Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,2,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(14.8202346151\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.17557\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | 3.07768 | 1.77690 | 0.888451 | − | 0.458972i | \(-0.151782\pi\) | ||||
0.888451 | + | 0.458972i | \(0.151782\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.23607 | 1.89443 | 0.947214 | − | 0.320603i | \(-0.103886\pi\) | ||||
0.947214 | + | 0.320603i | \(0.103886\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.35114 | 0.888648 | 0.444324 | − | 0.895866i | \(-0.353444\pi\) | ||||
0.444324 | + | 0.895866i | \(0.353444\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.47214 | 2.15738 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.53077 | −1.36608 | −0.683039 | − | 0.730382i | \(-0.739342\pi\) | ||||
−0.683039 | + | 0.730382i | \(0.739342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.76393 | 0.489227 | 0.244613 | − | 0.969621i | \(-0.421339\pi\) | ||||
0.244613 | + | 0.969621i | \(0.421339\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.0373 | 3.36621 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.23607 | −1.26993 | −0.634967 | − | 0.772540i | \(-0.718986\pi\) | ||||
−0.634967 | + | 0.772540i | \(0.718986\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.15537 | −1.41214 | −0.706069 | − | 0.708143i | \(-0.749533\pi\) | ||||
−0.706069 | + | 0.708143i | \(0.749533\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.23607 | 1.57904 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.80423 | −0.793236 | −0.396618 | − | 0.917984i | \(-0.629816\pi\) | ||||
−0.396618 | + | 0.917984i | \(0.629816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.9443 | 2.58885 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.6861 | 2.05655 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.726543 | 0.130491 | 0.0652454 | − | 0.997869i | \(-0.479217\pi\) | ||||
0.0652454 | + | 0.997869i | \(0.479217\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13.9443 | −2.42739 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.95959 | 1.68348 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.47214 | −0.406417 | −0.203208 | − | 0.979136i | \(-0.565137\pi\) | ||||
−0.203208 | + | 0.979136i | \(0.565137\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.42882 | 0.869308 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.23607 | −1.13008 | −0.565042 | − | 0.825062i | \(-0.691140\pi\) | ||||
−0.565042 | + | 0.825062i | \(0.691140\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.98385 | 0.912529 | 0.456265 | − | 0.889844i | \(-0.349187\pi\) | ||||
0.456265 | + | 0.889844i | \(0.349187\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 27.4164 | 4.08700 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.42882 | −0.791875 | −0.395938 | − | 0.918277i | \(-0.629580\pi\) | ||||
−0.395938 | + | 0.918277i | \(0.629580\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.47214 | −0.210305 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.1150 | −2.25655 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.76393 | 0.517016 | 0.258508 | − | 0.966009i | \(-0.416769\pi\) | ||||
0.258508 | + | 0.966009i | \(0.416769\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.1926 | −2.58794 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.9443 | −2.50923 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.71040 | −0.873619 | −0.436810 | − | 0.899554i | \(-0.643892\pi\) | ||||
−0.436810 | + | 0.899554i | \(0.643892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.76393 | 0.353885 | 0.176943 | − | 0.984221i | \(-0.443379\pi\) | ||||
0.176943 | + | 0.984221i | \(0.443379\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.2169 | 1.91715 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.47214 | 0.926804 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3107 | 1.50400 | 0.751998 | − | 0.659166i | \(-0.229090\pi\) | ||||
0.751998 | + | 0.659166i | \(0.229090\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.7082 | −1.40950 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.24920 | −0.385609 | −0.192804 | − | 0.981237i | \(-0.561758\pi\) | ||||
−0.192804 | + | 0.981237i | \(0.561758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.94427 | −0.578683 | −0.289342 | − | 0.957226i | \(-0.593436\pi\) | ||||
−0.289342 | + | 0.957226i | \(0.593436\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 39.8384 | 4.60014 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.6525 | −1.21396 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.17963 | −0.245227 | −0.122614 | − | 0.992454i | \(-0.539128\pi\) | ||||
−0.122614 | + | 0.992454i | \(0.539128\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.4721 | 1.49690 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.1150 | −1.76885 | −0.884423 | − | 0.466685i | \(-0.845448\pi\) | ||||
−0.884423 | + | 0.466685i | \(0.845448\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.1803 | −2.40580 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.07768 | −0.329962 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.70820 | 0.181069 | 0.0905346 | − | 0.995893i | \(-0.471142\pi\) | ||||
0.0905346 | + | 0.995893i | \(0.471142\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.14725 | 0.434750 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.23607 | 0.231869 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26.0746 | −2.67519 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.70820 | 0.985719 | 0.492859 | − | 0.870109i | \(-0.335952\pi\) | ||||
0.492859 | + | 0.870109i | \(0.335952\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −29.3238 | −2.94715 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4164 | 1.53399 | 0.766995 | − | 0.641653i | \(-0.221751\pi\) | ||||
0.766995 | + | 0.641653i | \(0.221751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.24920 | 0.320153 | 0.160076 | − | 0.987105i | \(-0.448826\pi\) | ||||
0.160076 | + | 0.987105i | \(0.448826\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30.6525 | 2.99138 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.35114 | −0.227293 | −0.113647 | − | 0.993521i | \(-0.536253\pi\) | ||||
−0.113647 | + | 0.993521i | \(0.536253\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.76393 | 0.168954 | 0.0844770 | − | 0.996425i | \(-0.473078\pi\) | ||||
