Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(1727,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1727");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(101.955300490\) |
Analytic rank: | \(0\) |
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: | \( x^{12} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + 6854 x^{2} - 888 x + 9496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{12} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1727.9 | ||
Root | \(-1.29835 + 1.36719i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1727 |
Dual form | 1728.4.c.j.1727.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.83890i | 0.522247i | 0.965305 | + | 0.261124i | \(0.0840930\pi\) | ||||
−0.965305 | + | 0.261124i | \(0.915907\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 8.83113i | − 0.476836i | −0.971163 | − | 0.238418i | \(-0.923371\pi\) | ||||
0.971163 | − | 0.238418i | \(-0.0766288\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 23.6146 | 0.647279 | 0.323639 | − | 0.946180i | \(-0.395094\pi\) | ||||
0.323639 | + | 0.946180i | \(0.395094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −54.6531 | −1.16600 | −0.583001 | − | 0.812471i | \(-0.698122\pi\) | ||||
−0.583001 | + | 0.812471i | \(0.698122\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 117.211i | − 1.67223i | −0.548553 | − | 0.836116i | \(-0.684821\pi\) | ||||
0.548553 | − | 0.836116i | \(-0.315179\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 109.576i | − 1.32308i | −0.749910 | − | 0.661539i | \(-0.769903\pi\) | ||||
0.749910 | − | 0.661539i | \(-0.230097\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 33.5763 | 0.304397 | 0.152199 | − | 0.988350i | \(-0.451365\pi\) | ||||
0.152199 | + | 0.988350i | \(0.451365\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 90.9072 | 0.727258 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 40.0490i | − 0.256445i | −0.991745 | − | 0.128223i | \(-0.959073\pi\) | ||||
0.991745 | − | 0.128223i | \(-0.0409272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 292.510i | 1.69472i | 0.531020 | + | 0.847359i | \(0.321809\pi\) | ||||
−0.531020 | + | 0.847359i | \(0.678191\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 51.5641 | 0.249026 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −283.265 | −1.25861 | −0.629304 | − | 0.777159i | \(-0.716660\pi\) | ||||
−0.629304 | + | 0.777159i | \(0.716660\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 367.472i | 1.39974i | 0.714269 | + | 0.699871i | \(0.246759\pi\) | ||||
−0.714269 | + | 0.699871i | \(0.753241\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 323.337i | 1.14671i | 0.819308 | + | 0.573354i | \(0.194358\pi\) | ||||
−0.819308 | + | 0.573354i | \(0.805642\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −66.2249 | −0.205530 | −0.102765 | − | 0.994706i | \(-0.532769\pi\) | ||||
−0.102765 | + | 0.994706i | \(0.532769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 265.011 | 0.772627 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 158.506i | − 0.410801i | −0.978678 | − | 0.205401i | \(-0.934150\pi\) | ||||
0.978678 | − | 0.205401i | \(-0.0658498\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 137.883i | 0.338040i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −848.630 | −1.87258 | −0.936290 | − | 0.351228i | \(-0.885764\pi\) | ||||
−0.936290 | + | 0.351228i | \(0.885764\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 348.716 | 0.731943 | 0.365972 | − | 0.930626i | \(-0.380737\pi\) | ||||
0.365972 | + | 0.930626i | \(0.380737\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 319.114i | − 0.608942i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 194.285i | − 0.354264i | −0.984187 | − | 0.177132i | \(-0.943318\pi\) | ||||
0.984187 | − | 0.177132i | \(-0.0566819\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −939.761 | −1.57083 | −0.785417 | − | 0.618968i | \(-0.787551\pi\) | ||||
−0.785417 | + | 0.618968i | \(0.787551\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −473.826 | −0.759686 | −0.379843 | − | 0.925051i | \(-0.624022\pi\) | ||||
−0.379843 | + | 0.925051i | \(0.624022\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 208.544i | − 0.308646i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 273.221i | − 0.389112i | −0.980891 | − | 0.194556i | \(-0.937673\pi\) | ||||
0.980891 | − | 0.194556i | \(-0.0623265\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 338.366 | 0.447476 | 0.223738 | − | 0.974649i | \(-0.428174\pi\) | ||||
