Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6044,2,Mod(1,6044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6044, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6044 = 2^{2} \cdot 1511 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6044.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: | \(48.2615829817\) |
Analytic rank: | \(1\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6044.1 |
$q$-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 | ||||||||
\(3\) | −3.43683 | −1.98425 | −0.992127 | − | 0.125239i | \(-0.960030\pi\) | ||||
−0.992127 | + | 0.125239i | \(0.960030\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.31396 | 0.587622 | 0.293811 | − | 0.955863i | \(-0.405076\pi\) | ||||
0.293811 | + | 0.955863i | \(0.405076\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.97589 | 1.12478 | 0.562391 | − | 0.826871i | \(-0.309882\pi\) | ||||
0.562391 | + | 0.826871i | \(0.309882\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.81178 | 2.93726 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.04814 | −0.919048 | −0.459524 | − | 0.888165i | \(-0.651980\pi\) | ||||
−0.459524 | + | 0.888165i | \(0.651980\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.12747 | 1.14475 | 0.572377 | − | 0.819991i | \(-0.306021\pi\) | ||||
0.572377 | + | 0.819991i | \(0.306021\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.51587 | −1.16599 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.31007 | 0.317738 | 0.158869 | − | 0.987300i | \(-0.449215\pi\) | ||||
0.158869 | + | 0.987300i | \(0.449215\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.92060 | 0.440616 | 0.220308 | − | 0.975430i | \(-0.429294\pi\) | ||||
0.220308 | + | 0.975430i | \(0.429294\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.2276 | −2.23185 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.38694 | 0.497711 | 0.248855 | − | 0.968541i | \(-0.419946\pi\) | ||||
0.248855 | + | 0.968541i | \(0.419946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.27350 | −0.654700 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19.9741 | −3.84402 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.127258 | −0.0236313 | −0.0118156 | − | 0.999930i | \(-0.503761\pi\) | ||||
−0.0118156 | + | 0.999930i | \(0.503761\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.273738 | −0.0491649 | −0.0245824 | − | 0.999698i | \(-0.507826\pi\) | ||||
−0.0245824 | + | 0.999698i | \(0.507826\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.4759 | 1.82362 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.91021 | 0.660947 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.5818 | −1.73964 | −0.869820 | − | 0.493370i | \(-0.835765\pi\) | ||||
−0.869820 | + | 0.493370i | \(0.835765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.1854 | −2.27148 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.48068 | −0.855938 | −0.427969 | − | 0.903793i | \(-0.640771\pi\) | ||||
−0.427969 | + | 0.903793i | \(0.640771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.698763 | −0.106560 | −0.0532802 | − | 0.998580i | \(-0.516968\pi\) | ||||
−0.0532802 | + | 0.998580i | \(0.516968\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.5784 | 1.72600 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.7050 | −1.99908 | −0.999538 | − | 0.0303977i | \(-0.990323\pi\) | ||||
−0.999538 | + | 0.0303977i | \(0.990323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.85594 | 0.265134 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50248 | −0.630473 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.84971 | 0.528799 | 0.264399 | − | 0.964413i | \(-0.414826\pi\) | ||||
0.264399 | + | 0.964413i | \(0.414826\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00514 | −0.540053 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.60077 | −0.874293 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.08417 | −0.792091 | −0.396046 | − | 0.918231i | \(-0.629618\pi\) | ||||
−0.396046 | + | 0.918231i | \(0.629618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.5724 | −1.60974 | −0.804868 | − | 0.593454i | \(-0.797764\pi\) | ||||
−0.804868 | + | 0.593454i | \(0.797764\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 26.2229 | 3.30378 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.42334 | 0.672683 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.19524 | −1.12338 | −0.561689 | − | 0.827349i | \(-0.689848\pi\) | ||||
−0.561689 | + | 0.827349i | \(0.689848\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.20349 | −0.987585 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.97288 | 0.946207 | 0.473104 | − | 0.881007i | \(-0.343134\pi\) | ||||
0.473104 | + | 0.881007i | \(0.343134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.98119 | 1.16821 | 0.584105 | − | 0.811678i | \(-0.301446\pi\) | ||||
0.584105 | + | 0.811678i | \(0.301446\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.2505 | 1.29909 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.07093 | −1.03373 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0822 | −1.69688 | −0.848439 | − | 0.529294i | \(-0.822457\pi\) | ||||
−0.848439 | + | 0.529294i | \(0.822457\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 42.2122 | 4.69024 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.25697 | −0.467263 | −0.233632 | − | 0.972325i | \(-0.575061\pi\) | ||||
−0.233632 | + | 0.972325i | \(0.575061\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.72138 | 0.186710 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.437365 | 0.0468904 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6184 | 1.12555 | 0.562774 | − | 0.826611i | \(-0.309734\pi\) | ||||
0.562774 | + | 0.826611i | \(0.309734\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2829 | 1.28760 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.940792 | 0.0975556 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.52360 | 0.258916 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.6409 | 1.58809 | 0.794046 | − | 0.607857i | \(-0.207971\pi\) | ||||
0.794046 | + | 0.607857i | \(0.207971\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −26.8595 | −2.69948 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.37551 | 0.236372 | 0.118186 | − | 0.992991i | \(-0.462292\pi\) | ||||
0.118186 | + | 0.992991i | \(0.462292\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.3325 | −1.70782 | −0.853909 | − | 0.520423i | \(-0.825774\pi\) | ||||
