Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 30 x^{17} + 132 x^{16} + 332 x^{15} - 1714 x^{14} - 1598 x^{13} + 11179 x^{12} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-0.0800487\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-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 | ||||||||
\(3\) | 0.0800487 | 0.0462161 | 0.0231081 | − | 0.999733i | \(-0.492644\pi\) | ||||
0.0231081 | + | 0.999733i | \(0.492644\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.442813 | 0.198032 | 0.0990159 | − | 0.995086i | \(-0.468431\pi\) | ||||
0.0990159 | + | 0.995086i | \(0.468431\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.60518 | 0.984667 | 0.492333 | − | 0.870407i | \(-0.336144\pi\) | ||||
0.492333 | + | 0.870407i | \(0.336144\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99359 | −0.997864 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.05333 | −0.619102 | −0.309551 | − | 0.950883i | \(-0.600179\pi\) | ||||
−0.309551 | + | 0.950883i | \(0.600179\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.33968 | 0.648911 | 0.324456 | − | 0.945901i | \(-0.394819\pi\) | ||||
0.324456 | + | 0.945901i | \(0.394819\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0354466 | 0.00915226 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.04003 | 0.494779 | 0.247390 | − | 0.968916i | \(-0.420427\pi\) | ||||
0.247390 | + | 0.968916i | \(0.420427\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.208542 | 0.0455075 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.75394 | −1.40829 | −0.704147 | − | 0.710054i | \(-0.748670\pi\) | ||||
−0.704147 | + | 0.710054i | \(0.748670\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80392 | −0.960783 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.479779 | −0.0923335 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.161496 | −0.0299890 | −0.0149945 | − | 0.999888i | \(-0.504773\pi\) | ||||
−0.0149945 | + | 0.999888i | \(0.504773\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.92315 | −1.42304 | −0.711520 | − | 0.702666i | \(-0.751993\pi\) | ||||
−0.711520 | + | 0.702666i | \(0.751993\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.164366 | −0.0286125 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.15361 | 0.194995 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.74579 | 0.615804 | 0.307902 | − | 0.951418i | \(-0.400373\pi\) | ||||
0.307902 | + | 0.951418i | \(0.400373\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.187289 | 0.0299902 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.17031 | −0.807467 | −0.403734 | − | 0.914877i | \(-0.632288\pi\) | ||||
−0.403734 | + | 0.914877i | \(0.632288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.07281 | −0.621097 | −0.310549 | − | 0.950557i | \(-0.600513\pi\) | ||||
−0.310549 | + | 0.950557i | \(0.600513\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.32560 | −0.197609 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.84920 | 0.415598 | 0.207799 | − | 0.978172i | \(-0.433370\pi\) | ||||
0.207799 | + | 0.978172i | \(0.433370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.213017 | −0.0304310 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.163302 | 0.0228668 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.909239 | −0.122602 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0800487 | −0.0106027 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.26122 | 1.07552 | 0.537759 | − | 0.843098i | \(-0.319271\pi\) | ||||
0.537759 | + | 0.843098i | \(0.319271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.20321 | −0.538165 | −0.269083 | − | 0.963117i | \(-0.586721\pi\) | ||||
−0.269083 | + | 0.963117i | \(0.586721\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.79886 | −0.982564 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.03604 | 0.128505 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7790 | −1.31687 | −0.658434 | − | 0.752638i | \(-0.728781\pi\) | ||||
−0.658434 | + | 0.752638i | \(0.728781\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.540644 | −0.0650859 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.25972 | −0.505535 | −0.252768 | − | 0.967527i | \(-0.581341\pi\) | ||||
−0.252768 | + | 0.967527i | \(0.581341\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.99568 | 0.350618 | 0.175309 | − | 0.984513i | \(-0.443908\pi\) | ||||
0.175309 | + | 0.984513i | \(0.443908\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.384547 | −0.0444037 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.34930 | −0.609609 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.77749 | 0.199983 | 0.0999915 | − | 0.994988i | \(-0.468118\pi\) | ||||
0.0999915 | + | 0.994988i | \(0.468118\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.94237 | 0.993597 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1358 | 1.44184 | 0.720920 | − | 0.693018i | \(-0.243719\pi\) | ||||
0.720920 | + | 0.693018i | \(0.243719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.903350 | 0.0979821 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0129275 | −0.00138597 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.31561 | −0.881453 | −0.440727 | − | 0.897641i | \(-0.645279\pi\) | ||||
−0.440727 | + | 0.897641i | \(0.645279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.09530 | 0.638962 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.634237 | −0.0657674 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.442813 | −0.0454316 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1455 | −1.33472 | −0.667360 | − | 0.744736i | \(-0.732576\pi\) | ||||
−0.667360 | + | 0.744736i | \(0.732576\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.14683 | 0.617779 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0172236 | 0.00171381 | 0.000856907 | − | 1.00000i | \(-0.499727\pi\) | ||||
0.000856907 | 1.00000i | \(0.499727\pi\) | ||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.31935 | 0.425598 | 0.212799 | − | 0.977096i | \(-0.431742\pi\) | ||||
0.212799 | + | 0.977096i | \(0.431742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0923448 | 0.00901193 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5615 | −1.31104 | −0.655519 | − | 0.755179i | \(-0.727550\pi\) | ||||
−0.655519 | + | 0.755179i | \(0.727550\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.87340 | 0.466787 | 0.233394 | − | 0.972382i | \(-0.425017\pi\) | ||||