0.223738 | + | 0.974649i | \(0.428174\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 684.386 | 0.873318 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 739.884i | − 0.881208i | −0.897702 | − | 0.440604i | \(-0.854764\pi\) | ||||
0.897702 | − | 0.440604i | \(-0.145236\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 482.648i | 0.555992i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 639.805 | 0.690974 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −448.629 | −0.469602 | −0.234801 | − | 0.972044i | \(-0.575444\pi\) | ||||
−0.234801 | + | 0.972044i | \(0.575444\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1152.87i | 1.13580i | 0.823099 | + | 0.567898i | \(0.192243\pi\) | ||||
−0.823099 | + | 0.567898i | \(0.807757\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1389.90i | − 1.32962i | −0.747013 | − | 0.664809i | \(-0.768513\pi\) | ||||
0.747013 | − | 0.664809i | \(-0.231487\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 245.479 | 0.221788 | 0.110894 | − | 0.993832i | \(-0.464629\pi\) | ||||
0.110894 | + | 0.993832i | \(0.464629\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 644.998 | 0.566785 | 0.283393 | − | 0.959004i | \(-0.408540\pi\) | ||||
0.283393 | + | 0.959004i | \(0.408540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 825.442i | 0.687177i | 0.939120 | + | 0.343589i | \(0.111643\pi\) | ||||
−0.939120 | + | 0.343589i | \(0.888357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 196.049i | 0.158971i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1035.11 | −0.797380 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −773.351 | −0.581030 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1260.66i | 0.902056i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 754.649i | − 0.527278i | −0.964621 | − | 0.263639i | \(-0.915077\pi\) | ||||
0.964621 | − | 0.263639i | \(-0.0849228\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2026.43 | −1.35153 | −0.675765 | − | 0.737117i | \(-0.736186\pi\) | ||||
−0.675765 | + | 0.737117i | \(0.736186\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −967.681 | −0.630892 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1882.88i | 1.17420i | 0.809515 | + | 0.587099i | \(0.199730\pi\) | ||||
−0.809515 | + | 0.587099i | \(0.800270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 93.7277i | 0.0571934i | 0.999591 | + | 0.0285967i | \(0.00910385\pi\) | ||||
−0.999591 | + | 0.0285967i | \(0.990896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1290.61 | −0.754729 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 233.842 | 0.133928 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2764.69i | − 1.52008i | −0.649874 | − | 0.760042i | \(-0.725178\pi\) | ||||
0.649874 | − | 0.760042i | \(-0.274822\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3694.11i | 1.99088i | 0.0954051 | + | 0.995439i | \(0.469585\pi\) | ||||
−0.0954051 | + | 0.995439i | \(0.530415\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1707.94 | −0.885062 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −812.401 | −0.412972 | −0.206486 | − | 0.978450i | \(-0.566203\pi\) | ||||
−0.206486 | + | 0.978450i | \(0.566203\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 296.516i | − 0.145148i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1034.18i | − 0.496953i | −0.968638 | − | 0.248477i | \(-0.920070\pi\) | ||||
0.968638 | − | 0.248477i | \(-0.0799299\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1453.29 | −0.673409 | −0.336704 | − | 0.941610i | \(-0.609312\pi\) | ||||
−0.336704 | + | 0.941610i | \(0.609312\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 789.957 | 0.359562 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 634.902i | − 0.279022i | −0.990221 | − | 0.139511i | \(-0.955447\pi\) | ||||
0.990221 | − | 0.139511i | \(-0.0445530\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 802.813i | − 0.346783i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2909.35 | −1.21483 | −0.607417 | − | 0.794383i | \(-0.707794\pi\) | ||||
−0.607417 | + | 0.794383i | \(0.707794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1354.46 | −0.556222 | −0.278111 | − | 0.960549i | \(-0.589708\pi\) | ||||
−0.278111 | + | 0.960549i | \(0.589708\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 1653.96i | − 0.657305i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2767.90i | − 1.08240i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3488.40 | −1.32153 | −0.660765 | − | 0.750593i | \(-0.729768\pi\) | ||||
−0.660765 | + | 0.750593i | \(0.729768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2912.99 | 1.08643 | 0.543217 | − | 0.839592i | \(-0.317206\pi\) | ||||
