Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 15x^{7} + 45x^{6} + 64x^{5} - 201x^{4} - 53x^{3} + 252x^{2} - 69x - 26 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.829765\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.829765 | 0.479065 | 0.239532 | − | 0.970888i | \(-0.423006\pi\) | ||||
0.239532 | + | 0.970888i | \(0.423006\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.12811 | 1.84615 | 0.923073 | − | 0.384625i | \(-0.125669\pi\) | ||||
0.923073 | + | 0.384625i | \(0.125669\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.31149 | −0.770497 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.42536 | 0.884424 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.93739 | −0.712421 | −0.356211 | − | 0.934406i | \(-0.615931\pi\) | ||||
−0.356211 | + | 0.934406i | \(0.615931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.03162 | 1.38375 | 0.691874 | − | 0.722018i | \(-0.256785\pi\) | ||||
0.691874 | + | 0.722018i | \(0.256785\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.829765 | 0.181070 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.47216 | −0.932510 | −0.466255 | − | 0.884650i | \(-0.654397\pi\) | ||||
−0.466255 | + | 0.884650i | \(0.654397\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.0413 | 2.40826 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.40729 | −0.848183 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.33589 | −0.619459 | −0.309729 | − | 0.950825i | \(-0.600238\pi\) | ||||
−0.309729 | + | 0.950825i | \(0.600238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.08099 | −0.912572 | −0.456286 | − | 0.889833i | \(-0.650821\pi\) | ||||
−0.456286 | + | 0.889833i | \(0.650821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.829765 | 0.144444 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.12811 | 0.697778 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.82151 | 0.957051 | 0.478525 | − | 0.878074i | \(-0.341171\pi\) | ||||
0.478525 | + | 0.878074i | \(0.341171\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.829765 | −0.132869 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.76715 | 0.900678 | 0.450339 | − | 0.892858i | \(-0.351303\pi\) | ||||
0.450339 | + | 0.892858i | \(0.351303\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.45459 | 1.44181 | 0.720905 | − | 0.693033i | \(-0.243726\pi\) | ||||
0.720905 | + | 0.693033i | \(0.243726\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.54208 | −1.42245 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.47216 | 0.652331 | 0.326166 | − | 0.945313i | \(-0.394243\pi\) | ||||
0.326166 | + | 0.945313i | \(0.394243\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.43734 | −0.341296 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.60150 | 0.219983 | 0.109991 | − | 0.993933i | \(-0.464918\pi\) | ||||
0.109991 | + | 0.993933i | \(0.464918\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.12811 | 0.556634 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.00483 | 0.662905 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.48190 | 1.23444 | 0.617219 | − | 0.786791i | \(-0.288259\pi\) | ||||
0.617219 | + | 0.786791i | \(0.288259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.767842 | 0.0983121 | 0.0491561 | − | 0.998791i | \(-0.484347\pi\) | ||||
0.0491561 | + | 0.998791i | \(0.484347\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.31149 | −0.291220 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.12811 | −0.512029 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.951002 | 0.116183 | 0.0580917 | − | 0.998311i | \(-0.481498\pi\) | ||||
0.0580917 | + | 0.998311i | \(0.481498\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.71084 | −0.446733 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.32071 | −0.631452 | −0.315726 | − | 0.948850i | \(-0.602248\pi\) | ||||
−0.315726 | + | 0.948850i | \(0.602248\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.36820 | −0.160135 | −0.0800677 | − | 0.996789i | \(-0.525514\pi\) | ||||
−0.0800677 | + | 0.996789i | \(0.525514\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.99143 | 1.15371 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.68584 | −0.189672 | −0.0948361 | − | 0.995493i | \(-0.530233\pi\) | ||||
−0.0948361 | + | 0.995493i | \(0.530233\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.27746 | 0.364162 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.97176 | 0.984779 | 0.492389 | − | 0.870375i | \(-0.336124\pi\) | ||||
0.492389 | + | 0.870375i | \(0.336124\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.1259 | −1.31523 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.76800 | −0.296761 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.9049 | 1.79192 | 0.895959 | − | 0.444137i | \(-0.146490\pi\) | ||||
0.895959 | + | 0.444137i | \(0.146490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.21603 | −0.437181 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24.8992 | 2.55460 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.13254 | 0.927269 | 0.463634 | − | 0.886027i | \(-0.346545\pi\) | ||||
0.463634 | + | 0.886027i | \(0.346545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.31149 | −0.232314 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3587 | 1.03073 | 0.515364 | − | 0.856971i | \(-0.327657\pi\) | ||||
0.515364 | + | 0.856971i | \(0.327657\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0074 | −0.986061 | −0.493031 | − | 0.870012i | \(-0.664111\pi\) | ||||
−0.493031 | + | 0.870012i | \(0.664111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.42536 | 0.334281 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.17531 | −0.790337 | −0.395168 | − | 0.918609i | \(-0.629314\pi\) | ||||
−0.395168 | + | 0.918609i | \(0.629314\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.53533 | −0.625971 | −0.312985 | − | 0.949758i | \(-0.601329\pi\) | ||||
−0.312985 | + | 0.949758i | \(0.601329\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.83049 | 0.458490 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.1221 | 1.32849 | 0.664247 | − | 0.747513i | \(-0.268752\pi\) | ||||
