Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.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: | \(54.8093159474\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.2172244.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 8x^{3} + 16x^{2} + 5x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3432) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.758834\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-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 | ||||||||
\(5\) | 1.82899 | 0.817950 | 0.408975 | − | 0.912545i | \(-0.365886\pi\) | ||||
0.408975 | + | 0.912545i | \(0.365886\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.862883 | 0.326139 | 0.163070 | − | 0.986615i | \(-0.447860\pi\) | ||||
0.163070 | + | 0.986615i | \(0.447860\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.82899 | 0.472244 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.551559 | 0.133773 | 0.0668863 | − | 0.997761i | \(-0.478694\pi\) | ||||
0.0668863 | + | 0.997761i | \(0.478694\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.300773 | 0.0690021 | 0.0345011 | − | 0.999405i | \(-0.489016\pi\) | ||||
0.0345011 | + | 0.999405i | \(0.489016\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.862883 | 0.188297 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.71122 | 1.60790 | 0.803951 | − | 0.594696i | \(-0.202728\pi\) | ||||
0.803951 | + | 0.594696i | \(0.202728\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.65479 | −0.330957 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.56356 | −0.847431 | −0.423716 | − | 0.905795i | \(-0.639274\pi\) | ||||
−0.423716 | + | 0.905795i | \(0.639274\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.391103 | −0.0702441 | −0.0351221 | − | 0.999383i | \(-0.511182\pi\) | ||||
−0.0351221 | + | 0.999383i | \(0.511182\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.57821 | 0.266766 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.60944 | 1.57978 | 0.789891 | − | 0.613247i | \(-0.210137\pi\) | ||||
0.789891 | + | 0.613247i | \(0.210137\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.29667 | 0.827201 | 0.413601 | − | 0.910458i | \(-0.364271\pi\) | ||||
0.413601 | + | 0.910458i | \(0.364271\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7603 | 1.79343 | 0.896715 | − | 0.442608i | \(-0.145947\pi\) | ||||
0.896715 | + | 0.442608i | \(0.145947\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.82899 | 0.272650 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.50633 | −0.949045 | −0.474523 | − | 0.880243i | \(-0.657379\pi\) | ||||
−0.474523 | + | 0.880243i | \(0.657379\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.25543 | −0.893633 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.551559 | 0.0772337 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.76446 | −1.34125 | −0.670626 | − | 0.741796i | \(-0.733974\pi\) | ||||
−0.670626 | + | 0.741796i | \(0.733974\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.82899 | 0.246621 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.300773 | 0.0398384 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.49433 | 0.845490 | 0.422745 | − | 0.906249i | \(-0.361067\pi\) | ||||
0.422745 | + | 0.906249i | \(0.361067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.39575 | −0.946929 | −0.473464 | − | 0.880813i | \(-0.656997\pi\) | ||||
−0.473464 | + | 0.880813i | \(0.656997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.862883 | 0.108713 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.82899 | 0.226859 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.53702 | −1.04296 | −0.521481 | − | 0.853263i | \(-0.674620\pi\) | ||||
−0.521481 | + | 0.853263i | \(0.674620\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.71122 | 0.928322 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.58545 | 0.425515 | 0.212757 | − | 0.977105i | \(-0.431756\pi\) | ||||
0.212757 | + | 0.977105i | \(0.431756\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.795102 | 0.0930597 | 0.0465298 | − | 0.998917i | \(-0.485184\pi\) | ||||
0.0465298 | + | 0.998917i | \(0.485184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.65479 | −0.191078 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.862883 | 0.0983347 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.81445 | 1.10421 | 0.552106 | − | 0.833774i | \(-0.313824\pi\) | ||||
0.552106 | + | 0.833774i | \(0.313824\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.49023 | −0.602631 | −0.301315 | − | 0.953525i | \(-0.597426\pi\) | ||||
−0.301315 | + | 0.953525i | \(0.597426\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00880 | 0.109419 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.56356 | −0.489265 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.6585 | 1.44780 | 0.723901 | − | 0.689904i | \(-0.242347\pi\) | ||||
0.723901 | + | 0.689904i | \(0.242347\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.862883 | 0.0904547 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.391103 | −0.0405555 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.550112 | 0.0564403 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.57411 | 0.261361 | 0.130681 | − | 0.991425i | \(-0.458284\pi\) | ||||
0.130681 | + | 0.991425i | \(0.458284\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.8709 | 1.47971 | 0.739854 | − | 0.672767i | \(-0.234894\pi\) | ||||
0.739854 | + | 0.672767i | \(0.234894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.83634 | 0.279473 | 0.139737 | − | 0.990189i | \(-0.455374\pi\) | ||||
0.139737 | + | 0.990189i | \(0.455374\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.57821 | 0.154017 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.2024 | 1.46967 | 0.734833 | − | 0.678248i | \(-0.237260\pi\) | ||||
0.734833 | + | 0.678248i | \(0.237260\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.11832 | −0.202898 | −0.101449 | − | 0.994841i | \(-0.532348\pi\) | ||||
−0.101449 | + | 0.994841i | \(0.532348\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.60944 | 0.912088 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.5650 | −1.37016 | −0.685080 | − | 0.728468i | \(-0.740233\pi\) | ||||