0.543217 | + | 0.839592i | \(0.317206\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2432.66i | − 0.879795i | −0.898048 | − | 0.439897i | \(-0.855015\pi\) | ||||
0.898048 | − | 0.439897i | \(-0.144985\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 563.190i | − 0.200621i | −0.994956 | − | 0.100310i | \(-0.968016\pi\) | ||||
0.994956 | − | 0.100310i | \(-0.0319836\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −353.678 | −0.122282 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2145.63 | −0.731012 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 2587.60i | − 0.856401i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1447.62i | − 0.472314i | −0.971715 | − | 0.236157i | \(-0.924112\pi\) | ||||
0.971715 | − | 0.236157i | \(-0.0758879\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1887.93 | −0.598865 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2583.19 | 0.808103 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6405.96i | 1.94983i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5049.28i | − 1.51625i | −0.652107 | − | 0.758127i | \(-0.726115\pi\) | ||||
0.652107 | − | 0.758127i | \(-0.273885\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5716.54 | −1.67145 | −0.835727 | − | 0.549146i | \(-0.814953\pi\) | ||||
−0.835727 | + | 0.549146i | \(0.814953\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2582.55 | 0.745240 | 0.372620 | − | 0.927984i | \(-0.378460\pi\) | ||||
0.372620 | + | 0.927984i | \(0.378460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 587.204i | − 0.165103i | −0.996587 | − | 0.0825516i | \(-0.973693\pi\) | ||||
0.996587 | − | 0.0825516i | \(-0.0263069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 386.681i | − 0.107337i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5583.00 | −1.51102 | −0.755512 | − | 0.655135i | \(-0.772612\pi\) | ||||
−0.755512 | + | 0.655135i | \(0.772612\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2056.95 | −0.549791 | −0.274895 | − | 0.961474i | \(-0.588643\pi\) | ||||
−0.274895 | + | 0.961474i | \(0.588643\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1547.37i | 0.403503i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5988.67i | 1.54271i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1256.79 | −0.316047 | −0.158023 | − | 0.987435i | \(-0.550512\pi\) | ||||
−0.158023 | + | 0.987435i | \(0.550512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 792.890 | 0.197030 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 643.773i | 0.156255i | 0.996943 | + | 0.0781273i | \(0.0248941\pi\) | ||||
−0.996943 | + | 0.0781273i | \(0.975106\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2501.55i | 0.600150i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −917.108 | −0.215024 | −0.107512 | − | 0.994204i | \(-0.534288\pi\) | ||||
−0.107512 | + | 0.994204i | \(0.534288\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 925.501 | 0.214540 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 6577.00i | − 1.49073i | −0.666656 | − | 0.745366i | \(-0.732275\pi\) | ||||
0.666656 | − | 0.745366i | \(-0.267725\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4656.21i | 1.04371i | 0.853035 | + | 0.521854i | \(0.174759\pi\) | ||||
−0.853035 | + | 0.521854i | \(0.825241\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2146.74 | 0.470739 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2881.42 | 0.625010 | 0.312505 | − | 0.949916i | \(-0.398832\pi\) | ||||
0.312505 | + | 0.949916i | \(0.398832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2604.93i | 0.553015i | 0.961012 | + | 0.276507i | \(0.0891771\pi\) | ||||
−0.961012 | + | 0.276507i | \(0.910823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5786.02i | 1.21535i | 0.794187 | + | 0.607674i | \(0.207897\pi\) | ||||
−0.794187 | + | 0.607674i | \(0.792103\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3245.19 | 0.667448 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8825.50 | −1.79636 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3279.55i | 0.653902i | 0.945041 | + | 0.326951i | \(0.106021\pi\) | ||||
−0.945041 | + | 0.326951i | \(0.893979\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 4955.07i | − 0.977950i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1835.05 | −0.354928 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2855.43 | 0.546792 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2036.12i | 0.382255i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3014.47i | 0.560407i | 0.959941 | + | 0.280203i | \(0.0904019\pi\) | ||||
−0.959941 | + | 0.280203i | \(0.909598\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6230.80 | −1.13606 | −0.568032 | − | 0.823006i | \(-0.692295\pi\) | ||||
