Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.733.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.51820\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.34132 | −1.04707 | −0.523536 | − | 0.852003i | \(-0.675387\pi\) | ||||
−0.523536 | + | 0.852003i | \(0.675387\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.85952 | −0.862179 | −0.431089 | − | 0.902309i | \(-0.641871\pi\) | ||||
−0.431089 | + | 0.902309i | \(0.641871\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.518199 | −0.143722 | −0.0718612 | − | 0.997415i | \(-0.522894\pi\) | ||||
−0.0718612 | + | 0.997415i | \(0.522894\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.34132 | 0.604527 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.17687 | −0.527969 | −0.263985 | − | 0.964527i | \(-0.585037\pi\) | ||||
−0.263985 | + | 0.964527i | \(0.585037\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.14048 | 0.261643 | 0.130822 | − | 0.991406i | \(-0.458238\pi\) | ||||
0.130822 | + | 0.991406i | \(0.458238\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.481801 | 0.0963603 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.17687 | −0.404235 | −0.202118 | − | 0.979361i | \(-0.564782\pi\) | ||||
−0.202118 | + | 0.979361i | \(0.564782\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.89592 | −1.05894 | −0.529469 | − | 0.848329i | \(-0.677609\pi\) | ||||
−0.529469 | + | 0.848329i | \(0.677609\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.85952 | 0.497779 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.34132 | −0.395756 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.89592 | −1.62688 | −0.813440 | − | 0.581649i | \(-0.802408\pi\) | ||||
−0.813440 | + | 0.581649i | \(0.802408\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.518199 | 0.0829782 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.85952 | 1.07128 | 0.535639 | − | 0.844447i | \(-0.320071\pi\) | ||||
0.535639 | + | 0.844447i | \(0.320071\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.23725 | −0.341177 | −0.170588 | − | 0.985342i | \(-0.554567\pi\) | ||||
−0.170588 | + | 0.985342i | \(0.554567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.34132 | −0.349024 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.03640 | 0.734634 | 0.367317 | − | 0.930096i | \(-0.380276\pi\) | ||||
0.367317 | + | 0.930096i | \(0.380276\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.17687 | 0.304823 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.30493 | −0.179246 | −0.0896228 | − | 0.995976i | \(-0.528566\pi\) | ||||
−0.0896228 | + | 0.995976i | \(0.528566\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.69507 | 0.902763 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.14048 | −0.151060 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.41412 | 1.09543 | 0.547713 | − | 0.836667i | \(-0.315499\pi\) | ||||
0.547713 | + | 0.836667i | \(0.315499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.16445 | −0.789277 | −0.394639 | − | 0.918836i | \(-0.629130\pi\) | ||||
−0.394639 | + | 0.918836i | \(0.629130\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.21327 | 0.150488 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.4141 | 1.76096 | 0.880482 | − | 0.474079i | \(-0.157219\pi\) | ||||
0.880482 | + | 0.474079i | \(0.157219\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.51820 | −0.298855 | −0.149428 | − | 0.988773i | \(-0.547743\pi\) | ||||
−0.149428 | + | 0.988773i | \(0.547743\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.21327 | 0.844250 | 0.422125 | − | 0.906538i | \(-0.361284\pi\) | ||||
0.422125 | + | 0.906538i | \(0.361284\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.481801 | −0.0556336 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.85952 | −0.325873 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.85952 | 0.996774 | 0.498387 | − | 0.866955i | \(-0.333926\pi\) | ||||
0.498387 | + | 0.866955i | \(0.333926\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5786 | −1.38068 | −0.690339 | − | 0.723486i | \(-0.742538\pi\) | ||||
−0.690339 | + | 0.723486i | \(0.742538\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.09677 | 0.552822 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.17687 | 0.233385 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.5910 | −1.54664 | −0.773321 | − | 0.634015i | \(-0.781406\pi\) | ||||
−0.773321 | + | 0.634015i | \(0.781406\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.518199 | −0.0543220 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.89592 | 0.611379 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.67023 | −0.273959 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.82313 | 0.185110 | 0.0925552 | − | 0.995708i | \(-0.470497\pi\) | ||||
0.0925552 | + | 0.995708i | \(0.470497\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.85952 | −0.287393 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.0968 | −1.10417 | −0.552085 | − | 0.833788i | \(-0.686168\pi\) | ||||
−0.552085 | + | 0.833788i | \(0.686168\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.70750 | −0.463843 | −0.231922 | − | 0.972734i | \(-0.574501\pi\) | ||||
−0.231922 | + | 0.972734i | \(0.574501\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.34132 | 0.228490 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9563 | −1.15586 | −0.577929 | − | 0.816087i | \(-0.696139\pi\) | ||||
−0.577929 | + | 0.816087i | \(0.696139\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.70662 | −0.738161 | −0.369080 | − | 0.929398i | \(-0.620327\pi\) | ||||
−0.369080 | + | 0.929398i | \(0.620327\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.89592 | 0.939279 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0604 | −0.946400 | −0.473200 | − | 0.880955i | \(-0.656901\pi\) | ||||
−0.473200 | + | 0.880955i | \(0.656901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.34132 | 0.218330 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.518199 | −0.0479075 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.17687 | −0.199554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.82313 | −0.256648 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.85952 | −0.618502 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.5786 | 0.946176 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.5661 | 1.47001 | 0.735004 | − | 0.678063i | \(-0.237180\pi\) | ||||