0.0844770 | + | 0.996425i | \(0.473078\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.60845 | −0.722162 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.94427 | −0.276974 | −0.138487 | − | 0.990364i | \(-0.544224\pi\) | ||||
−0.138487 | + | 0.990364i | \(0.544224\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.1150 | −1.50273 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.4164 | 1.05545 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.3107 | −1.12852 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.52786 | 0.866169 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.2703 | −2.00805 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 33.6525 | 3.00997 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.15537 | 0.546201 | 0.273100 | − | 0.961986i | \(-0.411951\pi\) | ||||
0.273100 | + | 0.961986i | \(0.411951\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.4164 | 1.62147 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.35926 | 0.380870 | 0.190435 | − | 0.981700i | \(-0.439010\pi\) | ||||
0.190435 | + | 0.981700i | \(0.439010\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.4721 | −1.25489 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 45.2672 | 3.89598 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.4164 | 0.975370 | 0.487685 | − | 0.873020i | \(-0.337842\pi\) | ||||
0.487685 | + | 0.873020i | \(0.337842\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.898056 | −0.0761721 | −0.0380861 | − | 0.999274i | \(-0.512126\pi\) | ||||
−0.0380861 | + | 0.999274i | \(0.512126\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.7082 | −1.40708 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.99197 | −0.668322 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.23607 | −0.351786 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.53077 | −0.373691 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.23607 | 0.674725 | 0.337362 | − | 0.941375i | \(-0.390465\pi\) | ||||
0.337362 | + | 0.941375i | \(0.390465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −24.0664 | −1.95850 | −0.979250 | − | 0.202658i | \(-0.935042\pi\) | ||||
−0.979250 | + | 0.202658i | \(0.935042\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −33.8885 | −2.73973 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.07768 | 0.247205 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.70820 | 0.774799 | 0.387400 | − | 0.921912i | \(-0.373373\pi\) | ||||
0.387400 | + | 0.921912i | \(0.373373\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5842 | 0.918686 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.94427 | −0.704907 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.28157 | −0.100380 | −0.0501902 | − | 0.998740i | \(-0.515983\pi\) | ||||
−0.0501902 | + | 0.998740i | \(0.515983\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −59.0689 | −4.59851 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.8576 | −0.840190 | −0.420095 | − | 0.907480i | \(-0.638003\pi\) | ||||
−0.420095 | + | 0.907480i | \(0.638003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.88854 | −0.760657 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −39.8384 | −3.04652 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.4721 | 1.55647 | 0.778234 | − | 0.627975i | \(-0.216116\pi\) | ||||
0.778234 | + | 0.627975i | \(0.216116\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30.4338 | 2.30058 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.6525 | −1.55234 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.3723 | 1.59744 | 0.798719 | − | 0.601704i | \(-0.205511\pi\) | ||||
0.798719 | + | 0.601704i | \(0.205511\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.1803 | 1.42566 | 0.712832 | − | 0.701335i | \(-0.247412\pi\) | ||||
0.712832 | + | 0.701335i | \(0.247412\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.50651 | 0.628819 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.4721 | −0.769927 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.7234 | 1.73483 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.1246 | 1.82755 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.2784 | 1.75673 | 0.878363 | − | 0.477994i | \(-0.158636\pi\) | ||||
0.878363 | + | 0.477994i | \(0.158636\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.76393 | 0.630842 | 0.315421 | − | 0.948952i | \(-0.397854\pi\) | ||||
0.315421 | + | 0.948952i | \(0.397854\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 22.9969 | 1.64684 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9443 | 0.779747 | 0.389874 | − | 0.920868i | \(-0.372519\pi\) | ||||
0.389874 | + | 0.920868i | \(0.372519\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.3642 | −1.37269 | −0.686344 | − | 0.727277i | \(-0.740786\pi\) | ||||
−0.686344 | + | 0.727277i | \(0.740786\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 37.8885 | 2.67245 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.35114 | −0.165018 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −30.6525 | −2.14086 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −24.6215 | −1.71131 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.8885 | 1.92909 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.53077 | 0.311911 | 0.155955 | − | 0.987764i | \(-0.450154\pi\) | ||||
0.155955 | + | 0.987764i | \(0.450154\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.0000 | −0.685189 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.3480 | 1.72872 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.70820 | 0.115960 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.2169 | −1.02826 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.23607 | −0.621285 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.8707 | 1.86636 | 0.933179 | − | 0.359412i | \(-0.117023\pi\) | ||||
0.933179 | + | 0.359412i | \(0.117023\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 83.7771 | 5.58514 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8576 | 0.720647 | 0.360324 | − | 0.932827i | \(-0.382666\pi\) | ||||
0.360324 | + | 0.932827i | \(0.382666\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.7082 | −1.43452 | −0.717259 | − | 0.696806i | \(-0.754604\pi\) | ||||
−0.717259 | + | 0.696806i | \(0.754604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −32.7849 | −2.15709 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.9443 | −1.17557 | −0.587784 | − | 0.809018i | \(-0.700000\pi\) | ||||