0.664247 | + | 0.747513i | \(0.268752\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.4616 | −1.72155 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.31149 | 0.213697 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.93739 | −0.269270 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.78538 | 0.431483 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 29.0671 | 2.59984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.4780 | 1.55092 | 0.775460 | − | 0.631396i | \(-0.217518\pi\) | ||||
0.775460 | + | 0.631396i | \(0.217518\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.84508 | 0.690721 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9632 | 1.48208 | 0.741040 | − | 0.671461i | \(-0.234333\pi\) | ||||
0.741040 | + | 0.671461i | \(0.234333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.03162 | 0.523008 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18.1938 | −1.56587 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.4110 | −1.23122 | −0.615609 | − | 0.788052i | \(-0.711090\pi\) | ||||
−0.615609 | + | 0.788052i | \(0.711090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.86031 | −0.327427 | −0.163714 | − | 0.986508i | \(-0.552347\pi\) | ||||
−0.163714 | + | 0.986508i | \(0.552347\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.71084 | 0.312509 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.7709 | −1.14361 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.829765 | 0.0684379 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.1712 | −0.833257 | −0.416628 | − | 0.909077i | \(-0.636788\pi\) | ||||
−0.416628 | + | 0.909077i | \(0.636788\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7023 | 1.19645 | 0.598227 | − | 0.801327i | \(-0.295872\pi\) | ||||
0.598227 | + | 0.801327i | \(0.295872\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.78974 | 0.548918 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.9749 | −1.68474 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.54984 | −0.442926 | −0.221463 | − | 0.975169i | \(-0.571083\pi\) | ||||
−0.221463 | + | 0.975169i | \(0.571083\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.32887 | 0.105386 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.47216 | −0.352455 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.11233 | 0.0871247 | 0.0435623 | − | 0.999051i | \(-0.486129\pi\) | ||||
0.0435623 | + | 0.999051i | \(0.486129\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.42536 | 0.266664 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.80637 | 0.758840 | 0.379420 | − | 0.925225i | \(-0.376124\pi\) | ||||
0.379420 | + | 0.925225i | \(0.376124\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.9420 | −1.06617 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.77299 | −0.438913 | −0.219456 | − | 0.975622i | \(-0.570428\pi\) | ||||
−0.219456 | + | 0.975622i | \(0.570428\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.0413 | 0.910235 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.86775 | 0.591376 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.9988 | 1.64427 | 0.822133 | − | 0.569296i | \(-0.192784\pi\) | ||||
0.822133 | + | 0.569296i | \(0.192784\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.8520 | −1.92156 | −0.960782 | − | 0.277304i | \(-0.910559\pi\) | ||||
−0.960782 | + | 0.277304i | \(0.910559\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.637129 | 0.0470979 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.0318 | 1.76686 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.93739 | −0.214803 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.40729 | −0.320583 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.6902 | 1.06294 | 0.531472 | − | 0.847076i | \(-0.321639\pi\) | ||||
0.531472 | + | 0.847076i | \(0.321639\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.3863 | −1.68338 | −0.841691 | − | 0.539959i | \(-0.818440\pi\) | ||||
−0.841691 | + | 0.539959i | \(0.818440\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.42536 | −0.245295 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.97258 | 0.140540 | 0.0702702 | − | 0.997528i | \(-0.477614\pi\) | ||||
0.0702702 | + | 0.997528i | \(0.477614\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.39952 | −0.0992093 | −0.0496047 | − | 0.998769i | \(-0.515796\pi\) | ||||
−0.0496047 | + | 0.998769i | \(0.515796\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.789108 | 0.0556594 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.33589 | −0.234133 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.8074 | 1.66278 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.3374 | 0.718496 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.03162 | 0.417216 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3444 | 1.12519 | 0.562597 | − | 0.826731i | \(-0.309802\pi\) | ||||
0.562597 | + | 0.826731i | \(0.309802\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.41494 | −0.302506 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 39.0296 | 2.66179 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.08099 | −0.344920 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.13528 | −0.0767153 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.93739 | 0.197590 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.1235 | 0.878814 | 0.439407 | − | 0.898288i | \(-0.355189\pi\) | ||||
0.439407 | + | 0.898288i | \(0.355189\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −27.8333 | −1.85555 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.55421 | −0.103156 | −0.0515782 | − | 0.998669i | \(-0.516425\pi\) | ||||
−0.0515782 | + | 0.998669i | \(0.516425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.876231 | −0.0579030 | −0.0289515 | − | 0.999581i | \(-0.509217\pi\) | ||||
−0.0289515 | + | 0.999581i | \(0.509217\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.829765 | 0.0545945 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.72345 | −0.309444 | −0.154722 | − | 0.987958i | \(-0.549448\pi\) | ||||
−0.154722 | + | 0.987958i | \(0.549448\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.4616 | 1.20430 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.39885 | −0.0908653 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.8265 | −0.959048 | −0.479524 | − | 0.877529i | \(-0.659191\pi\) | ||||
−0.479524 | + | 0.877529i | \(0.659191\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.4642 | −1.89796 | −0.948979 | − | 0.315338i | \(-0.897882\pi\) | ||||
