Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.291367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | 2.14073 | 0.957364 | 0.478682 | − | 0.877988i | \(-0.341115\pi\) | ||||
0.478682 | + | 0.877988i | \(0.341115\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.72347 | 1.02937 | 0.514687 | − | 0.857378i | \(-0.327908\pi\) | ||||
0.514687 | + | 0.857378i | \(0.327908\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.451253 | −0.136058 | −0.0680290 | − | 0.997683i | \(-0.521671\pi\) | ||||
−0.0680290 | + | 0.997683i | \(0.521671\pi\) | |||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | −5.41294 | −1.50128 | −0.750640 | − | 0.660711i | \(-0.770255\pi\) | ||||
−0.750640 | + | 0.660711i | \(0.770255\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.14073 | −0.552735 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −3.24046 | −0.785927 | −0.392963 | − | 0.919554i | \(-0.628550\pi\) | ||||
−0.392963 | + | 0.919554i | \(0.628550\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.89595 | −0.893792 | −0.446896 | − | 0.894586i | \(-0.647471\pi\) | ||||
−0.446896 | + | 0.894586i | \(0.647471\pi\) | |||||||
\(20\) | −4.28146 | −0.957364 | ||||||||
\(21\) | −2.72347 | −0.594309 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.417266 | −0.0834532 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −5.44693 | −1.02937 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.55800 | −0.279825 | −0.139912 | − | 0.990164i | \(-0.544682\pi\) | ||||
−0.139912 | + | 0.990164i | \(0.544682\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.451253 | 0.0785531 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.83021 | 0.985485 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −4.21572 | −0.693061 | −0.346530 | − | 0.938039i | \(-0.612640\pi\) | ||||
−0.346530 | + | 0.938039i | \(0.612640\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.41294 | 0.866765 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.10674 | 0.485192 | 0.242596 | − | 0.970127i | \(-0.422001\pi\) | ||||
0.242596 | + | 0.970127i | \(0.422001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.6287 | 1.62086 | 0.810428 | − | 0.585838i | \(-0.199234\pi\) | ||||
0.810428 | + | 0.585838i | \(0.199234\pi\) | |||||||
\(44\) | 0.902507 | 0.136058 | ||||||||
\(45\) | 2.14073 | 0.319121 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.14073 | −0.312258 | −0.156129 | − | 0.987737i | \(-0.549902\pi\) | ||||
−0.156129 | + | 0.987737i | \(0.549902\pi\) | |||||||
\(48\) | −4.00000 | −0.577350 | ||||||||
\(49\) | 0.417266 | 0.0596095 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.24046 | 0.453755 | ||||||||
\(52\) | 10.8259 | 1.50128 | ||||||||
\(53\) | −0.834532 | −0.114632 | −0.0573159 | − | 0.998356i | \(-0.518254\pi\) | ||||
−0.0573159 | + | 0.998356i | \(0.518254\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.966013 | −0.130257 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.89595 | 0.516031 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.0049 | −1.82329 | −0.911643 | − | 0.410982i | \(-0.865186\pi\) | ||||
−0.911643 | + | 0.410982i | \(0.865186\pi\) | |||||||
\(60\) | 4.28146 | 0.552735 | ||||||||
\(61\) | 6.69441 | 0.857131 | 0.428566 | − | 0.903511i | \(-0.359019\pi\) | ||||
0.428566 | + | 0.903511i | \(0.359019\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.72347 | 0.343124 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −11.5877 | −1.43727 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.44693 | −0.665449 | −0.332724 | − | 0.943024i | \(-0.607968\pi\) | ||||
−0.332724 | + | 0.943024i | \(0.607968\pi\) | |||||||
\(68\) | 6.48092 | 0.785927 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.82528 | −0.216621 | −0.108310 | − | 0.994117i | \(-0.534544\pi\) | ||||
−0.108310 | + | 0.994117i | \(0.534544\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.72347 | −1.02100 | −0.510502 | − | 0.859876i | \(-0.670540\pi\) | ||||
−0.510502 | + | 0.859876i | \(0.670540\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.417266 | 0.0481818 | ||||||||
\(76\) | 7.79190 | 0.893792 | ||||||||
\(77\) | −1.22897 | −0.140055 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.73048 | −0.982256 | −0.491128 | − | 0.871087i | \(-0.663415\pi\) | ||||
−0.491128 | + | 0.871087i | \(0.663415\pi\) | |||||||
\(80\) | 8.56293 | 0.957364 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.403693 | 0.0443110 | 0.0221555 | − | 0.999755i | \(-0.492947\pi\) | ||||
0.0221555 | + | 0.999755i | \(0.492947\pi\) | |||||||
\(84\) | 5.44693 | 0.594309 | ||||||||
\(85\) | −6.93696 | −0.752418 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.22498 | 0.447847 | 0.223923 | − | 0.974607i | \(-0.428113\pi\) | ||||
0.223923 | + | 0.974607i | \(0.428113\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.7420 | −1.54538 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | 1.55800 | 0.161557 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.34019 | −0.855685 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.86852 | −0.189719 | −0.0948597 | − | 0.995491i | \(-0.530240\pi\) | ||||
−0.0948597 | + | 0.995491i | \(0.530240\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.451253 | −0.0453527 | ||||||||
\(100\) | 0.834532 | 0.0834532 | ||||||||
\(101\) | 3.17472 | 0.315896 | 0.157948 | − | 0.987447i | \(-0.449512\pi\) | ||||
0.157948 | + | 0.987447i | \(0.449512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.66042 | −0.754804 | −0.377402 | − | 0.926050i | \(-0.623182\pi\) | ||||
−0.377402 | + | 0.926050i | \(0.623182\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.83021 | −0.568970 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.15924 | 0.402088 | 0.201044 | − | 0.979582i | \(-0.435567\pi\) | ||||
0.201044 | + | 0.979582i | \(0.435567\pi\) | |||||||
\(108\) | 2.00000 | 0.192450 | ||||||||
\(109\) | −14.4334 | −1.38246 | −0.691232 | − | 0.722632i | \(-0.742932\pi\) | ||||
−0.691232 | + | 0.722632i | \(0.742932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.21572 | 0.400139 | ||||||||
\(112\) | 10.8939 | 1.02937 | ||||||||
\(113\) | −3.03399 | −0.285414 | −0.142707 | − | 0.989765i | \(-0.545581\pi\) | ||||
−0.142707 | + | 0.989765i | \(0.545581\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.14073 | 0.199624 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | −5.41294 | −0.500427 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.82528 | −0.809012 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7964 | −0.981488 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.10674 | −0.280126 | ||||||||
