Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 13 x^{10} + 60 x^{9} + 48 x^{8} - 289 x^{7} - 89 x^{6} + 602 x^{5} + 161 x^{4} + \cdots + 82 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.85534\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.85534 | −1.07118 | −0.535590 | − | 0.844478i | \(-0.679911\pi\) | ||||
−0.535590 | + | 0.844478i | \(0.679911\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.75753 | −1.68042 | −0.840210 | − | 0.542261i | \(-0.817568\pi\) | ||||
−0.840210 | + | 0.542261i | \(0.817568\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.33364 | −1.26000 | −0.629999 | − | 0.776596i | \(-0.716945\pi\) | ||||
−0.629999 | + | 0.776596i | \(0.716945\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.442279 | 0.147426 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.31567 | 0.698200 | 0.349100 | − | 0.937085i | \(-0.386487\pi\) | ||||
0.349100 | + | 0.937085i | \(0.386487\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.30252 | −0.361253 | −0.180627 | − | 0.983552i | \(-0.557813\pi\) | ||||
−0.180627 | + | 0.983552i | \(0.557813\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.97149 | 1.80003 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.32303 | −0.303524 | −0.151762 | − | 0.988417i | \(-0.548495\pi\) | ||||
−0.151762 | + | 0.988417i | \(0.548495\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.18503 | 1.34968 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.50661 | −0.522664 | −0.261332 | − | 0.965249i | \(-0.584162\pi\) | ||||
−0.261332 | + | 0.965249i | \(0.584162\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.11905 | 1.82381 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.74544 | 0.913260 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.82690 | 1.26772 | 0.633862 | − | 0.773446i | \(-0.281469\pi\) | ||||
0.633862 | + | 0.773446i | \(0.281469\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.79295 | 1.39966 | 0.699828 | − | 0.714312i | \(-0.253260\pi\) | ||||
0.699828 | + | 0.714312i | \(0.253260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.29635 | −0.747898 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.5263 | 2.11733 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.02635 | 0.333130 | 0.166565 | − | 0.986030i | \(-0.446732\pi\) | ||||
0.166565 | + | 0.986030i | \(0.446732\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.41661 | 0.386967 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.45582 | 1.00823 | 0.504115 | − | 0.863637i | \(-0.331819\pi\) | ||||
0.504115 | + | 0.863637i | \(0.331819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.87421 | −0.743310 | −0.371655 | − | 0.928371i | \(-0.621210\pi\) | ||||
−0.371655 | + | 0.928371i | \(0.621210\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.66188 | −0.247738 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.41036 | −1.08091 | −0.540456 | − | 0.841372i | \(-0.681748\pi\) | ||||
−0.540456 | + | 0.841372i | \(0.681748\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.11316 | 0.587595 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.85534 | 0.259799 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.619651 | −0.0851156 | −0.0425578 | − | 0.999094i | \(-0.513551\pi\) | ||||
−0.0425578 | + | 0.999094i | \(0.513551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.70120 | −1.17327 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.45467 | 0.325129 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.42317 | −0.182219 | −0.0911093 | − | 0.995841i | \(-0.529041\pi\) | ||||
−0.0911093 | + | 0.995841i | \(0.529041\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.47440 | −0.185757 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.89425 | 0.607057 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.724862 | 0.0885559 | 0.0442780 | − | 0.999019i | \(-0.485901\pi\) | ||||
0.0442780 | + | 0.999019i | \(0.485901\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.65060 | 0.559867 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.70782 | 1.03343 | 0.516714 | − | 0.856158i | \(-0.327155\pi\) | ||||
0.516714 | + | 0.856158i | \(0.327155\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.8925 | −1.27487 | −0.637435 | − | 0.770504i | \(-0.720005\pi\) | ||||
−0.637435 | + | 0.770504i | \(0.720005\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.9189 | −1.95363 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.71961 | −0.879731 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.5916 | 1.64169 | 0.820843 | − | 0.571154i | \(-0.193504\pi\) | ||||
0.820843 | + | 0.571154i | \(0.193504\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1312 | −1.12569 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.49687 | −0.164303 | −0.0821515 | − | 0.996620i | \(-0.526179\pi\) | ||||
−0.0821515 | + | 0.996620i | \(0.526179\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.75753 | 0.407562 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.6662 | −1.35796 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.21141 | −0.658408 | −0.329204 | − | 0.944259i | \(-0.606780\pi\) | ||||
−0.329204 | + | 0.944259i | \(0.606780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.34213 | 0.455179 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.4586 | −1.49928 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.97134 | 0.510048 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.07138 | −0.413386 | −0.206693 | − | 0.978406i | \(-0.566270\pi\) | ||||
−0.206693 | + | 0.978406i | \(0.566270\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.02417 | 0.102933 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.13480 | 0.709939 | 0.354970 | − | 0.934878i | \(-0.384491\pi\) | ||||
0.354970 | + | 0.934878i | \(0.384491\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.16352 | 0.311711 | 0.155856 | − | 0.987780i | \(-0.450187\pi\) | ||||
0.155856 | + | 0.987780i | \(0.450187\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −23.2405 | −2.26804 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.34450 | −0.226651 | −0.113326 | − | 0.993558i | \(-0.536150\pi\) | ||||
−0.113326 | + | 0.993558i | \(0.536150\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.44291 | 0.904467 | 0.452234 | − | 0.891900i | \(-0.350627\pi\) | ||||