0.233394 | + | 0.972382i | \(0.425017\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.299846 | 0.0284601 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5045 | −0.988184 | −0.494092 | − | 0.869410i | \(-0.664499\pi\) | ||||
−0.494092 | + | 0.869410i | \(0.664499\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.99073 | −0.278887 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.00406 | −0.647525 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.31465 | 0.487193 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.78385 | −0.616713 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.413877 | −0.0373180 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.34130 | −0.388298 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.11653 | 0.187812 | 0.0939058 | − | 0.995581i | \(-0.470065\pi\) | ||||
0.0939058 | + | 0.995581i | \(0.470065\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.326023 | −0.0287047 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.17455 | −0.452102 | −0.226051 | − | 0.974115i | \(-0.572582\pi\) | ||||
−0.226051 | + | 0.974115i | \(0.572582\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.60518 | −0.225898 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.212452 | −0.0182850 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.5877 | 0.990004 | 0.495002 | − | 0.868892i | \(-0.335167\pi\) | ||||
0.495002 | + | 0.868892i | \(0.335167\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.1807 | −1.88135 | −0.940673 | − | 0.339315i | \(-0.889805\pi\) | ||||
−0.940673 | + | 0.339315i | \(0.889805\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.228074 | 0.0192073 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.80414 | −0.401742 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0715123 | −0.00593877 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0170517 | −0.00140640 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.1654 | 0.914703 | 0.457352 | − | 0.889286i | \(-0.348798\pi\) | ||||
0.457352 | + | 0.889286i | \(0.348798\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.8788 | −1.78047 | −0.890237 | − | 0.455497i | \(-0.849461\pi\) | ||||
−0.890237 | + | 0.455497i | \(0.849461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.10701 | −0.493723 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.50847 | −0.281807 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.15969 | −0.571405 | −0.285703 | − | 0.958318i | \(-0.592227\pi\) | ||||
−0.285703 | + | 0.958318i | \(0.592227\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0800487 | 0.00634827 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.5953 | −1.38670 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.1676 | 1.34467 | 0.672334 | − | 0.740248i | \(-0.265292\pi\) | ||||
0.672334 | + | 0.740248i | \(0.265292\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0727834 | −0.00566618 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.2803 | 1.33719 | 0.668595 | − | 0.743627i | \(-0.266896\pi\) | ||||
0.668595 | + | 0.743627i | \(0.266896\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.52588 | −0.578914 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.99359 | 0.228926 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.1836 | 1.00233 | 0.501164 | − | 0.865352i | \(-0.332905\pi\) | ||||
0.501164 | + | 0.865352i | \(0.332905\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.5151 | −0.946052 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.661299 | 0.0497063 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.00811 | 0.374324 | 0.187162 | − | 0.982329i | \(-0.440071\pi\) | ||||
0.187162 | + | 0.982329i | \(0.440071\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.15207 | 0.159962 | 0.0799810 | − | 0.996796i | \(-0.474514\pi\) | ||||
0.0799810 | + | 0.996796i | \(0.474514\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.336461 | −0.0248719 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.65868 | 0.121949 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.18884 | −0.306319 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.24991 | −0.0909178 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.9716 | 1.58981 | 0.794905 | − | 0.606734i | \(-0.207521\pi\) | ||||
0.794905 | + | 0.606734i | \(0.207521\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.78614 | 0.272533 | 0.136266 | − | 0.990672i | \(-0.456490\pi\) | ||||
0.136266 | + | 0.990672i | \(0.456490\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0829337 | 0.00593901 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.05465 | 0.502623 | 0.251312 | − | 0.967906i | \(-0.419138\pi\) | ||||
0.251312 | + | 0.967906i | \(0.419138\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.2692 | −1.22418 | −0.612091 | − | 0.790788i | \(-0.709671\pi\) | ||||
−0.612091 | + | 0.790788i | \(0.709671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.862847 | −0.0608606 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.420726 | −0.0295292 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.28948 | −0.159904 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.2185 | 1.40529 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.05333 | 0.142032 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.5576 | −1.62177 | −0.810886 | − | 0.585204i | \(-0.801014\pi\) | ||||
−0.810886 | + | 0.585204i | \(0.801014\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.340985 | −0.0233639 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.80349 | −0.122997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.6413 | −1.40122 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.239800 | 0.0162042 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.77302 | 0.321068 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.2802 | 1.15717 | 0.578584 | − | 0.815623i | \(-0.303605\pi\) | ||||
0.578584 | + | 0.815623i | \(0.303605\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.3810 | 0.958731 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.177530 | −0.0117831 | −0.00589155 | − | 0.999983i | \(-0.501875\pi\) | ||||
−0.00589155 | + | 0.999983i | \(0.501875\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.8364 | −0.782171 | −0.391086 | − | 0.920354i | \(-0.627900\pi\) | ||||
−0.391086 | + | 0.920354i | \(0.627900\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.428204 | −0.0281738 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.5076 | 1.40901 | 0.704505 | − | 0.709699i | \(-0.251169\pi\) | ||||