−0.948979 | + | 0.315338i | \(0.897882\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.9414 | 1.02264 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.12811 | 0.263735 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.03162 | −0.383783 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.44445 | 0.471773 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.7318 | −1.37170 | −0.685848 | − | 0.727745i | \(-0.740569\pi\) | ||||
−0.685848 | + | 0.727745i | \(0.740569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.47216 | −0.281162 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.0616 | −0.630082 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.3078 | −1.57866 | −0.789329 | − | 0.613971i | \(-0.789571\pi\) | ||||
−0.789329 | + | 0.613971i | \(0.789571\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.82151 | 0.361731 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.71087 | 0.477291 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.9144 | 1.22797 | 0.613986 | − | 0.789317i | \(-0.289565\pi\) | ||||
0.613986 | + | 0.789317i | \(0.289565\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.61117 | 0.406121 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.0271 | 0.858445 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.5469 | −1.43568 | −0.717840 | − | 0.696208i | \(-0.754869\pi\) | ||||
−0.717840 | + | 0.696208i | \(0.754869\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.7577 | −0.896469 | −0.448235 | − | 0.893916i | \(-0.647947\pi\) | ||||
−0.448235 | + | 0.893916i | \(0.647947\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.829765 | −0.0502197 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.0413 | 0.726116 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.7616 | 1.60795 | 0.803975 | − | 0.594663i | \(-0.202715\pi\) | ||||
0.803975 | + | 0.594663i | \(0.202715\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.7447 | 0.703134 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.83046 | −0.467126 | −0.233563 | − | 0.972342i | \(-0.575038\pi\) | ||||
−0.233563 | + | 0.972342i | \(0.575038\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.6976 | 0.814238 | 0.407119 | − | 0.913375i | \(-0.366533\pi\) | ||||
0.407119 | + | 0.913375i | \(0.366533\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 20.6605 | 1.22382 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.76715 | 0.340424 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.37176 | −0.492456 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.57786 | 0.444222 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.22597 | −0.0716217 | −0.0358109 | − | 0.999359i | \(-0.511401\pi\) | ||||
−0.0358109 | + | 0.999359i | \(0.511401\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 39.1423 | 2.27895 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.40729 | −0.255737 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.47216 | 0.258632 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.45459 | 0.544953 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.59528 | 0.493786 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.16974 | 0.181499 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.7628 | −0.842555 | −0.421277 | − | 0.906932i | \(-0.638418\pi\) | ||||
−0.421277 | + | 0.906932i | \(0.638418\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.30381 | −0.472387 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.1137 | −0.857017 | −0.428508 | − | 0.903538i | \(-0.640961\pi\) | ||||
−0.428508 | + | 0.903538i | \(0.640961\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.81459 | −0.498230 | −0.249115 | − | 0.968474i | \(-0.580140\pi\) | ||||
−0.249115 | + | 0.968474i | \(0.580140\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.54208 | −0.537635 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.1450 | −1.13146 | −0.565728 | − | 0.824592i | \(-0.691405\pi\) | ||||
−0.565728 | + | 0.824592i | \(0.691405\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.33589 | −0.186774 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.78358 | −0.378623 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.7172 | −0.985812 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0413 | −0.667930 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.42279 | −0.299881 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.47216 | 0.246558 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.250156 | −0.0137498 | −0.00687492 | − | 0.999976i | \(-0.502188\pi\) | ||||
−0.00687492 | + | 0.999976i | \(0.502188\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.4564 | −0.737405 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.92584 | 0.214491 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0879 | 1.20321 | 0.601603 | − | 0.798795i | \(-0.294529\pi\) | ||||
0.601603 | + | 0.798795i | \(0.294529\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.7180 | 0.636435 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.08099 | −0.275151 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.3187 | −0.824734 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.3480 | −1.09234 | −0.546169 | − | 0.837675i | \(-0.683915\pi\) | ||||
−0.546169 | + | 0.837675i | \(0.683915\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.5565 | −0.672135 | −0.336067 | − | 0.941838i | \(-0.609097\pi\) | ||||
−0.336067 | + | 0.941838i | \(0.609097\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.40729 | 0.235244 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.8811 | −1.00494 | −0.502469 | − | 0.864595i | \(-0.667575\pi\) | ||||
−0.502469 | + | 0.864595i | \(0.667575\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.9645 | −1.16575 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.43734 | −0.128998 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.82369 | 0.518475 | 0.259237 | − | 0.965814i | \(-0.416529\pi\) | ||||
0.259237 | + | 0.965814i | \(0.416529\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3804 | 0.914760 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.829765 | 0.0435514 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.64807 | −0.295633 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.451078 | 0.0235461 | 0.0117731 | − | 0.999931i | \(-0.496252\pi\) | ||||