−0.587784 | + | 0.809018i | \(0.700000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.9969 | −1.50015 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.70820 | −0.435745 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.898056 | 0.0580904 | 0.0290452 | − | 0.999578i | \(-0.490753\pi\) | ||||
0.0290452 | + | 0.999578i | \(0.490753\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.94427 | −0.254073 | −0.127036 | − | 0.991898i | \(-0.540547\pi\) | ||||
−0.127036 | + | 0.991898i | \(0.540547\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.40456 | 0.603303 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.23607 | −0.398408 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.8576 | −0.690856 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −49.5967 | −3.14307 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.89002 | 0.561133 | 0.280567 | − | 0.959835i | \(-0.409478\pi\) | ||||
0.280567 | + | 0.959835i | \(0.409478\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.2361 | 1.08362 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −68.2641 | −4.27486 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.47214 | 0.0918293 | 0.0459147 | − | 0.998945i | \(-0.485380\pi\) | ||||
0.0459147 | + | 0.998945i | \(0.485380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.81234 | −0.361161 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.47214 | −0.400615 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.726543 | 0.0448005 | 0.0224003 | − | 0.999749i | \(-0.492869\pi\) | ||||
0.0224003 | + | 0.999749i | \(0.492869\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.9443 | 0.979449 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.25731 | 0.321742 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.70820 | 0.469977 | 0.234989 | − | 0.971998i | \(-0.424495\pi\) | ||||
0.234989 | + | 0.971998i | \(0.424495\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.3803 | 0.812796 | 0.406398 | − | 0.913696i | \(-0.366785\pi\) | ||||
0.406398 | + | 0.913696i | \(0.366785\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.7639 | 0.772508 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −58.6475 | −3.53658 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8885 | 0.954650 | 0.477325 | − | 0.878727i | \(-0.341606\pi\) | ||||
0.477325 | + | 0.878727i | \(0.341606\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.70228 | 0.281518 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.5279 | −0.628040 | −0.314020 | − | 0.949416i | \(-0.601676\pi\) | ||||
−0.314020 | + | 0.949416i | \(0.601676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.898056 | −0.0533839 | −0.0266919 | − | 0.999644i | \(-0.508497\pi\) | ||||
−0.0266919 | + | 0.999644i | \(0.508497\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −80.2492 | −4.75355 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.0130 | −1.00425 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.8788 | 1.75153 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.41641 | −0.550112 | −0.275056 | − | 0.961428i | \(-0.588696\pi\) | ||||
−0.275056 | + | 0.961428i | \(0.588696\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.4257 | −1.65501 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −48.4164 | −2.80940 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.71040 | −0.388072 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.0689 | 0.810917 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 47.4468 | 2.72575 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.7082 | 0.670410 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.6992 | 1.58087 | 0.790437 | − | 0.612543i | \(-0.209853\pi\) | ||||
0.790437 | + | 0.612543i | \(0.209853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0000 | 0.568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.5599 | −0.882323 | −0.441161 | − | 0.897428i | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4164 | 0.814864 | 0.407432 | − | 0.913236i | \(-0.366424\pi\) | ||||
0.407432 | + | 0.913236i | \(0.366424\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 64.4598 | 3.63190 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.291796 | −0.0163889 | −0.00819445 | − | 0.999966i | \(-0.502608\pi\) | ||||
−0.00819445 | + | 0.999966i | \(0.502608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.53077 | 0.253674 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.23607 | −0.403878 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.2299 | 1.79332 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.8328 | 1.26654 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.42882 | 0.300215 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.7639 | −0.703698 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.171513 | −0.00942723 | −0.00471362 | − | 0.999989i | \(-0.501500\pi\) | ||||
−0.00471362 | + | 0.999989i | \(0.501500\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.0000 | −0.876795 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 52.1491 | 2.84921 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.1246 | −1.47757 | −0.738786 | − | 0.673940i | \(-0.764601\pi\) | ||||
−0.738786 | + | 0.673940i | \(0.764601\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.06154 | −0.492155 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.29180 | −0.178261 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9192 | −1.07553 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −49.5967 | −2.67020 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.4661 | 0.991312 | 0.495656 | − | 0.868519i | \(-0.334928\pi\) | ||||
0.495656 | + | 0.868519i | \(0.334928\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.34752 | 0.232718 | 0.116359 | − | 0.993207i | \(-0.462878\pi\) | ||||
0.116359 | + | 0.993207i | \(0.462878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.8496 | 1.00612 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.94427 | 0.156708 | 0.0783539 | − | 0.996926i | \(-0.475034\pi\) | ||||
0.0783539 | + | 0.996926i | \(0.475034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7638 | −0.730508 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −37.8885 | −2.00527 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.383516 | −0.0202412 | −0.0101206 | − | 0.999949i | \(-0.503222\pi\) | ||||
