Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 26x^{14} + 268x^{12} - 1395x^{10} + 3876x^{8} - 5635x^{6} + 4042x^{4} - 1272x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 693) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(2.68084\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.68084 | 1.89564 | 0.947821 | − | 0.318804i | \(-0.103281\pi\) | ||||
0.947821 | + | 0.318804i | \(0.103281\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.18691 | 2.59346 | ||||||||
\(5\) | −1.17039 | −0.523415 | −0.261708 | − | 0.965147i | \(-0.584286\pi\) | ||||
−0.261708 | + | 0.965147i | \(0.584286\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 8.54361 | 3.02062 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.13763 | −0.992207 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.68268 | −0.466693 | −0.233346 | − | 0.972394i | \(-0.574968\pi\) | ||||
−0.233346 | + | 0.972394i | \(0.574968\pi\) | |||||||
\(14\) | 2.68084 | 0.716485 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.5302 | 3.13256 | ||||||||
\(17\) | 5.59675 | 1.35741 | 0.678706 | − | 0.734410i | \(-0.262541\pi\) | ||||
0.678706 | + | 0.734410i | \(0.262541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35416 | 0.998913 | 0.499456 | − | 0.866339i | \(-0.333533\pi\) | ||||
0.499456 | + | 0.866339i | \(0.333533\pi\) | |||||||
\(20\) | −6.07072 | −1.35745 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.119612 | 0.0249408 | 0.0124704 | − | 0.999922i | \(-0.496030\pi\) | ||||
0.0124704 | + | 0.999922i | \(0.496030\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.63018 | −0.726037 | ||||||||
\(26\) | −4.51101 | −0.884682 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.18691 | 0.980234 | ||||||||
\(29\) | 4.39599 | 0.816315 | 0.408157 | − | 0.912912i | \(-0.366171\pi\) | ||||
0.408157 | + | 0.912912i | \(0.366171\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.31294 | −1.13384 | −0.566919 | − | 0.823774i | \(-0.691865\pi\) | ||||
−0.566919 | + | 0.823774i | \(0.691865\pi\) | |||||||
\(32\) | 16.5044 | 2.91759 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.0040 | 2.57317 | ||||||||
\(35\) | −1.17039 | −0.197832 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.85418 | 0.962421 | 0.481210 | − | 0.876605i | \(-0.340197\pi\) | ||||
0.481210 | + | 0.876605i | \(0.340197\pi\) | |||||||
\(38\) | 11.6728 | 1.89358 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.99937 | −1.58104 | ||||||||
\(41\) | 11.0165 | 1.72049 | 0.860244 | − | 0.509883i | \(-0.170311\pi\) | ||||
0.860244 | + | 0.509883i | \(0.170311\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.97227 | 0.910762 | 0.455381 | − | 0.890297i | \(-0.349503\pi\) | ||||
0.455381 | + | 0.890297i | \(0.349503\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.320661 | 0.0472789 | ||||||||
\(47\) | −12.5812 | −1.83516 | −0.917580 | − | 0.397552i | \(-0.869860\pi\) | ||||
−0.917580 | + | 0.397552i | \(0.869860\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −9.73195 | −1.37631 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.72794 | −1.21035 | ||||||||
\(53\) | −0.417004 | −0.0572800 | −0.0286400 | − | 0.999590i | \(-0.509118\pi\) | ||||
−0.0286400 | + | 0.999590i | \(0.509118\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.54361 | 1.14169 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.7849 | 1.54744 | ||||||||
\(59\) | 0.723544 | 0.0941974 | 0.0470987 | − | 0.998890i | \(-0.485002\pi\) | ||||
0.0470987 | + | 0.998890i | \(0.485002\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.85799 | −1.13415 | −0.567075 | − | 0.823666i | \(-0.691925\pi\) | ||||
−0.567075 | + | 0.823666i | \(0.691925\pi\) | |||||||
\(62\) | −16.9240 | −2.14935 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 19.1851 | 2.39814 | ||||||||
\(65\) | 1.96940 | 0.244274 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.78741 | 1.07355 | 0.536777 | − | 0.843724i | \(-0.319642\pi\) | ||||
0.536777 | + | 0.843724i | \(0.319642\pi\) | |||||||
\(68\) | 29.0299 | 3.52039 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.13763 | −0.375019 | ||||||||
\(71\) | −3.21286 | −0.381297 | −0.190648 | − | 0.981658i | \(-0.561059\pi\) | ||||
−0.190648 | + | 0.981658i | \(0.561059\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.5891 | −1.70752 | −0.853762 | − | 0.520664i | \(-0.825685\pi\) | ||||
−0.853762 | + | 0.520664i | \(0.825685\pi\) | |||||||
\(74\) | 15.6941 | 1.82440 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 22.5846 | 2.59064 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.4761 | 1.62869 | 0.814347 | − | 0.580378i | \(-0.197095\pi\) | ||||
0.814347 | + | 0.580378i | \(0.197095\pi\) | |||||||
\(80\) | −14.6653 | −1.63963 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 29.5335 | 3.26143 | ||||||||
\(83\) | 3.45931 | 0.379709 | 0.189854 | − | 0.981812i | \(-0.439198\pi\) | ||||
0.189854 | + | 0.981812i | \(0.439198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.55039 | −0.710490 | ||||||||
\(86\) | 16.0107 | 1.72648 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0621 | 1.27858 | 0.639292 | − | 0.768964i | \(-0.279228\pi\) | ||||
0.639292 | + | 0.768964i | \(0.279228\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.68268 | −0.176393 | ||||||||
\(92\) | 0.620417 | 0.0646830 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −33.7283 | −3.47880 | ||||||||
\(95\) | −5.09607 | −0.522846 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.99575 | −0.608776 | −0.304388 | − | 0.952548i | \(-0.598452\pi\) | ||||
−0.304388 | + | 0.952548i | \(0.598452\pi\) | |||||||
\(98\) | 2.68084 | 0.270806 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.8294 | −1.88294 | ||||||||
\(101\) | −0.101612 | −0.0101108 | −0.00505540 | − | 0.999987i | \(-0.501609\pi\) | ||||
−0.00505540 | + | 0.999987i | \(0.501609\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.73990 | −0.171438 | −0.0857188 | − | 0.996319i | \(-0.527319\pi\) | ||||
−0.0857188 | + | 0.996319i | \(0.527319\pi\) | |||||||
\(104\) | −14.3762 | −1.40970 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.11792 | −0.108582 | ||||||||
\(107\) | −11.0032 | −1.06372 | −0.531861 | − | 0.846831i | \(-0.678507\pi\) | ||||
−0.531861 | + | 0.846831i | \(0.678507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.5040 | 1.58080 | 0.790400 | − | 0.612592i | \(-0.209873\pi\) | ||||
0.790400 | + | 0.612592i | \(0.209873\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.5302 | 1.18400 | ||||||||
\(113\) | 6.28108 | 0.590875 | 0.295437 | − | 0.955362i | \(-0.404535\pi\) | ||||
0.295437 | + | 0.955362i | \(0.404535\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.139993 | −0.0130544 | ||||||||
\(116\) | 22.8016 | 2.11708 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.93971 | 0.178564 | ||||||||
\(119\) | 5.59675 | 0.513053 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −23.7469 | −2.14994 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −32.7447 | −2.94056 | ||||||||
\(125\) | 10.1007 | 0.903434 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.2379 | 1.52962 | 0.764809 | − | 0.644257i | \(-0.222833\pi\) | ||||
0.764809 | + | 0.644257i | \(0.222833\pi\) | |||||||
\(128\) | 18.4235 | 1.62843 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.27965 | 0.463056 | ||||||||
\(131\) | 0.324063 | 0.0283135 | 0.0141567 | − | 0.999900i | \(-0.495494\pi\) | ||||
0.0141567 | + | 0.999900i | \(0.495494\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.35416 | 0.377553 | ||||||||
\(134\) | 23.5577 | 2.03507 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 47.8165 | 4.10023 | ||||||||
\(137\) | −10.3726 | −0.886188 | −0.443094 | − | 0.896475i | \(-0.646119\pi\) | ||||
−0.443094 | + | 0.896475i | \(0.646119\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.3776 | 1.13467 | 0.567336 | − | 0.823486i | \(-0.307974\pi\) | ||||
0.567336 | + | 0.823486i | \(0.307974\pi\) | |||||||
\(140\) | −6.07072 | −0.513069 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.61317 | −0.722801 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.14503 | −0.427271 | ||||||||
\(146\) | −39.1110 | −3.23685 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 30.3651 | 2.49600 | ||||||||
\(149\) | −9.66988 | −0.792188 | −0.396094 | − | 0.918210i | \(-0.629635\pi\) | ||||
−0.396094 | + | 0.918210i | \(0.629635\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.56082 | 0.208396 | 0.104198 | − | 0.994557i | \(-0.466772\pi\) | ||||
0.104198 | + | 0.994557i | \(0.466772\pi\) | |||||||
\(152\) | 37.2002 | 3.01734 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.38862 | 0.593468 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.5092 | 1.47719 | 0.738597 | − | 0.674148i | \(-0.235489\pi\) | ||||
0.738597 | + | 0.674148i | \(0.235489\pi\) | |||||||
\(158\) | 38.8083 | 3.08742 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −19.3166 | −1.52711 | ||||||||
\(161\) | 0.119612 | 0.00942675 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.47823 | 0.507414 | 0.253707 | − | 0.967281i | \(-0.418350\pi\) | ||||
0.253707 | + | 0.967281i | \(0.418350\pi\) | |||||||
\(164\) | 57.1416 | 4.46201 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.27386 | 0.719791 | ||||||||
\(167\) | −25.2567 | −1.95442 | −0.977212 | − | 0.212266i | \(-0.931916\pi\) | ||||
−0.977212 | + | 0.212266i | \(0.931916\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1686 | −0.782198 | ||||||||
\(170\) | −17.5606 | −1.34683 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 30.9776 | 2.36202 | ||||||||
\(173\) | −9.26804 | −0.704636 | −0.352318 | − | 0.935880i | \(-0.614606\pi\) | ||||
−0.352318 | + | 0.935880i | \(0.614606\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.63018 | −0.274416 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 32.3367 | 2.42373 | ||||||||
\(179\) | −15.4438 | −1.15432 | −0.577161 | − | 0.816630i | \(-0.695840\pi\) | ||||
−0.577161 | + | 0.816630i | \(0.695840\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5318 | 0.782824 | 0.391412 | − | 0.920215i | \(-0.371987\pi\) | ||||
0.391412 | + | 0.920215i | \(0.371987\pi\) | |||||||
\(182\) | −4.51101 | −0.334378 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.02192 | 0.0753369 | ||||||||
\(185\) | −6.85168 | −0.503746 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −65.2577 | −4.75940 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.6618 | −0.991128 | ||||||||
\(191\) | −6.86336 | −0.496615 | −0.248308 | − | 0.968681i | \(-0.579874\pi\) | ||||
−0.248308 | + | 0.968681i | \(0.579874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.3297 | 1.60733 | 0.803663 | − | 0.595085i | \(-0.202881\pi\) | ||||
0.803663 | + | 0.595085i | \(0.202881\pi\) | |||||||
\(194\) | −16.0737 | −1.15402 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.18691 | 0.370494 | ||||||||
\(197\) | 4.45203 | 0.317194 | 0.158597 | − | 0.987343i | \(-0.449303\pi\) | ||||
0.158597 | + | 0.987343i | \(0.449303\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.0993 | −1.07036 | −0.535180 | − | 0.844738i | \(-0.679756\pi\) | ||||
−0.535180 | + | 0.844738i | \(0.679756\pi\) | |||||||
\(200\) | −31.0149 | −2.19308 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.272406 | −0.0191665 | ||||||||
\(203\) | 4.39599 | 0.308538 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.8936 | −0.900529 | ||||||||
\(206\) | −4.66440 | −0.324984 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −21.0844 | −1.46194 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.8486 | −1.57296 | −0.786480 | − | 0.617616i | \(-0.788099\pi\) | ||||
−0.786480 | + | 0.617616i | \(0.788099\pi\) | |||||||
\(212\) | −2.16297 | −0.148553 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −29.4979 | −2.01644 | ||||||||
\(215\) | −6.98989 | −0.476707 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.31294 | −0.428551 | ||||||||
\(218\) | 44.2447 | 2.99663 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.41757 | −0.633494 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.71068 | 0.650275 | 0.325137 | − | 0.945667i | \(-0.394589\pi\) | ||||
0.325137 | + | 0.945667i | \(0.394589\pi\) | |||||||
\(224\) | 16.5044 | 1.10274 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.8386 | 1.12009 | ||||||||
\(227\) | −18.6174 | −1.23568 | −0.617838 | − | 0.786305i | \(-0.711991\pi\) | ||||
−0.617838 | + | 0.786305i | \(0.711991\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.04273 | 0.597561 | 0.298780 | − | 0.954322i | \(-0.403420\pi\) | ||||
0.298780 | + | 0.954322i | \(0.403420\pi\) | |||||||
\(230\) | −0.375299 | −0.0247465 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 37.5576 | 2.46578 | ||||||||
\(233\) | 8.62319 | 0.564924 | 0.282462 | − | 0.959278i | \(-0.408849\pi\) | ||||
0.282462 | + | 0.959278i | \(0.408849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.7250 | 0.960550 | ||||||||
\(236\) | 3.75296 | 0.244297 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.0040 | 0.972565 | ||||||||
\(239\) | −20.6870 | −1.33813 | −0.669067 | − | 0.743202i | \(-0.733306\pi\) | ||||
−0.669067 | + | 0.743202i | \(0.733306\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.8415 | −1.60018 | −0.800090 | − | 0.599880i | \(-0.795215\pi\) | ||||
−0.800090 | + | 0.599880i | \(0.795215\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −45.9456 | −2.94137 | ||||||||
\(245\) | −1.17039 | −0.0747736 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.32668 | −0.466185 | ||||||||
\(248\) | −53.9353 | −3.42490 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 27.0784 | 1.71259 | ||||||||
\(251\) | 10.5076 | 0.663236 | 0.331618 | − | 0.943414i | \(-0.392405\pi\) | ||||
0.331618 | + | 0.943414i | \(0.392405\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 46.2121 | 2.89961 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.0203 | 0.688771 | ||||||||
\(257\) | −3.68093 | −0.229610 | −0.114805 | − | 0.993388i | \(-0.536624\pi\) | ||||
−0.114805 | + | 0.993388i | \(0.536624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.85418 | 0.363761 | ||||||||
\(260\) | 10.2151 | 0.633514 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.868760 | 0.0536722 | ||||||||
\(263\) | −10.1816 | −0.627824 | −0.313912 | − | 0.949452i | \(-0.601640\pi\) | ||||
−0.313912 | + | 0.949452i | \(0.601640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.488059 | 0.0299812 | ||||||||
\(266\) | 11.6728 | 0.715706 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 45.5795 | 2.78421 | ||||||||
\(269\) | −32.0196 | −1.95227 | −0.976135 | − | 0.217163i | \(-0.930320\pi\) | ||||
−0.976135 | + | 0.217163i | \(0.930320\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.7478 | −1.26034 | −0.630169 | − | 0.776458i | \(-0.717014\pi\) | ||||
−0.630169 | + | 0.776458i | \(0.717014\pi\) | |||||||
\(272\) | 70.1286 | 4.25217 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −27.8072 | −1.67990 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1464 | 0.910057 | 0.455028 | − | 0.890477i | \(-0.349629\pi\) | ||||
0.455028 | + | 0.890477i | \(0.349629\pi\) | |||||||
\(278\) | 35.8632 | 2.15093 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.99937 | −0.597577 | ||||||||
\(281\) | 25.7257 | 1.53467 | 0.767335 | − | 0.641247i | \(-0.221583\pi\) | ||||
0.767335 | + | 0.641247i | \(0.221583\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.9944 | 1.06966 | 0.534828 | − | 0.844961i | \(-0.320376\pi\) | ||||
0.534828 | + | 0.844961i | \(0.320376\pi\) | |||||||
\(284\) | −16.6648 | −0.988876 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.0165 | 0.650283 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.3236 | 0.842567 | ||||||||
\(290\) | −13.7930 | −0.809953 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −75.6723 | −4.42839 | ||||||||
\(293\) | −30.9599 | −1.80870 | −0.904349 | − | 0.426794i | \(-0.859643\pi\) | ||||
−0.904349 | + | 0.426794i | \(0.859643\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.846830 | −0.0493043 | ||||||||
\(296\) | 50.0158 | 2.90711 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −25.9234 | −1.50170 | ||||||||
\(299\) | −0.201269 | −0.0116397 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.97227 | 0.344236 | ||||||||
\(302\) | 6.86514 | 0.395045 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 54.5586 | 3.12915 | ||||||||
\(305\) | 10.3673 | 0.593631 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0193 | −0.571830 | −0.285915 | − | 0.958255i | \(-0.592298\pi\) | ||||
−0.285915 | + | 0.958255i | \(0.592298\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 19.8077 | 1.12500 | ||||||||
\(311\) | −16.3344 | −0.926240 | −0.463120 | − | 0.886296i | \(-0.653270\pi\) | ||||
−0.463120 | + | 0.886296i | \(0.653270\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.47058 | 0.252692 | 0.126346 | − | 0.991986i | \(-0.459675\pi\) | ||||
0.126346 | + | 0.991986i | \(0.459675\pi\) | |||||||
\(314\) | 49.6202 | 2.80023 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 75.0865 | 4.22395 | ||||||||
\(317\) | 11.9782 | 0.672765 | 0.336382 | − | 0.941725i | \(-0.390797\pi\) | ||||
0.336382 | + | 0.941725i | \(0.390797\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −22.4541 | −1.25522 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.320661 | 0.0178697 | ||||||||
\(323\) | 24.3692 | 1.35594 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.10845 | 0.338836 | ||||||||
\(326\) | 17.3671 | 0.961876 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 94.1206 | 5.19694 | ||||||||
\(329\) | −12.5812 | −0.693625 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.0873 | −0.994168 | −0.497084 | − | 0.867702i | \(-0.665596\pi\) | ||||
−0.497084 | + | 0.867702i | \(0.665596\pi\) | |||||||
\(332\) | 17.9431 | 0.984758 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −67.7093 | −3.70489 | ||||||||
\(335\) | −10.2847 | −0.561914 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.0858 | 1.03967 | 0.519836 | − | 0.854266i | \(-0.325993\pi\) | ||||
0.519836 | + | 0.854266i | \(0.325993\pi\) | |||||||
\(338\) | −27.2603 | −1.48277 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −33.9763 | −1.84262 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 51.0247 | 2.75107 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.8462 | −1.33574 | ||||||||
\(347\) | −5.31766 | −0.285467 | −0.142733 | − | 0.989761i | \(-0.545589\pi\) | ||||
−0.142733 | + | 0.989761i | \(0.545589\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.6262 | −1.10410 | −0.552048 | − | 0.833813i | \(-0.686153\pi\) | ||||
−0.552048 | + | 0.833813i | \(0.686153\pi\) | |||||||
\(350\) | −9.73195 | −0.520194 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.31745 | 0.389468 | 0.194734 | − | 0.980856i | \(-0.437616\pi\) | ||||
0.194734 | + | 0.980856i | \(0.437616\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.76031 | 0.199576 | ||||||||
\(356\) | 62.5652 | 3.31595 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −41.4023 | −2.18818 | ||||||||
\(359\) | 24.2290 | 1.27876 | 0.639378 | − | 0.768892i | \(-0.279192\pi\) | ||||
0.639378 | + | 0.768892i | \(0.279192\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0412986 | −0.00217361 | ||||||||
\(362\) | 28.2342 | 1.48395 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.72794 | −0.457468 | ||||||||
\(365\) | 17.0749 | 0.893744 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.5059 | −1.17480 | −0.587399 | − | 0.809298i | \(-0.699848\pi\) | ||||
−0.587399 | + | 0.809298i | \(0.699848\pi\) | |||||||
\(368\) | 1.49877 | 0.0781287 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −18.3683 | −0.954921 | ||||||||
\(371\) | −0.417004 | −0.0216498 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.25290 | 0.323763 | 0.161881 | − | 0.986810i | \(-0.448244\pi\) | ||||
0.161881 | + | 0.986810i | \(0.448244\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −107.489 | −5.54332 | ||||||||
\(377\) | −7.39706 | −0.380968 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.8192 | 0.658480 | 0.329240 | − | 0.944246i | \(-0.393207\pi\) | ||||
0.329240 | + | 0.944246i | \(0.393207\pi\) | |||||||
\(380\) | −26.4329 | −1.35598 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.3996 | −0.941405 | ||||||||
\(383\) | 6.46736 | 0.330467 | 0.165233 | − | 0.986255i | \(-0.447162\pi\) | ||||
0.165233 | + | 0.986255i | \(0.447162\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 59.8624 | 3.04691 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −31.0994 | −1.57883 | ||||||||
\(389\) | −14.8967 | −0.755295 | −0.377647 | − | 0.925949i | \(-0.623267\pi\) | ||||
−0.377647 | + | 0.925949i | \(0.623267\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.669439 | 0.0338550 | ||||||||
\(392\) | 8.54361 | 0.431517 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.9352 | 0.601286 | ||||||||
\(395\) | −16.9428 | −0.852483 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.85862 | 0.0932813 | 0.0466407 | − | 0.998912i | \(-0.485148\pi\) | ||||
0.0466407 | + | 0.998912i | \(0.485148\pi\) | |||||||
\(398\) | −40.4788 | −2.02902 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −45.4871 | −2.27435 | ||||||||
\(401\) | −8.74249 | −0.436579 | −0.218290 | − | 0.975884i | \(-0.570048\pi\) | ||||
−0.218290 | + | 0.975884i | \(0.570048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.6227 | 0.529154 | ||||||||
\(404\) | −0.527054 | −0.0262219 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.7849 | 0.584877 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.7198 | 0.628952 | 0.314476 | − | 0.949265i | \(-0.398171\pi\) | ||||
0.314476 | + | 0.949265i | \(0.398171\pi\) | |||||||
\(410\) | −34.5657 | −1.70708 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.02472 | −0.444616 | ||||||||
\(413\) | 0.723544 | 0.0356033 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.04875 | −0.198745 | ||||||||
\(416\) | −27.7716 | −1.36162 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.09885 | −0.395655 | −0.197827 | − | 0.980237i | \(-0.563389\pi\) | ||||
−0.197827 | + | 0.980237i | \(0.563389\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.4786 | −1.29049 | −0.645243 | − | 0.763977i | \(-0.723244\pi\) | ||||
−0.645243 | + | 0.763977i | \(0.723244\pi\) | |||||||
\(422\) | −61.2534 | −2.98177 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.56272 | −0.173021 | ||||||||
\(425\) | −20.3172 | −0.985531 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.85799 | −0.428668 | ||||||||
\(428\) | −57.0728 | −2.75872 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.7388 | −0.903665 | ||||||||
\(431\) | −0.356446 | −0.0171694 | −0.00858471 | − | 0.999963i | \(-0.502733\pi\) | ||||
−0.00858471 | + | 0.999963i | \(0.502733\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.2884 | −0.878886 | −0.439443 | − | 0.898270i | \(-0.644824\pi\) | ||||
−0.439443 | + | 0.898270i | \(0.644824\pi\) | |||||||
\(434\) | −16.9240 | −0.812378 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 85.6049 | 4.09973 | ||||||||
\(437\) | 0.520810 | 0.0249137 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.67633 | 0.318644 | 0.159322 | − | 0.987227i | \(-0.449069\pi\) | ||||
0.159322 | + | 0.987227i | \(0.449069\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −25.2470 | −1.20088 | ||||||||
\(443\) | −20.4403 | −0.971146 | −0.485573 | − | 0.874196i | \(-0.661389\pi\) | ||||
−0.485573 | + | 0.874196i | \(0.661389\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.1174 | −0.669230 | ||||||||
\(446\) | 26.0328 | 1.23269 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19.1851 | 0.906411 | ||||||||
\(449\) | 5.51429 | 0.260236 | 0.130118 | − | 0.991499i | \(-0.458464\pi\) | ||||
0.130118 | + | 0.991499i | \(0.458464\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 32.5794 | 1.53241 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −49.9102 | −2.34240 | ||||||||
\(455\) | 1.96940 | 0.0923269 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00275 | 0.0936849 | 0.0468424 | − | 0.998902i | \(-0.485084\pi\) | ||||
0.0468424 | + | 0.998902i | \(0.485084\pi\) | |||||||
\(458\) | 24.2421 | 1.13276 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.726131 | −0.0338561 | ||||||||
\(461\) | −8.17436 | −0.380718 | −0.190359 | − | 0.981715i | \(-0.560965\pi\) | ||||
−0.190359 | + | 0.981715i | \(0.560965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.26686 | −0.198298 | −0.0991488 | − | 0.995073i | \(-0.531612\pi\) | ||||
−0.0991488 | + | 0.995073i | \(0.531612\pi\) | |||||||
\(464\) | 55.0828 | 2.55715 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.1174 | 1.07089 | ||||||||
\(467\) | 40.5138 | 1.87476 | 0.937378 | − | 0.348315i | \(-0.113246\pi\) | ||||
0.937378 | + | 0.348315i | \(0.113246\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.78741 | 0.405765 | ||||||||
\(470\) | 39.4753 | 1.82086 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.18168 | 0.284535 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.8064 | −0.725247 | ||||||||
\(476\) | 29.0299 | 1.33058 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −55.4587 | −2.53662 | ||||||||
\(479\) | 8.24083 | 0.376533 | 0.188267 | − | 0.982118i | \(-0.439713\pi\) | ||||
0.188267 | + | 0.982118i | \(0.439713\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.85073 | −0.449155 | ||||||||
\(482\) | −66.5960 | −3.03337 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.01738 | 0.318643 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.964882 | −0.0437230 | −0.0218615 | − | 0.999761i | \(-0.506959\pi\) | ||||
−0.0218615 | + | 0.999761i | \(0.506959\pi\) | |||||||
\(488\) | −75.6792 | −3.42584 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.13763 | −0.141744 | ||||||||
\(491\) | −30.4284 | −1.37321 | −0.686607 | − | 0.727029i | \(-0.740901\pi\) | ||||
−0.686607 | + | 0.727029i | \(0.740901\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.6033 | 1.10808 | ||||||||
\(494\) | −19.6417 | −0.883720 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −79.1027 | −3.55181 | ||||||||
\(497\) | −3.21286 | −0.144117 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.5590 | −1.68137 | −0.840687 | − | 0.541522i | \(-0.817848\pi\) | ||||
−0.840687 | + | 0.541522i | \(0.817848\pi\) | |||||||
\(500\) | 52.3914 | 2.34302 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.1693 | 1.25726 | ||||||||
\(503\) | 22.9897 | 1.02506 | 0.512530 | − | 0.858669i | \(-0.328708\pi\) | ||||
0.512530 | + | 0.858669i | \(0.328708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.118926 | 0.00529214 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 89.4116 | 3.96700 | ||||||||
\(509\) | 4.19559 | 0.185966 | 0.0929831 | − | 0.995668i | \(-0.470360\pi\) | ||||
0.0929831 | + | 0.995668i | \(0.470360\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.5891 | −0.645383 | ||||||||
\(512\) | −7.30328 | −0.322763 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.86798 | −0.435258 | ||||||||
\(515\) | 2.03637 | 0.0897330 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 15.6941 | 0.689560 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16.8258 | 0.737859 | ||||||||
\(521\) | −36.9418 | −1.61845 | −0.809225 | − | 0.587499i | \(-0.800113\pi\) | ||||
−0.809225 | + | 0.587499i | \(0.800113\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.84645 | −0.0807395 | −0.0403697 | − | 0.999185i | \(-0.512854\pi\) | ||||
−0.0403697 | + | 0.999185i | \(0.512854\pi\) | |||||||
\(524\) | 1.68088 | 0.0734298 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.2953 | −1.19013 | ||||||||
\(527\) | −35.3320 | −1.53909 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9857 | −0.999378 | ||||||||
\(530\) | 1.30841 | 0.0568336 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 22.5846 | 0.979168 | ||||||||
\(533\) | −18.5373 | −0.802939 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.8781 | 0.556769 | ||||||||
\(536\) | 75.0762 | 3.24280 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −85.8395 | −3.70081 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.73546 | −0.418560 | −0.209280 | − | 0.977856i | \(-0.567112\pi\) | ||||
−0.209280 | + | 0.977856i | \(0.567112\pi\) | |||||||
\(542\) | −55.6215 | −2.38915 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 92.3708 | 3.96037 | ||||||||
\(545\) | −19.3162 | −0.827414 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.27745 | −0.0546199 | −0.0273100 | − | 0.999627i | \(-0.508694\pi\) | ||||
−0.0273100 | + | 0.999627i | \(0.508694\pi\) | |||||||
\(548\) | −53.8016 | −2.29829 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.1408 | 0.815427 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.4761 | 0.615588 | ||||||||
\(554\) | 40.6050 | 1.72514 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 69.3884 | 2.94272 | ||||||||
\(557\) | −36.7874 | −1.55873 | −0.779366 | − | 0.626569i | \(-0.784459\pi\) | ||||
−0.779366 | + | 0.626569i | \(0.784459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.0494 | −0.425046 | ||||||||
\(560\) | −14.6653 | −0.619721 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 68.9667 | 2.90918 | ||||||||
\(563\) | 14.6601 | 0.617849 | 0.308924 | − | 0.951087i | \(-0.400031\pi\) | ||||
0.308924 | + | 0.951087i | \(0.400031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.35133 | −0.309273 | ||||||||
\(566\) | 48.2402 | 2.02769 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.4494 | −1.15175 | ||||||||
\(569\) | −27.8442 | −1.16729 | −0.583645 | − | 0.812009i | \(-0.698374\pi\) | ||||
−0.583645 | + | 0.812009i | \(0.698374\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.5879 | 0.610485 | 0.305243 | − | 0.952275i | \(-0.401262\pi\) | ||||
0.305243 | + | 0.952275i | \(0.401262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 29.5335 | 1.23270 | ||||||||
\(575\) | −0.434214 | −0.0181080 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.1147 | −1.08717 | −0.543584 | − | 0.839355i | \(-0.682933\pi\) | ||||
−0.543584 | + | 0.839355i | \(0.682933\pi\) | |||||||
\(578\) | 38.3994 | 1.59721 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −26.6868 | −1.10811 | ||||||||
\(581\) | 3.45931 | 0.143516 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −124.643 | −5.15778 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −82.9987 | −3.42864 | ||||||||
\(587\) | −14.6634 | −0.605222 | −0.302611 | − | 0.953114i | \(-0.597858\pi\) | ||||
−0.302611 | + | 0.953114i | \(0.597858\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.4876 | −1.13261 | ||||||||
\(590\) | −2.27022 | −0.0934633 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 73.3542 | 3.01484 | ||||||||
\(593\) | −17.7060 | −0.727100 | −0.363550 | − | 0.931575i | \(-0.618435\pi\) | ||||
−0.363550 | + | 0.931575i | \(0.618435\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.55039 | −0.268540 | ||||||||
\(596\) | −50.1568 | −2.05450 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.539572 | −0.0220647 | ||||||||
\(599\) | −20.2930 | −0.829148 | −0.414574 | − | 0.910016i | \(-0.636069\pi\) | ||||
−0.414574 | + | 0.910016i | \(0.636069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.9477 | −0.446566 | −0.223283 | − | 0.974754i | \(-0.571677\pi\) | ||||
−0.223283 | + | 0.974754i | \(0.571677\pi\) | |||||||
\(602\) | 16.0107 | 0.652548 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.2827 | 0.540467 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.9487 | −1.37793 | −0.688967 | − | 0.724793i | \(-0.741936\pi\) | ||||
−0.688967 | + | 0.724793i | \(0.741936\pi\) | |||||||
\(608\) | 71.8626 | 2.91441 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 27.7931 | 1.12531 | ||||||||
\(611\) | 21.1702 | 0.856455 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.46975 | 0.301700 | 0.150850 | − | 0.988557i | \(-0.451799\pi\) | ||||
0.150850 | + | 0.988557i | \(0.451799\pi\) | |||||||
\(614\) | −26.8601 | −1.08399 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.3727 | 1.18250 | 0.591250 | − | 0.806489i | \(-0.298635\pi\) | ||||
0.591250 | + | 0.806489i | \(0.298635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.1344 | 1.45236 | 0.726181 | − | 0.687503i | \(-0.241293\pi\) | ||||
0.726181 | + | 0.687503i | \(0.241293\pi\) | |||||||
\(620\) | 38.3241 | 1.53913 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −43.7900 | −1.75582 | ||||||||
\(623\) | 12.0621 | 0.483259 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.32915 | 0.253166 | ||||||||
\(626\) | 11.9849 | 0.479014 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 96.0055 | 3.83104 | ||||||||
\(629\) | 32.7644 | 1.30640 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.1360 | 1.55798 | 0.778990 | − | 0.627036i | \(-0.215732\pi\) | ||||
0.778990 | + | 0.627036i | \(0.215732\pi\) | |||||||
\(632\) | 123.679 | 4.91967 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 32.1118 | 1.27532 | ||||||||
\(635\) | −20.1751 | −0.800625 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.68268 | −0.0666704 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.5627 | −0.852342 | ||||||||
\(641\) | 27.8586 | 1.10035 | 0.550174 | − | 0.835050i | \(-0.314561\pi\) | ||||
0.550174 | + | 0.835050i | \(0.314561\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.1417 | 0.518258 | 0.259129 | − | 0.965843i | \(-0.416565\pi\) | ||||
0.259129 | + | 0.965843i | \(0.416565\pi\) | |||||||
\(644\) | 0.620417 | 0.0244479 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 65.3298 | 2.57037 | ||||||||
\(647\) | 3.36604 | 0.132333 | 0.0661663 | − | 0.997809i | \(-0.478923\pi\) | ||||
0.0661663 | + | 0.997809i | \(0.478923\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 16.3758 | 0.642312 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 33.6020 | 1.31596 | ||||||||
\(653\) | 24.8798 | 0.973622 | 0.486811 | − | 0.873507i | \(-0.338160\pi\) | ||||
0.486811 | + | 0.873507i | \(0.338160\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.379280 | −0.0148197 | ||||||||
\(656\) | 138.039 | 5.38953 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −33.7283 | −1.31486 | ||||||||
\(659\) | −30.5058 | −1.18834 | −0.594169 | − | 0.804340i | \(-0.702519\pi\) | ||||
−0.594169 | + | 0.804340i | \(0.702519\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.2042 | 0.396899 | 0.198449 | − | 0.980111i | \(-0.436409\pi\) | ||||
0.198449 | + | 0.980111i | \(0.436409\pi\) | |||||||
\(662\) | −48.4892 | −1.88459 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.5550 | 1.14696 | ||||||||
\(665\) | −5.09607 | −0.197617 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.525813 | 0.0203596 | ||||||||
\(668\) | −131.004 | −5.06871 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −27.5717 | −1.06519 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.7196 | −1.87800 | −0.939001 | − | 0.343914i | \(-0.888247\pi\) | ||||
−0.939001 | + | 0.343914i | \(0.888247\pi\) | |||||||
\(674\) | 51.1661 | 1.97085 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −52.7435 | −2.02860 | ||||||||
\(677\) | −16.0041 | −0.615087 | −0.307543 | − | 0.951534i | \(-0.599507\pi\) | ||||
−0.307543 | + | 0.951534i | \(0.599507\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.99575 | −0.230096 | ||||||||
\(680\) | −55.9640 | −2.14612 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.6991 | 1.02161 | 0.510805 | − | 0.859696i | \(-0.329347\pi\) | ||||
0.510805 | + | 0.859696i | \(0.329347\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.1400 | 0.463844 | ||||||||
\(686\) | 2.68084 | 0.102355 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 74.8339 | 2.85302 | ||||||||
\(689\) | 0.701687 | 0.0267321 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.7496 | 0.599143 | 0.299571 | − | 0.954074i | \(-0.403156\pi\) | ||||
0.299571 | + | 0.954074i | \(0.403156\pi\) | |||||||
\(692\) | −48.0725 | −1.82744 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.2558 | −0.541143 | ||||||||
\(695\) | −15.6570 | −0.593905 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61.6566 | 2.33541 | ||||||||
\(698\) | −55.2956 | −2.09297 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18.8294 | −0.711686 | ||||||||
\(701\) | −32.1718 | −1.21511 | −0.607557 | − | 0.794276i | \(-0.707850\pi\) | ||||
−0.607557 | + | 0.794276i | \(0.707850\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.4900 | 0.961374 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.6169 | 0.738293 | ||||||||
\(707\) | −0.101612 | −0.00382152 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.52842 | −0.132513 | −0.0662564 | − | 0.997803i | \(-0.521106\pi\) | ||||
−0.0662564 | + | 0.997803i | \(0.521106\pi\) | |||||||
\(710\) | 10.0808 | 0.378325 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 103.054 | 3.86212 | ||||||||
\(713\) | −0.755104 | −0.0282789 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −80.1055 | −2.99368 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 64.9540 | 2.42406 | ||||||||
\(719\) | 37.1145 | 1.38414 | 0.692069 | − | 0.721831i | \(-0.256699\pi\) | ||||
0.692069 | + | 0.721831i | \(0.256699\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.73990 | −0.0647973 | ||||||||
\(722\) | −0.110715 | −0.00412039 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 54.6277 | 2.03022 | ||||||||
\(725\) | −15.9582 | −0.592674 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.85215 | −0.291220 | −0.145610 | − | 0.989342i | \(-0.546514\pi\) | ||||
−0.145610 | + | 0.989342i | \(0.546514\pi\) | |||||||
\(728\) | −14.3762 | −0.532817 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 45.7752 | 1.69422 | ||||||||
\(731\) | 33.4253 | 1.23628 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.0960 | −1.07468 | −0.537342 | − | 0.843365i | \(-0.680571\pi\) | ||||
−0.537342 | + | 0.843365i | \(0.680571\pi\) | |||||||
\(734\) | −60.3347 | −2.22699 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.97412 | 0.0727671 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.18580 | −0.264334 | −0.132167 | − | 0.991227i | \(-0.542194\pi\) | ||||
−0.132167 | + | 0.991227i | \(0.542194\pi\) | |||||||
\(740\) | −35.5391 | −1.30644 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.11792 | −0.0410402 | ||||||||
\(743\) | 10.6220 | 0.389684 | 0.194842 | − | 0.980835i | \(-0.437581\pi\) | ||||
0.194842 | + | 0.980835i | \(0.437581\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.3175 | 0.414643 | ||||||||
\(746\) | 16.7630 | 0.613739 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0032 | −0.402049 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0045 | 0.584014 | 0.292007 | − | 0.956416i | \(-0.405677\pi\) | ||||
0.292007 | + | 0.956416i | \(0.405677\pi\) | |||||||
\(752\) | −157.646 | −5.74874 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19.8304 | −0.722179 | ||||||||
\(755\) | −2.99716 | −0.109078 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.61194 | −0.313006 | −0.156503 | − | 0.987677i | \(-0.550022\pi\) | ||||
−0.156503 | + | 0.987677i | \(0.550022\pi\) | |||||||
\(758\) | 34.3664 | 1.24824 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −43.5388 | −1.57932 | ||||||||
\(761\) | 15.5310 | 0.563000 | 0.281500 | − | 0.959561i | \(-0.409168\pi\) | ||||
0.281500 | + | 0.959561i | \(0.409168\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.5040 | 0.597486 | ||||||||
\(764\) | −35.5997 | −1.28795 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.3380 | 0.626446 | ||||||||
\(767\) | −1.21750 | −0.0439612 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.4797 | 1.85640 | 0.928202 | − | 0.372076i | \(-0.121354\pi\) | ||||
0.928202 | + | 0.372076i | \(0.121354\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 115.822 | 4.16853 | ||||||||
\(773\) | −20.2078 | −0.726823 | −0.363411 | − | 0.931629i | \(-0.618388\pi\) | ||||
−0.363411 | + | 0.931629i | \(0.618388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.9171 | 0.823208 | ||||||||
\(776\) | −51.2253 | −1.83888 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −39.9358 | −1.43177 | ||||||||
\(779\) | 47.9676 | 1.71862 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.79466 | 0.0641769 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.5302 | 0.447508 | ||||||||
\(785\) | −21.6630 | −0.773185 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.5330 | 1.76566 | 0.882831 | − | 0.469692i | \(-0.155635\pi\) | ||||
0.882831 | + | 0.469692i | \(0.155635\pi\) | |||||||
\(788\) | 23.0923 | 0.822629 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −45.4209 | −1.61600 | ||||||||
\(791\) | 6.28108 | 0.223330 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9052 | 0.529299 | ||||||||
\(794\) | 4.98266 | 0.176828 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −78.3187 | −2.77593 | ||||||||
\(797\) | −26.6619 | −0.944414 | −0.472207 | − | 0.881488i | \(-0.656543\pi\) | ||||
−0.472207 | + | 0.881488i | \(0.656543\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −70.4140 | −2.49107 | ||||||||
\(800\) | −59.9139 | −2.11827 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.4372 | −0.827597 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.139993 | −0.00493411 | ||||||||
\(806\) | 28.4778 | 1.00309 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.868135 | −0.0305409 | ||||||||
\(809\) | 51.2793 | 1.80288 | 0.901442 | − | 0.432900i | \(-0.142510\pi\) | ||||
0.901442 | + | 0.432900i | \(0.142510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.9340 | 0.945782 | 0.472891 | − | 0.881121i | \(-0.343210\pi\) | ||||
0.472891 | + | 0.881121i | \(0.343210\pi\) | |||||||
\(812\) | 22.8016 | 0.800180 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.58207 | −0.265588 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.0042 | 0.909772 | ||||||||
\(818\) | 34.0997 | 1.19227 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −66.8781 | −2.33548 | ||||||||
\(821\) | −36.3229 | −1.26768 | −0.633839 | − | 0.773465i | \(-0.718522\pi\) | ||||
−0.633839 | + | 0.773465i | \(0.718522\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4540 | −0.399262 | −0.199631 | − | 0.979871i | \(-0.563974\pi\) | ||||
−0.199631 | + | 0.979871i | \(0.563974\pi\) | |||||||
\(824\) | −14.8650 | −0.517848 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.93971 | 0.0674910 | ||||||||
\(827\) | −18.8743 | −0.656324 | −0.328162 | − | 0.944621i | \(-0.606429\pi\) | ||||
−0.328162 | + | 0.944621i | \(0.606429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.0160 | −0.417331 | −0.208666 | − | 0.977987i | \(-0.566912\pi\) | ||||
−0.208666 | + | 0.977987i | \(0.566912\pi\) | |||||||
\(830\) | −10.8541 | −0.376750 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −32.2825 | −1.11919 | ||||||||
\(833\) | 5.59675 | 0.193916 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.5603 | 1.02297 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.7117 | −0.750019 | ||||||||
\(839\) | 5.34302 | 0.184461 | 0.0922307 | − | 0.995738i | \(-0.470600\pi\) | ||||
0.0922307 | + | 0.995738i | \(0.470600\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.67528 | −0.333630 | ||||||||
\(842\) | −70.9849 | −2.44630 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −118.513 | −4.07940 | ||||||||
\(845\) | 11.9012 | 0.409414 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.22516 | −0.179433 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −54.4673 | −1.86821 | ||||||||
\(851\) | 0.700230 | 0.0240036 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.05041 | 0.0359655 | 0.0179827 | − | 0.999838i | \(-0.494276\pi\) | ||||
0.0179827 | + | 0.999838i | \(0.494276\pi\) | |||||||
\(854\) | −23.7469 | −0.812601 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −94.0073 | −3.21310 | ||||||||
\(857\) | 13.9506 | 0.476542 | 0.238271 | − | 0.971199i | \(-0.423419\pi\) | ||||
0.238271 | + | 0.971199i | \(0.423419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.5493 | 1.75884 | 0.879419 | − | 0.476048i | \(-0.157931\pi\) | ||||
0.879419 | + | 0.476048i | \(0.157931\pi\) | |||||||
\(860\) | −36.2560 | −1.23632 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.955576 | −0.0325470 | ||||||||
\(863\) | −33.1894 | −1.12978 | −0.564890 | − | 0.825166i | \(-0.691082\pi\) | ||||
−0.564890 | + | 0.825166i | \(0.691082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8472 | 0.368817 | ||||||||
\(866\) | −49.0284 | −1.66605 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −32.7447 | −1.11143 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.7864 | −0.501020 | ||||||||
\(872\) | 141.004 | 4.77500 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.39621 | 0.0472275 | ||||||||
\(875\) | 10.1007 | 0.341466 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.2380 | −1.69642 | −0.848208 | − | 0.529663i | \(-0.822318\pi\) | ||||
−0.848208 | + | 0.529663i | \(0.822318\pi\) | |||||||
\(878\) | 17.8982 | 0.604034 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.9209 | 1.31128 | 0.655639 | − | 0.755074i | \(-0.272399\pi\) | ||||
0.655639 | + | 0.755074i | \(0.272399\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.3534 | −0.348420 | −0.174210 | − | 0.984709i | \(-0.555737\pi\) | ||||
−0.174210 | + | 0.984709i | \(0.555737\pi\) | |||||||
\(884\) | −48.8481 | −1.64294 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −54.7971 | −1.84094 | ||||||||
\(887\) | −24.6430 | −0.827432 | −0.413716 | − | 0.910406i | \(-0.635769\pi\) | ||||
−0.413716 | + | 0.910406i | \(0.635769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.2379 | 0.578141 | ||||||||
\(890\) | −37.8466 | −1.26862 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 50.3684 | 1.68646 | ||||||||
\(893\) | −54.7806 | −1.83316 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0753 | 0.604190 | ||||||||
\(896\) | 18.4235 | 0.615487 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.7829 | 0.493313 | ||||||||
\(899\) | −27.7516 | −0.925569 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.33387 | −0.0777525 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 53.6631 | 1.78481 | ||||||||
\(905\) | −12.3264 | −0.409742 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.0708 | 1.43014 | 0.715071 | − | 0.699052i | \(-0.246394\pi\) | ||||
0.715071 | + | 0.699052i | \(0.246394\pi\) | |||||||
\(908\) | −96.5666 | −3.20467 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.27965 | 0.175019 | ||||||||
\(911\) | −45.4296 | −1.50515 | −0.752574 | − | 0.658508i | \(-0.771188\pi\) | ||||
−0.752574 | + | 0.658508i | \(0.771188\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 5.36907 | 0.177593 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46.9039 | 1.54975 | ||||||||
\(917\) | 0.324063 | 0.0107015 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.7647 | 0.553015 | 0.276508 | − | 0.961012i | \(-0.410823\pi\) | ||||
0.276508 | + | 0.961012i | \(0.410823\pi\) | |||||||
\(920\) | −1.19605 | −0.0394324 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.9142 | −0.721705 | ||||||||
\(923\) | 5.40623 | 0.177948 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.2517 | −0.698753 | ||||||||
\(926\) | −11.4388 | −0.375901 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 72.5530 | 2.38167 | ||||||||
\(929\) | 22.5588 | 0.740131 | 0.370065 | − | 0.929006i | \(-0.379335\pi\) | ||||
0.370065 | + | 0.929006i | \(0.379335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.35416 | 0.142702 | ||||||||
\(932\) | 44.7278 | 1.46511 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 108.611 | 3.55386 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.56458 | 0.247124 | 0.123562 | − | 0.992337i | \(-0.460568\pi\) | ||||
0.123562 | + | 0.992337i | \(0.460568\pi\) | |||||||
\(938\) | 23.5577 | 0.769185 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 76.3770 | 2.49114 | ||||||||
\(941\) | −48.7593 | −1.58951 | −0.794754 | − | 0.606932i | \(-0.792400\pi\) | ||||
−0.794754 | + | 0.606932i | \(0.792400\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.31771 | 0.0429104 | ||||||||
\(944\) | 9.06618 | 0.295079 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.4056 | −0.468119 | −0.234060 | − | 0.972222i | \(-0.575201\pi\) | ||||
−0.234060 | + | 0.972222i | \(0.575201\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.5488 | 0.796889 | ||||||||
\(950\) | −42.3744 | −1.37481 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 47.8165 | 1.54974 | ||||||||
\(953\) | −31.4716 | −1.01947 | −0.509733 | − | 0.860333i | \(-0.670256\pi\) | ||||
−0.509733 | + | 0.860333i | \(0.670256\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.03282 | 0.259936 | ||||||||
\(956\) | −107.302 | −3.47039 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.0924 | 0.713772 | ||||||||
\(959\) | −10.3726 | −0.334948 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.85325 | 0.285589 | ||||||||
\(962\) | −26.4083 | −0.851436 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −128.851 | −4.15000 | ||||||||
\(965\) | −26.1345 | −0.841299 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.1109 | 0.614566 | 0.307283 | − | 0.951618i | \(-0.400580\pi\) | ||||
0.307283 | + | 0.951618i | \(0.400580\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18.8125 | 0.604032 | ||||||||
\(971\) | −42.7809 | −1.37291 | −0.686453 | − | 0.727174i | \(-0.740833\pi\) | ||||
−0.686453 | + | 0.727174i | \(0.740833\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.3776 | 0.428866 | ||||||||
\(974\) | −2.58670 | −0.0828831 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −110.993 | −3.55279 | ||||||||
\(977\) | 40.2273 | 1.28699 | 0.643493 | − | 0.765452i | \(-0.277485\pi\) | ||||
0.643493 | + | 0.765452i | \(0.277485\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.07072 | −0.193922 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −81.5737 | −2.60312 | ||||||||
\(983\) | −23.9559 | −0.764074 | −0.382037 | − | 0.924147i | \(-0.624777\pi\) | ||||
−0.382037 | + | 0.924147i | \(0.624777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.21062 | −0.166024 | ||||||||
\(986\) | 65.9574 | 2.10051 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.0028 | −1.20903 | ||||||||
\(989\) | 0.714356 | 0.0227152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.7275 | −0.626665 | −0.313332 | − | 0.949644i | \(-0.601445\pi\) | ||||
−0.313332 | + | 0.949644i | \(0.601445\pi\) | |||||||
\(992\) | −104.191 | −3.30807 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.61317 | −0.273193 | ||||||||
\(995\) | 17.6721 | 0.560243 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.90849 | 0.0604426 | 0.0302213 | − | 0.999543i | \(-0.490379\pi\) | ||||
0.0302213 | + | 0.999543i | \(0.490379\pi\) | |||||||
\(998\) | −100.690 | −3.18728 | ||||||||
\(999\) | 0 | 0 |
(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 | 7623.2.a.dc.1.16 | 16 | ||
3.2 | odd | 2 | inner | 7623.2.a.dc.1.1 | 16 | ||
11.5 | even | 5 | 693.2.m.k.190.1 | ✓ | 32 | ||
11.9 | even | 5 | 693.2.m.k.631.1 | yes | 32 | ||
11.10 | odd | 2 | 7623.2.a.db.1.1 | 16 | |||
33.5 | odd | 10 | 693.2.m.k.190.8 | yes | 32 | ||
33.20 | odd | 10 | 693.2.m.k.631.8 | yes | 32 | ||
33.32 | even | 2 | 7623.2.a.db.1.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.2.m.k.190.1 | ✓ | 32 | 11.5 | even | 5 | ||
693.2.m.k.190.8 | yes | 32 | 33.5 | odd | 10 | ||
693.2.m.k.631.1 | yes | 32 | 11.9 | even | 5 | ||
693.2.m.k.631.8 | yes | 32 | 33.20 | odd | 10 | ||
7623.2.a.db.1.1 | 16 | 11.10 | odd | 2 | |||
7623.2.a.db.1.16 | 16 | 33.32 | even | 2 | |||
7623.2.a.dc.1.1 | 16 | 3.2 | odd | 2 | inner | ||
7623.2.a.dc.1.16 | 16 | 1.1 | even | 1 | trivial |