0.0117731 | + | 0.999931i | \(0.496252\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.3307 | −0.693969 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.60150 | 0.0831457 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.8111 | −1.85423 | −0.927115 | − | 0.374778i | \(-0.877719\pi\) | ||||
−0.927115 | + | 0.374778i | \(0.877719\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.1189 | 1.24549 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.33589 | 0.171807 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.2983 | −0.734454 | −0.367227 | − | 0.930131i | \(-0.619693\pi\) | ||||
−0.367227 | + | 0.930131i | \(0.619693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.5026 | 0.742992 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.25912 | 0.370924 | 0.185462 | − | 0.982651i | \(-0.440622\pi\) | ||||
0.185462 | + | 0.982651i | \(0.440622\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.12811 | 0.210388 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.8542 | −1.11091 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −37.5285 | −1.90277 | −0.951386 | − | 0.308001i | \(-0.900340\pi\) | ||||
−0.951386 | + | 0.308001i | \(0.900340\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.1365 | 0.664339 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.0754 | 0.710012 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.95934 | −0.350163 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.27221 | −0.465359 | −0.232680 | − | 0.972553i | \(-0.574749\pi\) | ||||
−0.232680 | + | 0.972553i | \(0.574749\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.00483 | 0.250555 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.1124 | 0.904492 | 0.452246 | − | 0.891893i | \(-0.350623\pi\) | ||||
0.452246 | + | 0.891893i | \(0.350623\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.08099 | 0.253102 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.5297 | 0.672296 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.82151 | 0.288562 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.97525 | −0.196564 | −0.0982818 | − | 0.995159i | \(-0.531335\pi\) | ||||
−0.0982818 | + | 0.995159i | \(0.531335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.9578 | −0.589833 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.48190 | 0.466574 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37.0364 | 1.81805 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.20315 | −0.156859 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.61499 | 0.372017 | 0.186008 | − | 0.982548i | \(-0.440445\pi\) | ||||
0.186008 | + | 0.982548i | \(0.440445\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.9412 | −0.776926 | −0.388463 | − | 0.921464i | \(-0.626994\pi\) | ||||
−0.388463 | + | 0.921464i | \(0.626994\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.3374 | −0.502619 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −35.3699 | −1.71569 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.767842 | 0.0371585 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.829765 | −0.0400614 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.41109 | −0.260643 | −0.130322 | − | 0.991472i | \(-0.541601\pi\) | ||||
−0.130322 | + | 0.991472i | \(0.541601\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0511 | −1.25194 | −0.625968 | − | 0.779849i | \(-0.715296\pi\) | ||||
−0.625968 | + | 0.779849i | \(0.715296\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.4266 | −0.547864 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.9744 | −1.29036 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.3660 | −1.25838 | −0.629191 | − | 0.777250i | \(-0.716614\pi\) | ||||
−0.629191 | + | 0.777250i | \(0.716614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.31149 | −0.110071 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.43273 | −0.400651 | −0.200325 | − | 0.979729i | \(-0.564200\pi\) | ||||
−0.200325 | + | 0.979729i | \(0.564200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 69.7853 | 3.30814 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.43970 | −0.399184 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.9509 | 0.564000 | 0.282000 | − | 0.959414i | \(-0.409002\pi\) | ||||
0.282000 | + | 0.959414i | \(0.409002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.76715 | 0.271565 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.1994 | 0.573179 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.12811 | −0.193529 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.2542 | 1.69590 | 0.847951 | − | 0.530074i | \(-0.177836\pi\) | ||||
0.847951 | + | 0.530074i | \(0.177836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.9459 | 0.604263 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.1950 | −0.940573 | −0.470287 | − | 0.882514i | \(-0.655849\pi\) | ||||
−0.470287 | + | 0.882514i | \(0.655849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.5119 | −0.720901 | −0.360451 | − | 0.932778i | \(-0.617377\pi\) | ||||
−0.360451 | + | 0.932778i | \(0.617377\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.4042 | −0.807101 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.2692 | −1.67834 | −0.839169 | − | 0.543871i | \(-0.816958\pi\) | ||||
−0.839169 | + | 0.543871i | \(0.816958\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.951002 | 0.0439132 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.60506 | −0.212190 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.45459 | 0.434722 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 72.6284 | 3.33242 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.70185 | −0.169496 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0795 | 0.460545 | 0.230273 | − | 0.973126i | \(-0.426038\pi\) | ||||
0.230273 | + | 0.973126i | \(0.426038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.82151 | −0.265438 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.71084 | −0.168849 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 37.7001 | 1.71187 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.5017 | −1.47279 | −0.736396 | − | 0.676550i | \(-0.763474\pi\) | ||||