−0.0101206 | + | 0.999949i | \(0.503222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8885 | 0.994134 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.3238 | 1.53910 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.9443 | −1.09627 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.8576 | 0.566765 | 0.283382 | − | 0.959007i | \(-0.408543\pi\) | ||||
0.283382 | + | 0.959007i | \(0.408543\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −46.8328 | −2.43802 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.84953 | 0.459445 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.76393 | −0.0913329 | −0.0456665 | − | 0.998957i | \(-0.514541\pi\) | ||||
−0.0456665 | + | 0.998957i | \(0.514541\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 103.572 | 5.34842 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.76393 | −0.0908471 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.8707 | −1.43162 | −0.715810 | − | 0.698295i | \(-0.753942\pi\) | ||||
−0.715810 | + | 0.698295i | \(0.753942\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.9443 | 0.970544 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.3804 | 1.19468 | 0.597341 | − | 0.801987i | \(-0.296224\pi\) | ||||
0.597341 | + | 0.801987i | \(0.296224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −45.1246 | −2.29976 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 38.7283 | 1.96867 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.0000 | −0.811232 | −0.405616 | − | 0.914044i | \(-0.632943\pi\) | ||||
−0.405616 | + | 0.914044i | \(0.632943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.9192 | 1.00736 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.4164 | 0.676768 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.23305 | −0.464565 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.7639 | 0.991923 | 0.495962 | − | 0.868344i | \(-0.334816\pi\) | ||||
0.495962 | + | 0.868344i | \(0.334816\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −44.5407 | −2.22982 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.0000 | 1.34832 | 0.674158 | − | 0.738587i | \(-0.264507\pi\) | ||||
0.674158 | + | 0.738587i | \(0.264507\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.28157 | 0.0638396 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 57.0689 | 2.83578 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.2007 | 0.555197 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.8885 | 0.587851 | 0.293925 | − | 0.955828i | \(-0.405038\pi\) | ||||
0.293925 | + | 0.955828i | \(0.405038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35.1361 | 1.73314 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.7771 | −0.776340 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −68.2641 | −3.35095 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.76393 | −0.135350 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.4791 | −1.73327 | −0.866634 | − | 0.498944i | \(-0.833721\pi\) | ||||
−0.866634 | + | 0.498944i | \(0.833721\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.29180 | 0.404117 | 0.202059 | − | 0.979373i | \(-0.435237\pi\) | ||||
0.202059 | + | 0.979373i | \(0.435237\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −35.1361 | −1.70838 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −67.7771 | −3.28767 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.49839 | 0.314479 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.5967 | −1.18754 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.60034 | 0.269759 | 0.134879 | − | 0.990862i | \(-0.456935\pi\) | ||||
0.134879 | + | 0.990862i | \(0.456935\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.8885 | 1.05190 | 0.525948 | − | 0.850517i | \(-0.323711\pi\) | ||||
0.525948 | + | 0.850517i | \(0.323711\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.0373 | −0.625090 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.4164 | 1.12016 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.2088 | 0.630421 | 0.315211 | − | 0.949022i | \(-0.397925\pi\) | ||||
0.315211 | + | 0.949022i | \(0.397925\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.52786 | −0.453708 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.1684 | −1.10076 | −0.550382 | − | 0.834913i | \(-0.685518\pi\) | ||||
−0.550382 | + | 0.834913i | \(0.685518\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.23607 | 0.343023 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.3480 | 1.19892 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.4164 | −1.76579 | −0.882895 | − | 0.469571i | \(-0.844409\pi\) | ||||
−0.882895 | + | 0.469571i | \(0.844409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.7849 | 1.54378 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −74.0689 | −3.48006 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.5680 | 0.823603 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.8328 | −1.16163 | −0.580815 | − | 0.814036i | \(-0.697266\pi\) | ||||
−0.580815 | + | 0.814036i | \(0.697266\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −55.9533 | −2.61168 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.8885 | −1.67150 | −0.835748 | − | 0.549113i | \(-0.814966\pi\) | ||||
−0.835748 | + | 0.549113i | \(0.814966\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.8172 | −0.967459 | −0.483730 | − | 0.875217i | \(-0.660718\pi\) | ||||
−0.483730 | + | 0.875217i | \(0.660718\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.47214 | 0.439260 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.23305 | −0.427255 | −0.213627 | − | 0.976915i | \(-0.568528\pi\) | ||||
−0.213627 | + | 0.976915i | \(0.568528\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.9443 | 1.33652 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.8788 | 1.37674 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.1115 | −1.24659 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −79.6767 | −3.65582 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.3607 | 1.11540 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.5649 | −1.85346 | −0.926729 | − | 0.375730i | \(-0.877392\pi\) | ||||
−0.926729 | + | 0.375730i | \(0.877392\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.36068 | −0.198830 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −27.5276 | −1.25255 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 41.1246 | 1.86737 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.7719 | 0.714695 | 0.357347 | − | 0.933972i | \(-0.383681\pi\) | ||||