\(124\) | 3.11600 | 0.279825 | ||||||||
\(125\) | −11.5969 | −1.03726 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.47599 | −0.663387 | −0.331693 | − | 0.943387i | \(-0.607620\pi\) | ||||
−0.331693 | + | 0.943387i | \(0.607620\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.6287 | −0.935802 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0185035 | −0.00161666 | −0.000808329 | − | 1.00000i | \(-0.500257\pi\) | ||||
−0.000808329 | 1.00000i | \(0.500257\pi\) | ||||||||
\(132\) | −0.902507 | −0.0785531 | ||||||||
\(133\) | −10.6105 | −0.920046 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.14073 | −0.184245 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.61942 | −0.394663 | −0.197332 | − | 0.980337i | \(-0.563228\pi\) | ||||
−0.197332 | + | 0.980337i | \(0.563228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.51476 | 0.213299 | 0.106650 | − | 0.994297i | \(-0.465988\pi\) | ||||
0.106650 | + | 0.994297i | \(0.465988\pi\) | |||||||
\(140\) | −11.6604 | −0.985485 | ||||||||
\(141\) | 2.14073 | 0.180282 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.44261 | 0.204261 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 2.14073 | 0.177778 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.417266 | −0.0344155 | ||||||||
\(148\) | 8.43145 | 0.693061 | ||||||||
\(149\) | −13.2475 | −1.08528 | −0.542638 | − | 0.839967i | \(-0.682574\pi\) | ||||
−0.542638 | + | 0.839967i | \(0.682574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.267282 | −0.0217511 | −0.0108756 | − | 0.999941i | \(-0.503462\pi\) | ||||
−0.0108756 | + | 0.999941i | \(0.503462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.24046 | −0.261976 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.33526 | −0.267894 | ||||||||
\(156\) | −10.8259 | −0.866765 | ||||||||
\(157\) | 16.4152 | 1.31007 | 0.655037 | − | 0.755597i | \(-0.272653\pi\) | ||||
0.655037 | + | 0.755597i | \(0.272653\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.834532 | 0.0661827 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.72347 | 0.214639 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.0438 | 1.02167 | 0.510836 | − | 0.859678i | \(-0.329336\pi\) | ||||
0.510836 | + | 0.859678i | \(0.329336\pi\) | |||||||
\(164\) | −6.21349 | −0.485192 | ||||||||
\(165\) | 0.966013 | 0.0752040 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.0531 | −1.86128 | −0.930642 | − | 0.365930i | \(-0.880751\pi\) | ||||
−0.930642 | + | 0.365930i | \(0.880751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.3000 | 1.25384 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.89595 | −0.297931 | ||||||||
\(172\) | −21.2573 | −1.62086 | ||||||||
\(173\) | 15.7968 | 1.20101 | 0.600505 | − | 0.799621i | \(-0.294966\pi\) | ||||
0.600505 | + | 0.799621i | \(0.294966\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.13641 | −0.0859045 | ||||||||
\(176\) | −1.80501 | −0.136058 | ||||||||
\(177\) | 14.0049 | 1.05267 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.3204 | −1.89253 | −0.946267 | − | 0.323386i | \(-0.895179\pi\) | ||||
−0.946267 | + | 0.323386i | \(0.895179\pi\) | |||||||
\(180\) | −4.28146 | −0.319121 | ||||||||
\(181\) | 15.7284 | 1.16908 | 0.584541 | − | 0.811364i | \(-0.301275\pi\) | ||||
0.584541 | + | 0.811364i | \(0.301275\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.69441 | −0.494865 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.02474 | −0.663512 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.46227 | 0.106932 | ||||||||
\(188\) | 4.28146 | 0.312258 | ||||||||
\(189\) | −2.72347 | −0.198103 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.87122 | −0.641899 | −0.320949 | − | 0.947096i | \(-0.604002\pi\) | ||||
−0.320949 | + | 0.947096i | \(0.604002\pi\) | |||||||
\(192\) | 8.00000 | 0.577350 | ||||||||
\(193\) | −0.330935 | −0.0238212 | −0.0119106 | − | 0.999929i | \(-0.503791\pi\) | ||||
−0.0119106 | + | 0.999929i | \(0.503791\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.5877 | 0.829810 | ||||||||
\(196\) | −0.834532 | −0.0596095 | ||||||||
\(197\) | −15.9414 | −1.13578 | −0.567890 | − | 0.823105i | \(-0.692240\pi\) | ||||
−0.567890 | + | 0.823105i | \(0.692240\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.51537 | 0.178310 | 0.0891548 | − | 0.996018i | \(-0.471583\pi\) | ||||
0.0891548 | + | 0.996018i | \(0.471583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.44693 | 0.384197 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.72347 | 0.191150 | ||||||||
\(204\) | −6.48092 | −0.453755 | ||||||||
\(205\) | 6.65071 | 0.464506 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −21.6518 | −1.50128 | ||||||||
\(209\) | 1.75806 | 0.121608 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.33587 | 0.367336 | 0.183668 | − | 0.982988i | \(-0.441203\pi\) | ||||
0.183668 | + | 0.982988i | \(0.441203\pi\) | |||||||
\(212\) | 1.66906 | 0.114632 | ||||||||
\(213\) | 1.82528 | 0.125066 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.7531 | 1.55175 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.24316 | −0.288044 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.72347 | 0.589477 | ||||||||
\(220\) | 1.93203 | 0.130257 | ||||||||
\(221\) | 17.5404 | 1.17990 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1272 | 0.678165 | 0.339082 | − | 0.940757i | \(-0.389883\pi\) | ||||
0.339082 | + | 0.940757i | \(0.389883\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.417266 | −0.0278177 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.16849 | −0.542162 | −0.271081 | − | 0.962557i | \(-0.587381\pi\) | ||||
−0.271081 | + | 0.962557i | \(0.587381\pi\) | |||||||
\(228\) | −7.79190 | −0.516031 | ||||||||
\(229\) | 28.5084 | 1.88388 | 0.941942 | − | 0.335774i | \(-0.108998\pi\) | ||||
0.941942 | + | 0.335774i | \(0.108998\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.22897 | 0.0808605 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.07723 | 0.0705714 | 0.0352857 | − | 0.999377i | \(-0.488766\pi\) | ||||
0.0352857 | + | 0.999377i | \(0.488766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.58273 | −0.298945 | ||||||||
\(236\) | 28.0099 | 1.82329 | ||||||||
\(237\) | 8.73048 | 0.567106 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.8197 | −1.86419 | −0.932094 | − | 0.362216i | \(-0.882020\pi\) | ||||
−0.932094 | + | 0.362216i | \(0.882020\pi\) | |||||||
\(240\) | −8.56293 | −0.552735 | ||||||||