−0.736396 | + | 0.676550i | \(0.763474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.922975 | 0.0417384 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.34874 | −0.196256 | −0.0981280 | − | 0.995174i | \(-0.531285\pi\) | ||||
−0.0981280 | + | 0.995174i | \(0.531285\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.79879 | 0.441315 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.54208 | −0.428885 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.32071 | −0.238666 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.57133 | −0.249407 | −0.124704 | − | 0.992194i | \(-0.539798\pi\) | ||||
−0.124704 | + | 0.992194i | \(0.539798\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.13698 | 0.363534 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.6064 | 1.94431 | 0.972157 | − | 0.234330i | \(-0.0752897\pi\) | ||||
0.972157 | + | 0.234330i | \(0.0752897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.7618 | 1.90287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.829765 | 0.0368512 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.5763 | −0.956354 | −0.478177 | − | 0.878263i | \(-0.658702\pi\) | ||||
−0.478177 | + | 0.878263i | \(0.658702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.36820 | −0.0605255 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −26.5831 | −1.17367 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −41.3117 | −1.82041 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.47216 | 0.196685 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.79023 | −0.210268 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.0561274 | −0.00245899 | −0.00122949 | − | 0.999999i | \(-0.500391\pi\) | ||||
−0.00122949 | + | 0.999999i | \(0.500391\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.0264 | 1.40042 | 0.700209 | − | 0.713938i | \(-0.253090\pi\) | ||||
0.700209 | + | 0.713938i | \(0.253090\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.99143 | 0.436062 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.9248 | 0.650136 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.99980 | −0.130426 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.9173 | −0.951131 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.76715 | −0.249803 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.7486 | −1.45908 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.2538 | 0.787710 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3027 | 1.13084 | 0.565420 | − | 0.824803i | \(-0.308714\pi\) | ||||
0.565420 | + | 0.824803i | \(0.308714\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.4511 | −0.920554 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.9785 | −1.15563 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.46262 | −0.319079 | −0.159539 | − | 0.987192i | \(-0.551001\pi\) | ||||
−0.159539 | + | 0.987192i | \(0.551001\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.77486 | −0.0757492 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.1208 | −0.857175 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.68584 | −0.0716894 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.9408 | 0.846439 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.8144 | 0.585335 | 0.292667 | − | 0.956214i | \(-0.405457\pi\) | ||||
0.292667 | + | 0.956214i | \(0.405457\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.45459 | −0.399886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.43734 | −0.102905 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.1499 | −1.43925 | −0.719624 | − | 0.694364i | \(-0.755686\pi\) | ||||
−0.719624 | + | 0.694364i | \(0.755686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 58.2975 | 2.45259 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.27746 | 0.137640 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.1747 | 1.39076 | 0.695379 | − | 0.718643i | \(-0.255237\pi\) | ||||
0.695379 | + | 0.718643i | \(0.255237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.7096 | −1.11776 | −0.558881 | − | 0.829248i | \(-0.688769\pi\) | ||||
−0.558881 | + | 0.829248i | \(0.688769\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.1894 | 0.509219 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −53.8505 | −2.24572 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.01972 | 0.208974 | 0.104487 | − | 0.994526i | \(-0.466680\pi\) | ||||
0.104487 | + | 0.994526i | \(0.466680\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.4051 | −0.806449 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.97176 | 0.372211 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.60150 | 0.0663274 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.54208 | 0.394517 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.99583 | −0.206200 | −0.103100 | − | 0.994671i | \(-0.532876\pi\) | ||||
−0.103100 | + | 0.994671i | \(0.532876\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.6466 | −1.26277 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.63678 | 0.0673280 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.2892 | −1.20276 | −0.601382 | − | 0.798961i | \(-0.705383\pi\) | ||||
−0.601382 | + | 0.798961i | \(0.705383\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.1259 | −0.497111 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.16127 | −0.0475277 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.0732 | 1.71907 | 0.859533 | − | 0.511081i | \(-0.170755\pi\) | ||||
0.859533 | + | 0.511081i | \(0.170755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.3963 | 1.36227 | 0.681133 | − | 0.732160i | \(-0.261488\pi\) | ||||
0.681133 | + | 0.732160i | \(0.261488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.19823 | −0.0895189 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.12811 | 0.167831 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.6117 | 0.836604 | 0.418302 | − | 0.908308i | \(-0.362625\pi\) | ||||
0.418302 | + | 0.908308i | \(0.362625\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.76800 | −0.112165 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.47216 | −0.180924 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.2550 | −1.38354 | −0.691772 | − | 0.722116i | \(-0.743170\pi\) | ||||
−0.691772 | + | 0.722116i | \(0.743170\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.7546 | 0.796581 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.50685 | 0.342473 | 0.171236 | − | 0.985230i | \(-0.445224\pi\) | ||||