0.357347 | + | 0.933972i | \(0.383681\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.94427 | −0.178366 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.32688 | 0.285528 | 0.142764 | − | 0.989757i | \(-0.454401\pi\) | ||||
0.142764 | + | 0.989757i | \(0.454401\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.23607 | 0.235821 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −124.217 | −5.58316 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.63932 | −0.342670 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.6134 | −1.01231 | −0.506156 | − | 0.862442i | \(-0.668934\pi\) | ||||
−0.506156 | + | 0.862442i | \(0.668934\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.4164 | −1.49294 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.08580 | 0.226765 | 0.113382 | − | 0.993551i | \(-0.463832\pi\) | ||||
0.113382 | + | 0.993551i | \(0.463832\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 65.3050 | 2.90603 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.4338 | −1.35161 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.18034 | −0.0523176 | −0.0261588 | − | 0.999658i | \(-0.508328\pi\) | ||||
−0.0261588 | + | 0.999658i | \(0.508328\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.6247 | −0.514246 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −65.7771 | −2.90413 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.7638 | 0.606506 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.5967 | 1.08176 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 63.0068 | 2.76569 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −44.8885 | −1.96660 | −0.983301 | − | 0.181984i | \(-0.941748\pi\) | ||||
−0.983301 | + | 0.181984i | \(0.941748\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.7315 | 1.12516 | 0.562581 | − | 0.826742i | \(-0.309809\pi\) | ||||
0.562581 | + | 0.826742i | \(0.309809\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 93.6656 | 4.08790 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.80423 | −0.165715 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.52786 | −0.370777 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −43.4306 | −1.88473 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.7639 | −0.552867 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.95959 | −0.430591 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 65.7771 | 2.83849 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.66991 | 0.287293 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.3607 | −1.73524 | −0.867621 | − | 0.497227i | \(-0.834352\pi\) | ||||
−0.867621 | + | 0.497227i | \(0.834352\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 59.0310 | 2.53326 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.47214 | 0.320071 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.2703 | −0.952210 | −0.476105 | − | 0.879388i | \(-0.657952\pi\) | ||||
−0.476105 | + | 0.879388i | \(0.657952\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.8885 | 0.763464 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.15537 | 0.262227 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.12461 | −0.217921 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32.2299 | −1.36808 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.3607 | −1.28642 | −0.643212 | − | 0.765688i | \(-0.722398\pi\) | ||||
−0.643212 | + | 0.765688i | \(0.722398\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.5551 | 0.446434 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 73.0132 | 3.08262 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.07768 | −0.129709 | −0.0648544 | − | 0.997895i | \(-0.520658\pi\) | ||||
−0.0648544 | + | 0.997895i | \(0.520658\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.4721 | −0.524707 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.6749 | 1.33022 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.0000 | −0.586911 | −0.293455 | − | 0.955973i | \(-0.594805\pi\) | ||||
−0.293455 | + | 0.955973i | \(0.594805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.6377 | 1.19845 | 0.599225 | − | 0.800581i | \(-0.295475\pi\) | ||||
0.599225 | + | 0.800581i | \(0.295475\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 74.7214 | 3.12153 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −49.2429 | −2.05357 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.12461 | 0.296601 | 0.148301 | − | 0.988942i | \(-0.452620\pi\) | ||||
0.148301 | + | 0.988942i | \(0.452620\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.9726 | 1.12094 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.8885 | −1.57188 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.0535 | −0.706284 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 48.3607 | 1.99947 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.6296 | −1.09912 | −0.549560 | − | 0.835454i | \(-0.685205\pi\) | ||||
−0.549560 | + | 0.835454i | \(0.685205\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.47214 | −0.184271 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.6830 | 1.38553 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.8328 | 0.650176 | 0.325088 | − | 0.945684i | \(-0.394606\pi\) | ||||
0.325088 | + | 0.945684i | \(0.394606\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −52.1491 | −2.13790 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −59.5967 | −2.43913 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −43.8141 | −1.79020 | −0.895098 | − | 0.445869i | \(-0.852895\pi\) | ||||
−0.895098 | + | 0.445869i | \(0.852895\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.7639 | −1.33647 | −0.668234 | − | 0.743951i | \(-0.732950\pi\) | ||||
−0.668234 | + | 0.743951i | \(0.732950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 79.6767 | 3.24469 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 40.3607 | 1.64089 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.9402 | −1.17465 | −0.587324 | − | 0.809352i | \(-0.699819\pi\) | ||||
−0.587324 | + | 0.809352i | \(0.699819\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.23607 | −0.293220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.57608 | −0.387407 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.65248 | −0.0667429 | −0.0333714 | − | 0.999443i | \(-0.510624\pi\) | ||||
−0.0333714 | + | 0.999443i | \(0.510624\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −94.3386 | −3.80410 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.3607 | 0.980724 | 0.490362 | − | 0.871519i | \(-0.336865\pi\) | ||||