0.735004 | + | 0.678063i | \(0.237180\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.23725 | 0.196978 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.56702 | −0.835874 | −0.417937 | − | 0.908476i | \(-0.637247\pi\) | ||||
−0.417937 | + | 0.908476i | \(0.637247\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.14048 | 0.0988919 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.34132 | 0.201509 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.57857 | −0.732917 | −0.366458 | − | 0.930434i | \(-0.619430\pi\) | ||||
−0.366458 | + | 0.930434i | \(0.619430\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.97603 | 0.422061 | 0.211031 | − | 0.977479i | \(-0.432318\pi\) | ||||
0.211031 | + | 0.977479i | \(0.432318\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.03640 | −0.424141 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.48180 | 0.123914 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.09677 | 0.423264 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.4017 | −1.83522 | −0.917609 | − | 0.397484i | \(-0.869884\pi\) | ||||
−0.917609 | + | 0.397484i | \(0.869884\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.4745 | 1.34068 | 0.670338 | − | 0.742056i | \(-0.266149\pi\) | ||||
0.670338 | + | 0.742056i | \(0.266149\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.17687 | −0.175990 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.8043 | 1.10879 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.68265 | −0.373716 | −0.186858 | − | 0.982387i | \(-0.559830\pi\) | ||||
−0.186858 | + | 0.982387i | \(0.559830\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.30493 | 0.103487 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4141 | 1.28565 | 0.642827 | − | 0.766012i | \(-0.277762\pi\) | ||||
0.642827 | + | 0.766012i | \(0.277762\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.69507 | −0.521211 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5786 | −0.818594 | −0.409297 | − | 0.912401i | \(-0.634226\pi\) | ||||
−0.409297 | + | 0.912401i | \(0.634226\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7315 | −0.979344 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.14048 | 0.0872144 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.21327 | 0.548415 | 0.274207 | − | 0.961671i | \(-0.411585\pi\) | ||||
0.274207 | + | 0.961671i | \(0.411585\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.481801 | 0.0364208 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.41412 | −0.632444 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.69507 | −0.500413 | −0.250207 | − | 0.968192i | \(-0.580499\pi\) | ||||
−0.250207 | + | 0.968192i | \(0.580499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.0531 | 1.71352 | 0.856760 | − | 0.515715i | \(-0.172474\pi\) | ||||
0.856760 | + | 0.515715i | \(0.172474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.16445 | 0.455689 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.1696 | 1.70346 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.22482 | 0.455204 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.4017 | 1.33150 | 0.665750 | − | 0.746175i | \(-0.268112\pi\) | ||||
0.665750 | + | 0.746175i | \(0.268112\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0364 | 1.08234 | 0.541172 | − | 0.840912i | \(-0.317981\pi\) | ||||
0.541172 | + | 0.840912i | \(0.317981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.21327 | −0.0868842 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6274 | 0.828417 | 0.414209 | − | 0.910182i | \(-0.364058\pi\) | ||||
0.414209 | + | 0.910182i | \(0.364058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.7679 | 1.75575 | 0.877874 | − | 0.478892i | \(-0.158961\pi\) | ||||
0.877874 | + | 0.478892i | \(0.158961\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.4141 | −1.01669 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.17687 | −0.152787 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.0604 | −1.12170 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.26122 | −0.225583 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0167 | 1.24032 | 0.620159 | − | 0.784476i | \(-0.287068\pi\) | ||||
0.620159 | + | 0.784476i | \(0.287068\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.51820 | 0.172544 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.23812 | 0.357237 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.89592 | −0.400241 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.21327 | −0.487428 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.12805 | 0.0758811 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9760 | 0.868939 | 0.434469 | − | 0.900687i | \(-0.356936\pi\) | ||||
0.434469 | + | 0.900687i | \(0.356936\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.481801 | 0.0321201 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.73147 | −0.114922 | −0.0574609 | − | 0.998348i | \(-0.518300\pi\) | ||||
−0.0574609 | + | 0.998348i | \(0.518300\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.4985 | −1.02417 | −0.512084 | − | 0.858936i | \(-0.671126\pi\) | ||||
−0.512084 | + | 0.858936i | \(0.671126\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.85952 | 0.188143 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.01242 | −0.524911 | −0.262456 | − | 0.964944i | \(-0.584532\pi\) | ||||
−0.262456 | + | 0.964944i | \(0.584532\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.7918 | −0.769215 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.85952 | −0.575488 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.36617 | −0.153055 | −0.0765275 | − | 0.997067i | \(-0.524383\pi\) | ||||
−0.0765275 | + | 0.997067i | \(0.524383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.54217 | 0.228171 | 0.114086 | − | 0.993471i | \(-0.463606\pi\) | ||||
0.114086 | + | 0.993471i | \(0.463606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.34132 | −0.149582 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.590993 | −0.0376040 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.5786 | 0.797134 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.5473 | 1.54941 | 0.774705 | − | 0.632322i | \(-0.217898\pi\) | ||||