0.452234 | + | 0.891900i | \(0.350627\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.75956 | −0.356842 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.66821 | 0.439149 | 0.219574 | − | 0.975596i | \(-0.429533\pi\) | ||||
0.219574 | + | 0.975596i | \(0.429533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.41866 | 0.878294 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.576077 | −0.0532583 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.33364 | 0.305594 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.63768 | −0.512517 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.9777 | −1.07999 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15.4775 | −1.38435 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2936 | 1.09088 | 0.545439 | − | 0.838151i | \(-0.316363\pi\) | ||||
0.545439 | + | 0.838151i | \(0.316363\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.04331 | 0.796219 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.2561 | −1.24557 | −0.622783 | − | 0.782395i | \(-0.713998\pi\) | ||||
−0.622783 | + | 0.782395i | \(0.713998\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.41051 | 0.382440 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.8311 | −1.53466 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.26542 | 0.535291 | 0.267646 | − | 0.963517i | \(-0.413754\pi\) | ||||
0.267646 | + | 0.963517i | \(0.413754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.32589 | −0.282098 | −0.141049 | − | 0.990003i | \(-0.545048\pi\) | ||||
−0.141049 | + | 0.990003i | \(0.545048\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.7487 | 1.15785 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.01620 | −0.252227 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −25.6523 | −2.13031 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.63131 | −0.629420 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.0987 | 1.07309 | 0.536544 | − | 0.843872i | \(-0.319729\pi\) | ||||
0.536544 | + | 0.843872i | \(0.319729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.44446 | −0.361685 | −0.180842 | − | 0.983512i | \(-0.557882\pi\) | ||||
−0.180842 | + | 0.983512i | \(0.557882\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.442279 | −0.0357562 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −29.2823 | −2.35201 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.6740 | 1.33073 | 0.665366 | − | 0.746517i | \(-0.268275\pi\) | ||||
0.665366 | + | 0.746517i | \(0.268275\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.14966 | 0.0911741 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.35613 | 0.658555 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.2534 | −0.803110 | −0.401555 | − | 0.915835i | \(-0.631530\pi\) | ||||
−0.401555 | + | 0.915835i | \(0.631530\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.1437 | 1.25678 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.1224 | −1.78926 | −0.894632 | − | 0.446804i | \(-0.852562\pi\) | ||||
−0.894632 | + | 0.446804i | \(0.852562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3034 | −0.869496 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.585150 | −0.0447475 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.1860 | −1.83883 | −0.919413 | − | 0.393294i | \(-0.871335\pi\) | ||||
−0.919413 | + | 0.393294i | \(0.871335\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −30.3997 | −2.29800 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.85534 | −0.139456 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.42312 | −0.106369 | −0.0531844 | − | 0.998585i | \(-0.516937\pi\) | ||||
−0.0531844 | + | 0.998585i | \(0.516937\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.43803 | −0.255547 | −0.127773 | − | 0.991803i | \(-0.540783\pi\) | ||||
−0.127773 | + | 0.991803i | \(0.540783\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.64047 | 0.195189 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.61408 | −0.559798 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.31567 | −0.169338 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.8196 | −1.15071 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.7509 | −1.71855 | −0.859276 | − | 0.511512i | \(-0.829086\pi\) | ||||
−0.859276 | + | 0.511512i | \(0.829086\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.29389 | 0.237099 | 0.118550 | − | 0.992948i | \(-0.462176\pi\) | ||||
0.118550 | + | 0.992948i | \(0.462176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.08050 | −0.650268 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.7650 | 0.980715 | 0.490358 | − | 0.871521i | \(-0.336866\pi\) | ||||
0.490358 | + | 0.871521i | \(0.336866\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.49296 | 0.672938 | 0.336469 | − | 0.941694i | \(-0.390767\pi\) | ||||
0.336469 | + | 0.941694i | \(0.390767\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.34486 | −0.0948593 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22.7584 | −1.59733 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.2579 | −1.69425 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.10862 | −0.0770544 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.06370 | −0.211921 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.313416 | 0.0215765 | 0.0107882 | − | 0.999942i | \(-0.496566\pi\) | ||||
0.0107882 | + | 0.999942i | \(0.496566\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.1560 | −1.10699 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.3150 | 1.24907 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.9789 | −1.76356 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.2093 | 1.36562 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.30252 | 0.0876168 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.29570 | 0.153732 | 0.0768658 | − | 0.997041i | \(-0.475509\pi\) | ||||
0.0768658 | + | 0.997041i | \(0.475509\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.03317 | 0.268878 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.08017 | 0.536300 | 0.268150 | − | 0.963377i | \(-0.413588\pi\) | ||||
0.268150 | + | 0.963377i | \(0.413588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.4214 | 1.08516 | 0.542580 | − | 0.840004i | \(-0.317448\pi\) | ||||
0.542580 | + | 0.840004i | \(0.317448\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.3225 | 0.942350 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.47619 | 0.424269 | 0.212135 | − | 0.977240i | \(-0.431958\pi\) | ||||