−0.568032 | + | 0.823006i | \(0.692295\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3922.49 | −0.708346 | −0.354173 | − | 0.935180i | \(-0.615238\pi\) | ||||
−0.354173 | + | 0.935180i | \(0.615238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6882.19i | − 1.21938i | −0.792641 | − | 0.609689i | \(-0.791295\pi\) | ||||
0.792641 | − | 0.609689i | \(-0.208705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 945.741i | − 0.165992i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12843.6 | −2.21249 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4968.36 | −0.847984 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 584.841i | 0.0980040i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9489.08i | 1.57573i | 0.615847 | + | 0.787866i | \(0.288814\pi\) | ||||
−0.615847 | + | 0.787866i | \(0.711186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1134.41 | 0.185013 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4578.52 | 0.740083 | 0.370041 | − | 0.929015i | \(-0.379344\pi\) | ||||
0.370041 | + | 0.929015i | \(0.379344\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6907.50i | 1.09696i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 5369.42i | − 0.845253i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 942.483 | 0.145807 | 0.0729037 | − | 0.997339i | \(-0.476773\pi\) | ||||
0.0729037 | + | 0.997339i | \(0.476773\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2124.84 | 0.325903 | 0.162951 | − | 0.986634i | \(-0.447899\pi\) | ||||
0.162951 | + | 0.986634i | \(0.447899\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3881.60i | 0.585260i | 0.956226 | + | 0.292630i | \(0.0945304\pi\) | ||||
−0.956226 | + | 0.292630i | \(0.905470\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 5487.18i | − 0.820363i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8050.44 | −1.18353 | −0.591763 | − | 0.806112i | \(-0.701568\pi\) | ||||
−0.591763 | + | 0.806112i | \(0.701568\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5147.94 | −0.750537 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2766.62i | − 0.396744i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6890.96i | 0.980123i | 0.871688 | + | 0.490062i | \(0.163026\pi\) | ||||
−0.871688 | + | 0.490062i | \(0.836974\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1399.79 | −0.195885 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10512.5 | 1.45930 | 0.729649 | − | 0.683822i | \(-0.239684\pi\) | ||||
0.729649 | + | 0.683822i | \(0.239684\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2188.80i | 0.299016i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3139.69i | − 0.425528i | −0.977104 | − | 0.212764i | \(-0.931753\pi\) | ||||
0.977104 | − | 0.212764i | \(-0.0682466\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5117.53 | −0.682751 | −0.341375 | − | 0.939927i | \(-0.610893\pi\) | ||||
−0.341375 | + | 0.939927i | \(0.610893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1217.67 | 0.161190 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 787.004i | 0.102578i | 0.998684 | + | 0.0512888i | \(0.0163329\pi\) | ||||
−0.998684 | + | 0.0512888i | \(0.983667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 3935.52i | − 0.509023i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1595.31 | 0.203212 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11160.6 | −1.41092 | −0.705458 | − | 0.708752i | \(-0.749259\pi\) | ||||
−0.705458 | + | 0.708752i | \(0.749259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 13224.6i | − 1.64689i | −0.567394 | − | 0.823447i | \(-0.692048\pi\) | ||||
0.567394 | − | 0.823447i | \(-0.307952\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 15986.5i | − 1.97605i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6689.20 | −0.814671 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8153.09 | 0.985683 | 0.492841 | − | 0.870119i | \(-0.335958\pi\) | ||||
0.492841 | + | 0.870119i | \(0.335958\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7494.36i | 0.892914i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1975.69i | 0.233693i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11682.5 | −1.36212 | −0.681061 | − | 0.732226i | \(-0.738481\pi\) | ||||
−0.681061 | + | 0.732226i | \(0.738481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9595.77 | −1.11085 | −0.555426 | − | 0.831566i | \(-0.687445\pi\) | ||||
−0.555426 | + | 0.831566i | \(0.687445\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 10655.4i | − 1.21614i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3079.56i | − 0.349017i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4294.48 | 0.479948 | 0.239974 | − | 0.970779i | \(-0.422861\pi\) | ||||