0.774705 | + | 0.632322i | \(0.217898\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.85952 | 0.179777 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.09677 | −0.319172 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.4629 | 1.33882 | 0.669411 | − | 0.742893i | \(-0.266547\pi\) | ||||
0.669411 | + | 0.742893i | \(0.266547\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.89592 | −0.614903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.17687 | −0.134745 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.9075 | −0.919234 | −0.459617 | − | 0.888117i | \(-0.652013\pi\) | ||||
−0.459617 | + | 0.888117i | \(0.652013\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.05526 | 0.187683 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.5910 | 0.892954 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.52975 | 0.581039 | 0.290520 | − | 0.956869i | \(-0.406172\pi\) | ||||
0.290520 | + | 0.956869i | \(0.406172\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.50578 | 0.516689 | 0.258345 | − | 0.966053i | \(-0.416823\pi\) | ||||
0.258345 | + | 0.966053i | \(0.416823\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.518199 | 0.0313628 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.37772 | −0.0830798 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.51820 | −0.511809 | −0.255904 | − | 0.966702i | \(-0.582373\pi\) | ||||
−0.255904 | + | 0.966702i | \(0.582373\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.89592 | −0.352980 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.3289 | 1.09341 | 0.546705 | − | 0.837325i | \(-0.315882\pi\) | ||||
0.546705 | + | 0.837325i | \(0.315882\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.69507 | 0.279093 | 0.139547 | − | 0.990216i | \(-0.455436\pi\) | ||||
0.139547 | + | 0.990216i | \(0.455436\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.67023 | 0.158171 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.85952 | 0.404905 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.2612 | −0.721248 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.82313 | −0.106874 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.63470 | 0.153921 | 0.0769604 | − | 0.997034i | \(-0.475478\pi\) | ||||
0.0769604 | + | 0.997034i | \(0.475478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.7002 | −1.14699 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.85952 | 0.165926 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.518199 | 0.0299682 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.23725 | −0.128953 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.0968 | 0.637493 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.4330 | 0.826430 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.45783 | 0.368568 | 0.184284 | − | 0.982873i | \(-0.441003\pi\) | ||||
0.184284 | + | 0.982873i | \(0.441003\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.70750 | 0.267800 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6753 | 0.888867 | 0.444433 | − | 0.895812i | \(-0.353405\pi\) | ||||
0.444433 | + | 0.895812i | \(0.353405\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.4496 | 1.94721 | 0.973605 | − | 0.228242i | \(-0.0732976\pi\) | ||||
0.973605 | + | 0.228242i | \(0.0732976\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.34132 | −0.131919 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.98758 | −0.223965 | −0.111982 | − | 0.993710i | \(-0.535720\pi\) | ||||
−0.111982 | + | 0.993710i | \(0.535720\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.22482 | 0.348523 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.9563 | 0.667335 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.48267 | −0.138140 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.249669 | −0.0138491 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.70662 | 0.426177 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.03640 | 0.277666 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.7190 | −0.754067 | −0.377034 | − | 0.926200i | \(-0.623056\pi\) | ||||
−0.377034 | + | 0.926200i | \(0.623056\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.89592 | −0.542293 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −33.7481 | −1.84386 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.3580 | 1.21792 | 0.608959 | − | 0.793202i | \(-0.291588\pi\) | ||||
0.608959 | + | 0.793202i | \(0.291588\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.0604 | 0.546404 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.8595 | 0.912994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.34132 | −0.126053 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −31.7357 | −1.70366 | −0.851831 | − | 0.523817i | \(-0.824508\pi\) | ||||
−0.851831 | + | 0.523817i | \(0.824508\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.670226 | 0.0358764 | 0.0179382 | − | 0.999839i | \(-0.494290\pi\) | ||||
0.0179382 | + | 0.999839i | \(0.494290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.518199 | 0.0276594 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.9323 | 1.53991 | 0.769956 | − | 0.638097i | \(-0.220278\pi\) | ||||
0.769956 | + | 0.638097i | \(0.220278\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.89592 | 0.312923 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.17687 | 0.115212 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.0355 | −0.846323 | −0.423161 | − | 0.906054i | \(-0.639080\pi\) | ||||
−0.423161 | + | 0.906054i | \(0.639080\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6993 | −0.931543 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.82313 | 0.148176 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.8886 | −0.883990 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.566147 | −0.0295526 | −0.0147763 | − | 0.999891i | \(-0.504704\pi\) | ||||
−0.0147763 | + | 0.999891i | \(0.504704\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.85952 | 0.357093 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.30493 | −0.0677484 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.9687 | −1.44817 | −0.724083 | − | 0.689713i | \(-0.757737\pi\) | ||||