0.212135 | + | 0.977240i | \(0.431958\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.8447 | 1.81639 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.0724 | −1.75854 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.9063 | −1.35232 | −0.676158 | − | 0.736757i | \(-0.736356\pi\) | ||||
−0.676158 | + | 0.736757i | \(0.736356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.60994 | 0.554615 | 0.277307 | − | 0.960781i | \(-0.410558\pi\) | ||||
0.277307 | + | 0.960781i | \(0.410558\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.56054 | 0.292559 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.4553 | −0.987406 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.72327 | 0.109649 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.77720 | 0.175998 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.8758 | −1.63327 | −0.816633 | − | 0.577157i | \(-0.804162\pi\) | ||||
−0.816633 | + | 0.577157i | \(0.804162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.80447 | −0.364924 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.97149 | −0.436572 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.5391 | 0.719787 | 0.359893 | − | 0.932993i | \(-0.382813\pi\) | ||||
0.359893 | + | 0.932993i | \(0.382813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.75512 | −0.419743 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.01940 | 0.186896 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.4215 | −0.642615 | −0.321308 | − | 0.946975i | \(-0.604122\pi\) | ||||
−0.321308 | + | 0.946975i | \(0.604122\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.32836 | 0.143030 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.5243 | 0.705274 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.8465 | 1.63686 | 0.818429 | − | 0.574608i | \(-0.194845\pi\) | ||||
0.818429 | + | 0.574608i | \(0.194845\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.2274 | −0.742761 | −0.371381 | − | 0.928481i | \(-0.621116\pi\) | ||||
−0.371381 | + | 0.928481i | \(0.621116\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.05611 | −0.487578 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.1167 | 1.27338 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.3809 | 1.76533 | 0.882664 | − | 0.470004i | \(-0.155748\pi\) | ||||
0.882664 | + | 0.470004i | \(0.155748\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.44666 | 0.206346 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.83346 | −0.169030 | −0.0845150 | − | 0.996422i | \(-0.526934\pi\) | ||||
−0.0845150 | + | 0.996422i | \(0.526934\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.2973 | −1.02822 | −0.514109 | − | 0.857725i | \(-0.671877\pi\) | ||||
−0.514109 | + | 0.857725i | \(0.671877\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.22351 | −0.546354 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.5214 | −1.27037 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.55379 | 0.442811 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.7358 | 1.03614 | 0.518068 | − | 0.855339i | \(-0.326651\pi\) | ||||
0.518068 | + | 0.855339i | \(0.326651\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.75753 | −0.218772 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.9889 | 0.637638 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.26490 | 0.188814 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.2489 | 0.936570 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.2375 | −0.760473 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.34762 | 0.306204 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.9930 | −0.912769 | −0.456385 | − | 0.889783i | \(-0.650856\pi\) | ||||
−0.456385 | + | 0.889783i | \(0.650856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.86940 | −0.333899 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.1535 | −0.632457 | −0.316229 | − | 0.948683i | \(-0.602417\pi\) | ||||
−0.316229 | + | 0.948683i | \(0.602417\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.7340 | −0.606721 | −0.303361 | − | 0.952876i | \(-0.598109\pi\) | ||||
−0.303361 | + | 0.952876i | \(0.598109\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.54011 | 0.312150 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.66865 | 0.262218 | 0.131109 | − | 0.991368i | \(-0.458146\pi\) | ||||
0.131109 | + | 0.991368i | \(0.458146\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.8088 | 0.885125 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.34984 | 0.242784 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.32303 | 0.0736155 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.8777 | −0.658858 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.5198 | −0.968847 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.7035 | 1.36195 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.03028 | 0.496349 | 0.248174 | − | 0.968715i | \(-0.420169\pi\) | ||||
0.248174 | + | 0.968715i | \(0.420169\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.896213 | 0.0491122 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.72369 | −0.148811 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6963 | 0.582663 | 0.291331 | − | 0.956622i | \(-0.405902\pi\) | ||||
0.291331 | + | 0.956622i | \(0.405902\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.66111 | −0.470407 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.0459 | 0.977239 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.62368 | 0.519630 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.4748 | −0.940811 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.6983 | 1.48692 | 0.743462 | − | 0.668778i | \(-0.233182\pi\) | ||||
0.743462 | + | 0.668778i | \(0.233182\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.72901 | −0.0925519 | −0.0462760 | − | 0.998929i | \(-0.514735\pi\) | ||||
−0.0462760 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.18102 | −0.329918 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.82177 | −0.309862 | −0.154931 | − | 0.987925i | \(-0.549515\pi\) | ||||
−0.154931 | + | 0.987925i | \(0.549515\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.7199 | −1.73659 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.18503 | −0.327347 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.912868 | −0.0481793 | −0.0240897 | − | 0.999710i | \(-0.507669\pi\) | ||||