\(241\) | −17.2388 | −1.11045 | −0.555225 | − | 0.831700i | \(-0.687368\pi\) | ||||
−0.555225 | + | 0.831700i | \(0.687368\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −13.3888 | −0.857131 | ||||||||
\(245\) | 0.893255 | 0.0570680 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.0886 | 1.34183 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.403693 | −0.0255830 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.7552 | −0.741983 | −0.370991 | − | 0.928636i | \(-0.620982\pi\) | ||||
−0.370991 | + | 0.928636i | \(0.620982\pi\) | |||||||
\(252\) | −5.44693 | −0.343124 | ||||||||
\(253\) | −0.451253 | −0.0283701 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.93696 | 0.434409 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 9.34558 | 0.582961 | 0.291481 | − | 0.956577i | \(-0.405852\pi\) | ||||
0.291481 | + | 0.956577i | \(0.405852\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.4814 | −0.713418 | ||||||||
\(260\) | 23.1753 | 1.43727 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.2956 | −1.31315 | −0.656573 | − | 0.754263i | \(-0.727995\pi\) | ||||
−0.656573 | + | 0.754263i | \(0.727995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.78651 | −0.109744 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.22498 | −0.258564 | ||||||||
\(268\) | 10.8939 | 0.665449 | ||||||||
\(269\) | 4.00000 | 0.243884 | 0.121942 | − | 0.992537i | \(-0.461088\pi\) | ||||
0.121942 | + | 0.992537i | \(0.461088\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.1783 | 1.46873 | 0.734365 | − | 0.678755i | \(-0.237480\pi\) | ||||
0.734365 | + | 0.678755i | \(0.237480\pi\) | |||||||
\(272\) | −12.9618 | −0.785927 | ||||||||
\(273\) | 14.7420 | 0.892225 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.188293 | 0.0113545 | ||||||||
\(276\) | 2.00000 | 0.120386 | ||||||||
\(277\) | 17.6507 | 1.06053 | 0.530264 | − | 0.847832i | \(-0.322093\pi\) | ||||
0.530264 | + | 0.847832i | \(0.322093\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.55800 | −0.0932749 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.8784 | 0.947225 | 0.473612 | − | 0.880733i | \(-0.342950\pi\) | ||||
0.473612 | + | 0.880733i | \(0.342950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.88893 | −0.587836 | −0.293918 | − | 0.955831i | \(-0.594959\pi\) | ||||
−0.293918 | + | 0.955831i | \(0.594959\pi\) | |||||||
\(284\) | 3.65056 | 0.216621 | ||||||||
\(285\) | 8.34019 | 0.494030 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.46111 | 0.499444 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.49942 | −0.382319 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.86852 | 0.109535 | ||||||||
\(292\) | 17.4469 | 1.02100 | ||||||||
\(293\) | 11.5899 | 0.677089 | 0.338545 | − | 0.940950i | \(-0.390065\pi\) | ||||
0.338545 | + | 0.940950i | \(0.390065\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.9808 | −1.74555 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.451253 | 0.0261844 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.41294 | −0.313039 | ||||||||
\(300\) | −0.834532 | −0.0481818 | ||||||||
\(301\) | 28.9468 | 1.66847 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.17472 | −0.182383 | ||||||||
\(304\) | −15.5838 | −0.893792 | ||||||||
\(305\) | 14.3309 | 0.820587 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.4617 | 1.73854 | 0.869271 | − | 0.494336i | \(-0.164589\pi\) | ||||
0.869271 | + | 0.494336i | \(0.164589\pi\) | |||||||
\(308\) | 2.45795 | 0.140055 | ||||||||
\(309\) | 7.66042 | 0.435786 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.4314 | 0.818332 | 0.409166 | − | 0.912460i | \(-0.365820\pi\) | ||||
0.409166 | + | 0.912460i | \(0.365820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.1844 | 1.36698 | 0.683492 | − | 0.729958i | \(-0.260460\pi\) | ||||
0.683492 | + | 0.729958i | \(0.260460\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.83021 | 0.328495 | ||||||||
\(316\) | 17.4610 | 0.982256 | ||||||||
\(317\) | −20.1452 | −1.13147 | −0.565734 | − | 0.824588i | \(-0.691407\pi\) | ||||
−0.565734 | + | 0.824588i | \(0.691407\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.451253 | −0.0252653 | ||||||||
\(320\) | −17.1259 | −0.957364 | ||||||||
\(321\) | −4.15924 | −0.232146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.6247 | 0.702455 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | 2.25864 | 0.125287 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.4334 | 0.798167 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.83021 | −0.321430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.9618 | 1.26210 | 0.631048 | − | 0.775743i | \(-0.282625\pi\) | ||||
0.631048 | + | 0.775743i | \(0.282625\pi\) | |||||||
\(332\) | −0.807385 | −0.0443110 | ||||||||
\(333\) | −4.21572 | −0.231020 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.6604 | −0.637077 | ||||||||
\(336\) | −10.8939 | −0.594309 | ||||||||
\(337\) | −8.62420 | −0.469790 | −0.234895 | − | 0.972021i | \(-0.575475\pi\) | ||||
−0.234895 | + | 0.972021i | \(0.575475\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.03399 | 0.164784 | ||||||||
\(340\) | 13.8739 | 0.752418 | ||||||||
\(341\) | 0.703052 | 0.0380724 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.9279 | −0.968013 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.14073 | −0.115253 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.276534 | −0.0148451 | −0.00742257 | − | 0.999972i | \(-0.502363\pi\) | ||||
−0.00742257 | + | 0.999972i | \(0.502363\pi\) | |||||||
\(348\) | 2.00000 | 0.107211 | ||||||||
\(349\) | 10.1753 | 0.544673 | 0.272336 | − | 0.962202i | \(-0.412204\pi\) | ||||
0.272336 | + | 0.962202i | \(0.412204\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.41294 | 0.288922 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.8895 | 0.632816 | 0.316408 | − | 0.948623i | \(-0.397523\pi\) | ||||
0.316408 | + | 0.948623i | \(0.397523\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.90744 | −0.207385 | ||||||||
\(356\) | −8.44995 | −0.447847 | ||||||||
\(357\) | 8.82528 | 0.467083 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1923 | −0.590706 | −0.295353 | − | 0.955388i | \(-0.595437\pi\) | ||||
−0.295353 | + | 0.955388i | \(0.595437\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.82157 | −0.201135 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.7964 | 0.566662 | ||||||||
\(364\) | 29.4839 | 1.54538 | ||||||||
\(365\) | −18.6746 | −0.977473 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.37896 | 0.0719810 | 0.0359905 | − | 0.999352i | \(-0.488541\pi\) | ||||