−0.685080 | + | 0.728468i | \(0.740233\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.1038 | 1.31518 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.475931 | 0.0436285 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.29667 | 0.477585 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1716 | −1.08866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.638797 | −0.0566840 | −0.0283420 | − | 0.999598i | \(-0.509023\pi\) | ||||
−0.0283420 | + | 0.999598i | \(0.509023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.7603 | 1.03544 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.58611 | −0.750171 | −0.375086 | − | 0.926990i | \(-0.622387\pi\) | ||||
−0.375086 | + | 0.926990i | \(0.622387\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.259532 | 0.0225043 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.82899 | 0.157415 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.9652 | −1.27856 | −0.639282 | − | 0.768972i | \(-0.720768\pi\) | ||||
−0.639282 | + | 0.768972i | \(0.720768\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.26144 | 0.785546 | 0.392773 | − | 0.919636i | \(-0.371516\pi\) | ||||
0.392773 | + | 0.919636i | \(0.371516\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.50633 | −0.547932 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.34671 | −0.693157 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.25543 | −0.515939 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.73456 | −0.715563 | −0.357782 | − | 0.933805i | \(-0.616467\pi\) | ||||
−0.357782 | + | 0.933805i | \(0.616467\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.46033 | 0.688492 | 0.344246 | − | 0.938880i | \(-0.388135\pi\) | ||||
0.344246 | + | 0.938880i | \(0.388135\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.551559 | 0.0445909 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.715324 | −0.0574562 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.0020 | 1.27710 | 0.638549 | − | 0.769581i | \(-0.279535\pi\) | ||||
0.638549 | + | 0.769581i | \(0.279535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.76446 | −0.774372 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.65389 | 0.524400 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.89513 | 0.461742 | 0.230871 | − | 0.972984i | \(-0.425842\pi\) | ||||
0.230871 | + | 0.972984i | \(0.425842\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.82899 | 0.142387 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.402553 | 0.0311505 | 0.0155752 | − | 0.999879i | \(-0.495042\pi\) | ||||
0.0155752 | + | 0.999879i | \(0.495042\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.300773 | 0.0230007 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.1794 | −1.68627 | −0.843134 | − | 0.537703i | \(-0.819292\pi\) | ||||
−0.843134 | + | 0.537703i | \(0.819292\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.42789 | −0.107938 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.49433 | 0.488144 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.18156 | 0.462031 | 0.231016 | − | 0.972950i | \(-0.425795\pi\) | ||||
0.231016 | + | 0.972950i | \(0.425795\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.7958 | −1.32275 | −0.661374 | − | 0.750056i | \(-0.730026\pi\) | ||||
−0.661374 | + | 0.750056i | \(0.730026\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.39575 | −0.546710 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.5756 | 1.29218 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.551559 | 0.0403340 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.862883 | 0.0627655 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.2377 | 1.60906 | 0.804531 | − | 0.593910i | \(-0.202417\pi\) | ||||
0.804531 | + | 0.593910i | \(0.202417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.95876 | −0.140995 | −0.0704973 | − | 0.997512i | \(-0.522459\pi\) | ||||
−0.0704973 | + | 0.997512i | \(0.522459\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.82899 | 0.130977 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0652 | 1.28709 | 0.643547 | − | 0.765406i | \(-0.277462\pi\) | ||||
0.643547 | + | 0.765406i | \(0.277462\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.7521 | −1.61285 | −0.806425 | − | 0.591336i | \(-0.798601\pi\) | ||||
−0.806425 | + | 0.591336i | \(0.798601\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.53702 | −0.602155 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.93782 | −0.276381 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.68758 | 0.676610 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.71122 | 0.535967 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.300773 | 0.0208049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.7562 | −1.84197 | −0.920987 | − | 0.389594i | \(-0.872615\pi\) | ||||
−0.920987 | + | 0.389594i | \(0.872615\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.58545 | 0.245671 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.5095 | 1.46694 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.337476 | −0.0229094 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.795102 | 0.0537280 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.551559 | 0.0371019 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.84264 | 0.257322 | 0.128661 | − | 0.991689i | \(-0.458932\pi\) | ||||
0.128661 | + | 0.991689i | \(0.458932\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.65479 | −0.110319 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.8941 | 1.51954 | 0.759768 | − | 0.650194i | \(-0.225312\pi\) | ||||
0.759768 | + | 0.650194i | \(0.225312\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.22979 | −0.345594 | −0.172797 | − | 0.984957i | \(-0.555281\pi\) | ||||
−0.172797 | + | 0.984957i | \(0.555281\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.862883 | 0.0567735 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.48832 | 0.425064 | 0.212532 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212532 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.9000 | −0.776272 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.81445 | 0.637517 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.1498 | 1.82086 | 0.910429 | − | 0.413666i | \(-0.135752\pi\) | ||||
0.910429 | + | 0.413666i | \(0.135752\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.31293 | 0.406652 | 0.203326 | − | 0.979111i | \(-0.434825\pi\) | ||||
0.203326 | + | 0.979111i | \(0.434825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.4411 | −0.730948 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.300773 | 0.0191377 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.49023 | −0.347929 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.48709 | −0.283222 | −0.141611 | − | 0.989922i | \(-0.545228\pi\) | ||||
−0.141611 | + | 0.989922i | \(0.545228\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.71122 | 0.484801 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.00880 | 0.0631733 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.4505 | −1.40043 | −0.700213 | − | 0.713934i | \(-0.746912\pi\) | ||||
−0.700213 | + | 0.713934i | \(0.746912\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.29183 | 0.515229 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.56356 | −0.282477 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0854 | 0.745216 | 0.372608 | − | 0.927989i | \(-0.378464\pi\) | ||||
0.372608 | + | 0.927989i | \(0.378464\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.8591 | −1.09708 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.6585 | 0.835889 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.7885 | 1.32847 | 0.664233 | − | 0.747526i | \(-0.268758\pi\) | ||||
0.664233 | + | 0.747526i | \(0.268758\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.38761 | −0.570257 | −0.285128 | − | 0.958489i | \(-0.592036\pi\) | ||||
−0.285128 | + | 0.958489i | \(0.592036\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.862883 | 0.0522241 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.65479 | −0.0997873 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.07524 | 0.244857 | 0.122429 | − | 0.992477i | \(-0.460932\pi\) | ||||
0.122429 | + | 0.992477i | \(0.460932\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.391103 | −0.0234147 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.7933 | −1.47904 | −0.739522 | − | 0.673132i | \(-0.764949\pi\) | ||||
−0.739522 | + | 0.673132i | \(0.764949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3247 | 0.673181 | 0.336591 | − | 0.941651i | \(-0.390726\pi\) | ||||
0.336591 | + | 0.941651i | \(0.390726\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.550112 | 0.0325858 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.57041 | 0.269783 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6958 | −0.982105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.57411 | 0.150897 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.05389 | 0.412093 | 0.206046 | − | 0.978542i | \(-0.433940\pi\) | ||||
0.206046 | + | 0.978542i | \(0.433940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.8781 | 0.691569 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.71122 | 0.445952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.1478 | 0.584908 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.8709 | 0.854310 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.5268 | −0.774541 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.4440 | 1.16680 | 0.583402 | − | 0.812184i | \(-0.301721\pi\) | ||||
0.583402 | + | 0.812184i | \(0.301721\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.83634 | 0.161354 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.9342 | −0.903546 | −0.451773 | − | 0.892133i | \(-0.649208\pi\) | ||||
−0.451773 | + | 0.892133i | \(0.649208\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.1754 | 1.47952 | 0.739761 | − | 0.672870i | \(-0.234939\pi\) | ||||
0.739761 | + | 0.672870i | \(0.234939\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.57821 | 0.0889219 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.2142 | 0.910683 | 0.455341 | − | 0.890317i | \(-0.349517\pi\) | ||||
0.455341 | + | 0.890317i | \(0.349517\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.56356 | −0.255510 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.2024 | 0.848513 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.165894 | 0.00923060 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.65479 | −0.0917910 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.11832 | −0.117143 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.61420 | −0.309521 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.9140 | −1.25947 | −0.629733 | − | 0.776812i | \(-0.716836\pi\) | ||||
−0.629733 | + | 0.776812i | \(0.716836\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.60944 | 0.526594 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.6141 | −0.853092 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1335 | −0.933322 | −0.466661 | − | 0.884436i | \(-0.654543\pi\) | ||||
−0.466661 | + | 0.884436i | \(0.654543\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.5650 | −0.791062 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.391103 | −0.0211794 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4379 | −0.617588 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.1038 | 0.759322 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.4563 | 0.937103 | 0.468551 | − | 0.883436i | \(-0.344776\pi\) | ||||
0.468551 | + | 0.883436i | \(0.344776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.9240 | −1.17357 | −0.586783 | − | 0.809744i | \(-0.699606\pi\) | ||||
−0.586783 | + | 0.809744i | \(0.699606\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.8729 | −1.74965 | −0.874824 | − | 0.484442i | \(-0.839023\pi\) | ||||
−0.874824 | + | 0.484442i | \(0.839023\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.55776 | 0.348050 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.475931 | 0.0251889 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.28533 | −0.437283 | −0.218642 | − | 0.975805i | \(-0.570163\pi\) | ||||
−0.218642 | + | 0.975805i | \(0.570163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9095 | −0.995239 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.45424 | 0.0761182 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.5967 | 0.918541 | 0.459270 | − | 0.888297i | \(-0.348111\pi\) | ||||
0.459270 | + | 0.888297i | \(0.348111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.29667 | 0.275734 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.42559 | −0.437435 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5890 | −0.962502 | −0.481251 | − | 0.876583i | \(-0.659817\pi\) | ||||
−0.481251 | + | 0.876583i | \(0.659817\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1716 | −0.628536 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.56356 | −0.235035 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.3018 | −1.71060 | −0.855300 | − | 0.518134i | \(-0.826627\pi\) | ||||
−0.855300 | + | 0.518134i | \(0.826627\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.638797 | −0.0327265 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.9082 | 0.710677 | 0.355339 | − | 0.934738i | \(-0.384366\pi\) | ||||
0.355339 | + | 0.934738i | \(0.384366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.57821 | 0.0804329 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.7603 | 0.597810 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.0627 | 1.42283 | 0.711417 | − | 0.702770i | \(-0.248054\pi\) | ||||
0.711417 | + | 0.702770i | \(0.248054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.25319 | 0.215093 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.58611 | −0.433112 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.9506 | 0.903191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7618 | −1.19257 | −0.596284 | − | 0.802773i | \(-0.703357\pi\) | ||||
−0.596284 | + | 0.802773i | \(0.703357\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.259532 | 0.0129929 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.0470 | −1.45054 | −0.725270 | − | 0.688465i | \(-0.758285\pi\) | ||||
−0.725270 | + | 0.688465i | \(0.758285\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.391103 | −0.0194822 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.82899 | 0.0908834 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.60944 | 0.476322 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.0997 | 1.04331 | 0.521657 | − | 0.853155i | \(-0.325314\pi\) | ||||
0.521657 | + | 0.853155i | \(0.325314\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.9652 | −0.738179 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.60385 | 0.275747 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0416 | −0.492922 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.26144 | 0.453535 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.5151 | −1.14879 | −0.574394 | − | 0.818579i | \(-0.694762\pi\) | ||||
−0.574394 | + | 0.818579i | \(0.694762\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0322 | 1.65863 | 0.829315 | − | 0.558782i | \(-0.188731\pi\) | ||||
0.829315 | + | 0.558782i | \(0.188731\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.50633 | −0.316348 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.912712 | −0.0442730 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.38167 | −0.308831 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.920660 | 0.0443466 | 0.0221733 | − | 0.999754i | \(-0.492941\pi\) | ||||
0.0221733 | + | 0.999754i | \(0.492941\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.7393 | 1.38112 | 0.690560 | − | 0.723275i | \(-0.257364\pi\) | ||||
0.690560 | + | 0.723275i | \(0.257364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.34671 | −0.400194 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.31933 | 0.110949 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.91779 | −0.425623 | −0.212811 | − | 0.977093i | \(-0.568262\pi\) | ||||
−0.212811 | + | 0.977093i | \(0.568262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.25543 | −0.297878 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.42885 | −0.0678867 | −0.0339433 | − | 0.999424i | \(-0.510807\pi\) | ||||
−0.0339433 | + | 0.999424i | \(0.510807\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.9814 | 1.18423 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.73456 | −0.413131 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.4742 | −1.48536 | −0.742680 | − | 0.669647i | \(-0.766446\pi\) | ||||
−0.742680 | + | 0.669647i | \(0.766446\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.29667 | 0.249411 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.46033 | 0.397501 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.57821 | 0.0739875 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.6132 | 1.10458 | 0.552290 | − | 0.833652i | \(-0.313754\pi\) | ||||
0.552290 | + | 0.833652i | \(0.313754\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.551559 | 0.0257446 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.90904 | −0.228637 | −0.114318 | − | 0.993444i | \(-0.536468\pi\) | ||||
−0.114318 | + | 0.993444i | \(0.536468\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.4072 | −0.623085 | −0.311543 | − | 0.950232i | \(-0.600846\pi\) | ||||
−0.311543 | + | 0.950232i | \(0.600846\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.715324 | −0.0331724 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.0824 | 1.34577 | 0.672887 | − | 0.739745i | \(-0.265054\pi\) | ||||
0.672887 | + | 0.739745i | \(0.265054\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.36645 | −0.340151 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0020 | 0.737333 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.7603 | 0.540740 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.497715 | −0.0228367 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.76446 | −0.447084 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.8915 | 1.59423 | 0.797116 | − | 0.603826i | \(-0.206358\pi\) | ||||
0.797116 | + | 0.603826i | \(0.206358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.60944 | 0.438153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.65389 | 0.302762 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.70802 | 0.213780 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.3699 | 1.42151 | 0.710753 | − | 0.703441i | \(-0.248354\pi\) | ||||
0.710753 | + | 0.703441i | \(0.248354\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.89513 | 0.266587 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.4504 | 1.28395 | 0.641974 | − | 0.766726i | \(-0.278116\pi\) | ||||
0.641974 | + | 0.766726i | \(0.278116\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.51707 | −0.113363 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.82899 | 0.0822071 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.09382 | 0.138777 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.7818 | −1.19892 | −0.599460 | − | 0.800405i | \(-0.704618\pi\) | ||||
−0.599460 | + | 0.800405i | \(0.704618\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.402553 | 0.0179847 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.685123 | −0.0305481 | −0.0152741 | − | 0.999883i | \(-0.504862\pi\) | ||||
−0.0152741 | + | 0.999883i | \(0.504862\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.1987 | 1.21033 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.33920 | 0.325304 | 0.162652 | − | 0.986683i | \(-0.447995\pi\) | ||||
0.162652 | + | 0.986683i | \(0.447995\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.686080 | 0.0303504 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.300773 | 0.0132795 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.18765 | 0.228595 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.50633 | −0.286148 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.1794 | −0.973568 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.64738 | 0.203606 | 0.101803 | − | 0.994805i | \(-0.467539\pi\) | ||||
0.101803 | + | 0.994805i | \(0.467539\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.4724 | −1.28874 | −0.644370 | − | 0.764714i | \(-0.722880\pi\) | ||||
−0.644370 | + | 0.764714i | \(0.722880\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.42789 | −0.0623181 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.215716 | −0.00939674 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.4630 | 1.58535 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.49433 | 0.281830 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.29667 | 0.229424 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.8050 | 1.20211 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.18156 | 0.266754 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.25543 | −0.269441 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.9737 | 0.471798 | 0.235899 | − | 0.971778i | \(-0.424197\pi\) | ||||
0.235899 | + | 0.971778i | \(0.424197\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.7958 | −0.763689 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.87438 | −0.165960 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.7231 | 0.458487 | 0.229244 | − | 0.973369i | \(-0.426375\pi\) | ||||
0.229244 | + | 0.973369i | \(0.426375\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.39575 | −0.315643 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.37260 | −0.0584746 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.46872 | 0.360127 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.5756 | 0.746043 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.8392 | −0.544016 | −0.272008 | − | 0.962295i | \(-0.587688\pi\) | ||||
−0.272008 | + | 0.962295i | \(0.587688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.7603 | 0.497408 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.551559 | 0.0232868 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.32091 | −0.350685 | −0.175342 | − | 0.984508i | \(-0.556103\pi\) | ||||
−0.175342 | + | 0.984508i | \(0.556103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.6393 | −1.12072 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.862883 | 0.0362377 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.9917 | −0.544642 | −0.272321 | − | 0.962206i | \(-0.587791\pi\) | ||||
−0.272321 | + | 0.962206i | \(0.587791\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.9797 | −1.42200 | −0.711002 | − | 0.703190i | \(-0.751759\pi\) | ||||
−0.711002 | + | 0.703190i | \(0.751759\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.2377 | 0.928993 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.7604 | −0.532146 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.9415 | 1.41300 | 0.706502 | − | 0.707711i | \(-0.250272\pi\) | ||||
0.706502 | + | 0.707711i | \(0.250272\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.95876 | −0.0814032 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.73743 | −0.196542 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.76446 | −0.404403 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.82899 | 0.0756195 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.7614 | −1.51730 | −0.758652 | − | 0.651496i | \(-0.774142\pi\) | ||||
−0.758652 | + | 0.651496i | \(0.774142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.117633 | −0.00484699 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0652 | 0.743105 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.4759 | 1.45682 | 0.728410 | − | 0.685142i | \(-0.240260\pi\) | ||||
0.728410 | + | 0.685142i | \(0.240260\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.870474 | 0.0356860 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.7521 | −0.931180 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.54787 | −0.226680 | −0.113340 | − | 0.993556i | \(-0.536155\pi\) | ||||
−0.113340 | + | 0.993556i | \(0.536155\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0593 | 0.859028 | 0.429514 | − | 0.903060i | \(-0.358685\pi\) | ||||
0.429514 | + | 0.903060i | \(0.358685\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.53702 | −0.347654 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.82899 | 0.0743591 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.638797 | −0.0259280 | −0.0129640 | − | 0.999916i | \(-0.504127\pi\) | ||||
−0.0129640 | + | 0.999916i | \(0.504127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.93782 | −0.159568 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.50633 | −0.263218 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2683 | −0.616682 | −0.308341 | − | 0.951276i | \(-0.599774\pi\) | ||||
−0.308341 | + | 0.951276i | \(0.599774\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.68758 | 0.390641 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.2360 | 0.693895 | 0.346948 | − | 0.937885i | \(-0.387218\pi\) | ||||
0.346948 | + | 0.937885i | \(0.387218\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.8099 | −0.635452 | −0.317726 | − | 0.948183i | \(-0.602919\pi\) | ||||
−0.317726 | + | 0.948183i | \(0.602919\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.71122 | 0.309441 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.7857 | 0.472185 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9878 | −0.559510 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.300773 | 0.0120117 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.30018 | 0.211332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.8232 | −1.54553 | −0.772765 | − | 0.634693i | \(-0.781127\pi\) | ||||
−0.772765 | + | 0.634693i | \(0.781127\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.7562 | −1.06346 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.16835 | −0.0463647 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.25543 | −0.247849 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.58545 | 0.141838 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.4165 | 1.63585 | 0.817927 | − | 0.575322i | \(-0.195123\pi\) | ||||
0.817927 | + | 0.575322i | \(0.195123\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.0908 | −1.14723 | −0.573615 | − | 0.819125i | \(-0.694459\pi\) | ||||
−0.573615 | + | 0.819125i | \(0.694459\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.5095 | 0.846937 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.2691 | −0.600289 | −0.300145 | − | 0.953894i | \(-0.597035\pi\) | ||||
−0.300145 | + | 0.953894i | \(0.597035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.49433 | 0.254925 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.337476 | −0.0132267 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.714425 | −0.0279576 | −0.0139788 | − | 0.999902i | \(-0.504450\pi\) | ||||
−0.0139788 | + | 0.999902i | \(0.504450\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.7039 | −0.613603 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.795102 | 0.0310199 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.6563 | 0.609884 | 0.304942 | − | 0.952371i | \(-0.401363\pi\) | ||||
0.304942 | + | 0.952371i | \(0.401363\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.83528 | 0.110280 | 0.0551399 | − | 0.998479i | \(-0.482440\pi\) | ||||
0.0551399 | + | 0.998479i | \(0.482440\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.551559 | 0.0214208 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.474683 | 0.0184074 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.1906 | −1.36259 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.84264 | 0.148565 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.39575 | −0.285510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.6316 | −1.45059 | −0.725297 | − | 0.688437i | \(-0.758297\pi\) | ||||
−0.725297 | + | 0.688437i | \(0.758297\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.65479 | −0.0636927 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.0092 | 1.38394 | 0.691972 | − | 0.721924i | \(-0.256742\pi\) | ||||
0.691972 | + | 0.721924i | \(0.256742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.22115 | 0.0852401 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.8941 | 0.877305 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.9680 | −0.764054 | −0.382027 | − | 0.924151i | \(-0.624774\pi\) | ||||
−0.382027 | + | 0.924151i | \(0.624774\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.3713 | −1.04580 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.22979 | −0.199529 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.76446 | −0.371996 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.6854 | −1.35754 | −0.678769 | − | 0.734352i | \(-0.737486\pi\) | ||||
−0.678769 | + | 0.734352i | \(0.737486\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.862883 | 0.0327782 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.9391 | 0.642537 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.92143 | 0.110657 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.48832 | 0.245411 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.4890 | −0.887166 | −0.443583 | − | 0.896233i | \(-0.646293\pi\) | ||||
−0.443583 | + | 0.896233i | \(0.646293\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.89026 | 0.109008 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.9000 | −0.448181 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.8318 | 0.482591 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.6568 | −1.15134 | −0.575671 | − | 0.817681i | \(-0.695259\pi\) | ||||
−0.575671 | + | 0.817681i | \(0.695259\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.81445 | 0.368071 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.01588 | −0.112946 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.82899 | 0.0684005 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.1498 | 1.05127 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.5661 | −1.51286 | −0.756430 | − | 0.654075i | \(-0.773058\pi\) | ||||
−0.756430 | + | 0.654075i | \(0.773058\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.44743 | 0.0911472 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.31293 | 0.234780 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.55171 | 0.280463 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.18066 | 0.303404 | 0.151702 | − | 0.988426i | \(-0.451525\pi\) | ||||
0.151702 | + | 0.988426i | \(0.451525\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.48651 | 0.239912 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.2907 | 0.823325 | 0.411662 | − | 0.911336i | \(-0.364948\pi\) | ||||
0.411662 | + | 0.911336i | \(0.364948\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.4411 | −0.422013 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.53702 | −0.314465 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.2328 | −0.744275 | −0.372137 | − | 0.928178i | \(-0.621375\pi\) | ||||
−0.372137 | + | 0.928178i | \(0.621375\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.300773 | 0.0110492 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5586 | 0.387358 | 0.193679 | − | 0.981065i | \(-0.437958\pi\) | ||||
0.193679 | + | 0.981065i | \(0.437958\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.9755 | −0.585295 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.49023 | −0.200877 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.1179 | 0.479316 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5954 | 0.532594 | 0.266297 | − | 0.963891i | \(-0.414200\pi\) | ||||
0.266297 | + | 0.963891i | \(0.414200\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.48709 | −0.163519 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.4739 | 0.563152 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.76356 | 0.136789 | 0.0683945 | − | 0.997658i | \(-0.478212\pi\) | ||||
0.0683945 | + | 0.997658i | \(0.478212\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.71122 | 0.279900 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.80319 | −0.101615 | −0.0508077 | − | 0.998708i | \(-0.516180\pi\) | ||||
−0.0508077 | + | 0.998708i | \(0.516180\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.82786 | −0.0661729 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.00880 | 0.0364731 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.49433 | 0.234497 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.3119 | −0.443977 | −0.221989 | − | 0.975049i | \(-0.571255\pi\) | ||||
−0.221989 | + | 0.975049i | \(0.571255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.4505 | −0.808537 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.4627 | 1.49131 | 0.745655 | − | 0.666333i | \(-0.232137\pi\) | ||||
0.745655 | + | 0.666333i | \(0.232137\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.647191 | 0.0232478 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.29183 | 0.297468 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.59310 | 0.0570787 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.58545 | 0.128297 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.56356 | −0.163088 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.2675 | 1.04460 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.1807 | −1.21841 | −0.609205 | − | 0.793013i | \(-0.708511\pi\) | ||||
−0.609205 | + | 0.793013i | \(0.708511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.0854 | 0.430251 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.5679 | −0.446863 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.39575 | −0.262631 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.8591 | −0.633398 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.5951 | 0.587830 | 0.293915 | − | 0.955832i | \(-0.405042\pi\) | ||||
0.293915 | + | 0.955832i | \(0.405042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.58862 | −0.126956 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.6585 | 0.482601 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.795102 | 0.0280586 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.1699 | 0.428933 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.7885 | 0.766990 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.8533 | 0.592530 | 0.296265 | − | 0.955106i | \(-0.404259\pi\) | ||||
0.296265 | + | 0.955106i | \(0.404259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.97346 | −0.209757 | −0.104878 | − | 0.994485i | \(-0.533445\pi\) | ||||
−0.104878 | + | 0.994485i | \(0.533445\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.38761 | −0.329238 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.7821 | 0.377682 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.53719 | 0.123751 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.862883 | 0.0301516 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.5104 | 0.820518 | 0.410259 | − | 0.911969i | \(-0.365438\pi\) | ||||
0.410259 | + | 0.911969i | \(0.365438\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.2908 | −0.637576 | −0.318788 | − | 0.947826i | \(-0.603276\pi\) | ||||
−0.318788 | + | 0.947826i | \(0.603276\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.65479 | −0.0576122 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.8892 | −1.45663 | −0.728315 | − | 0.685243i | \(-0.759696\pi\) | ||||
−0.728315 | + | 0.685243i | \(0.759696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.5062 | 1.37211 | 0.686054 | − | 0.727550i | \(-0.259341\pi\) | ||||
0.686054 | + | 0.727550i | \(0.259341\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.07524 | 0.141369 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.45024 | −0.119544 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.736267 | 0.0254796 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.391103 | −0.0135185 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.9994 | 1.89879 | 0.949394 | − | 0.314086i | \(-0.101698\pi\) | ||||
0.949394 | + | 0.314086i | \(0.101698\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.17395 | −0.281860 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.7933 | −0.853927 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.82899 | 0.0629193 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.862883 | 0.0296490 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.3247 | 0.388661 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 74.1006 | 2.54014 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.02579 | −0.206319 | −0.103160 | − | 0.994665i | \(-0.532895\pi\) | ||||
−0.103160 | + | 0.994665i | \(0.532895\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.550112 | 0.0188134 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.12058 | −0.311553 | −0.155776 | − | 0.987792i | \(-0.549788\pi\) | ||||
−0.155776 | + | 0.987792i | \(0.549788\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.9607 | 0.715169 | 0.357584 | − | 0.933881i | \(-0.383600\pi\) | ||||
0.357584 | + | 0.933881i | \(0.383600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.57041 | 0.155759 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.6380 | 0.668485 | 0.334242 | − | 0.942487i | \(-0.391520\pi\) | ||||
0.334242 | + | 0.942487i | \(0.391520\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.5660 | −1.37928 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.6958 | −0.567019 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.81445 | 0.332932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.53702 | −0.289266 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.57411 | 0.0871203 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.5026 | −0.355054 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.2011 | −0.715910 | −0.357955 | − | 0.933739i | \(-0.616526\pi\) | ||||
−0.357955 | + | 0.933739i | \(0.616526\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.05389 | 0.237922 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.7783 | 0.396822 | 0.198411 | − | 0.980119i | \(-0.436422\pi\) | ||||
0.198411 | + | 0.980119i | \(0.436422\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.0887 | 0.911609 | 0.455804 | − | 0.890080i | \(-0.349352\pi\) | ||||
0.455804 | + | 0.890080i | \(0.349352\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.8781 | 0.399277 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.58252 | 0.153866 | 0.0769330 | − | 0.997036i | \(-0.475487\pi\) | ||||
0.0769330 | + | 0.997036i | \(0.475487\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.551207 | −0.0184869 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.95693 | −0.0654862 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.3060 | 0.377919 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.71122 | 0.257470 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.78482 | 0.0595271 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.38568 | −0.179423 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.1478 | 0.337697 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −32.5483 | −1.08194 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.8736 | −1.52321 | −0.761604 | − | 0.648042i | \(-0.775588\pi\) | ||||
−0.761604 | + | 0.648042i | \(0.775588\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.8709 | 0.493236 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.7205 | −0.388316 | −0.194158 | − | 0.980970i | \(-0.562197\pi\) | ||||
−0.194158 | + | 0.980970i | \(0.562197\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.49023 | −0.181700 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.5268 | −0.447181 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.40881 | −0.244660 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.18872 | −0.204147 | −0.102074 | − | 0.994777i | \(-0.532548\pi\) | ||||
−0.102074 | + | 0.994777i | \(0.532548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.4440 | 0.673654 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.58545 | 0.118017 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.9016 | −0.522840 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.83634 | 0.0931577 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.788059 | −0.0258554 | −0.0129277 | − | 0.999916i | \(-0.504115\pi\) | ||||
−0.0129277 | + | 0.999916i | \(0.504115\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.88147 | −0.0616626 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.9342 | −0.521663 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.00880 | 0.0329912 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.7726 | 0.743948 | 0.371974 | − | 0.928243i | \(-0.378681\pi\) | ||||
0.371974 | + | 0.928243i | \(0.378681\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.1754 | 0.854202 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.1370 | −0.917240 | −0.458620 | − | 0.888632i | \(-0.651656\pi\) | ||||
−0.458620 | + | 0.888632i | \(0.651656\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.8438 | 1.33006 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.57821 | 0.0513391 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.73345 | 0.218808 | 0.109404 | − | 0.993997i | \(-0.465106\pi\) | ||||
0.109404 | + | 0.993997i | \(0.465106\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.795102 | 0.0258101 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.2142 | 0.525783 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.990105 | −0.0320726 | −0.0160363 | − | 0.999871i | \(-0.505105\pi\) | ||||
−0.0160363 | + | 0.999871i | \(0.505105\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.6726 | 1.31613 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.56356 | −0.147519 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.9132 | −0.416990 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8470 | −0.995066 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.2024 | 0.489889 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.58256 | −0.115327 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.6223 | −0.920430 | −0.460215 | − | 0.887808i | \(-0.652228\pi\) | ||||
−0.460215 | + | 0.887808i | \(0.652228\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.165894 | 0.00532929 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.46377 | 0.143249 | 0.0716247 | − | 0.997432i | \(-0.477182\pi\) | ||||
0.0716247 | + | 0.997432i | \(0.477182\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.99155 | 0.256197 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.65479 | −0.0529955 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.969686 | 0.0310230 | 0.0155115 | − | 0.999880i | \(-0.495062\pi\) | ||||
0.0155115 | + | 0.999880i | \(0.495062\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.6585 | 0.436529 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.11832 | −0.0676326 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.6060 | 0.880495 | 0.440247 | − | 0.897877i | \(-0.354891\pi\) | ||||
0.440247 | + | 0.897877i | \(0.354891\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.0412 | 1.05278 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.61420 | −0.178702 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 90.6864 | 2.88366 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.7750 | −0.469342 | −0.234671 | − | 0.972075i | \(-0.575401\pi\) | ||||
−0.234671 | + | 0.972075i | \(0.575401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.9140 | −0.727153 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.6134 | −1.31923 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.8328 | −0.849804 | −0.424902 | − | 0.905239i | \(-0.639692\pi\) | ||||
−0.424902 | + | 0.905239i | \(0.639692\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.60944 | 0.304029 |
(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 | 6864.2.a.cf.1.4 | 5 | ||
4.3 | odd | 2 | 3432.2.a.w.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3432.2.a.w.1.4 | ✓ | 5 | 4.3 | odd | 2 | ||
6864.2.a.cf.1.4 | 5 | 1.1 | even | 1 | trivial |