0.704505 | + | 0.709699i | \(0.251169\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.26166 | 0.0823016 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.142286 | 0.00924244 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.78149 | −0.568027 | −0.284014 | − | 0.958820i | \(-0.591666\pi\) | ||||
−0.284014 | + | 0.958820i | \(0.591666\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.2194 | −1.36686 | −0.683432 | − | 0.730014i | \(-0.739513\pi\) | ||||
−0.683432 | + | 0.730014i | \(0.739513\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.15516 | 0.138254 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.0943265 | −0.00602630 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.33968 | −0.148870 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.05150 | 0.0666363 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.5509 | −1.92836 | −0.964179 | − | 0.265252i | \(-0.914545\pi\) | ||||
−0.964179 | + | 0.265252i | \(0.914545\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.8681 | 0.871877 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0723120 | 0.00452835 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2946 | −0.704535 | −0.352268 | − | 0.935899i | \(-0.614589\pi\) | ||||
−0.352268 | + | 0.935899i | \(0.614589\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.75848 | 0.606362 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.483452 | 0.0299249 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.0775000 | −0.00477885 | −0.00238943 | − | 0.999997i | \(-0.500761\pi\) | ||||
−0.00238943 | + | 0.999997i | \(0.500761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.442813 | 0.0272018 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.665654 | −0.0407374 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.5966 | −1.31677 | −0.658385 | − | 0.752681i | \(-0.728760\pi\) | ||||
−0.658385 | + | 0.752681i | \(0.728760\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.03169 | 0.366399 | 0.183199 | − | 0.983076i | \(-0.441355\pi\) | ||||
0.183199 | + | 0.983076i | \(0.441355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.487921 | 0.0295303 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.86401 | 0.594822 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.7533 | 1.66753 | 0.833766 | − | 0.552117i | \(-0.186180\pi\) | ||||
0.833766 | + | 0.552117i | \(0.186180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.7187 | 1.42000 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4658 | 0.743647 | 0.371824 | − | 0.928303i | \(-0.378733\pi\) | ||||
0.371824 | + | 0.928303i | \(0.378733\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.6112 | 1.70076 | 0.850378 | − | 0.526172i | \(-0.176373\pi\) | ||||
0.850378 | + | 0.526172i | \(0.176373\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0354466 | −0.00209967 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.4696 | −0.795086 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8383 | −0.755193 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.05228 | −0.0616856 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.23617 | 0.0722178 | 0.0361089 | − | 0.999348i | \(-0.488504\pi\) | ||||
0.0361089 | + | 0.999348i | \(0.488504\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.65817 | 0.212987 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.985144 | 0.0571638 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.8021 | −0.913858 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.6104 | −0.611574 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.00137873 | 7.92059e−5 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.86123 | −0.106574 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.5868 | −1.80275 | −0.901376 | − | 0.433038i | \(-0.857442\pi\) | ||||
−0.901376 | + | 0.433038i | \(0.857442\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.345758 | 0.0196695 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.1076 | −1.48043 | −0.740213 | − | 0.672373i | \(-0.765275\pi\) | ||||
−0.740213 | + | 0.672373i | \(0.765275\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9883 | 0.677618 | 0.338809 | − | 0.940855i | \(-0.389976\pi\) | ||||
0.338809 | + | 0.940855i | \(0.389976\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.45343 | −0.194579 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.2848 | 0.633817 | 0.316909 | − | 0.948456i | \(-0.397355\pi\) | ||||
0.316909 | + | 0.948456i | \(0.397355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.331603 | 0.0185662 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.08558 | −0.0605911 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.04003 | −0.113510 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.2396 | −0.623463 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.390109 | 0.0215731 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.42268 | 0.409226 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.5123 | −1.84200 | −0.921002 | − | 0.389558i | \(-0.872628\pi\) | ||||
−0.921002 | + | 0.389558i | \(0.872628\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.2134 | −0.614489 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.77309 | −0.260782 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.52540 | 0.246514 | 0.123257 | − | 0.992375i | \(-0.460666\pi\) | ||||
0.123257 | + | 0.992375i | \(0.460666\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.840875 | −0.0456701 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.2688 | 0.881006 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7912 | −1.01463 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.239404 | −0.0128891 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.4767 | −1.85081 | −0.925403 | − | 0.378985i | \(-0.876273\pi\) | ||||
−0.925403 | + | 0.378985i | \(0.876273\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3968 | 0.824173 | 0.412086 | − | 0.911145i | \(-0.364800\pi\) | ||||
0.412086 | + | 0.911145i | \(0.364800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.12253 | −0.0599163 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.39183 | −0.393427 | −0.196714 | − | 0.980461i | \(-0.563027\pi\) | ||||
−0.196714 | + | 0.980461i | \(0.563027\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.88626 | −0.100112 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.425430 | 0.0225162 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.8118 | −1.67896 | −0.839481 | − | 0.543389i | \(-0.817141\pi\) | ||||