0.171236 | + | 0.985230i | \(0.445224\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.16839 | −0.127348 | −0.0636742 | − | 0.997971i | \(-0.520282\pi\) | ||||
−0.0636742 | + | 0.997971i | \(0.520282\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.7101 | 0.790939 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9049 | 0.677281 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 59.7859 | 2.39144 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.00483 | 0.199874 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.1000 | −0.681823 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.6741 | −1.26092 | −0.630462 | − | 0.776220i | \(-0.717135\pi\) | ||||
−0.630462 | + | 0.776220i | \(0.717135\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.5620 | 0.539041 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 72.1510 | 2.86323 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.2988 | 0.486532 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.0040 | −1.10609 | −0.553046 | − | 0.833150i | \(-0.686535\pi\) | ||||
−0.553046 | + | 0.833150i | \(0.686535\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.5194 | 1.51906 | 0.759528 | − | 0.650474i | \(-0.225430\pi\) | ||||
0.759528 | + | 0.650474i | \(0.225430\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.3853 | 1.27517 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.2557 | 1.62193 | 0.810964 | − | 0.585097i | \(-0.198943\pi\) | ||||
0.810964 | + | 0.585097i | \(0.198943\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.48190 | 0.372197 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.21603 | −0.165239 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.51770 | −0.255057 | −0.127529 | − | 0.991835i | \(-0.540704\pi\) | ||||
−0.127529 | + | 0.991835i | \(0.540704\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 70.0258 | 2.73613 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.16257 | 0.123384 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.8407 | 1.00661 | 0.503305 | − | 0.864109i | \(-0.332117\pi\) | ||||
0.503305 | + | 0.864109i | \(0.332117\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.40006 | 0.365620 | 0.182810 | − | 0.983148i | \(-0.441481\pi\) | ||||
0.182810 | + | 0.983148i | \(0.441481\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.43734 | 0.0946585 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.8992 | 0.965549 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.9186 | 0.577651 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.8894 | 0.421009 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.767842 | 0.0296422 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.8867 | 1.42188 | 0.710938 | − | 0.703255i | \(-0.248271\pi\) | ||||
0.710938 | + | 0.703255i | \(0.248271\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −53.0694 | −2.04264 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.5835 | 1.63662 | 0.818308 | − | 0.574780i | \(-0.194912\pi\) | ||||
0.818308 | + | 0.574780i | \(0.194912\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.13254 | 0.350475 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.28963 | −0.0494186 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −46.1158 | −1.76457 | −0.882286 | − | 0.470713i | \(-0.843997\pi\) | ||||
−0.882286 | + | 0.470713i | \(0.843997\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −59.4903 | −2.27301 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.727066 | −0.0277393 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.60150 | −0.0610123 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.7814 | −1.32315 | −0.661574 | − | 0.749880i | \(-0.730111\pi\) | ||||
−0.661574 | + | 0.749880i | \(0.730111\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.31149 | −0.0878063 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.9358 | −0.604478 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.9404 | −0.641662 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.91935 | −0.148244 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.3275 | 0.843298 | 0.421649 | − | 0.906759i | \(-0.361451\pi\) | ||||
0.421649 | + | 0.906759i | \(0.361451\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.1132 | 1.32432 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.3187 | 0.576937 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.3587 | 0.389579 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.8408 | −0.594915 | −0.297458 | − | 0.954735i | \(-0.596139\pi\) | ||||
−0.297458 | + | 0.954735i | \(0.596139\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.89681 | 0.146142 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.7230 | 0.850982 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.12811 | −0.154382 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.3025 | −0.459446 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.2766 | −0.681602 | −0.340801 | − | 0.940135i | \(-0.610698\pi\) | ||||
−0.340801 | + | 0.940135i | \(0.610698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0074 | −0.372696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.4484 | −0.909246 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.1683 | −1.49181 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.8528 | 0.439597 | 0.219798 | − | 0.975545i | \(-0.429460\pi\) | ||||
0.219798 | + | 0.975545i | \(0.429460\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.39523 | 0.125749 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.7718 | −1.02718 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.8421 | 0.806757 | 0.403379 | − | 0.915033i | \(-0.367836\pi\) | ||||
0.403379 | + | 0.915033i | \(0.367836\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.42536 | 0.126346 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.951002 | 0.0350306 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.5532 | 0.388207 | 0.194103 | − | 0.980981i | \(-0.437820\pi\) | ||||
0.194103 | + | 0.980981i | \(0.437820\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.00483 | −0.183857 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 53.1325 | 1.94924 | 0.974620 | − | 0.223864i | \(-0.0718672\pi\) | ||||