0.490362 | + | 0.871519i | \(0.336865\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.1037 | −1.49132 | −0.745662 | − | 0.666324i | \(-0.767867\pi\) | ||||
−0.745662 | + | 0.666324i | \(0.767867\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −40.6525 | −1.63133 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.01623 | 0.160907 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 77.8328 | 3.11331 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 85.8321 | 3.42780 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.9443 | 0.516122 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.5892 | 1.45659 | 0.728296 | − | 0.685263i | \(-0.240313\pi\) | ||||
0.728296 | + | 0.685263i | \(0.240313\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.9443 | 0.554235 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 26.0746 | 1.03474 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.59675 | −0.102887 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.0292 | −0.831904 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.2361 | −0.680784 | −0.340392 | − | 0.940284i | \(-0.610560\pi\) | ||||
−0.340392 | + | 0.940284i | \(0.610560\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.14725 | 0.163552 | 0.0817758 | − | 0.996651i | \(-0.473941\pi\) | ||||
0.0817758 | + | 0.996651i | \(0.473941\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 78.0132 | 3.07177 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.8303 | −1.48726 | −0.743630 | − | 0.668591i | \(-0.766898\pi\) | ||||
−0.743630 | + | 0.668591i | \(0.766898\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.4033 | 1.19343 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.25731 | 0.206050 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.2361 | −0.439701 | −0.219851 | − | 0.975534i | \(-0.570557\pi\) | ||||
−0.219851 | + | 0.975534i | \(0.570557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.4661 | 0.721530 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32.0000 | −1.24844 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.9030 | 1.00904 | 0.504520 | − | 0.863400i | \(-0.331670\pi\) | ||||
0.504520 | + | 0.863400i | \(0.331670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.3050 | −1.21762 | −0.608811 | − | 0.793315i | \(-0.708353\pi\) | ||||
−0.608811 | + | 0.793315i | \(0.708353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −28.4257 | −1.10396 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −61.3050 | −2.37730 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.80423 | 0.147300 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 85.7771 | 3.31633 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.5227 | −0.483435 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.8328 | −0.687405 | −0.343702 | − | 0.939079i | \(-0.611681\pi\) | ||||
−0.343702 | + | 0.939079i | \(0.611681\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 138.324 | 5.32410 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.3607 | −0.398193 | −0.199097 | − | 0.979980i | \(-0.563801\pi\) | ||||
−0.199097 | + | 0.979980i | \(0.563801\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.8254 | 0.875957 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.4164 | 1.28052 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.59222 | 0.137453 | 0.0687263 | − | 0.997636i | \(-0.478106\pi\) | ||||
0.0687263 | + | 0.997636i | \(0.478106\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.3607 | 1.84777 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −66.8110 | −2.54900 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.63932 | 0.252938 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.8091 | 0.715533 | 0.357766 | − | 0.933811i | \(-0.383538\pi\) | ||||
0.357766 | + | 0.933811i | \(0.383538\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −68.9443 | −2.61898 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.80423 | −0.144303 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.8885 | 1.43513 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −55.2268 | −2.08887 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.0132 | 1.81343 | 0.906716 | − | 0.421742i | \(-0.138581\pi\) | ||||
0.906716 | + | 0.421742i | \(0.138581\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2169 | 0.573916 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −70.7771 | −2.66562 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.2461 | 1.36318 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.6525 | 1.33896 | 0.669478 | − | 0.742832i | \(-0.266518\pi\) | ||||
0.669478 | + | 0.742832i | \(0.266518\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.1068 | −0.529048 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.76393 | −0.103510 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.8545 | −1.26609 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.76393 | 0.103221 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.8061 | 1.93204 | 0.966020 | − | 0.258466i | \(-0.0832170\pi\) | ||||
0.966020 | + | 0.258466i | \(0.0832170\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.63932 | 0.284503 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.1392 | −0.451462 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.9443 | −0.480738 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2784 | 0.900438 | 0.450219 | − | 0.892918i | \(-0.351346\pi\) | ||||
0.450219 | + | 0.892918i | \(0.351346\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.4721 | −0.424894 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.3319 | −1.15885 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.94427 | 0.182621 | 0.0913104 | − | 0.995822i | \(-0.470894\pi\) | ||||
0.0913104 | + | 0.995822i | \(0.470894\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.1926 | −0.707931 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −55.7771 | −2.05458 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.6669 | −1.45917 | −0.729585 | − | 0.683891i | \(-0.760287\pi\) | ||||
−0.729585 | + | 0.683891i | \(0.760287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.4164 | −1.22758 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.1038 | 1.72807 | 0.864035 | − | 0.503431i | \(-0.167929\pi\) | ||||