−0.724083 | + | 0.689713i | \(0.757737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5786 | −0.546275 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.12805 | 0.0580977 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.426543 | 0.0219100 | 0.0109550 | − | 0.999940i | \(-0.496513\pi\) | ||||
0.0109550 | + | 0.999940i | \(0.496513\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.5661 | −0.848709 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.9323 | 1.37618 | 0.688089 | − | 0.725627i | \(-0.258450\pi\) | ||||
0.688089 | + | 0.725627i | \(0.258450\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.69507 | 0.341213 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.23725 | −0.113726 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.6878 | 0.693997 | 0.346999 | − | 0.937866i | \(-0.387201\pi\) | ||||
0.346999 | + | 0.937866i | \(0.387201\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.17687 | 0.110089 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.56702 | 0.482592 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.7430 | −1.04369 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.4132 | 0.873946 | 0.436973 | − | 0.899475i | \(-0.356051\pi\) | ||||
0.436973 | + | 0.899475i | \(0.356051\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.14048 | −0.0570952 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.82313 | −0.490544 | −0.245272 | − | 0.969454i | \(-0.578877\pi\) | ||||
−0.245272 | + | 0.969454i | \(0.578877\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.05526 | 0.152193 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.34132 | −0.116341 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.2976 | 1.40266 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.6993 | 1.41909 | 0.709545 | − | 0.704660i | \(-0.248901\pi\) | ||||
0.709545 | + | 0.704660i | \(0.248901\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.57857 | 0.423150 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.41412 | 0.414032 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.4505 | 1.44567 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.97603 | −0.243677 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.3893 | 0.507549 | 0.253775 | − | 0.967263i | \(-0.418328\pi\) | ||||
0.253775 | + | 0.967263i | \(0.418328\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.55460 | −0.173240 | −0.0866202 | − | 0.996241i | \(-0.527607\pi\) | ||||
−0.0866202 | + | 0.996241i | \(0.527607\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.03640 | 0.244878 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.04882 | −0.0508753 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.16445 | −0.298319 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.48180 | −0.0715420 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.6389 | −1.47583 | −0.737913 | − | 0.674896i | \(-0.764189\pi\) | ||||
−0.737913 | + | 0.674896i | \(0.764189\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3289 | 1.26529 | 0.632643 | − | 0.774443i | \(-0.281970\pi\) | ||||
0.632643 | + | 0.774443i | \(0.281970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.09677 | −0.244371 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.14048 | −0.0545564 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1769 | 0.581170 | 0.290585 | − | 0.956849i | \(-0.406150\pi\) | ||||
0.290585 | + | 0.956849i | \(0.406150\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.8034 | 0.608308 | 0.304154 | − | 0.952623i | \(-0.401626\pi\) | ||||
0.304154 | + | 0.952623i | \(0.401626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 34.1623 | 1.61945 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.4017 | 1.05956 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.6702 | 0.786717 | 0.393358 | − | 0.919385i | \(-0.371313\pi\) | ||||
0.393358 | + | 0.919385i | \(0.371313\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.6150 | −0.923633 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.4745 | −0.774039 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.21327 | 0.0568790 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.4754 | 0.723907 | 0.361953 | − | 0.932196i | \(-0.382110\pi\) | ||||
0.361953 | + | 0.932196i | \(0.382110\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.17687 | 0.101608 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.1696 | −1.17226 | −0.586132 | − | 0.810216i | \(-0.699350\pi\) | ||||
−0.586132 | + | 0.810216i | \(0.699350\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.55372 | −0.304577 | −0.152289 | − | 0.988336i | \(-0.548664\pi\) | ||||
−0.152289 | + | 0.988336i | \(0.548664\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.8043 | −0.640157 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.56702 | −0.165062 | −0.0825310 | − | 0.996588i | \(-0.526300\pi\) | ||||
−0.0825310 | + | 0.996588i | \(0.526300\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.4141 | 0.665582 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.68265 | 0.215765 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.39746 | 0.294155 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.549483 | 0.0252120 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.30493 | −0.0597485 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.6034 | 0.667247 | 0.333624 | − | 0.942706i | \(-0.391729\pi\) | ||||
0.333624 | + | 0.942706i | \(0.391729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.12805 | 0.233819 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.26853 | −0.193824 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7606 | −1.25795 | −0.628975 | − | 0.777425i | \(-0.716525\pi\) | ||||
−0.628975 | + | 0.777425i | \(0.716525\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.4141 | −0.742272 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.3828 | −0.739347 | −0.369673 | − | 0.929162i | \(-0.620530\pi\) | ||||
−0.369673 | + | 0.929162i | \(0.620530\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.73878 | 0.213424 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.69507 | 0.300921 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.51820 | −0.112957 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.6951 | 1.37410 | 0.687050 | − | 0.726610i | \(-0.258905\pi\) | ||||