−0.853909 | + | 0.520423i | \(0.825774\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.4387 | −1.31149 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.0669 | −0.973200 | −0.486600 | − | 0.873625i | \(-0.661763\pi\) | ||||
−0.486600 | + | 0.873625i | \(0.661763\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.62668 | −0.538938 | −0.269469 | − | 0.963009i | \(-0.586848\pi\) | ||||
−0.269469 | + | 0.963009i | \(0.586848\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 36.3679 | 3.45188 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5469 | −0.992166 | −0.496083 | − | 0.868275i | \(-0.665229\pi\) | ||||
−0.496083 | + | 0.868275i | \(0.665229\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.13635 | 0.292466 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 36.3704 | 3.36244 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.89862 | 0.357386 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.70886 | −0.155351 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.8361 | 1.69840 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8711 | −0.972339 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1798 | −0.903311 | −0.451655 | − | 0.892192i | \(-0.649166\pi\) | ||||
−0.451655 | + | 0.892192i | \(0.649166\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.40153 | 0.211443 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.4177 | −0.910196 | −0.455098 | − | 0.890441i | \(-0.650396\pi\) | ||||
−0.455098 | + | 0.890441i | \(0.650396\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.71550 | 0.495597 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −26.2452 | −2.25883 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.5230 | 1.15535 | 0.577676 | − | 0.816266i | \(-0.303960\pi\) | ||||
0.577676 | + | 0.816266i | \(0.303960\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.612591 | 0.0519593 | 0.0259797 | − | 0.999662i | \(-0.491729\pi\) | ||||
0.0259797 | + | 0.999662i | \(0.491729\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 47.1016 | 3.96667 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.5811 | −1.05208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.167213 | −0.0138863 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.37854 | −0.526093 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.4821 | 1.26834 | 0.634171 | − | 0.773193i | \(-0.281342\pi\) | ||||
0.634171 | + | 0.773193i | \(0.281342\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.2485 | 1.48504 | 0.742521 | − | 0.669822i | \(-0.233630\pi\) | ||||
0.742521 | + | 0.669822i | \(0.233630\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.5440 | 0.933280 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.359682 | −0.0288904 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.1637 | −1.60924 | −0.804620 | − | 0.593790i | \(-0.797631\pi\) | ||||
−0.804620 | + | 0.593790i | \(0.797631\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.2308 | −1.04927 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.10327 | 0.559816 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.45585 | 0.427335 | 0.213668 | − | 0.976906i | \(-0.431459\pi\) | ||||
0.213668 | + | 0.976906i | \(0.431459\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.7650 | 1.07160 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.8449 | 1.07135 | 0.535675 | − | 0.844424i | \(-0.320057\pi\) | ||||
0.535675 | + | 0.844424i | \(0.320057\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.03600 | 0.310461 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.9239 | 1.29420 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.4674 | 1.63213 | 0.816067 | − | 0.577957i | \(-0.196150\pi\) | ||||
0.816067 | + | 0.577957i | \(0.196150\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.74159 | −0.736395 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.9102 | 1.57171 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.3962 | 1.22551 | 0.612754 | − | 0.790274i | \(-0.290062\pi\) | ||||
0.612754 | + | 0.790274i | \(0.290062\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.4204 | −1.88949 | −0.944743 | − | 0.327812i | \(-0.893689\pi\) | ||||
−0.944743 | + | 0.327812i | \(0.893689\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 43.2093 | 3.19412 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.9041 | −1.02225 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.99327 | −0.292017 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −59.4408 | −4.32368 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.4317 | −1.26131 | −0.630656 | − | 0.776063i | \(-0.717214\pi\) | ||||
−0.630656 | + | 0.776063i | \(0.717214\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.88543 | −0.135716 | −0.0678581 | − | 0.997695i | \(-0.521617\pi\) | ||||
−0.0678581 | + | 0.997695i | \(0.521617\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.6391 | −1.33477 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.72400 | −0.621559 | −0.310779 | − | 0.950482i | \(-0.600590\pi\) | ||||
−0.310779 | + | 0.950482i | \(0.600590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.450808 | −0.0319569 | −0.0159785 | − | 0.999872i | \(-0.505086\pi\) | ||||
−0.0159785 | + | 0.999872i | \(0.505086\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.6025 | 2.22907 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.378707 | −0.0265800 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.20141 | −0.502968 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.0332 | 1.46191 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.85425 | −0.404947 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3506 | 1.12562 | 0.562812 | − | 0.826585i | \(-0.309720\pi\) | ||||
0.562812 | + | 0.826585i | \(0.309720\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −27.4014 | −1.87751 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.918149 | −0.0626172 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.814616 | −0.0552998 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −34.3036 | −2.31802 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.40727 | 0.363732 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.38285 | −0.494392 | −0.247196 | − | 0.968965i | \(-0.579509\pi\) | ||||
−0.247196 | + | 0.968965i | \(0.579509\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −28.8454 | −1.92302 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.4615 | 0.959843 | 0.479922 | − | 0.877311i | \(-0.340665\pi\) | ||||