−0.839481 | + | 0.543389i | \(0.817141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.543038 | −0.0285021 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.32653 | 0.0694335 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.60800 | −0.136136 | −0.0680682 | − | 0.997681i | \(-0.521684\pi\) | ||||
−0.0680682 | + | 0.997681i | \(0.521684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.4778 | 0.805743 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.60518 | 0.135254 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.546587 | 0.0283012 | 0.0141506 | − | 0.999900i | \(-0.495496\pi\) | ||||
0.0141506 | + | 0.999900i | \(0.495496\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.347515 | −0.0179456 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.377848 | −0.0194602 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.5170 | −1.77302 | −0.886510 | − | 0.462709i | \(-0.846878\pi\) | ||||
−0.886510 | + | 0.462709i | \(0.846878\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.169425 | 0.00867993 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.5252 | 0.537813 | 0.268906 | − | 0.963166i | \(-0.413338\pi\) | ||||
0.268906 | + | 0.963166i | \(0.413338\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.36874 | −0.120722 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.1923 | 0.619771 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.1600 | −1.78268 | −0.891342 | − | 0.453331i | \(-0.850236\pi\) | ||||
−0.891342 | + | 0.453331i | \(0.850236\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.7782 | −0.696795 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.414216 | −0.0208944 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.787094 | 0.0396030 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.6583 | −1.43832 | −0.719158 | − | 0.694846i | \(-0.755472\pi\) | ||||
−0.719158 | + | 0.694846i | \(0.755472\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.208542 | −0.0104401 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.8079 | 1.63835 | 0.819175 | − | 0.573544i | \(-0.194432\pi\) | ||||
0.819175 | + | 0.573544i | \(0.194432\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.5377 | −0.923426 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.95979 | 0.196764 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.69134 | −0.381245 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.2118 | −0.801620 | −0.400810 | − | 0.916161i | \(-0.631271\pi\) | ||||
−0.400810 | + | 0.916161i | \(0.631271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.927580 | 0.0457541 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.5220 | 1.05903 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.81670 | 0.285530 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.77554 | −0.0869485 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.8854 | −0.727200 | −0.363600 | − | 0.931555i | \(-0.618452\pi\) | ||||
−0.363600 | + | 0.931555i | \(0.618452\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.6578 | 1.20175 | 0.600874 | − | 0.799344i | \(-0.294819\pi\) | ||||
0.600874 | + | 0.799344i | \(0.294819\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.52933 | −0.414710 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.80012 | −0.475376 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.9501 | −0.529914 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.384565 | −0.0185670 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.3628 | 1.79970 | 0.899850 | − | 0.436199i | \(-0.143676\pi\) | ||||
0.899850 | + | 0.436199i | \(0.143676\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.55750 | 0.411247 | 0.205624 | − | 0.978631i | \(-0.434078\pi\) | ||||
0.205624 | + | 0.978631i | \(0.434078\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.00572446 | −0.000274467 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.75394 | 0.323085 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.9645 | 1.66876 | 0.834382 | − | 0.551187i | \(-0.185825\pi\) | ||||
0.834382 | + | 0.551187i | \(0.185825\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.637685 | 0.0303660 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.2168 | 1.05555 | 0.527777 | − | 0.849383i | \(-0.323026\pi\) | ||||
0.527777 | + | 0.849383i | \(0.323026\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.68226 | −0.174556 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.893774 | 0.0422740 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.2221 | 0.576795 | 0.288397 | − | 0.957511i | \(-0.406878\pi\) | ||||
0.288397 | + | 0.957511i | \(0.406878\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.6163 | 0.499904 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.75137 | −0.0822866 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.69908 | 0.126535 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3167 | 0.903597 | 0.451798 | − | 0.892120i | \(-0.350783\pi\) | ||||
0.451798 | + | 0.892120i | \(0.350783\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.978763 | −0.0456847 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.75002 | 0.360954 | 0.180477 | − | 0.983579i | \(-0.442236\pi\) | ||||
0.180477 | + | 0.983579i | \(0.442236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.6871 | −0.589622 | −0.294811 | − | 0.955556i | \(-0.595257\pi\) | ||||
−0.294811 | + | 0.955556i | \(0.595257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.280848 | −0.0130240 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.81309 | 0.454095 | 0.227048 | − | 0.973884i | \(-0.427093\pi\) | ||||
0.227048 | + | 0.973884i | \(0.427093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.0814 | −1.29668 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.573123 | −0.0264081 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.36281 | 0.384522 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.80392 | 0.220419 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.99359 | −0.137067 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.7465 | −1.35915 | −0.679576 | − | 0.733605i | \(-0.737836\pi\) | ||||
−0.679576 | + | 0.733605i | \(0.737836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.76396 | 0.399602 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.40848 | −0.0640879 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.82098 | −0.264317 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.1548 | 0.913299 | 0.456650 | − | 0.889647i | \(-0.349049\pi\) | ||||