−0.0240897 | + | 0.999710i | \(0.507669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2496 | −0.907873 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.4598 | 0.548998 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.9289 | 2.14232 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.83714 | 0.200297 | 0.100149 | − | 0.994972i | \(-0.468068\pi\) | ||||
0.100149 | + | 0.994972i | \(0.468068\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.85527 | 0.148640 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.06569 | 0.107245 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.3125 | 0.585736 | 0.292868 | − | 0.956153i | \(-0.405390\pi\) | ||||
0.292868 | + | 0.956153i | \(0.405390\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 28.7160 | 1.48289 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.89216 | −0.457970 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.54089 | −0.284617 | −0.142308 | − | 0.989822i | \(-0.545452\pi\) | ||||
−0.142308 | + | 0.989822i | \(0.545452\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.8087 | −1.16853 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.46082 | −0.279035 | −0.139517 | − | 0.990220i | \(-0.544555\pi\) | ||||
−0.139517 | + | 0.990220i | \(0.544555\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.0067 | 1.47832 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.15576 | −0.109584 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.88390 | −0.349028 | −0.174514 | − | 0.984655i | \(-0.555835\pi\) | ||||
−0.174514 | + | 0.984655i | \(0.555835\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.50661 | 0.126765 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.4500 | 1.33422 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −54.8285 | −2.75872 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.9273 | 1.00012 | 0.500060 | − | 0.865991i | \(-0.333311\pi\) | ||||
0.500060 | + | 0.865991i | \(0.333311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.18300 | −0.409662 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.4500 | −0.821473 | −0.410736 | − | 0.911754i | \(-0.634728\pi\) | ||||
−0.410736 | + | 0.911754i | \(0.634728\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.1505 | −0.505630 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 38.0684 | 1.89163 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.69235 | 0.232591 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.2889 | −0.755989 | −0.377994 | − | 0.925808i | \(-0.623386\pi\) | ||||
−0.377994 | + | 0.925808i | \(0.623386\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.6245 | −0.573393 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.33364 | −0.164038 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.62455 | 0.276098 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.17065 | 0.302178 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.72035 | −0.132898 | −0.0664488 | − | 0.997790i | \(-0.521167\pi\) | ||||
−0.0664488 | + | 0.997790i | \(0.521167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.86840 | 0.432219 | 0.216110 | − | 0.976369i | \(-0.430663\pi\) | ||||
0.216110 | + | 0.976369i | \(0.430663\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.27745 | −0.159355 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.11905 | −0.442339 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.74435 | 0.229595 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.59607 | 0.270181 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.6159 | −0.896698 | −0.448349 | − | 0.893859i | \(-0.647988\pi\) | ||||
−0.448349 | + | 0.893859i | \(0.647988\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.6155 | 1.42323 | 0.711614 | − | 0.702570i | \(-0.247964\pi\) | ||||
0.711614 | + | 0.702570i | \(0.247964\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 47.5937 | 2.28194 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.31632 | 0.158641 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.72431 | 0.177752 | 0.0888759 | − | 0.996043i | \(-0.471673\pi\) | ||||
0.0888759 | + | 0.996043i | \(0.471673\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.81917 | 0.0866270 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.22885 | 0.248430 | 0.124215 | − | 0.992255i | \(-0.460359\pi\) | ||||
0.124215 | + | 0.992255i | \(0.460359\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.3396 | 1.10640 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.3025 | −1.14947 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.0624 | −1.27716 | −0.638578 | − | 0.769557i | \(-0.720477\pi\) | ||||
−0.638578 | + | 0.769557i | \(0.720477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.9495 | 0.703946 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.24597 | 0.387430 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.3157 | −0.764891 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −41.0564 | −1.92054 | −0.960268 | − | 0.279080i | \(-0.909971\pi\) | ||||
−0.960268 | + | 0.279080i | \(0.909971\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.74544 | −0.221498 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.16975 | 0.147630 | 0.0738150 | − | 0.997272i | \(-0.476483\pi\) | ||||
0.0738150 | + | 0.997272i | \(0.476483\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.9669 | −1.02089 | −0.510445 | − | 0.859911i | \(-0.670519\pi\) | ||||
−0.510445 | + | 0.859911i | \(0.670519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 54.3285 | 2.51942 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.73251 | 0.218995 | 0.109497 | − | 0.993987i | \(-0.465076\pi\) | ||||
0.109497 | + | 0.993987i | \(0.465076\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.41643 | −0.111580 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.9360 | −1.42545 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.2871 | −0.518979 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.0648 | −0.553571 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.274059 | −0.0125483 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.48804 | −0.387828 | −0.193914 | − | 0.981018i | \(-0.562118\pi\) | ||||
−0.193914 | + | 0.981018i | \(0.562118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.63936 | −0.120344 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.5034 | −0.705431 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.2983 | 0.694662 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.8532 | −1.12620 | −0.563102 | − | 0.826387i | \(-0.690392\pi\) | ||||