0.239974 | + | 0.970779i | \(0.422861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 168.392 | 0.0186892 | 0.00934460 | − | 0.999956i | \(-0.497025\pi\) | ||||
0.00934460 | + | 0.999956i | \(0.497025\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3679.16i | − 0.402742i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1459.53i | 0.158677i | 0.996848 | + | 0.0793387i | \(0.0252809\pi\) | ||||
−0.996848 | + | 0.0793387i | \(0.974719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 333.411 | 0.0357581 | 0.0178790 | − | 0.999840i | \(-0.494309\pi\) | ||||
0.0178790 | + | 0.999840i | \(0.494309\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4320.11 | 0.460209 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11454.3i | 1.20393i | 0.798523 | + | 0.601964i | \(0.205615\pi\) | ||||
−0.798523 | + | 0.601964i | \(0.794385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8677.70i | 0.906024i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2818.14 | −0.290365 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9680.26 | 0.990861 | 0.495431 | − | 0.868648i | \(-0.335010\pi\) | ||||
0.495431 | + | 0.868648i | \(0.335010\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14806.9i | 1.49593i | 0.663737 | + | 0.747966i | \(0.268970\pi\) | ||||
−0.663737 | + | 0.747966i | \(0.731030\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3658.08i | − 0.367183i | −0.983003 | − | 0.183591i | \(-0.941228\pi\) | ||||
0.983003 | − | 0.183591i | \(-0.0587723\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9852.37 | 0.976260 | 0.488130 | − | 0.872771i | \(-0.337679\pi\) | ||||
0.488130 | + | 0.872771i | \(0.337679\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1715.75 | −0.168926 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7635.47i | 0.742240i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 9961.26i | − 0.962219i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11107.9 | 1.05957 | 0.529784 | − | 0.848133i | \(-0.322273\pi\) | ||||
0.529784 | + | 0.848133i | \(0.322273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15481.3 | 1.46754 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2619.50i | − 0.245248i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11703.7i | 1.08900i | 0.838761 | + | 0.544500i | \(0.183281\pi\) | ||||
−0.838761 | + | 0.544500i | \(0.816719\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2851.25 | 0.262067 | 0.131034 | − | 0.991378i | \(-0.458170\pi\) | ||||
0.131034 | + | 0.991378i | \(0.458170\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4694.20 | −0.428836 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8299.15i | 0.749030i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14936.0i | 1.33994i | 0.742389 | + | 0.669969i | \(0.233693\pi\) | ||||
−0.742389 | + | 0.669969i | \(0.766307\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9047.91 | −0.802041 | −0.401020 | − | 0.916069i | \(-0.631344\pi\) | ||||
−0.401020 | + | 0.916069i | \(0.631344\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6731.52 | −0.593166 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 15173.5i | − 1.32132i | −0.750683 | − | 0.660662i | \(-0.770276\pi\) | ||||
0.750683 | − | 0.660662i | \(-0.229724\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4184.41i | 0.362246i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8115.47 | 0.694389 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1563.87 | −0.133035 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 7375.96i | − 0.620243i | −0.950697 | − | 0.310121i | \(-0.899630\pi\) | ||||
0.950697 | − | 0.310121i | \(-0.100370\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8514.96i | − 0.711918i | −0.934502 | − | 0.355959i | \(-0.884154\pi\) | ||||
0.934502 | − | 0.355959i | \(-0.115846\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34285.4 | 2.83396 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11039.6 | −0.907342 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 20083.5i | − 1.63210i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1433.33i | 0.115828i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6258.13 | 0.500105 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2214.98 | 0.176025 | 0.0880125 | − | 0.996119i | \(-0.471948\pi\) | ||||
0.0880125 | + | 0.996119i | \(0.471948\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3766.08i | 0.296002i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3906.55i | 0.305360i | 0.988276 | + | 0.152680i | \(0.0487904\pi\) | ||||