0.479922 | + | 0.877311i | \(0.340665\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.7858 | −1.37356 | −0.686782 | − | 0.726863i | \(-0.740977\pi\) | ||||
−0.686782 | + | 0.726863i | \(0.740977\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 31.1752 | 2.05118 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.8030 | 1.10080 | 0.550400 | − | 0.834901i | \(-0.314475\pi\) | ||||
0.550400 | + | 0.834901i | \(0.314475\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0078 | −1.17470 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 51.8348 | 3.36703 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.38777 | −0.607244 | −0.303622 | − | 0.952792i | \(-0.598196\pi\) | ||||
−0.303622 | + | 0.952792i | \(0.598196\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.8491 | 0.956516 | 0.478258 | − | 0.878219i | \(-0.341268\pi\) | ||||
0.478258 | + | 0.878219i | \(0.341268\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −85.1536 | −5.46261 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.43864 | 0.155799 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.92722 | 0.504397 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.6305 | 0.927168 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.542070 | −0.0342152 | −0.0171076 | − | 0.999854i | \(-0.505446\pi\) | ||||
−0.0171076 | + | 0.999854i | \(0.505446\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.27571 | −0.457420 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.91609 | −0.370480 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.97182 | 0.372512 | 0.186256 | − | 0.982501i | \(-0.440365\pi\) | ||||
0.186256 | + | 0.982501i | \(0.440365\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.4903 | −1.95671 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.12137 | −0.0694112 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.67681 | −0.226722 | −0.113361 | − | 0.993554i | \(-0.536162\pi\) | ||||
−0.113361 | + | 0.993554i | \(0.536162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.05838 | 0.310734 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36.4936 | −2.23337 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.60618 | 0.280844 | 0.140422 | − | 0.990092i | \(-0.455154\pi\) | ||||
0.140422 | + | 0.990092i | \(0.455154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −31.7365 | −1.92786 | −0.963929 | − | 0.266161i | \(-0.914245\pi\) | ||||
−0.963929 | + | 0.266161i | \(0.914245\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −42.2142 | −2.55492 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.97808 | 0.601701 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.4328 | 1.16760 | 0.583800 | − | 0.811897i | \(-0.301565\pi\) | ||||
0.583800 | + | 0.811897i | \(0.301565\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.41212 | −0.144410 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.238157 | 0.0142072 | 0.00710362 | − | 0.999975i | \(-0.497739\pi\) | ||||
0.00710362 | + | 0.999975i | \(0.497739\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.8132 | −1.23721 | −0.618607 | − | 0.785701i | \(-0.712303\pi\) | ||||
−0.618607 | + | 0.785701i | \(0.712303\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.67317 | −0.513754 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.3099 | −0.962744 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2837 | −0.899042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −53.7551 | −3.15118 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.7369 | 1.38672 | 0.693361 | − | 0.720590i | \(-0.256129\pi\) | ||||
0.693361 | + | 0.720590i | \(0.256129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.99437 | −0.465450 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 60.8838 | 3.53283 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.85201 | 0.569757 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.07944 | −0.119857 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.16423 | −0.469023 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.5197 | −0.945917 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.529978 | 0.0302474 | 0.0151237 | − | 0.999886i | \(-0.495186\pi\) | ||||
0.0151237 | + | 0.999886i | \(0.495186\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 59.5687 | 3.38874 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.7427 | 1.11951 | 0.559754 | − | 0.828659i | \(-0.310896\pi\) | ||||
0.559754 | + | 0.828659i | \(0.310896\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.05191 | −0.229028 | −0.114514 | − | 0.993422i | \(-0.536531\pi\) | ||||
−0.114514 | + | 0.993422i | \(0.536531\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 34.4560 | 1.94137 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.0232 | −0.562959 | −0.281480 | − | 0.959567i | \(-0.590825\pi\) | ||||
−0.281480 | + | 0.959567i | \(0.590825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.387901 | 0.0217183 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 34.5981 | 1.93108 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.51612 | 0.140000 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.5113 | −0.749470 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.3379 | 1.06939 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −40.7845 | −2.24852 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.7200 | 0.973979 | 0.486989 | − | 0.873408i | \(-0.338095\pi\) | ||||
0.486989 | + | 0.873408i | \(0.338095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −93.2446 | −5.10977 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0822 | −0.660122 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.36241 | −0.128689 | −0.0643444 | − | 0.997928i | \(-0.520496\pi\) | ||||
−0.0643444 | + | 0.997928i | \(0.520496\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.2478 | 1.96871 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.834392 | 0.0451849 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.3082 | −0.826564 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.7791 | −0.580327 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.1626 | −1.35080 | −0.675399 | − | 0.737452i | \(-0.736029\pi\) | ||||
−0.675399 | + | 0.737452i | \(0.736029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.4417 | −0.826577 | −0.413288 | − | 0.910600i | \(-0.635620\pi\) | ||||
−0.413288 | + | 0.910600i | \(0.635620\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −82.4424 | −4.40045 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.1171 | −1.70942 | −0.854710 | − | 0.519105i | \(-0.826265\pi\) | ||||