0.687050 | + | 0.726610i | \(0.258905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.5786 | 0.472616 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.74302 | −0.389832 | −0.194916 | − | 0.980820i | \(-0.562443\pi\) | ||||
−0.194916 | + | 0.980820i | \(0.562443\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.9811 | 1.15615 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.7315 | 0.565424 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.24456 | −0.143812 | −0.0719062 | − | 0.997411i | \(-0.522908\pi\) | ||||
−0.0719062 | + | 0.997411i | \(0.522908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.21327 | 0.319096 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.14048 | −0.0503533 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.0218 | 0.485678 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.4017 | −0.633386 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.21327 | −0.316627 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.48911 | 0.196672 | 0.0983358 | − | 0.995153i | \(-0.468648\pi\) | ||||
0.0983358 | + | 0.995153i | \(0.468648\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.4150 | 0.499143 | 0.249571 | − | 0.968356i | \(-0.419710\pi\) | ||||
0.249571 | + | 0.968356i | \(0.419710\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.481801 | −0.0210275 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.8347 | 0.559087 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.41412 | 0.365142 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.55460 | −0.153967 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.9936 | 1.21027 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.69507 | 0.288914 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.85952 | −0.123168 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1935 | 0.524241 | 0.262121 | − | 0.965035i | \(-0.415578\pi\) | ||||
0.262121 | + | 0.965035i | \(0.415578\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.0531 | −0.989302 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.0437 | 0.772908 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.7679 | 1.23003 | 0.615013 | − | 0.788517i | \(-0.289151\pi\) | ||||
0.615013 | + | 0.788517i | \(0.289151\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.16445 | −0.263092 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.48267 | −0.105765 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.85952 | 0.376745 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23.1696 | −0.983493 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.8282 | 0.882521 | 0.441260 | − | 0.897379i | \(-0.354532\pi\) | ||||
0.441260 | + | 0.897379i | \(0.354532\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.15934 | 0.0490348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.22482 | −0.262812 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.6869 | 0.787559 | 0.393779 | − | 0.919205i | \(-0.371167\pi\) | ||||
0.393779 | + | 0.919205i | \(0.371167\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.5546 | 0.990949 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.6463 | −0.907458 | −0.453729 | − | 0.891140i | \(-0.649907\pi\) | ||||
−0.453729 | + | 0.891140i | \(0.649907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.6398 | 1.07299 | 0.536496 | − | 0.843903i | \(-0.319747\pi\) | ||||
0.536496 | + | 0.843903i | \(0.319747\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.4017 | −0.768742 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.481801 | −0.0200925 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.9490 | −1.12190 | −0.560950 | − | 0.827849i | \(-0.689564\pi\) | ||||
−0.560950 | + | 0.827849i | \(0.689564\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.0364 | −0.624891 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.5786 | −0.521847 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.73147 | 0.154542 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.21327 | 0.0501626 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.4672 | 1.46389 | 0.731944 | − | 0.681365i | \(-0.238613\pi\) | ||||
0.731944 | + | 0.681365i | \(0.238613\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.72416 | −0.277064 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.6274 | −0.478287 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.96360 | 0.368091 | 0.184046 | − | 0.982918i | \(-0.441081\pi\) | ||||
0.184046 | + | 0.982918i | \(0.441081\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.09677 | 0.208947 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.7679 | −1.01368 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.799152 | −0.0326525 | −0.0163262 | − | 0.999867i | \(-0.505197\pi\) | ||||
−0.0163262 | + | 0.999867i | \(0.505197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.4869 | 1.65150 | 0.825748 | − | 0.564039i | \(-0.190753\pi\) | ||||
0.825748 | + | 0.564039i | \(0.190753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.4141 | 0.586988 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.60985 | 0.268729 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.2985 | −0.864479 | −0.432240 | − | 0.901759i | \(-0.642276\pi\) | ||||
−0.432240 | + | 0.901759i | \(0.642276\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.17687 | 0.0882114 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.60985 | −0.105583 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.5786 | −0.750381 | −0.375191 | − | 0.926948i | \(-0.622423\pi\) | ||||
−0.375191 | + | 0.926948i | \(0.622423\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.0604 | 0.647617 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.4818 | 0.784308 | 0.392154 | − | 0.919900i | \(-0.371730\pi\) | ||||
0.392154 | + | 0.919900i | \(0.371730\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.3349 | −0.817328 | −0.408664 | − | 0.912685i | \(-0.634005\pi\) | ||||