0.864035 | + | 0.503431i | \(0.167929\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.8885 | 1.27822 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −104.298 | −3.81607 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.52786 | −0.201984 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.0746 | −0.951474 | −0.475737 | − | 0.879588i | \(-0.657819\pi\) | ||||
−0.475737 | + | 0.879588i | \(0.657819\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.3607 | 0.997079 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −101.947 | −3.71023 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8197 | 0.793049 | 0.396525 | − | 0.918024i | \(-0.370216\pi\) | ||||
0.396525 | + | 0.918024i | \(0.370216\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 53.0472 | 1.92549 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.8885 | −0.575959 | −0.287980 | − | 0.957637i | \(-0.592984\pi\) | ||||
−0.287980 | + | 0.957637i | \(0.592984\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.14725 | 0.150141 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −143.554 | −5.19021 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.8367 | −0.427398 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.2361 | 0.621549 | 0.310774 | − | 0.950484i | \(-0.399412\pi\) | ||||
0.310774 | + | 0.950484i | \(0.399412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.53077 | 0.163172 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.2361 | 1.12348 | 0.561742 | − | 0.827313i | \(-0.310132\pi\) | ||||
0.561742 | + | 0.827313i | \(0.310132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.40456 | 0.337822 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.8885 | −0.641748 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 44.5407 | 1.59583 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.7214 | 0.526772 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.6861 | −0.381891 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.1246 | 1.46780 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.4953 | 1.40786 | 0.703929 | − | 0.710271i | \(-0.251428\pi\) | ||||
0.703929 | + | 0.710271i | \(0.251428\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.23607 | 0.0796061 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.92240 | −0.246132 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.87539 | 0.173130 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 49.0714 | 1.74038 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.2361 | −1.03559 | −0.517797 | − | 0.855503i | \(-0.673248\pi\) | ||||
−0.517797 | + | 0.855503i | \(0.673248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.4257 | 1.00563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.0557 | 0.390635 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.4014 | 0.790527 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.8885 | −1.33540 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.7234 | 0.835104 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0557 | 0.388699 | 0.194349 | − | 0.980932i | \(-0.437740\pi\) | ||||
0.194349 | + | 0.980932i | \(0.437740\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.6749 | 1.11226 | 0.556128 | − | 0.831097i | \(-0.312286\pi\) | ||||
0.556128 | + | 0.831097i | \(0.312286\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.1803 | 1.44426 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.42882 | −0.190163 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.8328 | −1.28862 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 26.8416 | 0.937921 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.2361 | −1.47405 | −0.737024 | − | 0.675866i | \(-0.763770\pi\) | ||||
−0.737024 | + | 0.675866i | \(0.763770\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.06154 | −0.315865 | −0.157933 | − | 0.987450i | \(-0.550483\pi\) | ||||
−0.157933 | + | 0.987450i | \(0.550483\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −180.498 | −6.28415 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.5245 | −1.75691 | −0.878455 | − | 0.477826i | \(-0.841425\pi\) | ||||
−0.878455 | + | 0.477826i | \(0.841425\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.7082 | −0.545568 | −0.272784 | − | 0.962075i | \(-0.587945\pi\) | ||||
−0.272784 | + | 0.962075i | \(0.587945\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 48.8999 | 1.69632 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.70820 | 0.267073 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −45.9937 | −1.59168 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.76393 | 0.268361 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.5519 | −0.813102 | −0.406551 | − | 0.913628i | \(-0.633269\pi\) | ||||
−0.406551 | + | 0.913628i | \(0.633269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.4014 | −1.11596 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −41.8885 | −1.44101 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.4014 | 0.769720 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.76393 | −0.0948579 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.40456 | 0.322384 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.5836 | 0.362375 | 0.181188 | − | 0.983449i | \(-0.442006\pi\) | ||||
0.181188 | + | 0.983449i | \(0.442006\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −168.758 | −5.77140 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.0557 | −0.958365 | −0.479183 | − | 0.877715i | \(-0.659067\pi\) | ||||
−0.479183 | + | 0.877715i | \(0.659067\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.3561 | 0.933379 | 0.466689 | − | 0.884421i | \(-0.345447\pi\) | ||||
0.466689 | + | 0.884421i | \(0.345447\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −52.3607 | −1.78445 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.5729 | 1.10880 | 0.554398 | − | 0.832252i | \(-0.312949\pi\) | ||||
0.554398 | + | 0.832252i | \(0.312949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 86.7214 | 2.94861 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 32.0584 | 1.08876 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.87539 | 0.335000 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.7153 | 0.735795 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 62.8328 | 2.12657 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 79.1217 | 2.67480 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.81966 | 0.230284 | 0.115142 | − | 0.993349i | \(-0.463268\pi\) | ||||
0.115142 | + | 0.993349i | \(0.463268\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.9807 | −0.977496 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.3607 | −0.753350 | −0.376675 | − | 0.926345i | \(-0.622933\pi\) | ||||
−0.376675 | + | 0.926345i | \(0.622933\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.9758 | −0.470324 | −0.235162 | − | 0.971956i | \(-0.575562\pi\) | ||||
−0.235162 | + | 0.971956i | \(0.575562\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −87.4853 | −2.94079 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.3318 | 0.716251 | 0.358126 | − | 0.933673i | \(-0.383416\pi\) | ||||
0.358126 | + | 0.933673i | \(0.383416\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.4721 | 0.485380 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −61.0391 | −2.04489 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.4164 | 1.11824 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 90.5344 | 3.02623 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.6525 | −0.689566 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.726543 | −0.0242315 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.7082 | −0.656575 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 43.2996 | 1.44092 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 81.2492 | 2.70082 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.4791 | 1.17806 | 0.589032 | − | 0.808109i | \(-0.299509\pi\) | ||||
0.589032 | + | 0.808109i | \(0.299509\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 99.7771 | 3.30940 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.8141 | 1.45163 | 0.725813 | − | 0.687892i | \(-0.241464\pi\) | ||||
0.725813 | + | 0.687892i | \(0.241464\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 73.0132 | 2.41638 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.0341 | 1.19125 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.2492 | 0.338459 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.95148 | −0.262295 | −0.131148 | − | 0.991363i | \(-0.541866\pi\) | ||||
−0.131148 | + | 0.991363i | \(0.541866\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 85.2492 | 2.80906 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.73136 | −0.188650 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.0000 | −1.05215 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.0292 | 0.690691 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.0000 | 1.77168 | 0.885841 | − | 0.463988i | \(-0.153582\pi\) | ||||
0.885841 | + | 0.463988i | \(0.153582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.06154 | 0.296980 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −47.8885 | −1.56780 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 100.494 | 3.28650 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.3607 | 1.12251 | 0.561257 | − | 0.827641i | \(-0.310318\pi\) | ||||
0.561257 | + | 0.827641i | \(0.310318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 44.3691 | 1.44793 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.0132 | −1.63038 | −0.815191 | − | 0.579192i | \(-0.803368\pi\) | ||||
−0.815191 | + | 0.579192i | \(0.803368\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.5276 | 0.896423 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 106.430 | 3.46215 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.5600 | −0.830589 | −0.415294 | − | 0.909687i | \(-0.636321\pi\) | ||||
−0.415294 | + | 0.909687i | \(0.636321\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.72136 | −0.283107 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.898056 | −0.0291215 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.4164 | −0.402207 | −0.201103 | − | 0.979570i | \(-0.564453\pi\) | ||||
−0.201103 | + | 0.979570i | \(0.564453\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 102.845 | 3.32799 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.9443 | 0.450754 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.8416 | 0.866760 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4721 | −0.982972 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.2169 | −0.490358 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.1246 | 1.19508 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.2219 | 1.29345 | 0.646724 | − | 0.762724i | \(-0.276138\pi\) | ||||
0.646724 | + | 0.762724i | \(0.276138\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 99.1935 | 3.18655 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.45309 | −0.0466317 | −0.0233159 | − | 0.999728i | \(-0.507422\pi\) | ||||
−0.0233159 | + | 0.999728i | \(0.507422\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.11146 | −0.0676902 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 70.2722 | 2.25051 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.8328 | −1.40234 | −0.701168 | − | 0.712996i | \(-0.747338\pi\) | ||||
−0.701168 | + | 0.712996i | \(0.747338\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.73948 | −0.247355 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.4164 | 0.364498 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.52265 | −0.0804602 | −0.0402301 | − | 0.999190i | \(-0.512809\pi\) | ||||
−0.0402301 | + | 0.999190i | \(0.512809\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.3607 | 1.47717 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −39.2833 | −1.25040 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.7639 | −0.723851 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.8576 | 0.344905 | 0.172452 | − | 0.985018i | \(-0.444831\pi\) | ||||
0.172452 | + | 0.985018i | \(0.444831\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.527864 | −0.0167513 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −82.0279 | −2.60046 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.944272 | −0.0299054 | −0.0149527 | − | 0.999888i | \(-0.504760\pi\) | ||||
−0.0149527 | + | 0.999888i | \(0.504760\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.4176 | −0.835815 |
(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 | 1856.2.a.z.1.4 | 4 | ||
4.3 | odd | 2 | inner | 1856.2.a.z.1.1 | 4 | ||
8.3 | odd | 2 | 928.2.a.f.1.4 | yes | 4 | ||
8.5 | even | 2 | 928.2.a.f.1.1 | ✓ | 4 | ||
24.5 | odd | 2 | 8352.2.a.ba.1.4 | 4 | |||
24.11 | even | 2 | 8352.2.a.ba.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.2.a.f.1.1 | ✓ | 4 | 8.5 | even | 2 | ||
928.2.a.f.1.4 | yes | 4 | 8.3 | odd | 2 | ||
1856.2.a.z.1.1 | 4 | 4.3 | odd | 2 | inner | ||
1856.2.a.z.1.4 | 4 | 1.1 | even | 1 | trivial | ||
8352.2.a.ba.1.3 | 4 | 24.11 | even | 2 | |||
8352.2.a.ba.1.4 | 4 | 24.5 | odd | 2 |