−0.854710 | + | 0.519105i | \(0.826265\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4761 | 0.556012 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.3989 | −0.709145 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.3047 | −1.59942 | −0.799711 | − | 0.600385i | \(-0.795014\pi\) | ||||
−0.799711 | + | 0.600385i | \(0.795014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3113 | −0.805858 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.87305 | 0.308255 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.1149 | 0.686466 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.95465 | −0.363030 | −0.181515 | − | 0.983388i | \(-0.558100\pi\) | ||||
−0.181515 | + | 0.983388i | \(0.558100\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −48.2946 | −2.51411 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.4563 | 0.594783 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.3785 | −0.692713 | −0.346356 | − | 0.938103i | \(-0.612581\pi\) | ||||
−0.346356 | + | 0.938103i | \(0.612581\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 37.3620 | 1.92937 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.525255 | −0.0270520 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0746 | 0.671596 | 0.335798 | − | 0.941934i | \(-0.390994\pi\) | ||||
0.335798 | + | 0.941934i | \(0.390994\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.9862 | 1.79240 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.5105 | 0.996939 | 0.498470 | − | 0.866907i | \(-0.333896\pi\) | ||||
0.498470 | + | 0.866907i | \(0.333896\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.9189 | −0.607442 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.15735 | −0.312996 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.0781 | −0.663087 | −0.331544 | − | 0.943440i | \(-0.607569\pi\) | ||||
−0.331544 | + | 0.943440i | \(0.607569\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.12705 | 0.158142 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 35.8037 | 1.80606 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.8174 | −0.997123 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.3656 | −1.17268 | −0.586342 | − | 0.810064i | \(-0.699432\pi\) | ||||
−0.586342 | + | 0.810064i | \(0.699432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.6432 | −0.983389 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.79033 | −0.139343 | −0.0696713 | − | 0.997570i | \(-0.522195\pi\) | ||||
−0.0696713 | + | 0.997570i | \(0.522195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.12985 | −0.0562817 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 55.4652 | 2.75609 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.2548 | 1.59881 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7319 | −0.530658 | −0.265329 | − | 0.964158i | \(-0.585481\pi\) | ||||
−0.265329 | + | 0.964158i | \(0.585481\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −46.4763 | −2.29251 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.1058 | −0.890930 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.59350 | −0.274574 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.10537 | −0.103100 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.14851 | 0.398081 | 0.199040 | − | 0.979991i | \(-0.436218\pi\) | ||||
0.199040 | + | 0.979991i | \(0.436218\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.55862 | −0.465858 | −0.232929 | − | 0.972494i | \(-0.574831\pi\) | ||||
−0.232929 | + | 0.972494i | \(0.574831\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −120.765 | −5.87181 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.28851 | −0.208023 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −37.4142 | −1.81060 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 43.2390 | 2.08760 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.05762 | −0.195448 | −0.0977242 | − | 0.995214i | \(-0.531156\pi\) | ||||
−0.0977242 | + | 0.995214i | \(0.531156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.9993 | 0.672763 | 0.336381 | − | 0.941726i | \(-0.390797\pi\) | ||||
0.336381 | + | 0.941726i | \(0.390797\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.574681 | 0.0275539 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.58435 | 0.219299 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.1866 | 1.87027 | 0.935137 | − | 0.354288i | \(-0.115277\pi\) | ||||
0.935137 | + | 0.354288i | \(0.115277\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.3541 | 0.778768 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.0814 | 1.80930 | 0.904651 | − | 0.426153i | \(-0.140131\pi\) | ||||
0.904651 | + | 0.426153i | \(0.140131\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.9522 | 0.661397 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −53.2093 | −2.51671 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.9507 | 1.41346 | 0.706729 | − | 0.707484i | \(-0.250170\pi\) | ||||
0.706729 | + | 0.707484i | \(0.250170\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.7059 | 0.786648 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −62.7170 | −2.94670 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.1393 | 0.756622 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5239 | 0.726178 | 0.363089 | − | 0.931755i | \(-0.381722\pi\) | ||||
0.363089 | + | 0.931755i | \(0.381722\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.1674 | −1.22139 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.80886 | −0.223971 | −0.111985 | − | 0.993710i | \(-0.535721\pi\) | ||||
−0.111985 | + | 0.993710i | \(0.535721\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.76396 | 0.407296 | 0.203648 | − | 0.979044i | \(-0.434720\pi\) | ||||
0.203648 | + | 0.979044i | \(0.434720\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.23617 | 0.0573258 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.6178 | −1.60192 | −0.800961 | − | 0.598716i | \(-0.795678\pi\) | ||||
−0.800961 | + | 0.598716i | \(0.795678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.3641 | −1.26355 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 69.2992 | 3.19314 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.12993 | 0.0979341 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.28708 | −0.288471 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.9228 | 1.55322 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.37031 | −0.428141 | −0.214070 | − | 0.976818i | \(-0.568672\pi\) | ||||