−0.563102 | + | 0.826387i | \(0.690392\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.0236 | 0.860275 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.2916 | −1.09627 | −0.548133 | − | 0.836391i | \(-0.684661\pi\) | ||||
−0.548133 | + | 0.836391i | \(0.684661\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.82690 | −0.307468 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.84836 | −0.172971 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −29.0288 | −1.30212 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.7278 | 1.28603 | 0.643017 | − | 0.765852i | \(-0.277682\pi\) | ||||
0.643017 | + | 0.765852i | \(0.277682\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.8998 | 1.91662 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.9124 | 0.709499 | 0.354750 | − | 0.934961i | \(-0.384566\pi\) | ||||
0.354750 | + | 0.934961i | \(0.384566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.8093 | −1.19300 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.9717 | 0.931387 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.6646 | 0.871618 | 0.435809 | − | 0.900039i | \(-0.356462\pi\) | ||||
0.435809 | + | 0.900039i | \(0.356462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.3117 | 1.60633 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.27837 | −0.277197 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.8870 | −0.523805 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.1599 | −0.754693 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 44.8732 | 1.96971 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.18680 | 0.358670 | 0.179335 | − | 0.983788i | \(-0.442605\pi\) | ||||
0.179335 | + | 0.983788i | \(0.442605\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.4485 | −0.850423 | −0.425211 | − | 0.905094i | \(-0.639800\pi\) | ||||
−0.425211 | + | 0.905094i | \(0.639800\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 56.4016 | 2.46157 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.79295 | −0.339466 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.7169 | −0.726823 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.442279 | 0.0191933 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.40882 | −0.364226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.80953 | 0.380869 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.64036 | 0.113940 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.52472 | 0.410259 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6221 | 0.929605 | 0.464802 | − | 0.885414i | \(-0.346125\pi\) | ||||
0.464802 | + | 0.885414i | \(0.346125\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.37871 | 0.273737 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −35.4821 | −1.51988 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.4016 | 1.29988 | 0.649938 | − | 0.759987i | \(-0.274795\pi\) | ||||
0.649938 | + | 0.759987i | \(0.274795\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.629440 | −0.0268638 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.03221 | −0.384785 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −48.6432 | −2.06852 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.1267 | 0.599644 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.4359 | −0.781155 | −0.390577 | − | 0.920570i | \(-0.627725\pi\) | ||||
−0.390577 | + | 0.920570i | \(0.627725\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.34875 | 0.268523 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.29635 | 0.181392 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.8813 | −0.922188 | −0.461094 | − | 0.887351i | \(-0.652543\pi\) | ||||
−0.461094 | + | 0.887351i | \(0.652543\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.5410 | −0.737954 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 33.7739 | 1.41837 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.89113 | −0.205047 | −0.102523 | − | 0.994731i | \(-0.532692\pi\) | ||||
−0.102523 | + | 0.994731i | \(0.532692\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.9503 | 0.583804 | 0.291902 | − | 0.956448i | \(-0.405712\pi\) | ||||
0.291902 | + | 0.956448i | \(0.405712\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 44.0659 | 1.84088 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.8579 | −0.953239 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.1864 | 0.507326 | 0.253663 | − | 0.967293i | \(-0.418365\pi\) | ||||
0.253663 | + | 0.967293i | \(0.418365\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.11127 | −0.253976 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.99003 | 0.207022 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.43491 | −0.0594277 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.16463 | 0.0894963 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.143998 | 0.00594342 | 0.00297171 | − | 0.999996i | \(-0.499054\pi\) | ||||
0.00297171 | + | 0.999996i | \(0.499054\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.3103 | −0.424830 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.5387 | −1.05052 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.0804 | 0.578212 | 0.289106 | − | 0.957297i | \(-0.406642\pi\) | ||||
0.289106 | + | 0.957297i | \(0.406642\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.5263 | −0.513527 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.6127 | −0.720838 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.99932 | −0.0816899 | −0.0408450 | − | 0.999165i | \(-0.513005\pi\) | ||||
−0.0408450 | + | 0.999165i | \(0.513005\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.3950 | 0.668767 | 0.334383 | − | 0.942437i | \(-0.391472\pi\) | ||||
0.334383 | + | 0.942437i | \(0.391472\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.320591 | 0.0130555 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.1838 | 0.861243 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9240 | −0.808690 | −0.404345 | − | 0.914606i | \(-0.632501\pi\) | ||||
−0.404345 | + | 0.914606i | \(0.632501\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 42.2246 | 1.71103 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.65212 | 0.390483 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.07961 | −0.205164 | −0.102582 | − | 0.994725i | \(-0.532710\pi\) | ||||
−0.102582 | + | 0.994725i | \(0.532710\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 45.0067 | 1.81484 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.85737 | 0.356584 | 0.178292 | − | 0.983978i | \(-0.442943\pi\) | ||||
0.178292 | + | 0.983978i | \(0.442943\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.30527 | 0.0524632 | 0.0262316 | − | 0.999656i | \(-0.491649\pi\) | ||||
0.0262316 | + | 0.999656i | \(0.491649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.8949 | −0.477328 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.7066 | 0.829593 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5619 | 0.502475 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.68420 | 0.227005 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.02635 | −0.0807959 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.8589 | 1.70619 | 0.853094 | − | 0.521758i | \(-0.174723\pi\) | ||||
0.853094 | + | 0.521758i | \(0.174723\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.581493 | −0.0231123 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −46.1935 | −1.83313 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.35747 | −0.212271 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.85129 | 0.152355 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.6014 | −1.91964 | −0.959819 | − | 0.280618i | \(-0.909460\pi\) | ||||
−0.959819 | + | 0.280618i | \(0.909460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.7479 | 1.76469 | 0.882343 | − | 0.470607i | \(-0.155965\pi\) | ||||
0.882343 | + | 0.470607i | \(0.155965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.9805 | −1.33798 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.6310 | −1.16491 | −0.582457 | − | 0.812861i | \(-0.697909\pi\) | ||||
−0.582457 | + | 0.812861i | \(0.697909\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.31567 | 0.0908979 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 48.1996 | 1.88909 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.7112 | −0.771358 | −0.385679 | − | 0.922633i | \(-0.626033\pi\) | ||||
−0.385679 | + | 0.922633i | \(0.626033\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 53.5679 | 2.09307 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.81753 | −0.187950 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.8278 | −0.811335 | −0.405667 | − | 0.914021i | \(-0.632961\pi\) | ||||
−0.405667 | + | 0.914021i | \(0.632961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.1383 | 0.822186 | 0.411093 | − | 0.911593i | \(-0.365147\pi\) | ||||
0.411093 | + | 0.911593i | \(0.365147\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.41661 | −0.0938534 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.5727 | −0.642660 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.1124 | −0.662593 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.25930 | −0.164674 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.29560 | −0.127225 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.1361 | 0.891832 | 0.445916 | − | 0.895075i | \(-0.352878\pi\) | ||||
0.445916 | + | 0.895075i | \(0.352878\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 43.2739 | 1.66561 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.5934 | −1.17580 | −0.587899 | − | 0.808934i | \(-0.700045\pi\) | ||||
−0.587899 | + | 0.808934i | \(0.700045\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.5725 | 0.520866 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.9914 | −0.574473 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.8411 | 1.60100 | 0.800502 | − | 0.599330i | \(-0.204566\pi\) | ||||
0.800502 | + | 0.599330i | \(0.204566\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.5425 | −0.899514 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.4673 | −1.16240 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.807106 | 0.0307483 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.3358 | −1.11599 | −0.557993 | − | 0.829846i | \(-0.688428\pi\) | ||||
−0.557993 | + | 0.829846i | \(0.688428\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.41422 | −0.129696 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.4971 | 0.474044 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.45582 | −0.244531 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.0155 | −0.454469 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.0370 | 1.21002 | 0.605010 | − | 0.796218i | \(-0.293169\pi\) | ||||
0.605010 | + | 0.796218i | \(0.293169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.68093 | −0.101113 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −51.6613 | −1.94568 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.7849 | −0.894522 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.0818 | 1.58042 | 0.790208 | − | 0.612839i | \(-0.209973\pi\) | ||||
0.790208 | + | 0.612839i | \(0.209973\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.45357 | 0.242028 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.5339 | −0.731549 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.3335 | 0.423848 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 38.7882 | 1.44857 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.8796 | 0.405742 | 0.202871 | − | 0.979205i | \(-0.434973\pi\) | ||||
0.202871 | + | 0.979205i | \(0.434973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.5460 | −0.392755 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.9743 | −0.594092 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 62.2549 | 2.31209 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.9809 | 1.63116 | 0.815581 | − | 0.578643i | \(-0.196417\pi\) | ||||
0.815581 | + | 0.578643i | \(0.196417\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.9323 | 0.812309 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.87421 | 0.180279 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.17663 | 0.191203 | 0.0956016 | − | 0.995420i | \(-0.469523\pi\) | ||||
0.0956016 | + | 0.995420i | \(0.469523\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.6749 | 1.05769 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.67854 | 0.0618298 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.9165 | −0.548713 | −0.274357 | − | 0.961628i | \(-0.588465\pi\) | ||||
−0.274357 | + | 0.961628i | \(0.588465\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.19725 | −0.117454 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.7072 | −0.979792 | −0.489896 | − | 0.871781i | \(-0.662965\pi\) | ||||
−0.489896 | + | 0.871781i | \(0.662965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −49.2189 | −1.80324 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.662036 | −0.0242226 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.81572 | 0.285580 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.17483 | −0.298304 | −0.149152 | − | 0.988814i | \(-0.547654\pi\) | ||||
−0.149152 | + | 0.988814i | \(0.547654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 48.0084 | 1.74952 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.7002 | 0.607782 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.2068 | 0.625392 | 0.312696 | − | 0.949853i | \(-0.398768\pi\) | ||||
0.312696 | + | 0.949853i | \(0.398768\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.7692 | 0.390899 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.0300 | −0.871086 | −0.435543 | − | 0.900168i | \(-0.643444\pi\) | ||||
−0.435543 | + | 0.900168i | \(0.643444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.4793 | −1.13963 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.66188 | 0.0600854 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.30252 | −0.0470312 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.03458 | −0.181552 | −0.0907758 | − | 0.995871i | \(-0.528935\pi\) | ||||
−0.0907758 | + | 0.995871i | \(0.528935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.4089 | −0.771021 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.61254 | −0.309772 | −0.154886 | − | 0.987932i | \(-0.549501\pi\) | ||||
−0.154886 | + | 0.987932i | \(0.549501\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 71.0643 | 2.55271 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.5330 | 0.449620 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.54125 | −0.306022 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.1644 | 0.721540 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.3966 | 1.15776 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62.6532 | −2.23619 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.41439 | −0.228648 | −0.114324 | − | 0.993443i | \(-0.536470\pi\) | ||||
−0.114324 | + | 0.993443i | \(0.536470\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.3354 | 0.688357 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.5621 | −0.553326 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.85371 | 0.0658271 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.31989 | −0.153211 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.6551 | −1.29839 | −0.649196 | − | 0.760621i | \(-0.724894\pi\) | ||||
−0.649196 | + | 0.760621i | \(0.724894\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.41036 | 0.262160 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.74718 | −0.0970668 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.2234 | −0.890115 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.3984 | −1.10665 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −49.8093 | −1.75337 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.81501 | 0.239603 | 0.119801 | − | 0.992798i | \(-0.461774\pi\) | ||||
0.119801 | + | 0.992798i | \(0.461774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.5929 | −1.32006 | −0.660032 | − | 0.751237i | \(-0.729457\pi\) | ||||
−0.660032 | + | 0.751237i | \(0.729457\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.6860 | 0.795631 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.5276 | 1.34956 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.44874 | 0.225613 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.92043 | 0.0671054 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.3793 | 0.362240 | 0.181120 | − | 0.983461i | \(-0.442028\pi\) | ||||
0.181120 | + | 0.983461i | \(0.442028\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.53711 | 0.0884382 | 0.0442191 | − | 0.999022i | \(-0.485920\pi\) | ||||
0.0442191 | + | 0.999022i | \(0.485920\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −39.1786 | −1.36402 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.8288 | 0.724289 | 0.362145 | − | 0.932122i | \(-0.382045\pi\) | ||||
0.362145 | + | 0.932122i | \(0.382045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.9717 | −1.87452 | −0.937258 | − | 0.348638i | \(-0.886644\pi\) | ||||
−0.937258 | + | 0.348638i | \(0.886644\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −54.5115 | −1.89098 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.11316 | −0.142513 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 86.8831 | 3.00671 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.9810 | 1.27825 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −55.8041 | −1.92657 | −0.963286 | − | 0.268478i | \(-0.913479\pi\) | ||||
−0.963286 | + | 0.268478i | \(0.913479\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6066 | 0.607123 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.25703 | 0.181062 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.4731 | 1.46112 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.7940 | 0.645770 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.0923 | 1.10141 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.07926 | −0.174115 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.07550 | 0.208021 | 0.104011 | − | 0.994576i | \(-0.466832\pi\) | ||||
0.104011 | + | 0.994576i | \(0.466832\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.19872 | 0.0751946 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.8784 | −0.849831 | −0.424916 | − | 0.905233i | \(-0.639696\pi\) | ||||
−0.424916 | + | 0.905233i | \(0.639696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.1644 | 0.756239 | 0.378119 | − | 0.925757i | \(-0.376571\pi\) | ||||
0.378119 | + | 0.925757i | \(0.376571\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39.9294 | 1.36079 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.0075 | −1.80440 | −0.902198 | − | 0.431322i | \(-0.858047\pi\) | ||||
−0.902198 | + | 0.431322i | \(0.858047\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 90.8796 | 3.09000 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.85534 | −0.0630106 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.7894 | 1.14623 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.944145 | −0.0319911 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.80069 | −0.0609440 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.5964 | 1.74428 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.1445 | 0.376322 | 0.188161 | − | 0.982138i | \(-0.439747\pi\) | ||||
0.188161 | + | 0.982138i | \(0.439747\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.9059 | −1.10989 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.7999 | 1.30720 | 0.653601 | − | 0.756839i | \(-0.273257\pi\) | ||||
0.653601 | + | 0.756839i | \(0.273257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.3775 | −0.921327 | −0.460664 | − | 0.887575i | \(-0.652389\pi\) | ||||
−0.460664 | + | 0.887575i | \(0.652389\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.97149 | 0.234344 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.8543 | −1.23745 | −0.618723 | − | 0.785609i | \(-0.712350\pi\) | ||||
−0.618723 | + | 0.785609i | \(0.712350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.9823 | −1.37450 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.4606 | −0.785958 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.80414 | 0.328083 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.34741 | 0.178744 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.05749 | −0.202254 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 53.2017 | 1.77438 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.619651 | 0.0206436 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.1472 | −1.00323 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.9185 | 0.429426 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.8188 | −1.55459 | −0.777296 | − | 0.629136i | \(-0.783409\pi\) | ||||
−0.777296 | + | 0.629136i | \(0.783409\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.15558 | 0.104664 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.2475 | 1.10154 | 0.550770 | − | 0.834657i | \(-0.314334\pi\) | ||||
0.550770 | + | 0.834657i | \(0.314334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.46626 | −0.114716 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.92164 | −0.327999 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.5249 | 1.56941 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.7710 | 0.883094 | 0.441547 | − | 0.897238i | \(-0.354430\pi\) | ||||
0.441547 | + | 0.897238i | \(0.354430\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.6724 | 0.977740 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.3421 | −0.373330 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.4784 | 0.607566 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.39916 | 0.0459545 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.5662 | −0.937227 | −0.468613 | − | 0.883403i | \(-0.655246\pi\) | ||||
−0.468613 | + | 0.883403i | \(0.655246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.44185 | −0.178349 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.6935 | 0.677475 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.70120 | 0.284560 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.0107 | 1.47044 | 0.735218 | − | 0.677831i | \(-0.237080\pi\) | ||||
0.735218 | + | 0.677831i | \(0.237080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.9152 | 0.649907 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5546 | −0.344069 | −0.172035 | − | 0.985091i | \(-0.555034\pi\) | ||||
−0.172035 | + | 0.985091i | \(0.555034\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.1822 | −0.526965 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 59.4426 | 1.93367 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.5326 | −1.51211 | −0.756053 | − | 0.654511i | \(-0.772875\pi\) | ||||
−0.756053 | + | 0.654511i | \(0.772875\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.1877 | 0.460551 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.66193 | −0.280882 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.6950 | −1.05910 | −0.529548 | − | 0.848280i | \(-0.677638\pi\) | ||||
−0.529548 | + | 0.848280i | \(0.677638\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 89.2447 | 2.88789 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.3307 | −0.948128 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.8867 | −0.674466 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.7301 | 0.959035 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.03692 | −0.0334144 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.3769 | −0.398426 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.5525 | 1.01466 | 0.507329 | − | 0.861752i | \(-0.330633\pi\) | ||||
0.507329 | + | 0.861752i | \(0.330633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.45467 | −0.0788554 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.18250 | 0.262589 | 0.131294 | − | 0.991343i | \(-0.458087\pi\) | ||||
0.131294 | + | 0.991343i | \(0.458087\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0873 | 0.355443 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 22.0372 | 0.705755 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.0246 | 1.24851 | 0.624253 | − | 0.781222i | \(-0.285403\pi\) | ||||
0.624253 | + | 0.781222i | \(0.285403\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.3836 | −0.459701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.17641 | 0.133342 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.6447 | −0.530884 | −0.265442 | − | 0.964127i | \(-0.585518\pi\) | ||||
−0.265442 | + | 0.964127i | \(0.585518\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.7224 | −1.64801 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −45.8333 | −1.45889 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.2177 | 0.388501 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.9404 | 1.87230 | 0.936151 | − | 0.351598i | \(-0.114361\pi\) | ||||
0.936151 | + | 0.351598i | \(0.114361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.7542 | −0.531679 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35.6701 | −1.13082 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.6381 | 0.653616 | 0.326808 | − | 0.945091i | \(-0.394027\pi\) | ||||
0.326808 | + | 0.945091i | \(0.394027\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.61591 | 0.304234 |
(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 | 4012.2.a.g.1.4 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.g.1.4 | ✓ | 12 | 1.1 | even | 1 | trivial |