0.0359905 | + | 0.999352i | \(0.488541\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 3.10674 | 0.161731 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.27282 | −0.117999 | ||||||||
\(372\) | −3.11600 | −0.161557 | ||||||||
\(373\) | −5.90744 | −0.305875 | −0.152938 | − | 0.988236i | \(-0.548873\pi\) | ||||
−0.152938 | + | 0.988236i | \(0.548873\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.5969 | 0.598862 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.41294 | −0.278781 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.2114 | −1.39776 | −0.698878 | − | 0.715241i | \(-0.746317\pi\) | ||||
−0.698878 | + | 0.715241i | \(0.746317\pi\) | |||||||
\(380\) | 16.6804 | 0.855685 | ||||||||
\(381\) | 7.47599 | 0.383007 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.5939 | −0.643518 | −0.321759 | − | 0.946822i | \(-0.604274\pi\) | ||||
−0.321759 | + | 0.946822i | \(0.604274\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.63090 | −0.134083 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.6287 | 0.540286 | ||||||||
\(388\) | 3.73704 | 0.189719 | ||||||||
\(389\) | −12.6491 | −0.641334 | −0.320667 | − | 0.947192i | \(-0.603907\pi\) | ||||
−0.320667 | + | 0.947192i | \(0.603907\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.24046 | −0.163877 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.0185035 | 0.000933378 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.6896 | −0.940377 | ||||||||
\(396\) | 0.902507 | 0.0453527 | ||||||||
\(397\) | 17.4358 | 0.875076 | 0.437538 | − | 0.899200i | \(-0.355851\pi\) | ||||
0.437538 | + | 0.899200i | \(0.355851\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.6105 | 0.531189 | ||||||||
\(400\) | −1.66906 | −0.0834532 | ||||||||
\(401\) | −8.47228 | −0.423085 | −0.211543 | − | 0.977369i | \(-0.567849\pi\) | ||||
−0.211543 | + | 0.977369i | \(0.567849\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.43336 | 0.420095 | ||||||||
\(404\) | −6.34944 | −0.315896 | ||||||||
\(405\) | 2.14073 | 0.106374 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.90236 | 0.0942965 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.768468 | 0.0379983 | 0.0189992 | − | 0.999819i | \(-0.493952\pi\) | ||||
0.0189992 | + | 0.999819i | \(0.493952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.61942 | 0.227859 | ||||||||
\(412\) | 15.3208 | 0.754804 | ||||||||
\(413\) | −38.1419 | −1.87684 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.864198 | 0.0424218 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.51476 | −0.123148 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.2573 | 0.745370 | 0.372685 | − | 0.927958i | \(-0.378437\pi\) | ||||
0.372685 | + | 0.927958i | \(0.378437\pi\) | |||||||
\(420\) | 11.6604 | 0.568970 | ||||||||
\(421\) | 1.23855 | 0.0603632 | 0.0301816 | − | 0.999544i | \(-0.490391\pi\) | ||||
0.0301816 | + | 0.999544i | \(0.490391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.14073 | −0.104086 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.35213 | 0.0655881 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.2320 | 0.882308 | ||||||||
\(428\) | −8.31847 | −0.402088 | ||||||||
\(429\) | −2.44261 | −0.117930 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.8458 | 0.570594 | 0.285297 | − | 0.958439i | \(-0.407908\pi\) | ||||
0.285297 | + | 0.958439i | \(0.407908\pi\) | |||||||
\(432\) | −4.00000 | −0.192450 | ||||||||
\(433\) | −27.4131 | −1.31739 | −0.658695 | − | 0.752410i | \(-0.728891\pi\) | ||||
−0.658695 | + | 0.752410i | \(0.728891\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.14073 | −0.102640 | ||||||||
\(436\) | 28.8667 | 1.38246 | ||||||||
\(437\) | −3.89595 | −0.186369 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.5246 | 1.02731 | 0.513657 | − | 0.857996i | \(-0.328290\pi\) | ||||
0.513657 | + | 0.857996i | \(0.328290\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.417266 | 0.0198698 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.671122 | −0.0318860 | −0.0159430 | − | 0.999873i | \(-0.505075\pi\) | ||||
−0.0159430 | + | 0.999873i | \(0.505075\pi\) | |||||||
\(444\) | −8.43145 | −0.400139 | ||||||||
\(445\) | 9.04454 | 0.428752 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.2475 | 0.626584 | ||||||||
\(448\) | −21.7877 | −1.02937 | ||||||||
\(449\) | 21.9517 | 1.03597 | 0.517983 | − | 0.855391i | \(-0.326683\pi\) | ||||
0.517983 | + | 0.855391i | \(0.326683\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.40193 | −0.0660143 | ||||||||
\(452\) | 6.06797 | 0.285414 | ||||||||
\(453\) | 0.267282 | 0.0125580 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31.5586 | −1.47949 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.310521 | 0.0145256 | 0.00726279 | − | 0.999974i | \(-0.497688\pi\) | ||||
0.00726279 | + | 0.999974i | \(0.497688\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.24046 | 0.151252 | ||||||||
\(460\) | −4.28146 | −0.199624 | ||||||||
\(461\) | 15.9604 | 0.743349 | 0.371675 | − | 0.928363i | \(-0.378784\pi\) | ||||
0.371675 | + | 0.928363i | \(0.378784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6451 | 0.773563 | 0.386781 | − | 0.922171i | \(-0.373587\pi\) | ||||
0.386781 | + | 0.922171i | \(0.373587\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | 3.33526 | 0.154669 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.7126 | −0.588268 | −0.294134 | − | 0.955764i | \(-0.595031\pi\) | ||||
−0.294134 | + | 0.955764i | \(0.595031\pi\) | |||||||
\(468\) | 10.8259 | 0.500427 | ||||||||
\(469\) | −14.8345 | −0.684995 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.4152 | −0.756372 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.79622 | −0.220531 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.62565 | 0.0745899 | ||||||||
\(476\) | 17.6506 | 0.809012 | ||||||||
\(477\) | −0.834532 | −0.0382106 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.1686 | −1.51551 | −0.757757 | − | 0.652537i | \(-0.773705\pi\) | ||||
−0.757757 | + | 0.652537i | \(0.773705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.8195 | 1.04048 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.72347 | −0.123922 | ||||||||
\(484\) | 21.5927 | 0.981488 | ||||||||
\(485\) | −4.00000 | −0.181631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.8851 | −1.08234 | −0.541168 | − | 0.840915i | \(-0.682018\pi\) | ||||
−0.541168 | + | 0.840915i | \(0.682018\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.0438 | −0.589863 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.290716 | −0.0131198 | −0.00655991 | − | 0.999978i | \(-0.502088\pi\) | ||||