0.456650 | + | 0.889647i | \(0.349049\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.37424 | 0.0621454 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.9467 | −1.17096 | −0.585480 | − | 0.810687i | \(-0.699094\pi\) | ||||
−0.585480 | + | 0.810687i | \(0.699094\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.329455 | −0.0148379 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.72189 | 0.122340 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.0973 | −0.497784 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.1611 | 1.84262 | 0.921312 | − | 0.388823i | \(-0.127118\pi\) | ||||
0.921312 | + | 0.388823i | \(0.127118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.38327 | 0.0617997 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.0598213 | −0.00266730 | −0.00133365 | − | 0.999999i | \(-0.500425\pi\) | ||||
−0.00133365 | + | 0.999999i | \(0.500425\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.00762684 | 0.000339390 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.602437 | −0.0267552 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.9387 | 1.81458 | 0.907289 | − | 0.420508i | \(-0.138148\pi\) | ||||
0.907289 | + | 0.420508i | \(0.138148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.80430 | 0.345242 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.479779 | 0.0211828 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.91266 | 0.0842820 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.85033 | −0.257297 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.05533 | 0.0463237 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.3009 | 1.80943 | 0.904714 | − | 0.426021i | \(-0.140085\pi\) | ||||
0.904714 | + | 0.426021i | \(0.140085\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.06733 | −0.0903981 | −0.0451991 | − | 0.998978i | \(-0.514392\pi\) | ||||
−0.0451991 | + | 0.998978i | \(0.514392\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.00182 | −0.0437228 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.1634 | −0.704090 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.6157 | 0.983293 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.7307 | −1.07322 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0969 | −0.523975 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00520 | −0.259627 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.400893 | 0.0172998 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.437393 | 0.0188399 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.6525 | −1.05989 | −0.529946 | − | 0.848031i | \(-0.677788\pi\) | ||||
−0.529946 | + | 0.848031i | \(0.677788\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.172270 | 0.00739282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.15800 | 0.0924387 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.6190 | −0.667819 | −0.333909 | − | 0.942605i | \(-0.608368\pi\) | ||||
−0.333909 | + | 0.942605i | \(0.608368\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.5827 | 0.537016 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.161496 | 0.00687994 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.63068 | 0.196917 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.132775 | 0.00563600 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.0983 | 1.19056 | 0.595281 | − | 0.803518i | \(-0.297041\pi\) | ||||
0.595281 | + | 0.803518i | \(0.297041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.52908 | −0.403037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.335311 | −0.0141569 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.62749 | 0.0685904 | 0.0342952 | − | 0.999412i | \(-0.489081\pi\) | ||||
0.0342952 | + | 0.999412i | \(0.489081\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.65155 | −0.195692 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.2965 | 0.978362 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.9361 | −1.12922 | −0.564610 | − | 0.825358i | \(-0.690973\pi\) | ||||
−0.564610 | + | 0.825358i | \(0.690973\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.2736 | −1.64355 | −0.821775 | − | 0.569811i | \(-0.807016\pi\) | ||||
−0.821775 | + | 0.569811i | \(0.807016\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.75880 | 0.0734748 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.4454 | 1.35307 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.9871 | 0.623923 | 0.311961 | − | 0.950095i | \(-0.399014\pi\) | ||||
0.311961 | + | 0.950095i | \(0.399014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.303076 | 0.0125954 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.2212 | 1.41973 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.05333 | −0.0850401 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.10148 | −0.128231 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.9297 | 1.60680 | 0.803400 | − | 0.595439i | \(-0.203022\pi\) | ||||
0.803400 | + | 0.595439i | \(0.203022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.92315 | 0.326468 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.564716 | 0.0232293 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.6009 | −0.969174 | −0.484587 | − | 0.874743i | \(-0.661030\pi\) | ||||
−0.484587 | + | 0.874743i | \(0.661030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.35339 | 0.0964797 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.38238 | −0.0565769 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.9916 | −1.51144 | −0.755718 | − | 0.654897i | \(-0.772712\pi\) | ||||
−0.755718 | + | 0.654897i | \(0.772712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.7323 | 1.62071 | 0.810357 | − | 0.585936i | \(-0.199273\pi\) | ||||
0.810357 | + | 0.585936i | \(0.199273\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.2680 | 1.31406 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.00397 | −0.122129 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.9832 | 1.74464 | 0.872318 | − | 0.488939i | \(-0.162616\pi\) | ||||
0.872318 | + | 0.488939i | \(0.162616\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0336785 | −0.00136472 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.66622 | 0.269686 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.2633 | 0.818428 | 0.409214 | − | 0.912438i | \(-0.365803\pi\) | ||||
0.409214 | + | 0.912438i | \(0.365803\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.183270 | −0.00739015 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.4290 | 1.74839 | 0.874193 | − | 0.485579i | \(-0.161391\pi\) | ||||
0.874193 | + | 0.485579i | \(0.161391\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.6938 | −1.15330 | −0.576651 | − | 0.816991i | \(-0.695641\pi\) | ||||
−0.576651 | + | 0.816991i | \(0.695641\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.24040 | 0.130033 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.6637 | −0.867938 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.0972 | 0.883888 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.164366 | 0.00656415 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.64152 | 0.304687 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.0787 | 1.35665 | 0.678326 | − | 0.734761i | \(-0.262706\pi\) | ||||
0.678326 | + | 0.734761i | \(0.262706\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.88575 | −0.0749520 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.937226 | 0.0371927 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.498392 | −0.0197470 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.7519 | 0.504456 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 49.8468 | 1.96883 | 0.984414 | − | 0.175864i | \(-0.0562720\pi\) | ||||
0.984414 | + | 0.175864i | \(0.0562720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.7487 | −1.40979 | −0.704896 | − | 0.709311i | \(-0.749006\pi\) | ||||
−0.704896 | + | 0.709311i | \(0.749006\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.144367 | −0.00568445 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.6225 | −1.04664 | −0.523319 | − | 0.852137i | \(-0.675307\pi\) | ||||
−0.523319 | + | 0.852137i | \(0.675307\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.9630 | −0.665855 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.65231 | −0.0647589 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.5839 | −0.648977 | −0.324488 | − | 0.945890i | \(-0.605192\pi\) | ||||
−0.324488 | + | 0.945890i | \(0.605192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.29136 | −0.0895307 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.96785 | −0.349869 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7302 | 0.768580 | 0.384290 | − | 0.923212i | \(-0.374446\pi\) | ||||
0.384290 | + | 0.923212i | \(0.374446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.3031 | 0.945283 | 0.472641 | − | 0.881255i | \(-0.343301\pi\) | ||||
0.472641 | + | 0.881255i | \(0.343301\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.382074 | 0.0148385 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.15361 | −0.0447350 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.09073 | 0.0422333 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.38326 | 0.0534798 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.63056 | 0.333179 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.92628 | −0.344083 | −0.172041 | − | 0.985090i | \(-0.555036\pi\) | ||||
−0.172041 | + | 0.985090i | \(0.555036\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.30482 | 0.0887125 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.3563 | −1.01295 | −0.506477 | − | 0.862254i | \(-0.669052\pi\) | ||||
−0.506477 | + | 0.862254i | \(0.669052\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.2463 | −1.31425 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0142111 | −0.000544569 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.89120 | 0.187157 | 0.0935783 | − | 0.995612i | \(-0.470169\pi\) | ||||
0.0935783 | + | 0.995612i | \(0.470169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.13118 | 0.196052 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.947488 | −0.0361489 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.33968 | 0.0891348 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.2422 | 0.693965 | 0.346982 | − | 0.937872i | \(-0.387206\pi\) | ||||
0.346982 | + | 0.937872i | \(0.387206\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.0136 | 0.608307 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.82191 | −0.372566 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.5476 | −0.399518 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.72166 | 0.0651190 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.4734 | 1.26427 | 0.632136 | − | 0.774857i | \(-0.282178\pi\) | ||||
0.632136 | + | 0.774857i | \(0.282178\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.74579 | −0.141275 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.100994 | 0.00380366 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0448707 | 0.00168754 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.77292 | 0.291918 | 0.145959 | − | 0.989291i | \(-0.453373\pi\) | ||||
0.145959 | + | 0.989291i | \(0.453373\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.32108 | −0.199556 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 53.5125 | 2.00406 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.12733 | −0.0795577 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.702947 | −0.0262520 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.23898 | −0.232675 | −0.116337 | − | 0.993210i | \(-0.537115\pi\) | ||||
−0.116337 | + | 0.993210i | \(0.537115\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.2527 | 0.419072 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.69859 | −0.0631711 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.775811 | 0.0288129 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6584 | 0.543651 | 0.271826 | − | 0.962347i | \(-0.412373\pi\) | ||||
0.271826 | + | 0.962347i | \(0.412373\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.6546 | −0.987207 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.30864 | −0.307306 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.06986 | 0.224195 | 0.112098 | − | 0.993697i | \(-0.464243\pi\) | ||||
0.112098 | + | 0.993697i | \(0.464243\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.00755071 | −0.000278512 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.1329 | 0.815275 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.49102 | 0.165205 | 0.0826025 | − | 0.996583i | \(-0.473677\pi\) | ||||
0.0826025 | + | 0.996583i | \(0.473677\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.187289 | −0.00688022 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.7290 | −0.393607 | −0.196804 | − | 0.980443i | \(-0.563056\pi\) | ||||
−0.196804 | + | 0.980443i | \(0.563056\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.94417 | 0.181140 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −39.3232 | −1.43876 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.3302 | −1.29094 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.8939 | 1.78416 | 0.892081 | − | 0.451875i | \(-0.149245\pi\) | ||||
0.892081 | + | 0.451875i | \(0.149245\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.44556 | −0.0891213 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.68822 | −0.352591 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.7495 | −0.427041 | −0.213521 | − | 0.976939i | \(-0.568493\pi\) | ||||
−0.213521 | + | 0.976939i | \(0.568493\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.11012 | 0.0402948 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.70454 | −0.351789 | −0.175895 | − | 0.984409i | \(-0.556282\pi\) | ||||
−0.175895 | + | 0.984409i | \(0.556282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.6961 | 0.459630 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.70426 | −0.0977728 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.3286 | 0.697916 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.8869 | −0.536834 | −0.268417 | − | 0.963303i | \(-0.586500\pi\) | ||||
−0.268417 | + | 0.963303i | \(0.586500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.904114 | −0.0325609 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.74773 | −0.0988289 | −0.0494145 | − | 0.998778i | \(-0.515736\pi\) | ||||
−0.0494145 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.0621 | 1.36723 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.781153 | 0.0280237 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.17031 | 0.185246 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.74660 | 0.312978 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.0774822 | 0.00276899 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.17040 | −0.113156 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.24788 | −0.151421 | −0.0757103 | − | 0.997130i | \(-0.524122\pi\) | ||||
−0.0757103 | + | 0.997130i | \(0.524122\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.00620377 | −0.000220860 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.3663 | −0.973033 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.83417 | −0.349222 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0354466 | 0.00125716 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.42079 | 0.121171 | 0.0605854 | − | 0.998163i | \(-0.480703\pi\) | ||||
0.0605854 | + | 0.998163i | \(0.480703\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.81244 | 0.205629 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.8936 | 0.879571 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.15111 | −0.217068 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.79140 | −0.274611 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.72878 | −0.0608560 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.2668 | 0.712543 | 0.356272 | − | 0.934382i | \(-0.384048\pi\) | ||||
0.356272 | + | 0.934382i | \(0.384048\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.6631 | −0.585121 | −0.292561 | − | 0.956247i | \(-0.594507\pi\) | ||||
−0.292561 | + | 0.956247i | \(0.594507\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.482829 | 0.0169335 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.60202 | 0.266287 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.07281 | 0.142489 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.2469 | −0.637597 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.5886 | 1.41655 | 0.708277 | − | 0.705935i | \(-0.249473\pi\) | ||||
0.708277 | + | 0.705935i | \(0.249473\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.3801 | 0.989267 | 0.494634 | − | 0.869102i | \(-0.335302\pi\) | ||||
0.494634 | + | 0.869102i | \(0.335302\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.789601 | 0.0274904 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.6329 | −1.34340 | −0.671699 | − | 0.740824i | \(-0.734435\pi\) | ||||
−0.671699 | + | 0.740824i | \(0.734435\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.0546 | −0.835449 | −0.417725 | − | 0.908574i | \(-0.637172\pi\) | ||||
−0.417725 | + | 0.908574i | \(0.637172\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.22161 | 0.0770669 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.434560 | −0.0150566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.65194 | 0.264806 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.80136 | 0.131394 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.5322 | −0.432660 | −0.216330 | − | 0.976320i | \(-0.569409\pi\) | ||||
−0.216330 | + | 0.976320i | \(0.569409\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9739 | −0.999101 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.997871 | 0.0343685 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.33256 | −0.114643 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.6732 | −0.607257 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.29029 | 0.0786024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.2989 | −0.867234 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.0175 | 0.616908 | 0.308454 | − | 0.951239i | \(-0.400188\pi\) | ||||
0.308454 | + | 0.951239i | \(0.400188\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.32560 | 0.0453346 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.4522 | −0.937748 | −0.468874 | − | 0.883265i | \(-0.655340\pi\) | ||||
−0.468874 | + | 0.883265i | \(0.655340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.8818 | 1.22427 | 0.612136 | − | 0.790753i | \(-0.290311\pi\) | ||||
0.612136 | + | 0.790753i | \(0.290311\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.07823 | −0.0367458 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.0943 | 1.19463 | 0.597313 | − | 0.802008i | \(-0.296235\pi\) | ||||
0.597313 | + | 0.802008i | \(0.296235\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.83785 | 0.198493 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.02769 | −0.0349021 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.64977 | −0.123810 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.2195 | −0.854531 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 39.3522 | 1.33187 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.3099 | −0.382344 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.5063 | 1.09766 | 0.548829 | − | 0.835934i | \(-0.315074\pi\) | ||||