−0.408664 | + | 0.912685i | \(0.634005\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.5910 | −0.584576 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.1769 | −1.08707 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.26122 | 0.130241 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.5422 | 0.858943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.3340 | −0.849294 | −0.424647 | − | 0.905359i | \(-0.639602\pi\) | ||||
−0.424647 | + | 0.905359i | \(0.639602\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.0167 | −0.716098 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.7867 | −1.53920 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.518199 | −0.0205318 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.51820 | −0.0996184 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.7117 | 1.52902 | 0.764511 | − | 0.644611i | \(-0.222981\pi\) | ||||
0.764511 | + | 0.644611i | \(0.222981\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.0291 | 1.49972 | 0.749860 | − | 0.661596i | \(-0.230121\pi\) | ||||
0.749860 | + | 0.661596i | \(0.230121\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.23812 | −0.206251 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.1811 | −1.57968 | −0.789841 | − | 0.613311i | \(-0.789837\pi\) | ||||
−0.789841 | + | 0.613311i | \(0.789837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0604 | −0.944452 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.89592 | 0.231079 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.2060 | 0.712454 | 0.356227 | − | 0.934399i | \(-0.384063\pi\) | ||||
0.356227 | + | 0.934399i | \(0.384063\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.3995 | 0.875221 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.21327 | 0.281417 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.7242 | 1.89802 | 0.949012 | − | 0.315240i | \(-0.102085\pi\) | ||||
0.949012 | + | 0.315240i | \(0.102085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.0646 | −1.24717 | −0.623584 | − | 0.781756i | \(-0.714324\pi\) | ||||
−0.623584 | + | 0.781756i | \(0.714324\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.12805 | −0.0438100 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.67023 | −0.103547 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.17687 | 0.0842889 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.9760 | −0.501682 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.6274 | 0.680498 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.2612 | 0.511182 | 0.255591 | − | 0.966785i | \(-0.417730\pi\) | ||||
0.255591 | + | 0.966785i | \(0.417730\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.481801 | −0.0185445 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.6274 | −0.523743 | −0.261872 | − | 0.965103i | \(-0.584340\pi\) | ||||
−0.261872 | + | 0.965103i | \(0.584340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.82313 | 0.0699652 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.73147 | 0.0663501 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.77518 | −0.374037 | −0.187018 | − | 0.982356i | \(-0.559882\pi\) | ||||
−0.187018 | + | 0.982356i | \(0.559882\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.0852 | 0.767417 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.4985 | 0.591303 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.676212 | 0.0257616 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7002 | −0.749430 | −0.374715 | − | 0.927140i | \(-0.622260\pi\) | ||||
−0.374715 | + | 0.927140i | \(0.622260\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.85952 | −0.108624 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.6505 | −0.441928 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.9323 | −0.565602 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.01242 | 0.303058 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.6223 | −0.627815 | −0.313907 | − | 0.949454i | \(-0.601638\pi\) | ||||
−0.313907 | + | 0.949454i | \(0.601638\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.2861 | −0.425662 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.7918 | 0.444106 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.0968 | −0.417337 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.6389 | 1.45112 | 0.725558 | − | 0.688161i | \(-0.241582\pi\) | ||||
0.725558 | + | 0.688161i | \(0.241582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.85952 | 0.332258 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.89592 | 0.220804 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.46938 | −0.129747 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.36617 | 0.0883663 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.6878 | −0.957992 | −0.478996 | − | 0.877817i | \(-0.658999\pi\) | ||||
−0.478996 | + | 0.877817i | \(0.658999\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.70750 | −0.175316 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.54217 | −0.131735 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.04882 | −0.0389522 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2248 | −0.675921 | −0.337961 | − | 0.941160i | \(-0.609737\pi\) | ||||
−0.337961 | + | 0.941160i | \(0.609737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.87020 | 0.180131 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.46294 | 0.275650 | 0.137825 | − | 0.990457i | \(-0.455989\pi\) | ||||
0.137825 | + | 0.990457i | \(0.455989\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.34132 | 0.0863611 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41.2175 | −1.51827 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.3704 | −0.822909 | −0.411454 | − | 0.911430i | \(-0.634979\pi\) | ||||
−0.411454 | + | 0.911430i | \(0.634979\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.590993 | 0.0217107 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.3529 | 0.856734 | 0.428367 | − | 0.903605i | \(-0.359089\pi\) | ||||
0.428367 | + | 0.903605i | \(0.359089\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 52.4496 | 1.92161 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.5786 | −0.460226 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.9563 | −0.436873 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.3165 | 0.814340 | 0.407170 | − | 0.913352i | \(-0.366516\pi\) | ||||