0.974620 | + | 0.223864i | \(0.0718672\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −41.9878 | −1.53831 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.7381 | −0.758769 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.17531 | −0.298719 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.2243 | 0.920447 | 0.460224 | − | 0.887803i | \(-0.347769\pi\) | ||||
0.460224 | + | 0.887803i | \(0.347769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.0323 | −0.657132 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 60.6926 | 2.20883 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9861 | −0.581025 | −0.290512 | − | 0.956871i | \(-0.593826\pi\) | ||||
−0.290512 | + | 0.956871i | \(0.593826\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.71084 | −0.134695 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.5280 | −1.14289 | −0.571444 | − | 0.820641i | \(-0.693617\pi\) | ||||
−0.571444 | + | 0.820641i | \(0.693617\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.53533 | −0.236595 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 28.0288 | 1.01338 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.48190 | −0.342372 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.2315 | −0.621384 | −0.310692 | − | 0.950511i | \(-0.600561\pi\) | ||||
−0.310692 | + | 0.950511i | \(0.600561\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.9995 | −0.756280 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.9833 | 0.466978 | 0.233489 | − | 0.972359i | \(-0.424986\pi\) | ||||
0.233489 | + | 0.972359i | \(0.424986\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −61.1816 | −2.19771 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.83049 | 0.173293 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.7853 | 1.24631 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.32071 | −0.190390 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.7022 | 0.525414 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.9103 | −0.817705 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.36830 | −0.0844209 | −0.0422105 | − | 0.999109i | \(-0.513440\pi\) | ||||
−0.0422105 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.5242 | 0.588278 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.1221 | 0.502123 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.767842 | −0.0272669 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.48571 | 0.194558 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.0580 | −0.852176 | −0.426088 | − | 0.904682i | \(-0.640109\pi\) | ||||
−0.426088 | + | 0.904682i | \(0.640109\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.1365 | −0.464735 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.0755 | −1.38067 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.36820 | −0.0482826 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.4616 | −0.650684 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.5384 | −0.687784 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.9465 | 1.12318 | 0.561589 | − | 0.827416i | \(-0.310190\pi\) | ||||
0.561589 | + | 0.827416i | \(0.310190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.8926 | −0.874097 | −0.437049 | − | 0.899438i | \(-0.643976\pi\) | ||||
−0.437049 | + | 0.899438i | \(0.643976\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.2455 | −0.429467 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.59183 | 0.160845 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 57.0265 | 1.99510 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.31149 | 0.0807700 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.4488 | −0.957969 | −0.478985 | − | 0.877823i | \(-0.658995\pi\) | ||||
−0.478985 | + | 0.877823i | \(0.658995\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.68587 | −0.128481 | −0.0642407 | − | 0.997934i | \(-0.520463\pi\) | ||||
−0.0642407 | + | 0.997934i | \(0.520463\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.99143 | 0.347857 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.1209 | 0.525807 | 0.262903 | − | 0.964822i | \(-0.415320\pi\) | ||||
0.262903 | + | 0.964822i | \(0.415320\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.78178 | 0.166078 | 0.0830391 | − | 0.996546i | \(-0.473537\pi\) | ||||
0.0830391 | + | 0.996546i | \(0.473537\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.2058 | 0.770312 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.93739 | −0.101774 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.4818 | 1.40093 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.3934 | 0.774028 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.3658 | 1.42811 | 0.714053 | − | 0.700092i | \(-0.246858\pi\) | ||||
0.714053 | + | 0.700092i | \(0.246858\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.8719 | −0.616271 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.49744 | −0.223784 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.12811 | 0.142011 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.3658 | 0.390073 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.0347 | −0.892459 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.8152 | −0.746937 | −0.373469 | − | 0.927643i | \(-0.621832\pi\) | ||||
−0.373469 | + | 0.927643i | \(0.621832\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −57.5542 | −1.96831 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.8757 | 0.644783 | 0.322391 | − | 0.946606i | \(-0.395513\pi\) | ||||
0.322391 | + | 0.946606i | \(0.395513\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.3038 | 0.556279 | 0.278140 | − | 0.960541i | \(-0.410282\pi\) | ||||
0.278140 | + | 0.960541i | \(0.410282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.78538 | 0.163085 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.4059 | 0.524421 | 0.262211 | − | 0.965011i | \(-0.415548\pi\) | ||||
0.262211 | + | 0.965011i | \(0.415548\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.8315 | −0.810297 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.94659 | −0.235919 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.68584 | −0.0571883 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.951002 | −0.0322235 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.1098 | −0.714458 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.0671 | 0.982649 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.787645 | −0.0265969 | −0.0132984 | − | 0.999912i | \(-0.504233\pi\) | ||||