0.548829 | + | 0.835934i | \(0.315074\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.0989537 | 0.00333763 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.6801 | −0.966259 | −0.483129 | − | 0.875549i | \(-0.660500\pi\) | ||||
−0.483129 | + | 0.875549i | \(0.660500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.16251 | −0.207385 | −0.103692 | − | 0.994609i | \(-0.533066\pi\) | ||||
−0.103692 | + | 0.994609i | \(0.533066\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.292832 | 0.00984343 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.262178 | 0.00880309 | 0.00440154 | − | 0.999990i | \(-0.498599\pi\) | ||||
0.00440154 | + | 0.999990i | \(0.498599\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.51395 | 0.184932 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.3616 | −0.615137 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.84920 | −0.0953447 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.21765 | 0.0741280 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.26494 | −0.0422350 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.27955 | 0.0426755 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.04003 | 0.0679632 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.849349 | −0.0282646 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.952963 | 0.0316775 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.5866 | 1.28125 | 0.640624 | − | 0.767855i | \(-0.278676\pi\) | ||||
0.640624 | + | 0.767855i | \(0.278676\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.0515605 | −0.00171015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.7598 | 0.389619 | 0.194810 | − | 0.980841i | \(-0.437591\pi\) | ||||
0.194810 | + | 0.980841i | \(0.437591\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.9721 | −0.892646 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.148989 | −0.00492543 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.4807 | −0.445170 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.4742 | −0.378500 | −0.189250 | − | 0.981929i | \(-0.560606\pi\) | ||||
−0.189250 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.52848 | −0.0833162 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.96639 | −0.328048 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.9945 | −0.591655 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.9304 | −0.424689 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.1220 | 0.857035 | 0.428517 | − | 0.903534i | \(-0.359036\pi\) | ||||
0.428517 | + | 0.903534i | \(0.359036\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.213017 | 0.00698134 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.08988 | −0.0684195 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.85487 | −0.0606608 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.58835 | 0.117226 | 0.0586131 | − | 0.998281i | \(-0.481332\pi\) | ||||
0.0586131 | + | 0.998281i | \(0.481332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.959646 | 0.0313169 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55.1725 | −1.79857 | −0.899287 | − | 0.437359i | \(-0.855914\pi\) | ||||
−0.899287 | + | 0.437359i | \(0.855914\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.9200 | 1.13715 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.553477 | −0.0180046 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.9388 | 0.875393 | 0.437697 | − | 0.899123i | \(-0.355794\pi\) | ||||
0.437697 | + | 0.899123i | \(0.355794\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.00894 | 0.227520 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.903333 | 0.0292926 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.4776 | −1.34359 | −0.671796 | − | 0.740737i | \(-0.734477\pi\) | ||||
−0.671796 | + | 0.740737i | \(0.734477\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.72930 | 0.314833 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0265444 | 0.000858059 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.1881 | 0.974824 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.7763 | 1.02504 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.5975 | 1.30824 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.67655 | 0.0539701 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.2835 | −1.03817 | −0.519084 | − | 0.854723i | \(-0.673727\pi\) | ||||
−0.519084 | + | 0.854723i | \(0.673727\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.163302 | −0.00524600 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.53014 | 0.0491045 | 0.0245522 | − | 0.999699i | \(-0.492184\pi\) | ||||
0.0245522 | + | 0.999699i | \(0.492184\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −57.7849 | −1.85250 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.899719 | −0.0288141 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.5952 | 1.49071 | 0.745357 | − | 0.666666i | \(-0.232279\pi\) | ||||
0.745357 | + | 0.666666i | \(0.232279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.0747 | 0.545709 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.5890 | −0.465790 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.0055 | 0.638076 | 0.319038 | − | 0.947742i | \(-0.396640\pi\) | ||||
0.319038 | + | 0.947742i | \(0.396640\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.12389 | 0.0995354 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.594176 | 0.0189128 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.5075 | 0.874688 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00418 | 0.254261 | 0.127131 | − | 0.991886i | \(-0.459423\pi\) | ||||
0.127131 | + | 0.991886i | \(0.459423\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.68262 | −0.0851303 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.64702 | −0.242427 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.35634 | −0.106296 | −0.0531482 | − | 0.998587i | \(-0.516926\pi\) | ||||
−0.0531482 | + | 0.998587i | \(0.516926\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.79715 | −0.0568594 |
(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 | 4028.2.a.d.1.10 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.d.1.10 | ✓ | 19 | 1.1 | even | 1 | trivial |