−0.214070 | + | 0.976818i | \(0.568672\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.6761 | −1.99146 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.4127 | −1.11082 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.5516 | 0.933199 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.7625 | 0.759583 | 0.379791 | − | 0.925072i | \(-0.375996\pi\) | ||||
0.379791 | + | 0.925072i | \(0.375996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.7508 | −0.847941 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.9793 | −1.80424 | −0.902120 | − | 0.431486i | \(-0.857989\pi\) | ||||
−0.902120 | + | 0.431486i | \(0.857989\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.166717 | −0.00750856 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −35.2924 | −1.58628 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.7265 | 1.06428 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.21802 | 0.144058 | 0.0720291 | − | 0.997403i | \(-0.477053\pi\) | ||||
0.0720291 | + | 0.997403i | \(0.477053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −47.5825 | −2.12583 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 44.1707 | 1.96947 | 0.984737 | − | 0.174050i | \(-0.0556854\pi\) | ||||
0.984737 | + | 0.174050i | \(0.0556854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.12134 | 0.138898 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.8710 | −0.616034 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.99004 | −0.398476 | −0.199238 | − | 0.979951i | \(-0.563847\pi\) | ||||
−0.199238 | + | 0.979951i | \(0.563847\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.7029 | 1.31398 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −38.3622 | −1.69373 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.7742 | −1.00355 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.7746 | 1.83725 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −73.7797 | −3.23857 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.07009 | −0.178314 | −0.0891568 | − | 0.996018i | \(-0.528417\pi\) | ||||
−0.0891568 | + | 0.996018i | \(0.528417\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.38613 | −0.366700 | −0.183350 | − | 0.983048i | \(-0.558694\pi\) | ||||
−0.183350 | + | 0.983048i | \(0.558694\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 33.4802 | 1.46119 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.358616 | −0.0156216 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3025 | −0.752284 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −53.6123 | −2.32658 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.6213 | −0.979839 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.2275 | −0.571874 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −56.3509 | −2.43172 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.65716 | −0.243671 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.3465 | −1.43368 | −0.716839 | − | 0.697239i | \(-0.754412\pi\) | ||||
−0.716839 | + | 0.697239i | \(0.754412\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 87.3656 | 3.74922 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.39325 | −0.316692 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.3956 | −1.04308 | −0.521541 | − | 0.853226i | \(-0.674643\pi\) | ||||
−0.521541 | + | 0.853226i | \(0.674643\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −110.786 | −4.72821 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.244412 | −0.0104123 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −44.8829 | −1.90862 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 47.7860 | 2.02840 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.1152 | −1.27602 | −0.638011 | − | 0.770028i | \(-0.720242\pi\) | ||||
−0.638011 | + | 0.770028i | \(0.720242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.88412 | −0.121985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.7242 | 0.579435 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.6373 | 0.743322 | 0.371661 | − | 0.928369i | \(-0.378788\pi\) | ||||
0.371661 | + | 0.928369i | \(0.378788\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.8582 | −0.583019 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 125.619 | 5.27550 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.5360 | 0.860913 | 0.430456 | − | 0.902611i | \(-0.358353\pi\) | ||||
0.430456 | + | 0.902611i | \(0.358353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.2908 | 0.598053 | 0.299026 | − | 0.954245i | \(-0.403338\pi\) | ||||
0.299026 | + | 0.954245i | \(0.403338\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 59.9097 | 2.50276 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.81364 | −0.325851 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.3185 | 0.929130 | 0.464565 | − | 0.885539i | \(-0.346211\pi\) | ||||
0.464565 | + | 0.885539i | \(0.346211\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.47989 | 0.269295 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.6683 | −0.525569 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.7344 | −0.485991 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 47.7893 | 1.97584 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.25908 | −0.258340 | −0.129170 | − | 0.991622i | \(-0.541231\pi\) | ||||
−0.129170 | + | 0.991622i | \(0.541231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.525742 | −0.0216628 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.9829 | 1.23333 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.09671 | 0.0861014 | 0.0430507 | − | 0.999073i | \(-0.486292\pi\) | ||||
0.0430507 | + | 0.999073i | \(0.486292\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.12265 | 0.210008 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.54935 | 0.0634106 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.8150 | −0.482747 | −0.241373 | − | 0.970432i | \(-0.577598\pi\) | ||||
−0.241373 | + | 0.970432i | \(0.577598\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.9546 | 1.42583 | 0.712914 | − | 0.701251i | \(-0.247375\pi\) | ||||
0.712914 | + | 0.701251i | \(0.247375\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −81.0265 | −3.29965 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.24538 | −0.0912876 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.5048 | 0.669908 | 0.334954 | − | 0.942235i | \(-0.391279\pi\) | ||||