−0.0132984 | + | 0.999912i | \(0.504233\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.01726 | −0.0343115 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.2246 | 0.647694 | 0.323847 | − | 0.946109i | \(-0.395024\pi\) | ||||
0.323847 | + | 0.946109i | \(0.395024\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.7815 | 1.37241 | 0.686204 | − | 0.727409i | \(-0.259276\pi\) | ||||
0.686204 | + | 0.727409i | \(0.259276\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.4789 | 1.09177 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.1173 | −1.48131 | −0.740657 | − | 0.671884i | \(-0.765485\pi\) | ||||
−0.740657 | + | 0.671884i | \(0.765485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.4780 | 0.586193 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.27746 | 0.109799 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.9744 | 0.902663 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 90.8133 | 3.03555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.71084 | 0.123901 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.9496 | 0.565301 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.70423 | −0.156720 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.84508 | 0.261068 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −106.720 | −3.54749 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.1654 | 0.370741 | 0.185371 | − | 0.982669i | \(-0.440651\pi\) | ||||
0.185371 | + | 0.982669i | \(0.440651\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23.9440 | −0.794173 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.8784 | 0.658602 | 0.329301 | − | 0.944225i | \(-0.393187\pi\) | ||||
0.329301 | + | 0.944225i | \(0.393187\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.97176 | 0.296922 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.63014 | 0.0869496 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.9632 | 0.560173 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.7842 | −0.949504 | −0.474752 | − | 0.880120i | \(-0.657462\pi\) | ||||
−0.474752 | + | 0.880120i | \(0.657462\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.2496 | −0.403639 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.32071 | 0.175133 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 70.0984 | 2.30482 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.1321 | 0.759757 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.61071 | 0.216890 | 0.108445 | − | 0.994102i | \(-0.465413\pi\) | ||||
0.108445 | + | 0.994102i | \(0.465413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.03162 | 0.197678 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.5408 | −0.410567 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.1259 | −0.396558 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.7109 | 0.545921 | 0.272961 | − | 0.962025i | \(-0.411997\pi\) | ||||
0.272961 | + | 0.962025i | \(0.411997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.31404 | −0.238685 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.9377 | 0.812946 | 0.406473 | − | 0.913663i | \(-0.366759\pi\) | ||||
0.406473 | + | 0.913663i | \(0.366759\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.7916 | −0.839891 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.1938 | −0.591843 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.8721 | 0.385790 | 0.192895 | − | 0.981219i | \(-0.438212\pi\) | ||||
0.192895 | + | 0.981219i | \(0.438212\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.36820 | 0.0444136 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.7156 | −0.542041 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.5839 | −0.731564 | −0.365782 | − | 0.930700i | \(-0.619199\pi\) | ||||
−0.365782 | + | 0.930700i | \(0.619199\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 60.6427 | 1.96235 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.76800 | −0.0894768 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.4110 | −0.465356 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.18356 | −0.167212 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.8971 | 0.608952 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −96.5411 | −3.10777 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.3246 | −0.332017 | −0.166008 | − | 0.986124i | \(-0.553088\pi\) | ||||
−0.166008 | + | 0.986124i | \(0.553088\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.7011 | −0.472268 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.82234 | −0.154756 | −0.0773781 | − | 0.997002i | \(-0.524655\pi\) | ||||
−0.0773781 | + | 0.997002i | \(0.524655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.86031 | −0.123756 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.99143 | −0.319982 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.0395 | 0.769090 | 0.384545 | − | 0.923106i | \(-0.374358\pi\) | ||||
0.384545 | + | 0.923106i | \(0.374358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.9049 | 0.540283 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.1063 | 0.482308 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.9072 | −1.08147 | −0.540736 | − | 0.841193i | \(-0.681854\pi\) | ||||
−0.540736 | + | 0.841193i | \(0.681854\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.14302 | 0.259458 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.71084 | 0.118117 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.2824 | −1.34450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0541 | −0.509974 | −0.254987 | − | 0.966944i | \(-0.582071\pi\) | ||||
−0.254987 | + | 0.966944i | \(0.582071\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.207571 | −0.00658707 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.77737 | −0.183155 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55.1878 | 1.74781 | 0.873907 | − | 0.486093i | \(-0.161578\pi\) | ||||
0.873907 | + | 0.486093i | \(0.161578\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.6571 | −0.811754 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8008.2.a.q.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.q.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial |