.43174 | −0.715871 | − | 0.698233i | \(-0.753970\pi\) | ||||
−0.715871 | + | 0.698233i | \(0.753970\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.24943 | −1.28125 | −0.640625 | − | 0.767854i | \(-0.721325\pi\) | ||||
−0.640625 | + | 0.767854i | \(0.721325\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.15352 | −0.874629 | −0.437314 | − | 0.899309i | \(-0.644070\pi\) | ||||
−0.437314 | + | 0.899309i | \(0.644070\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.20147 | −0.826617 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.40294 | 1.06787 | 0.533935 | − | 0.845525i | \(-0.320713\pi\) | ||||
0.533935 | + | 0.845525i | \(0.320713\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.15352 | 0.723467 | 0.361734 | − | 0.932282i | \(-0.382185\pi\) | ||||
0.361734 | + | 0.932282i | \(0.382185\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.40294 | 0.918077 | 0.459039 | − | 0.888416i | \(-0.348194\pi\) | ||||
0.459039 | + | 0.888416i | \(0.348194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.24943 | 1.04989 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.20147 | −1.33728 | −0.668640 | − | 0.743586i | \(-0.733123\pi\) | ||||
−0.668640 | + | 0.743586i | \(0.733123\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.04795 | −0.367823 | −0.183912 | − | 0.982943i | \(-0.558876\pi\) | ||||
−0.183912 | + | 0.982943i | \(0.558876\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.24943 | −0.739730 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.65237 | 1.58684 | 0.793420 | − | 0.608675i | \(-0.208299\pi\) | ||||
0.793420 | + | 0.608675i | \(0.208299\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.15352 | −0.504967 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4989 | 1.63964 | 0.819822 | − | 0.572618i | \(-0.194072\pi\) | ||||
0.819822 | + | 0.572618i | \(0.194072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.750575 | −0.114462 | −0.0572308 | − | 0.998361i | \(-0.518227\pi\) | ||||
−0.0572308 | + | 0.998361i | \(0.518227\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.20147 | −0.477247 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.40294 | 0.350506 | 0.175253 | − | 0.984523i | \(-0.443926\pi\) | ||||
0.175253 | + | 0.984523i | \(0.443926\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.40294 | 0.616536 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.29738 | 0.452930 | 0.226465 | − | 0.974019i | \(-0.427283\pi\) | ||||
0.226465 | + | 0.974019i | \(0.427283\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.6044 | 1.83442 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.15352 | 0.417694 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.24943 | 1.07398 | 0.536992 | − | 0.843587i | \(-0.319561\pi\) | ||||
0.536992 | + | 0.843587i | \(0.319561\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.09591 | −1.03657 | −0.518287 | − | 0.855207i | \(-0.673430\pi\) | ||||
−0.518287 | + | 0.855207i | \(0.673430\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.0959 | 1.25224 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.15352 | −0.629603 | −0.314801 | − | 0.949158i | \(-0.601938\pi\) | ||||
−0.314801 | + | 0.949158i | \(0.601938\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.40294 | 0.530052 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.40294 | 0.759890 | 0.379945 | − | 0.925009i | \(-0.375943\pi\) | ||||
0.379945 | + | 0.925009i | \(0.375943\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.2494 | −1.78481 | −0.892405 | − | 0.451235i | \(-0.850984\pi\) | ||||
−0.892405 | + | 0.451235i | \(0.850984\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.24943 | 0.606151 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.4509 | −1.85087 | −0.925435 | − | 0.378906i | \(-0.876300\pi\) | ||||
−0.925435 | + | 0.378906i | \(0.876300\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.5565 | 1.59778 | 0.798890 | − | 0.601477i | \(-0.205421\pi\) | ||||
0.798890 | + | 0.601477i | \(0.205421\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.0959 | −1.52892 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.20147 | −0.772079 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.40294 | −0.254712 | −0.127356 | − | 0.991857i | \(-0.540649\pi\) | ||||
−0.127356 | + | 0.991857i | \(0.540649\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.04795 | −0.212363 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.0959 | −1.03582 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.24943 | −0.431464 | −0.215732 | − | 0.976453i | \(-0.569214\pi\) | ||||
−0.215732 | + | 0.976453i | \(0.569214\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.24943 | −0.427083 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.90409 | 0.388472 | 0.194236 | − | 0.980955i | \(-0.437777\pi\) | ||||
0.194236 | + | 0.980955i | \(0.437777\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.24943 | −0.911373 | −0.455686 | − | 0.890140i | \(-0.650606\pi\) | ||||
−0.455686 | + | 0.890140i | \(0.650606\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.5565 | −1.60057 | −0.800287 | − | 0.599617i | \(-0.795319\pi\) | ||||
−0.800287 | + | 0.599617i | \(0.795319\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.0553 | −1.92095 | −0.960475 | − | 0.278365i | \(-0.910208\pi\) | ||||
−0.960475 | + | 0.278365i | \(0.910208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.65237 | 0.916162 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.0959 | −1.31445 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.15352 | −0.291543 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.05761 | 0.641601 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.4989 | 0.946649 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.798528 | −0.0714225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4509 | 1.10484 | 0.552419 | − | 0.833566i | \(-0.313705\pi\) | ||||
0.552419 | + | 0.833566i | \(0.313705\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.750575 | −0.0660844 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.24943 | 0.371274 | 0.185637 | − | 0.982618i | \(-0.440565\pi\) | ||||
0.185637 | + | 0.982618i | \(0.440565\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.20147 | −0.275539 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.4029 | −0.888784 | −0.444392 | − | 0.895833i | \(-0.646580\pi\) | ||||
−0.444392 | + | 0.895833i | \(0.646580\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6524 | 0.988341 | 0.494171 | − | 0.869365i | \(-0.335472\pi\) | ||||
0.494171 | + | 0.869365i | \(0.335472\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.40294 | 0.202364 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.4006 | 1.12062 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23.0553 | 1.91464 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.4029 | −0.852242 | −0.426121 | − | 0.904666i | \(-0.640120\pi\) | ||||
−0.426121 | + | 0.904666i | \(0.640120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.0074 | −1.62818 | −0.814088 | − | 0.580742i | \(-0.802763\pi\) | ||||
−0.814088 | + | 0.580742i | \(0.802763\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.40294 | 0.355957 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.55646 | 0.526628 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.4989 | 1.15713 | 0.578567 | − | 0.815635i | \(-0.303612\pi\) | ||||
0.578567 | + | 0.815635i | \(0.303612\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.29738 | 0.261499 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7100 | 0.838871 | 0.419435 | − | 0.907785i | \(-0.362228\pi\) | ||||
0.419435 | + | 0.907785i | \(0.362228\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.6044 | 1.05910 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3047 | −1.33908 | −0.669540 | − | 0.742776i | \(-0.733509\pi\) | ||||
−0.669540 | + | 0.742776i | \(0.733509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.05531 | −0.235024 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.15352 | 0.241156 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.90409 | −0.296823 | −0.148411 | − | 0.988926i | \(-0.547416\pi\) | ||||
−0.148411 | + | 0.988926i | \(0.547416\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.24943 | 0.620065 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.8059 | −1.55511 | −0.777553 | − | 0.628818i | \(-0.783539\pi\) | ||||
−0.777553 | + | 0.628818i | \(0.783539\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2494 | −0.984822 | −0.492411 | − | 0.870363i | \(-0.663884\pi\) | ||||
−0.492411 | + | 0.870363i | \(0.663884\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.09591 | −0.598467 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −30.9018 | −2.27195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.7100 | −1.36821 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.19181 | 0.303309 | 0.151654 | − | 0.988434i | \(-0.451540\pi\) | ||||
0.151654 | + | 0.988434i | \(0.451540\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.3047 | −1.31760 | −0.658802 | − | 0.752316i | \(-0.728936\pi\) | ||||
−0.658802 | + | 0.752316i | \(0.728936\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.0959 | 0.722983 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9041 | −0.848132 | −0.424066 | − | 0.905631i | \(-0.639397\pi\) | ||||
−0.424066 | + | 0.905631i | \(0.639397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.805889 | −0.0571280 | −0.0285640 | − | 0.999592i | \(-0.509093\pi\) | ||||
−0.0285640 | + | 0.999592i | \(0.509093\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.15352 | −0.363501 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −33.6118 | −2.34755 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.40294 | 0.306026 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.4006 | −0.926942 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.49885 | −0.585085 | −0.292542 | − | 0.956253i | \(-0.594501\pi\) | ||||
−0.292542 | + | 0.956253i | \(0.594501\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.40294 | 0.438723 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.40294 | 0.163879 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.2494 | −1.03046 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.8848 | −0.933991 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.7985 | 1.12491 | 0.562456 | − | 0.826827i | \(-0.309856\pi\) | ||||
0.562456 | + | 0.826827i | \(0.309856\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.24943 | 0.349962 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.8635 | −1.11927 | −0.559635 | − | 0.828739i | \(-0.689059\pi\) | ||||
−0.559635 | + | 0.828739i | \(0.689059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.5542 | 1.35826 | 0.679129 | − | 0.734019i | \(-0.262358\pi\) | ||||
0.679129 | + | 0.734019i | \(0.262358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.90409 | 0.648839 | 0.324419 | − | 0.945913i | \(-0.394831\pi\) | ||||
0.324419 | + | 0.945913i | \(0.394831\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.69296 | −0.501833 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.4509 | −1.06860 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.40294 | 0.284803 | 0.142401 | − | 0.989809i | \(-0.454518\pi\) | ||||
0.142401 | + | 0.989809i | \(0.454518\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.8635 | −1.34394 | −0.671968 | − | 0.740580i | \(-0.734551\pi\) | ||||
−0.671968 | + | 0.740580i | \(0.734551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.94469 | −0.632765 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.5565 | 0.922478 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.44354 | 0.217354 | 0.108677 | − | 0.994077i | \(-0.465339\pi\) | ||||
0.108677 | + | 0.994077i | \(0.465339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.7100 | −1.17629 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.0959 | −0.882720 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.59706 | 0.349135 | 0.174567 | − | 0.984645i | \(-0.444147\pi\) | ||||
0.174567 | + | 0.984645i | \(0.444147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.20147 | −0.445760 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.59706 | −0.0984787 | −0.0492393 | − | 0.998787i | \(-0.515680\pi\) | ||||
−0.0492393 | + | 0.998787i | \(0.515680\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5565 | −0.648478 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.40294 | −0.147058 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.7003 | 1.07921 | 0.539604 | − | 0.841919i | \(-0.318574\pi\) | ||||
0.539604 | + | 0.841919i | \(0.318574\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.39558 | 0.145521 | 0.0727607 | − | 0.997349i | \(-0.476819\pi\) | ||||
0.0727607 | + | 0.997349i | \(0.476819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.3070 | −1.34517 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.24943 | 0.315407 | 0.157704 | − | 0.987486i | \(-0.449591\pi\) | ||||
0.157704 | + | 0.987486i | \(0.449591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.04795 | −0.122608 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0959 | 1.19882 | 0.599411 | − | 0.800442i | \(-0.295402\pi\) | ||||
0.599411 | + | 0.800442i | \(0.295402\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.2494 | −1.38203 | −0.691017 | − | 0.722838i | \(-0.742837\pi\) | ||||
−0.691017 | + | 0.722838i | \(0.742837\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.0959 | −0.598030 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.38592 | 0.140348 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.24943 | −0.249106 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2015 | 0.654397 | 0.327199 | − | 0.944956i | \(-0.393895\pi\) | ||||
0.327199 | + | 0.944956i | \(0.393895\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.4103 | −1.53767 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.24943 | −0.246577 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.8848 | −0.802977 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.90409 | 0.224284 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.9188 | 1.48411 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.9571 | −1.65267 | −0.826335 | − | 0.563179i | \(-0.809578\pi\) | ||||
−0.826335 | + | 0.563179i | \(0.809578\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.24943 | −0.526181 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.3047 | −1.54831 | −0.774155 | − | 0.632996i | \(-0.781825\pi\) | ||||
−0.774155 | + | 0.632996i | \(0.781825\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.49885 | 0.310813 | 0.155407 | − | 0.987851i | \(-0.450331\pi\) | ||||
0.155407 | + | 0.987851i | \(0.450331\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.60442 | 0.539438 | 0.269719 | − | 0.962939i | \(-0.413069\pi\) | ||||
0.269719 | + | 0.962939i | \(0.413069\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.6021 | 1.71339 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.5565 | −0.924092 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.8848 | 0.772569 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.5542 | −0.918260 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.0553 | −1.10906 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5565 | −0.855061 | −0.427530 | − | 0.904001i | \(-0.640616\pi\) | ||||
−0.427530 | + | 0.904001i | \(0.640616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.65237 | 0.528947 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.4989 | 0.901428 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.9977 | 0.980397 | 0.490199 | − | 0.871611i | \(-0.336924\pi\) | ||||
0.490199 | + | 0.871611i | \(0.336924\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.00000 | 0.434500 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.70262 | 0.471273 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.0959 | −0.758898 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.69296 | −0.305614 | −0.152807 | − | 0.988256i | \(-0.548831\pi\) | ||||
−0.152807 | + | 0.988256i | \(0.548831\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.1918 | −0.973785 | −0.486893 | − | 0.873462i | \(-0.661870\pi\) | ||||
−0.486893 | + | 0.873462i | \(0.661870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.15352 | −0.168322 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.9977 | 1.11759 | 0.558797 | − | 0.829304i | \(-0.311263\pi\) | ||||
0.558797 | + | 0.829304i | \(0.311263\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.4989 | −1.08797 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.6907 | −1.30312 | −0.651562 | − | 0.758596i | \(-0.725886\pi\) | ||||
−0.651562 | + | 0.758596i | \(0.725886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.05531 | −0.476595 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.05761 | 0.370429 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 48.8206 | 2.55539 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.85614 | 0.305688 | 0.152844 | − | 0.988250i | \(-0.451157\pi\) | ||||
0.152844 | + | 0.988250i | \(0.451157\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.4989 | 0.546548 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.635347 | −0.0328970 | −0.0164485 | − | 0.999865i | \(-0.505236\pi\) | ||||
−0.0164485 | + | 0.999865i | \(0.505236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.798528 | −0.0412358 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.7100 | 1.16962 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7506 | −0.552220 | −0.276110 | − | 0.961126i | \(-0.589045\pi\) | ||||
−0.276110 | + | 0.961126i | \(0.589045\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4509 | 0.637879 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.9977 | −0.766347 | −0.383173 | − | 0.923676i | \(-0.625169\pi\) | ||||
−0.383173 | + | 0.923676i | \(0.625169\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.750575 | −0.0381539 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.21113 | −0.314917 | −0.157458 | − | 0.987526i | \(-0.550330\pi\) | ||||
−0.157458 | + | 0.987526i | \(0.550330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.3859 | 0.980388 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.24943 | 0.214355 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 52.6671 | 2.64997 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.24943 | 0.0627068 | 0.0313534 | − | 0.999508i | \(-0.490018\pi\) | ||||
0.0313534 | + | 0.999508i | \(0.490018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.11523 | 0.105629 | 0.0528147 | − | 0.998604i | \(-0.483181\pi\) | ||||
0.0528147 | + | 0.998604i | \(0.483181\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.45826 | 0.321709 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.20147 | −0.159082 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −41.0170 | −2.03314 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.1129 | 0.796733 | 0.398367 | − | 0.917226i | \(-0.369577\pi\) | ||||
0.398367 | + | 0.917226i | \(0.369577\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.4029 | −0.513139 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −46.6021 | −2.28761 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.6524 | 0.570619 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.1106 | −0.982469 | −0.491234 | − | 0.871027i | \(-0.663454\pi\) | ||||
−0.491234 | + | 0.871027i | \(0.663454\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.96171 | −0.241819 | −0.120909 | − | 0.992664i | \(-0.538581\pi\) | ||||
−0.120909 | + | 0.992664i | \(0.538581\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.40294 | 0.116835 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.1129 | 1.12114 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.4006 | 0.646989 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.8059 | −1.00218 | −0.501092 | − | 0.865394i | \(-0.667068\pi\) | ||||
−0.501092 | + | 0.865394i | \(0.667068\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.05531 | 0.387114 | 0.193557 | − | 0.981089i | \(-0.437998\pi\) | ||||
0.193557 | + | 0.981089i | \(0.437998\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.0553 | 1.10542 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.8848 | 0.664199 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.1992 | 0.773144 | 0.386572 | − | 0.922259i | \(-0.373659\pi\) | ||||
0.386572 | + | 0.922259i | \(0.373659\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.4435 | −0.733745 | −0.366872 | − | 0.930271i | \(-0.619571\pi\) | ||||
−0.366872 | + | 0.930271i | \(0.619571\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.69296 | 0.364681 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.4029 | −0.492042 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.5159 | 1.48733 | 0.743663 | − | 0.668555i | \(-0.233087\pi\) | ||||
0.743663 | + | 0.668555i | \(0.233087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.6141 | −2.10079 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.0074 | −0.940028 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.1152 | −0.519948 | −0.259974 | − | 0.965616i | \(-0.583714\pi\) | ||||
−0.259974 | + | 0.965616i | \(0.583714\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.40294 | 0.205512 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.5971 | 0.633278 | 0.316639 | − | 0.948546i | \(-0.397446\pi\) | ||||
0.316639 | + | 0.948546i | \(0.397446\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.55876 | 0.118916 | 0.0594579 | − | 0.998231i | \(-0.481063\pi\) | ||||
0.0594579 | + | 0.998231i | \(0.481063\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.55646 | 0.304049 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.614078 | −0.0284161 | −0.0142081 | − | 0.999899i | \(-0.504523\pi\) | ||||
−0.0142081 | + | 0.999899i | \(0.504523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4989 | 0.668072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.18951 | 0.146654 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.5542 | 0.759557 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.29738 | 0.150977 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.0959 | −0.918205 | −0.459103 | − | 0.888383i | \(-0.651829\pi\) | ||||
−0.459103 | + | 0.888383i | \(0.651829\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.4389 | −1.38790 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.6044 | 0.617745 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.3720 | 1.05909 | 0.529544 | − | 0.848283i | \(-0.322363\pi\) | ||||
0.529544 | + | 0.848283i | \(0.322363\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.7100 | 0.484322 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.7483 | −1.02662 | −0.513308 | − | 0.858205i | \(-0.671580\pi\) | ||||
−0.513308 | + | 0.858205i | \(0.671580\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.7077 | −1.42804 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.6044 | 0.611473 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.53944 | 0.382278 | 0.191139 | − | 0.981563i | \(-0.438782\pi\) | ||||
0.191139 | + | 0.981563i | \(0.438782\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3047 | −0.773119 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.59706 | −0.338736 | −0.169368 | − | 0.985553i | \(-0.554173\pi\) | ||||
−0.169368 | + | 0.985553i | \(0.554173\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.4989 | −0.556192 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.05531 | −0.135691 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.99034 | −0.221193 | −0.110596 | − | 0.993865i | \(-0.535276\pi\) | ||||
−0.110596 | + | 0.993865i | \(0.535276\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.15352 | 0.139231 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.6118 | 1.30485 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2111 | −0.449085 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.90409 | −0.171371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.4989 | 0.547585 | 0.273792 | − | 0.961789i | \(-0.411722\pi\) | ||||
0.273792 | + | 0.961789i | \(0.411722\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.2618 | 1.93544 | 0.967718 | − | 0.252036i | \(-0.0811003\pi\) | ||||
0.967718 | + | 0.252036i | \(0.0811003\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.01702 | −0.392788 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.61408 | −0.157134 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.24943 | 0.357995 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.1083 | −1.43408 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 53.0051 | 2.29161 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.8059 | −0.897840 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.9594 | −1.11608 | −0.558041 | − | 0.829813i | \(-0.688447\pi\) | ||||
−0.558041 | + | 0.829813i | \(0.688447\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.2494 | −0.568587 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 64.2065 | 2.75031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.9018 | −0.979210 | −0.489605 | − | 0.871944i | \(-0.662859\pi\) | ||||
−0.489605 | + | 0.871944i | \(0.662859\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.09591 | −0.345525 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.7100 | −0.967478 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −30.9018 | −1.31171 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.50621 | 0.275677 | 0.137839 | − | 0.990455i | \(-0.455984\pi\) | ||||
0.137839 | + | 0.990455i | \(0.455984\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.36695 | 0.100111 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.7100 | −0.789936 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.2448 | −1.86470 | −0.932349 | − | 0.361561i | \(-0.882244\pi\) | ||||
−0.932349 | + | 0.361561i | \(0.882244\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.6118 | −1.07750 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.0170 | −0.545702 | −0.272851 | − | 0.962056i | \(-0.587967\pi\) | ||||
−0.272851 | + | 0.962056i | \(0.587967\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.1705 | −1.26260 | −0.631299 | − | 0.775540i | \(-0.717478\pi\) | ||||
−0.631299 | + | 0.775540i | \(0.717478\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.19181 | 0.175115 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.1129 | 0.963876 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.8059 | 1.24084 | 0.620418 | − | 0.784272i | \(-0.286963\pi\) | ||||
0.620418 | + | 0.784272i | \(0.286963\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.3047 | −0.760719 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.0120 | −0.580316 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.0959 | 0.417414 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.2494 | 0.753234 | 0.376617 | − | 0.926369i | \(-0.377087\pi\) | ||||
0.376617 | + | 0.926369i | \(0.377087\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.45826 | −0.266108 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.9041 | −0.489669 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.7889 | 0.976892 | 0.488446 | − | 0.872594i | \(-0.337564\pi\) | ||||
0.488446 | + | 0.872594i | \(0.337564\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.805889 | −0.0329829 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.5011 | −0.633360 | −0.316680 | − | 0.948532i | \(-0.602568\pi\) | ||||
−0.316680 | + | 0.948532i | \(0.602568\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.8059 | −0.644736 | −0.322368 | − | 0.946614i | \(-0.604479\pi\) | ||||
−0.322368 | + | 0.946614i | \(0.604479\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.15352 | −0.209868 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.5948 | −0.918607 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.95205 | −0.241586 | −0.120793 | − | 0.992678i | \(-0.538544\pi\) | ||||
−0.120793 | + | 0.992678i | \(0.538544\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.57773 | −0.306562 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.4029 | 1.14718 | 0.573592 | − | 0.819141i | \(-0.305549\pi\) | ||||
0.573592 | + | 0.819141i | \(0.305549\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −33.6118 | −1.35536 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.1918 | −0.410307 | −0.205153 | − | 0.978730i | \(-0.565769\pi\) | ||||
−0.205153 | + | 0.978730i | \(0.565769\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.8612 | 0.838483 | 0.419241 | − | 0.907875i | \(-0.362296\pi\) | ||||
0.419241 | + | 0.907875i | \(0.362296\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.40294 | 0.176684 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.6907 | −0.947626 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.4006 | −0.535170 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.4989 | 1.69454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.6191 | 1.65683 | 0.828416 | − | 0.560113i | \(-0.189242\pi\) | ||||
0.828416 | + | 0.560113i | \(0.189242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.49885 | −0.337799 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −39.8612 | −1.58184 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.40294 | 0.253297 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.8013 | −1.92754 | −0.963768 | − | 0.266744i | \(-0.914052\pi\) | ||||
−0.963768 | + | 0.266744i | \(0.914052\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.8442 | 0.467089 | 0.233544 | − | 0.972346i | \(-0.424968\pi\) | ||||
0.233544 | + | 0.972346i | \(0.424968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.40294 | 0.0946159 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.5159 | −1.31764 | −0.658822 | − | 0.752298i | \(-0.728945\pi\) | ||||
−0.658822 | + | 0.752298i | \(0.728945\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.0553 | −1.37604 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 46.5062 | 1.81993 | 0.909964 | − | 0.414686i | \(-0.136109\pi\) | ||||
0.909964 | + | 0.414686i | \(0.136109\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.6044 | −0.531569 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.2494 | −0.594937 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.1152 | 0.394033 | 0.197017 | − | 0.980400i | \(-0.436875\pi\) | ||||
0.197017 | + | 0.980400i | \(0.436875\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.2641 | 1.29383 | 0.646913 | − | 0.762564i | \(-0.276060\pi\) | ||||
0.646913 | + | 0.762564i | \(0.276060\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.8848 | −0.539240 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.7077 | −1.22773 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.7985 | 0.649469 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.4029 | 1.32811 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.4966 | −1.94650 | −0.973249 | − | 0.229751i | \(-0.926209\pi\) | ||||
−0.973249 | + | 0.229751i | \(0.926209\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.24943 | 0.202050 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.7985 | 1.10682 | 0.553409 | − | 0.832910i | \(-0.313327\pi\) | ||||
0.553409 | + | 0.832910i | \(0.313327\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.8635 | −0.646211 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.2471 | 0.506887 | 0.253444 | − | 0.967350i | \(-0.418437\pi\) | ||||
0.253444 | + | 0.967350i | \(0.418437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.3047 | 1.27251 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.5542 | 0.784190 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.3983 | −0.396145 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.6671 | −1.50901 | −0.754504 | − | 0.656296i | \(-0.772122\pi\) | ||||
−0.754504 | + | 0.656296i | \(0.772122\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −37.3047 | −1.41505 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.2259 | 1.75093 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.90409 | 0.374607 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.10787 | 0.0796130 | 0.0398065 | − | 0.999207i | \(-0.487326\pi\) | ||||
0.0398065 | + | 0.999207i | \(0.487326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.4389 | 1.14803 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.69296 | −0.289734 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.9977 | 0.563250 | 0.281625 | − | 0.959524i | \(-0.409127\pi\) | ||||
0.281625 | + | 0.959524i | \(0.409127\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.4509 | −0.616957 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.01702 | −0.337690 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.9018 | −1.60444 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.40294 | 0.164431 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.8059 | −0.850516 | −0.425258 | − | 0.905072i | \(-0.639817\pi\) | ||||
−0.425258 | + | 0.905072i | \(0.639817\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.8635 | −0.775922 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −37.8036 | −1.40399 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.9691 | −0.629348 | −0.314674 | − | 0.949200i | \(-0.601895\pi\) | ||||
−0.314674 | + | 0.949200i | \(0.601895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.30474 | −0.122230 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.34533 | 0.0496909 | 0.0248455 | − | 0.999691i | \(-0.492091\pi\) | ||||
0.0248455 | + | 0.999691i | \(0.492091\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.8995 | 0.806678 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.2641 | −1.66507 | −0.832534 | − | 0.553973i | \(-0.813111\pi\) | ||||
−0.832534 | + | 0.553973i | \(0.813111\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.94469 | −0.365327 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.8036 | −1.02001 | −0.510007 | − | 0.860170i | \(-0.670357\pi\) | ||||
−0.510007 | + | 0.860170i | \(0.670357\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.3047 | 1.22019 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.5565 | 0.532593 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.0627 | 1.09700 | 0.548501 | − | 0.836150i | \(-0.315199\pi\) | ||||
0.548501 | + | 0.836150i | \(0.315199\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.44354 | 0.125489 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 64.0530 | 2.33113 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.3241 | 0.629654 | 0.314827 | − | 0.949149i | \(-0.398054\pi\) | ||||
0.314827 | + | 0.949149i | \(0.398054\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.7100 | −0.679129 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.2111 | −0.442653 | −0.221327 | − | 0.975200i | \(-0.571039\pi\) | ||||
−0.221327 | + | 0.975200i | \(0.571039\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.0959 | −0.509639 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.0147 | −0.939337 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.1152 | −0.400825 | −0.200413 | − | 0.979712i | \(-0.564228\pi\) | ||||
−0.200413 | + | 0.979712i | \(0.564228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.59706 | 0.201573 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.287717 | −0.0103485 | −0.00517423 | − | 0.999987i | \(-0.501647\pi\) | ||||
−0.00517423 | + | 0.999987i | \(0.501647\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.7506 | −0.386172 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.1083 | 1.18623 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.2088 | −0.973609 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.20147 | −0.257360 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46.4177 | −1.65672 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.5011 | −0.409972 | −0.204986 | − | 0.978765i | \(-0.565715\pi\) | ||||
−0.204986 | + | 0.978765i | \(0.565715\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.59706 | −0.0568567 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.5306 | 0.906618 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.5565 | −0.374399 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.6980 | −0.662318 | −0.331159 | − | 0.943575i | \(-0.607440\pi\) | ||||
−0.331159 | + | 0.943575i | \(0.607440\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.5800 | 0.374295 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.40294 | −0.0849039 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 64.8013 | 2.28679 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.7003 | 0.623081 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −53.8036 | −1.89163 | −0.945817 | − | 0.324701i | \(-0.894736\pi\) | ||||
−0.945817 | + | 0.324701i | \(0.894736\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.7866 | −1.22152 | −0.610761 | − | 0.791815i | \(-0.709136\pi\) | ||||
−0.610761 | + | 0.791815i | \(0.709136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.39558 | 0.0840168 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.2877 | −1.20105 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.36695 | −0.0828092 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.8110 | −1.31961 | −0.659806 | − | 0.751436i | \(-0.729361\pi\) | ||||
−0.659806 | + | 0.751436i | \(0.729361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54.4177 | −1.89688 | −0.948440 | − | 0.316956i | \(-0.897339\pi\) | ||||
−0.948440 | + | 0.316956i | \(0.897339\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.3070 | −0.776631 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.86120 | 0.273361 | 0.136680 | − | 0.990615i | \(-0.456357\pi\) | ||||
0.136680 | + | 0.990615i | \(0.456357\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.45826 | 0.224305 | 0.112152 | − | 0.993691i | \(-0.464226\pi\) | ||||
0.112152 | + | 0.993691i | \(0.464226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.24943 | 0.182101 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 55.4006 | 1.91722 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.04795 | −0.0707876 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.3218 | 0.977776 | 0.488888 | − | 0.872347i | \(-0.337403\pi\) | ||||
0.488888 | + | 0.872347i | \(0.337403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8612 | 0.788317 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.0959 | 0.692140 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.78150 | 0.336494 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.2494 | −0.797918 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.4989 | 1.45684 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.75057 | 0.299614 | 0.149807 | − | 0.988715i | \(-0.452135\pi\) | ||||
0.149807 | + | 0.988715i | \(0.452135\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.0959 | −0.345273 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.6907 | 0.843417 | 0.421708 | − | 0.906731i | \(-0.361431\pi\) | ||||
0.421708 | + | 0.906731i | \(0.361431\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.49885 | −0.289977 | −0.144989 | − | 0.989433i | \(-0.546315\pi\) | ||||
−0.144989 | + | 0.989433i | \(0.546315\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.6141 | 0.633631 | 0.316815 | − | 0.948487i | \(-0.397386\pi\) | ||||
0.316815 | + | 0.948487i | \(0.397386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4989 | 0.424974 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.38592 | 0.0810302 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 69.9069 | 2.37143 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2517 | 0.550669 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.24943 | −0.143821 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.1106 | 1.48951 | 0.744755 | − | 0.667338i | \(-0.232566\pi\) | ||||
0.744755 | + | 0.667338i | \(0.232566\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.2015 | 0.377816 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.2900 | 0.380370 | 0.190185 | − | 0.981748i | \(-0.439091\pi\) | ||||
0.190185 | + | 0.981748i | \(0.439091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.2471 | 1.42173 | 0.710864 | − | 0.703329i | \(-0.248304\pi\) | ||||
0.710864 | + | 0.703329i | \(0.248304\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.4103 | −0.887773 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.98068 | 0.133658 | 0.0668290 | − | 0.997764i | \(-0.478712\pi\) | ||||
0.0668290 | + | 0.997764i | \(0.478712\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.24943 | −0.142361 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.57773 | 0.253579 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 66.6095 | 2.22651 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.8848 | −0.463599 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.7483 | 0.491883 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.5182 | 0.483670 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 42.4177 | 1.41001 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.5735 | 0.417496 | 0.208748 | − | 0.977969i | \(-0.433061\pi\) | ||||
0.208748 | + | 0.977969i | \(0.433061\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.90409 | 0.129491 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.09821 | 0.235174 | 0.117587 | − | 0.993063i | \(-0.462484\pi\) | ||||
0.117587 | + | 0.993063i | \(0.462484\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −61.8566 | −2.04715 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25.9188 | 0.856850 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.4412 | −1.23507 | −0.617536 | − | 0.786542i | \(-0.711869\pi\) | ||||
−0.617536 | + | 0.786542i | \(0.711869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.9571 | −0.954169 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.1918 | −0.664622 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.6694 | 1.66600 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.24943 | −0.303791 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.88477 | −0.258691 | −0.129345 | − | 0.991600i | \(-0.541288\pi\) | ||||
−0.129345 | + | 0.991600i | \(0.541288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.3047 | −0.893917 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 59.8995 | 1.95892 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.9954 | −1.20859 | −0.604294 | − | 0.796762i | \(-0.706545\pi\) | ||||
−0.604294 | + | 0.796762i | \(0.706545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.49885 | 0.179448 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.7026 | −0.414094 | −0.207047 | − | 0.978331i | \(-0.566385\pi\) | ||||
−0.207047 | + | 0.978331i | \(0.566385\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.2259 | 1.50532 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.1129 | 0.751069 | 0.375535 | − | 0.926808i | \(-0.377459\pi\) | ||||
0.375535 | + | 0.926808i | \(0.377459\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.0894 | 1.56105 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.60442 | 0.311445 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.4200 | −1.40651 | −0.703255 | − | 0.710937i | \(-0.748271\pi\) | ||||
−0.703255 | + | 0.710937i | \(0.748271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.4200 | −0.434260 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.6021 | 0.989226 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.8059 | −0.864706 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.5565 | −0.533525 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 58.6021 | 1.88647 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.6450 | −0.374478 | −0.187239 | − | 0.982314i | \(-0.559954\pi\) | ||||
−0.187239 | + | 0.982314i | \(0.559954\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.8848 | 0.446043 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.3624 | 1.07065 | 0.535324 | − | 0.844647i | \(-0.320189\pi\) | ||||
0.535324 | + | 0.844647i | \(0.320189\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.5542 | −0.530158 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.1895 | 0.613927 | 0.306963 | − | 0.951721i | \(-0.400687\pi\) | ||||
0.306963 | + | 0.951721i | \(0.400687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.2111 | 0.326349 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.0553 | −0.640317 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.07658 | −0.193813 | −0.0969065 | − | 0.995293i | \(-0.530895\pi\) | ||||
−0.0969065 | + | 0.995293i | \(0.530895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.1106 | 1.21431 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.30474 | −0.105085 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.6597 | 1.00570 | 0.502852 | − | 0.864372i | \(-0.332284\pi\) | ||||
0.502852 | + | 0.864372i | \(0.332284\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.5565 | −0.493669 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.58003 | 0.0817925 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.3601 | 0.486458 | 0.243229 | − | 0.969969i | \(-0.421793\pi\) | ||||
0.243229 | + | 0.969969i | \(0.421793\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.65237 | 0.305387 |
(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 | 9408.2.a.ei.1.1 | 3 | ||
4.3 | odd | 2 | 9408.2.a.eg.1.1 | 3 | |||
7.3 | odd | 6 | 1344.2.q.z.961.1 | 6 | |||
7.5 | odd | 6 | 1344.2.q.z.193.1 | 6 | |||
7.6 | odd | 2 | 9408.2.a.eh.1.3 | 3 | |||
8.3 | odd | 2 | 4704.2.a.bv.1.3 | 3 | |||
8.5 | even | 2 | 4704.2.a.bt.1.3 | 3 | |||
28.3 | even | 6 | 1344.2.q.y.961.1 | 6 | |||
28.19 | even | 6 | 1344.2.q.y.193.1 | 6 | |||
28.27 | even | 2 | 9408.2.a.ej.1.3 | 3 | |||
56.3 | even | 6 | 672.2.q.l.289.3 | yes | 6 | ||
56.5 | odd | 6 | 672.2.q.k.193.3 | ✓ | 6 | ||
56.13 | odd | 2 | 4704.2.a.bu.1.1 | 3 | |||
56.19 | even | 6 | 672.2.q.l.193.3 | yes | 6 | ||
56.27 | even | 2 | 4704.2.a.bs.1.1 | 3 | |||
56.45 | odd | 6 | 672.2.q.k.289.3 | yes | 6 | ||
168.5 | even | 6 | 2016.2.s.u.865.1 | 6 | |||
168.59 | odd | 6 | 2016.2.s.v.289.1 | 6 | |||
168.101 | even | 6 | 2016.2.s.u.289.1 | 6 | |||
168.131 | odd | 6 | 2016.2.s.v.865.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.q.k.193.3 | ✓ | 6 | 56.5 | odd | 6 | ||
672.2.q.k.289.3 | yes | 6 | 56.45 | odd | 6 | ||
672.2.q.l.193.3 | yes | 6 | 56.19 | even | 6 | ||
672.2.q.l.289.3 | yes | 6 | 56.3 | even | 6 | ||
1344.2.q.y.193.1 | 6 | 28.19 | even | 6 | |||
1344.2.q.y.961.1 | 6 | 28.3 | even | 6 | |||
1344.2.q.z.193.1 | 6 | 7.5 | odd | 6 | |||
1344.2.q.z.961.1 | 6 | 7.3 | odd | 6 | |||
2016.2.s.u.289.1 | 6 | 168.101 | even | 6 | |||
2016.2.s.u.865.1 | 6 | 168.5 | even | 6 | |||
2016.2.s.v.289.1 | 6 | 168.59 | odd | 6 | |||
2016.2.s.v.865.1 | 6 | 168.131 | odd | 6 | |||
4704.2.a.bs.1.1 | 3 | 56.27 | even | 2 | |||
4704.2.a.bt.1.3 | 3 | 8.5 | even | 2 | |||
4704.2.a.bu.1.1 | 3 | 56.13 | odd | 2 | |||
4704.2.a.bv.1.3 | 3 | 8.3 | odd | 2 | |||
9408.2.a.eg.1.1 | 3 | 4.3 | odd | 2 | |||
9408.2.a.eh.1.3 | 3 | 7.6 | odd | 2 | |||
9408.2.a.ei.1.1 | 3 | 1.1 | even | 1 | trivial | ||
9408.2.a.ej.1.3 | 3 | 28.27 | even | 2 |