0.334954 | + | 0.942235i | \(0.391279\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.30155 | 0.0527415 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −56.5668 | −2.28845 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.5280 | −1.79847 | −0.899234 | − | 0.437469i | \(-0.855875\pi\) | ||||
−0.899234 | + | 0.437469i | \(0.855875\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.7500 | 0.998017 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.7397 | 0.834951 | 0.417475 | − | 0.908688i | \(-0.362915\pi\) | ||||
0.417475 | + | 0.908688i | \(0.362915\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.5683 | 1.22865 | 0.614323 | − | 0.789055i | \(-0.289429\pi\) | ||||
0.614323 | + | 0.789055i | \(0.289429\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −47.6769 | −1.91321 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.5992 | 1.26600 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.08330 | 0.0833322 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.1201 | 0.803518 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.8629 | −0.552750 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.6401 | −1.57805 | −0.789025 | − | 0.614362i | \(-0.789414\pi\) | ||||
−0.789025 | + | 0.614362i | \(0.789414\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −56.1943 | −2.23352 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.3759 | −0.530806 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.66033 | 0.303513 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 70.2553 | 2.77926 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.0341 | −0.475318 | −0.237659 | − | 0.971349i | \(-0.576380\pi\) | ||||
−0.237659 | + | 0.971349i | \(0.576380\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.7562 | 1.80445 | 0.902225 | − | 0.431266i | \(-0.141933\pi\) | ||||
0.902225 | + | 0.431266i | \(0.141933\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.15552 | 0.124248 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.9438 | 1.25584 | 0.627919 | − | 0.778278i | \(-0.283907\pi\) | ||||
0.627919 | + | 0.778278i | \(0.283907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.5454 | 0.727970 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.79970 | 0.109729 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.2709 | 0.519330 | 0.259665 | − | 0.965699i | \(-0.416388\pi\) | ||||
0.259665 | + | 0.965699i | \(0.416388\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.6884 | −0.534852 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 87.9521 | 3.43134 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.02075 | 0.117672 | 0.0588358 | − | 0.998268i | \(-0.481261\pi\) | ||||
0.0588358 | + | 0.998268i | \(0.481261\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.7998 | −1.82030 | −0.910151 | − | 0.414276i | \(-0.864035\pi\) | ||||
−0.910151 | + | 0.414276i | \(0.864035\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.5838 | −0.721736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.50996 | 0.291224 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.303758 | −0.0117615 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.3736 | 0.980999 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.3225 | 1.47942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.26705 | 0.241577 | 0.120789 | − | 0.992678i | \(-0.461458\pi\) | ||||
0.120789 | + | 0.992678i | \(0.461458\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 65.3852 | 2.51668 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.28662 | 0.356914 | 0.178457 | − | 0.983948i | \(-0.442889\pi\) | ||||
0.178457 | + | 0.983948i | \(0.442889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 46.5456 | 1.78626 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −49.7017 | −1.90457 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.49380 | 0.325006 | 0.162503 | − | 0.986708i | \(-0.448043\pi\) | ||||
0.162503 | + | 0.986708i | \(0.448043\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.7688 | 0.678910 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 71.4372 | 2.72550 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.8896 | 0.605344 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.0759 | 0.991973 | 0.495987 | − | 0.868330i | \(-0.334806\pi\) | ||||
0.495987 | + | 0.868330i | \(0.334806\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −79.9311 | −3.03633 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.804923 | 0.0305325 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.18006 | −0.271964 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −57.7490 | −2.18427 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.55904 | 0.323271 | 0.161635 | − | 0.986851i | \(-0.448323\pi\) | ||||
0.161635 | + | 0.986851i | \(0.448323\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.3234 | −0.766513 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 61.8898 | 2.33091 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.06927 | 0.265867 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.569928 | −0.0214041 | −0.0107021 | − | 0.999943i | \(-0.503407\pi\) | ||||
−0.0107021 | + | 0.999943i | \(0.503407\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −132.901 | −4.98417 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.653397 | −0.0244699 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.5311 | −0.618228 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.2642 | 1.20493 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.7249 | 0.735616 | 0.367808 | − | 0.929902i | \(-0.380108\pi\) | ||||
0.367808 | + | 0.929902i | \(0.380108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −51.5795 | −1.92092 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −51.0339 | −1.89797 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.416580 | 0.0154714 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.06123 | −0.0393587 | −0.0196794 | − | 0.999806i | \(-0.506265\pi\) | ||||
−0.0196794 | + | 0.999806i | \(0.506265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 166.022 | 6.14896 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.915427 | −0.0338583 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.0915 | 1.44388 | 0.721939 | − | 0.691957i | \(-0.243251\pi\) | ||||
0.721939 | + | 0.691957i | \(0.243251\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.38117 | −0.309144 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.0284 | 1.03244 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.7905 | 1.27979 | 0.639895 | − | 0.768463i | \(-0.278978\pi\) | ||||
0.639895 | + | 0.768463i | \(0.278978\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.2445 | −1.00085 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 52.3955 | 1.92220 | 0.961102 | − | 0.276194i | \(-0.0890733\pi\) | ||||
0.961102 | + | 0.276194i | \(0.0890733\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.3429 | 0.745306 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −37.5115 | −1.37247 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.9579 | −1.09464 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.2741 | 0.812793 | 0.406397 | − | 0.913697i | \(-0.366785\pi\) | ||||
0.406397 | + | 0.913697i | \(0.366785\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.86300 | 0.0678915 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.9779 | 0.872644 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.78288 | −0.210182 | −0.105091 | − | 0.994463i | \(-0.533513\pi\) | ||||
−0.105091 | + | 0.994463i | \(0.533513\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.0054 | 0.907638 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.2058 | 1.27621 | 0.638105 | − | 0.769949i | \(-0.279718\pi\) | ||||
0.638105 | + | 0.769949i | \(0.279718\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.7444 | −0.606188 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.1684 | 0.548416 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.1122 | −0.906749 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.2409 | −0.405359 | −0.202679 | − | 0.979245i | \(-0.564965\pi\) | ||||
−0.202679 | + | 0.979245i | \(0.564965\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.5241 | −0.739157 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.72473 | 0.241872 | 0.120936 | − | 0.992660i | \(-0.461410\pi\) | ||||
0.120936 | + | 0.992660i | \(0.461410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.896083 | 0.0321882 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 108.227 | 3.88262 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.5262 | −0.377140 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.3024 | −0.869610 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.54187 | 0.0908390 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.4944 | −0.945625 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.5198 | 0.731451 | 0.365726 | − | 0.930723i | \(-0.380821\pi\) | ||||
0.365726 | + | 0.930723i | \(0.380821\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.6366 | 0.449873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.3864 | −1.11597 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51.8924 | −1.84275 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.3848 | −0.616575 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.8530 | 1.34082 | 0.670411 | − | 0.741990i | \(-0.266118\pi\) | ||||
0.670411 | + | 0.741990i | \(0.266118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.9544 | −0.635183 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 93.5670 | 3.30603 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30.4240 | −1.07364 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.33344 | 0.328961 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.8306 | −0.557265 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.84978 | −0.311142 | −0.155571 | − | 0.987825i | \(-0.549722\pi\) | ||||
−0.155571 | + | 0.987825i | \(0.549722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.72294 | 0.306304 | 0.153152 | − | 0.988203i | \(-0.451058\pi\) | ||||
0.153152 | + | 0.988203i | \(0.451058\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 109.073 | 3.82536 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.16879 | 0.251112 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.34204 | −0.0469522 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 108.234 | 3.78201 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.7577 | 0.724450 | 0.362225 | − | 0.932091i | \(-0.382017\pi\) | ||||
0.362225 | + | 0.932091i | \(0.382017\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.6422 | 0.858974 | 0.429487 | − | 0.903073i | \(-0.358694\pi\) | ||||
0.429487 | + | 0.903073i | \(0.358694\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −34.2929 | −1.19393 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.82099 | 0.132869 | 0.0664345 | − | 0.997791i | \(-0.478838\pi\) | ||||
0.0664345 | + | 0.997791i | \(0.478838\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0658 | −0.801109 | −0.400554 | − | 0.916273i | \(-0.631182\pi\) | ||||
−0.400554 | + | 0.916273i | \(0.631182\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −66.7870 | −2.31682 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.43141 | 0.0842433 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.1917 | 0.629549 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.46768 | 0.188991 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.41885 | −0.325175 | −0.162587 | − | 0.986694i | \(-0.551984\pi\) | ||||
−0.162587 | + | 0.986694i | \(0.551984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9838 | −0.999442 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.818504 | −0.0281908 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.30315 | 0.182434 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.08538 | −0.174736 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 71.5312 | 2.45495 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.2581 | −0.865838 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.84052 | 0.302694 | 0.151347 | − | 0.988481i | \(-0.451639\pi\) | ||||
0.151347 | + | 0.988481i | \(0.451639\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.2374 | 0.760503 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.6723 | 1.18438 | 0.592192 | − | 0.805797i | \(-0.298263\pi\) | ||||
0.592192 | + | 0.805797i | \(0.298263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.01068 | 0.205082 | 0.102541 | − | 0.994729i | \(-0.467303\pi\) | ||||
0.102541 | + | 0.994729i | \(0.467303\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 56.0544 | 1.91033 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.6487 | −0.634808 | −0.317404 | − | 0.948290i | \(-0.602811\pi\) | ||||
−0.317404 | + | 0.948290i | \(0.602811\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.2073 | 0.959079 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 52.5275 | 1.78393 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.9725 | 1.55951 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.9531 | −1.28599 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 137.824 | 4.66464 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32.3512 | −1.09367 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.3222 | −1.19275 | −0.596373 | − | 0.802707i | \(-0.703392\pi\) | ||||
−0.596373 | + | 0.802707i | \(0.703392\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −81.5795 | −2.75161 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.3739 | −1.36023 | −0.680116 | − | 0.733104i | \(-0.738071\pi\) | ||||
−0.680116 | + | 0.733104i | \(0.738071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.5817 | 0.759933 | 0.379967 | − | 0.925000i | \(-0.375935\pi\) | ||||
0.379967 | + | 0.925000i | \(0.375935\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27.4753 | 0.923571 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.8314 | −0.430837 | −0.215419 | − | 0.976522i | \(-0.569112\pi\) | ||||
−0.215419 | + | 0.976522i | \(0.569112\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.2940 | −1.01603 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −128.668 | −4.31055 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.3218 | −0.880824 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.5440 | 0.720136 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −33.8597 | −1.13054 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.0348355 | 0.00116183 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.04338 | 0.168019 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.14669 | 0.237827 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.4015 | −1.11030 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.6544 | −1.05107 | −0.525534 | − | 0.850773i | \(-0.676134\pi\) | ||||
−0.525534 | + | 0.850773i | \(0.676134\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.9325 | 0.694287 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.4132 | −0.477531 | −0.238765 | − | 0.971077i | \(-0.576743\pi\) | ||||
−0.238765 | + | 0.971077i | \(0.576743\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.9758 | 0.429437 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 56.7755 | 1.87694 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.0019 | −1.02377 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.0964 | −0.761879 | −0.380939 | − | 0.924600i | \(-0.624399\pi\) | ||||
−0.380939 | + | 0.924600i | \(0.624399\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.82144 | −0.0600185 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.9078 | 1.08317 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.6396 | 1.13894 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −152.730 | −5.01631 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.4077 | −0.702364 | −0.351182 | − | 0.936307i | \(-0.614220\pi\) | ||||
−0.351182 | + | 0.936307i | \(0.614220\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.56452 | 0.116822 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −67.8524 | −2.22139 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.24701 | −0.171595 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.8922 | 0.878531 | 0.439265 | − | 0.898357i | \(-0.355239\pi\) | ||||
0.439265 | + | 0.898357i | \(0.355239\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.9257 | 0.454449 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.4907 | −1.28736 | −0.643680 | − | 0.765295i | \(-0.722593\pi\) | ||||
−0.643680 | + | 0.765295i | \(0.722593\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.0820 | −0.426010 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −78.1030 | −2.54069 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.52937 | −0.0496980 | −0.0248490 | − | 0.999691i | \(-0.507910\pi\) | ||||
−0.0248490 | + | 0.999691i | \(0.507910\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.1970 | 1.33731 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.4480 | 1.11705 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.0571 | −1.20040 | −0.600199 | − | 0.799851i | \(-0.704912\pi\) | ||||
−0.600199 | + | 0.799851i | \(0.704912\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.9046 | −0.741175 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.33315 | −0.0430945 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40.2431 | 1.29952 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9251 | −0.997583 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −88.7070 | −2.85854 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.47738 | −0.0797498 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.0872 | 1.09617 | 0.548085 | − | 0.836423i | \(-0.315357\pi\) | ||||
0.548085 | + | 0.836423i | \(0.315357\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.64746 | −0.277796 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.7175 | −1.43505 | −0.717527 | − | 0.696531i | \(-0.754726\pi\) | ||||
−0.717527 | + | 0.696531i | \(0.754726\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.82301 | 0.0584429 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 46.4359 | 1.48714 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.8270 | −1.01824 | −0.509118 | − | 0.860696i | \(-0.670028\pi\) | ||||
−0.509118 | + | 0.860696i | \(0.670028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.3663 | −1.03443 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −49.5811 | −1.58300 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.7358 | −1.33117 | −0.665583 | − | 0.746324i | \(-0.731817\pi\) | ||||
−0.665583 | + | 0.746324i | \(0.731817\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.4630 | −0.365242 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 140.169 | 4.46164 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.66790 | −0.0530362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.86565 | 0.313393 | 0.156696 | − | 0.987647i | \(-0.449916\pi\) | ||||
0.156696 | + | 0.987647i | \(0.449916\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −60.9005 | −1.93262 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.592345 | −0.0187786 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.6133 | 1.03287 | 0.516437 | − | 0.856325i | \(-0.327258\pi\) | ||||
0.516437 | + | 0.856325i | \(0.327258\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 211.362 | 6.68720 |
(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 | 6044.2.a.a.1.1 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6044.2.a.a.1.1 | ✓ | 63 | 1.1 | even | 1 | trivial |