−0.988276 | + | 0.152680i | \(0.951210\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4388.41 | −0.339297 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2412.85 | −0.185542 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 2978.14i | − 0.226549i | −0.993564 | − | 0.113275i | \(-0.963866\pi\) | ||||
0.993564 | − | 0.113275i | \(-0.0361340\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 17671.4i | − 1.33706i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8786.44 | −0.657734 | −0.328867 | − | 0.944376i | \(-0.606667\pi\) | ||||
−0.328867 | + | 0.944376i | \(0.606667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4819.67 | −0.358876 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 19271.0i | − 1.41983i | −0.704288 | − | 0.709914i | \(-0.748734\pi\) | ||||
0.704288 | − | 0.709914i | \(-0.251266\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 15535.7i | − 1.13861i | −0.822125 | − | 0.569307i | \(-0.807212\pi\) | ||||
0.822125 | − | 0.569307i | \(-0.192788\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3052.33 | 0.221375 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3783.58 | 0.272985 | 0.136493 | − | 0.990641i | \(-0.456417\pi\) | ||||
0.136493 | + | 0.990641i | \(0.456417\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 2988.15i | − 0.213373i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 3743.06i | − 0.265903i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15515.4 | 1.09095 | 0.545477 | − | 0.838126i | \(-0.316349\pi\) | ||||
0.545477 | + | 0.838126i | \(0.316349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32052.1 | 2.24225 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 14098.1i | − 0.976292i | −0.872762 | − | 0.488146i | \(-0.837673\pi\) | ||||
0.872762 | − | 0.488146i | \(-0.162327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 6043.90i | − 0.416430i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −572.539 | −0.0390539 | −0.0195270 | − | 0.999809i | \(-0.506216\pi\) | ||||
−0.0195270 | + | 0.999809i | \(0.506216\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23463.4 | −1.59250 | −0.796249 | − | 0.604969i | \(-0.793185\pi\) | ||||
−0.796249 | + | 0.604969i | \(0.793185\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 4515.52i | − 0.303441i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1980.51i | 0.132433i | 0.997805 | + | 0.0662163i | \(0.0210927\pi\) | ||||
−0.997805 | + | 0.0662163i | \(0.978907\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3619.39 | 0.239648 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2479.01 | −0.163338 | −0.0816691 | − | 0.996660i | \(-0.526025\pi\) | ||||
−0.0816691 | + | 0.996660i | \(0.526025\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20002.8i | 1.30516i | 0.757722 | + | 0.652578i | \(0.226312\pi\) | ||||
−0.757722 | + | 0.652578i | \(0.773688\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22292.4i | 1.44751i | 0.690058 | + | 0.723754i | \(0.257585\pi\) | ||||
−0.690058 | + | 0.723754i | \(0.742415\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6534.01 | −0.420192 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4002.52 | 0.256161 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33201.9i | 2.10469i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 24203.8i | − 1.52700i | −0.645807 | − | 0.763501i | \(-0.723479\pi\) | ||||
0.645807 | − | 0.763501i | \(-0.276521\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4406.32 | 0.275370 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14483.7 | −0.900885 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4423.87i | 0.272593i | 0.990668 | + | 0.136297i | \(0.0435200\pi\) | ||||
−0.990668 | + | 0.136297i | \(0.956480\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11961.5i | 0.733619i | 0.930296 | + | 0.366810i | \(0.119550\pi\) | ||||
−0.930296 | + | 0.366810i | \(0.880450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6287.16 | 0.382030 | 0.191015 | − | 0.981587i | \(-0.438822\pi\) | ||||
0.191015 | + | 0.981587i | \(0.438822\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20040.1 | −1.21208 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18793.2i | 1.12624i | 0.826376 | + | 0.563119i | \(0.190399\pi\) | ||||
−0.826376 | + | 0.563119i | \(0.809601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 11832.2i | − 0.705833i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20827.2 | −1.23113 | −0.615563 | − | 0.788088i | \(-0.711071\pi\) | ||||
−0.615563 | + | 0.788088i | \(0.711071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6038.16 | 0.355306 | 0.177653 | − | 0.984093i | \(-0.443150\pi\) | ||||