−0.00655991 | + | 0.999978i | \(0.502088\pi\) | |||||||
\(492\) | 6.21349 | 0.280126 | ||||||||
\(493\) | −3.24046 | −0.145943 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.966013 | −0.0434190 | ||||||||
\(496\) | −6.23199 | −0.279825 | ||||||||
\(497\) | −4.97109 | −0.222984 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0735 | 0.719549 | 0.359775 | − | 0.933039i | \(-0.382854\pi\) | ||||
0.359775 | + | 0.933039i | \(0.382854\pi\) | |||||||
\(500\) | 23.1938 | 1.03726 | ||||||||
\(501\) | 24.0531 | 1.07461 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.77517 | −0.302090 | −0.151045 | − | 0.988527i | \(-0.548264\pi\) | ||||
−0.151045 | + | 0.988527i | \(0.548264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.79622 | 0.302428 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.3000 | −0.723907 | ||||||||
\(508\) | 14.9520 | 0.663387 | ||||||||
\(509\) | 38.8024 | 1.71988 | 0.859942 | − | 0.510391i | \(-0.170499\pi\) | ||||
0.859942 | + | 0.510391i | \(0.170499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.7581 | −1.05099 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.89595 | 0.172010 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.3989 | −0.722622 | ||||||||
\(516\) | 21.2573 | 0.935802 | ||||||||
\(517\) | 0.966013 | 0.0424852 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.7968 | −0.693404 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.2961 | −1.06443 | −0.532216 | − | 0.846609i | \(-0.678641\pi\) | ||||
−0.532216 | + | 0.846609i | \(0.678641\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.94682 | −0.303763 | −0.151882 | − | 0.988399i | \(-0.548533\pi\) | ||||
−0.151882 | + | 0.988399i | \(0.548533\pi\) | |||||||
\(524\) | 0.0370070 | 0.00161666 | ||||||||
\(525\) | 1.13641 | 0.0495970 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.04863 | 0.219922 | ||||||||
\(528\) | 1.80501 | 0.0785531 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.0049 | −0.607762 | ||||||||
\(532\) | 21.2210 | 0.920046 | ||||||||
\(533\) | −16.8166 | −0.728409 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.90381 | 0.384945 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.3204 | 1.09266 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.188293 | −0.00811035 | ||||||||
\(540\) | 4.28146 | 0.184245 | ||||||||
\(541\) | 10.0692 | 0.432908 | 0.216454 | − | 0.976293i | \(-0.430551\pi\) | ||||
0.216454 | + | 0.976293i | \(0.430551\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.7284 | −0.674970 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.8980 | −1.32352 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.63220 | −0.155302 | −0.0776509 | − | 0.996981i | \(-0.524742\pi\) | ||||
−0.0776509 | + | 0.996981i | \(0.524742\pi\) | |||||||
\(548\) | 9.23883 | 0.394663 | ||||||||
\(549\) | 6.69441 | 0.285710 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.89595 | −0.165973 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.7772 | −1.01111 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.02474 | 0.383079 | ||||||||
\(556\) | −5.02952 | −0.213299 | ||||||||
\(557\) | 17.0260 | 0.721413 | 0.360706 | − | 0.932679i | \(-0.382536\pi\) | ||||
0.360706 | + | 0.932679i | \(0.382536\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −57.5324 | −2.43336 | ||||||||
\(560\) | 23.3208 | 0.985485 | ||||||||
\(561\) | −1.46227 | −0.0617370 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.80051 | 0.244463 | 0.122231 | − | 0.992502i | \(-0.460995\pi\) | ||||
0.122231 | + | 0.992502i | \(0.460995\pi\) | |||||||
\(564\) | −4.28146 | −0.180282 | ||||||||
\(565\) | −6.49495 | −0.273245 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.72347 | 0.114375 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.6197 | 0.696736 | 0.348368 | − | 0.937358i | \(-0.386736\pi\) | ||||
0.348368 | + | 0.937358i | \(0.386736\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.26789 | 0.387849 | 0.193925 | − | 0.981016i | \(-0.437878\pi\) | ||||
0.193925 | + | 0.981016i | \(0.437878\pi\) | |||||||
\(572\) | −4.88522 | −0.204261 | ||||||||
\(573\) | 8.87122 | 0.370600 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.417266 | −0.0174012 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | 43.2098 | 1.79885 | 0.899423 | − | 0.437079i | \(-0.143987\pi\) | ||||
0.899423 | + | 0.437079i | \(0.143987\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.330935 | 0.0137532 | ||||||||
\(580\) | −4.28146 | −0.177778 | ||||||||
\(581\) | 1.09944 | 0.0456126 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.376586 | 0.0155966 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.5877 | −0.479091 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.2690 | −1.45571 | −0.727853 | − | 0.685733i | \(-0.759482\pi\) | ||||
−0.727853 | + | 0.685733i | \(0.759482\pi\) | |||||||
\(588\) | 0.834532 | 0.0344155 | ||||||||
\(589\) | 6.06988 | 0.250105 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.9414 | 0.655743 | ||||||||
\(592\) | −16.8629 | −0.693061 | ||||||||
\(593\) | 15.8508 | 0.650913 | 0.325457 | − | 0.945557i | \(-0.394482\pi\) | ||||
0.325457 | + | 0.945557i | \(0.394482\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.8926 | −0.774520 | ||||||||
\(596\) | 26.4950 | 1.08528 | ||||||||
\(597\) | −2.51537 | −0.102947 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.6357 | −1.49689 | −0.748447 | − | 0.663195i | \(-0.769200\pi\) | ||||
−0.748447 | + | 0.663195i | \(0.769200\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.28448 | −0.378722 | −0.189361 | − | 0.981908i | \(-0.560642\pi\) | ||||
−0.189361 | + | 0.981908i | \(0.560642\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.44693 | −0.221816 | ||||||||
\(604\) | 0.534565 | 0.0217511 | ||||||||
\(605\) | −23.1121 | −0.939642 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.75298 | −0.395861 | −0.197931 | − | 0.980216i | \(-0.563422\pi\) | ||||
−0.197931 | + | 0.980216i | \(0.563422\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.72347 | −0.110360 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.5877 | 0.468787 | ||||||||
\(612\) | 6.48092 | 0.261976 | ||||||||
\(613\) | −23.0624 | −0.931480 | −0.465740 | − | 0.884922i | \(-0.654212\pi\) | ||||
−0.465740 | + | 0.884922i | \(0.654212\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.65071 | −0.268182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.1963 | 1.25592 | 0.627959 | − | 0.778247i | \(-0.283891\pi\) | ||||
0.627959 | + | 0.778247i | \(0.283891\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.8368 | −0.837500 | −0.418750 | − | 0.908101i | \(-0.637532\pi\) | ||||
−0.418750 | + | 0.908101i | \(0.637532\pi\) | |||||||
\(620\) | 6.67051 | 0.267894 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.5066 | 0.461001 | ||||||||
\(624\) | 21.6518 | 0.866765 | ||||||||
\(625\) | −22.7396 | −0.909582 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.75806 | −0.0702102 | ||||||||
\(628\) | −32.8304 | −1.31007 | ||||||||
\(629\) | 13.6609 | 0.544695 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.18959 | −0.166785 | −0.0833926 | − | 0.996517i | \(-0.526576\pi\) | ||||
−0.0833926 | + | 0.996517i | \(0.526576\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.33587 | −0.212082 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.0041 | −0.635103 | ||||||||
\(636\) | −1.66906 | −0.0661827 | ||||||||
\(637\) | −2.25864 | −0.0894905 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.82528 | −0.0722070 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.9755 | 0.986475 | 0.493237 | − | 0.869895i | \(-0.335813\pi\) | ||||
0.493237 | + | 0.869895i | \(0.335813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.4455 | 0.490802 | 0.245401 | − | 0.969422i | \(-0.421080\pi\) | ||||
0.245401 | + | 0.969422i | \(0.421080\pi\) | |||||||
\(644\) | −5.44693 | −0.214639 | ||||||||
\(645\) | −22.7531 | −0.895904 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.3894 | −1.50924 | −0.754622 | − | 0.656160i | \(-0.772180\pi\) | ||||
−0.754622 | + | 0.656160i | \(0.772180\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.31977 | 0.248073 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.24316 | 0.166302 | ||||||||
\(652\) | −26.0877 | −1.02167 | ||||||||
\(653\) | 38.3414 | 1.50042 | 0.750208 | − | 0.661202i | \(-0.229954\pi\) | ||||
0.750208 | + | 0.661202i | \(0.229954\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0396110 | −0.00154773 | ||||||||
\(656\) | 12.4270 | 0.485192 | ||||||||
\(657\) | −8.72347 | −0.340335 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.3052 | −1.21948 | −0.609738 | − | 0.792603i | \(-0.708725\pi\) | ||||
−0.609738 | + | 0.792603i | \(0.708725\pi\) | |||||||
\(660\) | −1.93203 | −0.0752040 | ||||||||
\(661\) | −0.243763 | −0.00948129 | −0.00474065 | − | 0.999989i | \(-0.501509\pi\) | ||||
−0.00474065 | + | 0.999989i | \(0.501509\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.5404 | −0.681214 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.7142 | −0.880819 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 48.1062 | 1.86128 | ||||||||
\(669\) | −10.1272 | −0.391539 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.02088 | −0.116620 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.6506 | −0.641832 | −0.320916 | − | 0.947108i | \(-0.603991\pi\) | ||||
−0.320916 | + | 0.947108i | \(0.603991\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.417266 | 0.0160606 | ||||||||
\(676\) | −32.5999 | −1.25384 | ||||||||
\(677\) | 11.8162 | 0.454133 | 0.227066 | − | 0.973879i | \(-0.427087\pi\) | ||||
0.227066 | + | 0.973879i | \(0.427087\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.08885 | −0.195292 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.16849 | 0.313017 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.5343 | 1.43621 | 0.718106 | − | 0.695934i | \(-0.245009\pi\) | ||||
0.718106 | + | 0.695934i | \(0.245009\pi\) | |||||||
\(684\) | 7.79190 | 0.297931 | ||||||||
\(685\) | −9.88893 | −0.377837 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.5084 | −1.08766 | ||||||||
\(688\) | 42.5147 | 1.62086 | ||||||||
\(689\) | 4.51728 | 0.172095 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.1048 | −0.498531 | −0.249266 | − | 0.968435i | \(-0.580189\pi\) | ||||
−0.249266 | + | 0.968435i | \(0.580189\pi\) | |||||||
\(692\) | −31.5937 | −1.20101 | ||||||||
\(693\) | −1.22897 | −0.0466848 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.38343 | 0.204205 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.0673 | −0.381325 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.07723 | −0.0407444 | ||||||||
\(700\) | 2.27282 | 0.0859045 | ||||||||
\(701\) | 4.19113 | 0.158297 | 0.0791483 | − | 0.996863i | \(-0.474780\pi\) | ||||
0.0791483 | + | 0.996863i | \(0.474780\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.4243 | 0.619452 | ||||||||
\(704\) | 3.61003 | 0.136058 | ||||||||
\(705\) | 4.58273 | 0.172596 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.64624 | 0.325175 | ||||||||
\(708\) | −28.0099 | −1.05267 | ||||||||
\(709\) | 47.8449 | 1.79685 | 0.898426 | − | 0.439126i | \(-0.144712\pi\) | ||||
0.898426 | + | 0.439126i | \(0.144712\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.73048 | −0.327419 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.55800 | −0.0583475 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.22897 | 0.195553 | ||||||||
\(716\) | 50.6408 | 1.89253 | ||||||||
\(717\) | 28.8197 | 1.07629 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.5524 | 1.84799 | 0.923996 | − | 0.382402i | \(-0.124903\pi\) | ||||
0.923996 | + | 0.382402i | \(0.124903\pi\) | |||||||
\(720\) | 8.56293 | 0.319121 | ||||||||
\(721\) | −20.8629 | −0.776975 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.2388 | 0.641119 | ||||||||
\(724\) | −31.4568 | −1.16908 | ||||||||
\(725\) | −0.417266 | −0.0154969 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.3100 | 1.82881 | 0.914403 | − | 0.404805i | \(-0.132661\pi\) | ||||
0.914403 | + | 0.404805i | \(0.132661\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.4418 | −1.27387 | ||||||||
\(732\) | 13.3888 | 0.494865 | ||||||||
\(733\) | −5.79190 | −0.213929 | −0.106964 | − | 0.994263i | \(-0.534113\pi\) | ||||
−0.106964 | + | 0.994263i | \(0.534113\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.893255 | −0.0329482 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.45795 | 0.0905396 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.3623 | 1.15368 | 0.576841 | − | 0.816857i | \(-0.304285\pi\) | ||||
0.576841 | + | 0.816857i | \(0.304285\pi\) | |||||||
\(740\) | 18.0495 | 0.663512 | ||||||||
\(741\) | −21.0886 | −0.774708 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.2217 | 1.18210 | 0.591050 | − | 0.806635i | \(-0.298714\pi\) | ||||
0.591050 | + | 0.806635i | \(0.298714\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.3593 | −1.03900 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.403693 | 0.0147703 | ||||||||
\(748\) | −2.92454 | −0.106932 | ||||||||
\(749\) | 11.3275 | 0.413899 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0644 | 0.367257 | 0.183628 | − | 0.982996i | \(-0.441216\pi\) | ||||
0.183628 | + | 0.982996i | \(0.441216\pi\) | |||||||
\(752\) | −8.56293 | −0.312258 | ||||||||
\(753\) | 11.7552 | 0.428384 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.572180 | −0.0208238 | ||||||||
\(756\) | 5.44693 | 0.198103 | ||||||||
\(757\) | 12.9551 | 0.470862 | 0.235431 | − | 0.971891i | \(-0.424350\pi\) | ||||
0.235431 | + | 0.971891i | \(0.424350\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.451253 | 0.0163795 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.0304 | −0.943602 | −0.471801 | − | 0.881705i | \(-0.656396\pi\) | ||||
−0.471801 | + | 0.881705i | \(0.656396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.3088 | −1.42307 | ||||||||
\(764\) | 17.7424 | 0.641899 | ||||||||
\(765\) | −6.93696 | −0.250806 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 75.8079 | 2.73726 | ||||||||
\(768\) | −16.0000 | −0.577350 | ||||||||
\(769\) | 5.79831 | 0.209092 | 0.104546 | − | 0.994520i | \(-0.466661\pi\) | ||||
0.104546 | + | 0.994520i | \(0.466661\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.34558 | −0.336573 | ||||||||
\(772\) | 0.661870 | 0.0238212 | ||||||||
\(773\) | 44.6714 | 1.60672 | 0.803358 | − | 0.595496i | \(-0.203044\pi\) | ||||
0.803358 | + | 0.595496i | \(0.203044\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.650100 | 0.0233523 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.4814 | 0.411892 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.1037 | −0.433661 | ||||||||
\(780\) | −23.1753 | −0.829810 | ||||||||
\(781\) | 0.823664 | 0.0294730 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 1.66906 | 0.0596095 | ||||||||
\(785\) | 35.1405 | 1.25422 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.7171 | 0.595900 | 0.297950 | − | 0.954582i | \(-0.403697\pi\) | ||||
0.297950 | + | 0.954582i | \(0.403697\pi\) | |||||||
\(788\) | 31.8828 | 1.13578 | ||||||||
\(789\) | 21.2956 | 0.758145 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.26296 | −0.293797 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.2365 | −1.28679 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.78651 | 0.0633610 | ||||||||
\(796\) | −5.03074 | −0.178310 | ||||||||
\(797\) | −31.3789 | −1.11150 | −0.555748 | − | 0.831351i | \(-0.687568\pi\) | ||||
−0.555748 | + | 0.831351i | \(0.687568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.93696 | 0.245412 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.22498 | 0.149282 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.93649 | 0.138916 | ||||||||
\(804\) | −10.8939 | −0.384197 | ||||||||
\(805\) | 5.83021 | 0.205488 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.00000 | −0.140807 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.4174 | −0.366257 | −0.183128 | − | 0.983089i | \(-0.558622\pi\) | ||||
−0.183128 | + | 0.983089i | \(0.558622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.6886 | −1.42877 | −0.714386 | − | 0.699752i | \(-0.753294\pi\) | ||||
−0.714386 | + | 0.699752i | \(0.753294\pi\) | |||||||
\(812\) | −5.44693 | −0.191150 | ||||||||
\(813\) | −24.1783 | −0.847972 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.9234 | 0.978113 | ||||||||
\(816\) | 12.9618 | 0.453755 | ||||||||
\(817\) | −41.4088 | −1.44871 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.7420 | −0.515126 | ||||||||
\(820\) | −13.3014 | −0.464506 | ||||||||
\(821\) | 9.34688 | 0.326208 | 0.163104 | − | 0.986609i | \(-0.447849\pi\) | ||||
0.163104 | + | 0.986609i | \(0.447849\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.0610 | −1.50101 | −0.750506 | − | 0.660863i | \(-0.770190\pi\) | ||||
−0.750506 | + | 0.660863i | \(0.770190\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.188293 | −0.00655551 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.3168 | 1.81923 | 0.909617 | − | 0.415447i | \(-0.136375\pi\) | ||||
0.909617 | + | 0.415447i | \(0.136375\pi\) | |||||||
\(828\) | −2.00000 | −0.0695048 | ||||||||
\(829\) | 26.5597 | 0.922456 | 0.461228 | − | 0.887282i | \(-0.347409\pi\) | ||||
0.461228 | + | 0.887282i | \(0.347409\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.6507 | −0.612296 | ||||||||
\(832\) | 43.3036 | 1.50128 | ||||||||
\(833\) | −1.35213 | −0.0468487 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −51.4912 | −1.78193 | ||||||||
\(836\) | −3.51612 | −0.121608 | ||||||||
\(837\) | 1.55800 | 0.0538523 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.9318 | −1.34407 | −0.672037 | − | 0.740517i | \(-0.734581\pi\) | ||||
−0.672037 | + | 0.740517i | \(0.734581\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.8784 | −0.546880 | ||||||||
\(844\) | −10.6717 | −0.367336 | ||||||||
\(845\) | 34.8939 | 1.20039 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.4035 | −1.01032 | ||||||||
\(848\) | −3.33813 | −0.114632 | ||||||||
\(849\) | 9.88893 | 0.339387 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.21572 | −0.144513 | ||||||||
\(852\) | −3.65056 | −0.125066 | ||||||||
\(853\) | 33.8334 | 1.15843 | 0.579216 | − | 0.815174i | \(-0.303359\pi\) | ||||
0.579216 | + | 0.815174i | \(0.303359\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.34019 | −0.285228 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.9332 | −1.09082 | −0.545409 | − | 0.838170i | \(-0.683626\pi\) | ||||
−0.545409 | + | 0.838170i | \(0.683626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.13194 | 0.106860 | 0.0534302 | − | 0.998572i | \(-0.482985\pi\) | ||||
0.0534302 | + | 0.998572i | \(0.482985\pi\) | |||||||
\(860\) | −45.5063 | −1.55175 | ||||||||
\(861\) | −8.46111 | −0.288354 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.4962 | −1.17426 | −0.587132 | − | 0.809491i | \(-0.699743\pi\) | ||||
−0.587132 | + | 0.809491i | \(0.699743\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.8168 | 1.14981 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.49942 | 0.220732 | ||||||||
\(868\) | 8.48631 | 0.288044 | ||||||||
\(869\) | 3.93966 | 0.133644 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.4839 | 0.999025 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.86852 | −0.0632398 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.5838 | −1.06773 | ||||||||
\(876\) | −17.4469 | −0.589477 | ||||||||
\(877\) | −10.6747 | −0.360461 | −0.180230 | − | 0.983624i | \(-0.557684\pi\) | ||||
−0.180230 | + | 0.983624i | \(0.557684\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.5899 | −0.390918 | ||||||||
\(880\) | −3.86405 | −0.130257 | ||||||||
\(881\) | −18.4669 | −0.622166 | −0.311083 | − | 0.950383i | \(-0.600692\pi\) | ||||
−0.311083 | + | 0.950383i | \(0.600692\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.3253 | 0.885917 | 0.442959 | − | 0.896542i | \(-0.353929\pi\) | ||||
0.442959 | + | 0.896542i | \(0.353929\pi\) | |||||||
\(884\) | −35.0809 | −1.17990 | ||||||||
\(885\) | 29.9808 | 1.00779 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.0617 | 0.841491 | 0.420745 | − | 0.907179i | \(-0.361769\pi\) | ||||
0.420745 | + | 0.907179i | \(0.361769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.3606 | −0.682873 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.451253 | −0.0151176 | ||||||||
\(892\) | −20.2543 | −0.678165 | ||||||||
\(893\) | 8.34019 | 0.279094 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −54.2042 | −1.81184 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.41294 | 0.180733 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.55800 | −0.0519622 | ||||||||
\(900\) | 0.834532 | 0.0278177 | ||||||||
\(901\) | 2.70427 | 0.0900922 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −28.9468 | −0.963290 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.6703 | 1.11924 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.3691 | −1.14121 | −0.570604 | − | 0.821225i | \(-0.693291\pi\) | ||||
−0.570604 | + | 0.821225i | \(0.693291\pi\) | |||||||
\(908\) | 16.3370 | 0.542162 | ||||||||
\(909\) | 3.17472 | 0.105299 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.5447 | 0.746941 | 0.373470 | − | 0.927642i | \(-0.378168\pi\) | ||||
0.373470 | + | 0.927642i | \(0.378168\pi\) | |||||||
\(912\) | 15.5838 | 0.516031 | ||||||||
\(913\) | −0.182168 | −0.00602887 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.3309 | −0.473766 | ||||||||
\(916\) | −57.0167 | −1.88388 | ||||||||
\(917\) | −0.0503936 | −0.00166414 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.3790 | −0.573279 | −0.286639 | − | 0.958039i | \(-0.592538\pi\) | ||||
−0.286639 | + | 0.958039i | \(0.592538\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.4617 | −1.00375 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.88014 | 0.325209 | ||||||||
\(924\) | −2.45795 | −0.0808605 | ||||||||
\(925\) | 1.75908 | 0.0578382 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.66042 | −0.251601 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.4583 | 1.45863 | 0.729315 | − | 0.684178i | \(-0.239839\pi\) | ||||
0.729315 | + | 0.684178i | \(0.239839\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.62565 | −0.0532785 | ||||||||
\(932\) | −2.15445 | −0.0705714 | ||||||||
\(933\) | −14.4314 | −0.472464 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.13033 | 0.102373 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.0111 | 1.43778 | 0.718890 | − | 0.695124i | \(-0.244651\pi\) | ||||
0.718890 | + | 0.695124i | \(0.244651\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.1844 | −0.789229 | ||||||||
\(940\) | 9.16547 | 0.298945 | ||||||||
\(941\) | 43.8742 | 1.43026 | 0.715129 | − | 0.698992i | \(-0.246368\pi\) | ||||
0.715129 | + | 0.698992i | \(0.246368\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.10674 | 0.101170 | ||||||||
\(944\) | −56.0197 | −1.82329 | ||||||||
\(945\) | −5.83021 | −0.189657 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.9967 | −1.75466 | −0.877329 | − | 0.479889i | \(-0.840677\pi\) | ||||
−0.877329 | + | 0.479889i | \(0.840677\pi\) | |||||||
\(948\) | −17.4610 | −0.567106 | ||||||||
\(949\) | 47.2196 | 1.53281 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.1452 | 0.653253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.62727 | 0.0527126 | 0.0263563 | − | 0.999653i | \(-0.491610\pi\) | ||||
0.0263563 | + | 0.999653i | \(0.491610\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.9909 | −0.614531 | ||||||||
\(956\) | 57.6393 | 1.86419 | ||||||||
\(957\) | 0.451253 | 0.0145870 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.5808 | −0.406256 | ||||||||
\(960\) | 17.1259 | 0.552735 | ||||||||
\(961\) | −28.5726 | −0.921698 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.15924 | 0.134029 | ||||||||
\(964\) | 34.4777 | 1.11045 | ||||||||
\(965\) | −0.708443 | −0.0228056 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.3204 | 0.717775 | 0.358888 | − | 0.933381i | \(-0.383156\pi\) | ||||
0.358888 | + | 0.933381i | \(0.383156\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.6247 | −0.405563 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.5661 | −1.17346 | −0.586731 | − | 0.809782i | \(-0.699585\pi\) | ||||
−0.586731 | + | 0.809782i | \(0.699585\pi\) | |||||||
\(972\) | 2.00000 | 0.0641500 | ||||||||
\(973\) | 6.84886 | 0.219564 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.25864 | −0.0723343 | ||||||||
\(976\) | 26.7776 | 0.857131 | ||||||||
\(977\) | −14.7024 | −0.470373 | −0.235186 | − | 0.971950i | \(-0.575570\pi\) | ||||
−0.235186 | + | 0.971950i | \(0.575570\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.90653 | −0.0609331 | ||||||||
\(980\) | −1.78651 | −0.0570680 | ||||||||
\(981\) | −14.4334 | −0.460822 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.76221 | −0.311366 | −0.155683 | − | 0.987807i | \(-0.549758\pi\) | ||||
−0.155683 | + | 0.987807i | \(0.549758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.1263 | −1.08735 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.83021 | 0.185578 | ||||||||
\(988\) | −42.1771 | −1.34183 | ||||||||
\(989\) | 10.6287 | 0.337972 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.6899 | 0.403109 | 0.201555 | − | 0.979477i | \(-0.435401\pi\) | ||||
0.201555 | + | 0.979477i | \(0.435401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.9618 | −0.728672 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.38473 | 0.170707 | ||||||||
\(996\) | 0.807385 | 0.0255830 | ||||||||
\(997\) | 18.8584 | 0.597252 | 0.298626 | − | 0.954370i | \(-0.403472\pi\) | ||||
0.298626 | + | 0.954370i | \(0.403472\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.21572 | 0.133380 |
(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 | 2001.2.a.g.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 6003.2.a.g.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.g.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6003.2.a.g.1.1 | 4 | 3.2 | odd | 2 |