0.407170 | + | 0.913352i | \(0.366516\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.5473 | −0.894553 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.5721 | −1.40378 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.23812 | 0.190383 | 0.0951913 | − | 0.995459i | \(-0.469654\pi\) | ||||
0.0951913 | + | 0.995459i | \(0.469654\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.85952 | −0.103794 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7190 | 0.424815 | 0.212408 | − | 0.977181i | \(-0.431870\pi\) | ||||
0.212408 | + | 0.977181i | \(0.431870\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.70662 | −0.278999 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.09677 | 0.184274 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.36019 | −0.157437 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.7439 | −0.567739 | −0.283870 | − | 0.958863i | \(-0.591618\pi\) | ||||
−0.283870 | + | 0.958863i | \(0.591618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.4629 | −0.772969 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.6514 | 0.742778 | 0.371389 | − | 0.928477i | \(-0.378882\pi\) | ||||
0.371389 | + | 0.928477i | \(0.378882\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.84066 | −0.102040 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.89592 | 0.355014 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.82313 | 0.280293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.20085 | 0.257667 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.17687 | 0.0777951 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.9636 | 0.391308 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.83044 | 0.243479 | 0.121739 | − | 0.992562i | \(-0.461153\pi\) | ||||
0.121739 | + | 0.992562i | \(0.461153\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.9075 | 0.530720 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.0604 | −0.357706 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.19441 | 0.113437 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.05526 | −0.108359 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.67110 | −0.130037 | −0.0650185 | − | 0.997884i | \(-0.520711\pi\) | ||||
−0.0650185 | + | 0.997884i | \(0.520711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.9636 | −0.387864 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.5910 | −0.515547 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.6265 | −0.727894 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.34132 | 0.0825209 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.52975 | −0.335463 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.9083 | −0.488991 | −0.244496 | − | 0.969650i | \(-0.578622\pi\) | ||||
−0.244496 | + | 0.969650i | \(0.578622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.6398 | 0.689647 | 0.344824 | − | 0.938668i | \(-0.387939\pi\) | ||||
0.344824 | + | 0.938668i | \(0.387939\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.50578 | −0.298311 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.4308 | −1.34617 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.55153 | −0.0892666 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.518199 | −0.0181073 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.9752 | 0.627337 | 0.313669 | − | 0.949533i | \(-0.398442\pi\) | ||||
0.313669 | + | 0.949533i | \(0.398442\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.96448 | −0.138193 | −0.0690965 | − | 0.997610i | \(-0.522012\pi\) | ||||
−0.0690965 | + | 0.997610i | \(0.522012\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.37772 | 0.0479661 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.2570 | 0.739178 | 0.369589 | − | 0.929195i | \(-0.379499\pi\) | ||||
0.369589 | + | 0.929195i | \(0.379499\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.82313 | −0.202246 | −0.101123 | − | 0.994874i | \(-0.532243\pi\) | ||||
−0.101123 | + | 0.994874i | \(0.532243\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.51820 | 0.295493 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.17687 | −0.0754242 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.7679 | 0.857127 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.89592 | 0.203793 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.1760 | 0.662029 | 0.331015 | − | 0.943626i | \(-0.392609\pi\) | ||||
0.331015 | + | 0.943626i | \(0.392609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2612 | −0.836594 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.3289 | −0.631281 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.8085 | 1.02544 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.82313 | −0.0970038 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.69507 | −0.161134 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.89592 | 0.339228 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.32890 | 0.216697 | 0.108349 | − | 0.994113i | \(-0.465444\pi\) | ||||
0.108349 | + | 0.994113i | \(0.465444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.67023 | −0.0913198 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.4017 | 0.833546 | 0.416773 | − | 0.909011i | \(-0.363161\pi\) | ||||
0.416773 | + | 0.909011i | \(0.363161\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.9884 | −0.374921 | −0.187461 | − | 0.982272i | \(-0.560026\pi\) | ||||
−0.187461 | + | 0.982272i | \(0.560026\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.85952 | −0.233772 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −56.8282 | −1.93446 | −0.967228 | − | 0.253910i | \(-0.918283\pi\) | ||||
−0.967228 | + | 0.253910i | \(0.918283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.8886 | −0.574230 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.2612 | 0.416413 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.3340 | −0.859398 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.46938 | −0.253090 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.82313 | 0.0617035 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.5786 | 0.357621 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.71905 | −0.260654 | −0.130327 | − | 0.991471i | \(-0.541603\pi\) | ||||
−0.130327 | + | 0.991471i | \(0.541603\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.63470 | −0.0888663 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.8895 | 1.07438 | 0.537192 | − | 0.843460i | \(-0.319485\pi\) | ||||
0.537192 | + | 0.843460i | \(0.319485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.1396 | −0.610446 | −0.305223 | − | 0.952281i | \(-0.598731\pi\) | ||||
−0.305223 | + | 0.952281i | \(0.598731\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.7002 | 0.662214 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.0903 | 0.842451 | 0.421225 | − | 0.906956i | \(-0.361600\pi\) | ||||
0.421225 | + | 0.906956i | \(0.361600\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.5661 | 0.555611 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.85952 | −0.0957976 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.74389 | 0.192212 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.6753 | 0.523969 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.518199 | −0.0173022 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.8347 | 0.428060 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.84066 | 0.0946362 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.23725 | 0.0744509 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −53.9747 | −1.79418 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.0373 | −0.399691 | −0.199845 | − | 0.979827i | \(-0.564044\pi\) | ||||
−0.199845 | + | 0.979827i | \(0.564044\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.0968 | −0.368057 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.9636 | −0.495766 | −0.247883 | − | 0.968790i | \(-0.579735\pi\) | ||||
−0.247883 | + | 0.968790i | \(0.579735\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.9687 | 1.19039 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.4330 | −0.477140 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.56702 | −0.315931 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.04284 | −0.0344000 | −0.0172000 | − | 0.999852i | \(-0.505475\pi\) | ||||
−0.0172000 | + | 0.999852i | \(0.505475\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.45783 | −0.212793 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.30493 | 0.0429522 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.76787 | −0.156767 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.70750 | −0.154614 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.91478 | −0.194058 | −0.0970288 | − | 0.995282i | \(-0.530934\pi\) | ||||
−0.0970288 | + | 0.995282i | \(0.530934\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.14048 | 0.0373776 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.6753 | −0.513188 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.5743 | −0.476632 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.88262 | −0.290183 | −0.145091 | − | 0.989418i | \(-0.546348\pi\) | ||||
−0.145091 | + | 0.989418i | \(0.546348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.4496 | −1.12422 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.87619 | −0.0937610 | −0.0468805 | − | 0.998901i | \(-0.514928\pi\) | ||||
−0.0468805 | + | 0.998901i | \(0.514928\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.85952 | −0.223377 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.34132 | 0.0761633 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.3537 | 1.31132 | 0.655660 | − | 0.755056i | \(-0.272390\pi\) | ||||
0.655660 | + | 0.755056i | \(0.272390\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.73791 | −0.121338 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.98758 | 0.129306 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.8702 | 0.352120 | 0.176060 | − | 0.984379i | \(-0.443665\pi\) | ||||
0.176060 | + | 0.984379i | \(0.443665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43.0843 | −1.39418 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.22482 | −0.201220 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.57857 | −0.277016 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.76188 | 0.121351 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.9563 | −0.385286 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.2051 | −1.13329 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.01155 | −0.289792 | −0.144896 | − | 0.989447i | \(-0.546285\pi\) | ||||
−0.144896 | + | 0.989447i | \(0.546285\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.48267 | 0.0797550 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.0655 | 0.483474 | 0.241737 | − | 0.970342i | \(-0.422283\pi\) | ||||
0.241737 | + | 0.970342i | \(0.422283\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.97603 | 0.159524 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.249669 | 0.00799580 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.9083 | 0.572939 | 0.286469 | − | 0.958089i | \(-0.407518\pi\) | ||||
0.286469 | + | 0.958089i | \(0.407518\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.7233 | 1.33348 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.70662 | −0.246054 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.77518 | −0.311780 | −0.155890 | − | 0.987774i | \(-0.549824\pi\) | ||||
−0.155890 | + | 0.987774i | \(0.549824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.2235 | −0.867413 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.03640 | −0.160310 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.23725 | 0.0711403 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.1281 | −0.671155 | −0.335577 | − | 0.942013i | \(-0.608931\pi\) | ||||
−0.335577 | + | 0.942013i | \(0.608931\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.7190 | 0.435361 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −57.9896 | −1.83839 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.1769 | 1.08239 | 0.541196 | − | 0.840896i | \(-0.317972\pi\) | ||||
0.541196 | + | 0.840896i | \(0.317972\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.89592 | 0.313093 |
(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 | 7728.2.a.bq.1.2 | 3 | ||
4.3 | odd | 2 | 3864.2.a.o.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.o.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
7728.2.a.bq.1.2 | 3 | 1.1 | even | 1 | trivial |