0.177653 | + | 0.984093i | \(0.443150\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 5650.20i | − 0.329482i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1344.70i | − 0.0780612i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8234.79 | 0.473771 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19811.5 | −1.13474 | −0.567368 | − | 0.823464i | \(-0.692038\pi\) | ||||
−0.567368 | + | 0.823464i | \(0.692038\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22962.5i | 1.30357i | 0.758402 | + | 0.651787i | \(0.225980\pi\) | ||||
−0.758402 | + | 0.651787i | \(0.774020\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3961.90i | 0.223923i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33097.3 | 1.85422 | 0.927109 | − | 0.374791i | \(-0.122286\pi\) | ||||
0.927109 | + | 0.374791i | \(0.122286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10993.9 | −0.613222 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8662.84i | 0.478995i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21151.0i | 1.16443i | 0.813034 | + | 0.582216i | \(0.197814\pi\) | ||||
−0.813034 | + | 0.582216i | \(0.802186\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −547.267 | −0.0298691 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43071.9 | 2.34069 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 18752.3i | − 1.01036i | −0.863013 | − | 0.505182i | \(-0.831425\pi\) | ||||
0.863013 | − | 0.505182i | \(-0.168575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31039.1i | 1.66524i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10181.2 | 0.541588 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25964.1 | 1.37532 | 0.687660 | − | 0.726033i | \(-0.258638\pi\) | ||||
0.687660 | + | 0.726033i | \(0.258638\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9821.38i | 0.515868i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 7535.75i | − 0.394155i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11741.1 | 0.608998 | 0.304499 | − | 0.952513i | \(-0.401511\pi\) | ||||
0.304499 | + | 0.952513i | \(0.401511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12274.4 | −0.634010 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3640.74i | − 0.186502i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5637.87i | 0.287616i | 0.989606 | + | 0.143808i | \(0.0459348\pi\) | ||||
−0.989606 | + | 0.143808i | \(0.954065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37898.8 | 1.91756 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23807.3 | 1.19965 | 0.599825 | − | 0.800131i | \(-0.295237\pi\) | ||||
0.599825 | + | 0.800131i | \(0.295237\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 4587.96i | − 0.229307i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3556.31i | 0.177024i | 0.996075 | + | 0.0885122i | \(0.0282112\pi\) | ||||
−0.996075 | + | 0.0885122i | \(0.971789\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24054.6 | 1.18772 | 0.593860 | − | 0.804568i | \(-0.297603\pi\) | ||||
0.593860 | + | 0.804568i | \(0.297603\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16142.8 | 0.793860 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2167.86i | − 0.105757i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15373.0i | 0.746960i | 0.927638 | + | 0.373480i | \(0.121836\pi\) | ||||
−0.927638 | + | 0.373480i | \(0.878164\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21569.6 | −1.03973 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26000.8 | −1.24837 | −0.624184 | − | 0.781277i | \(-0.714569\pi\) | ||||
−0.624184 | + | 0.781277i | \(0.714569\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 9461.72i | − 0.450706i | −0.974277 | − | 0.225353i | \(-0.927646\pi\) | ||||
0.974277 | − | 0.225353i | \(-0.0723535\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 5696.06i | − 0.270264i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46380.2 | 2.18343 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11196.2 | 0.525028 | 0.262514 | − | 0.964928i | \(-0.415448\pi\) | ||||
0.262514 | + | 0.964928i | \(0.415448\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 39575.0i | − 1.84141i | −0.390255 | − | 0.920707i | \(-0.627613\pi\) | ||||
0.390255 | − | 0.920707i | \(-0.372387\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26591.2i | 1.23250i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40266.2 | 1.85197 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22192.1 | −1.01677 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 4743.53i | − 0.215674i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 25069.2i | − 1.13548i | −0.823209 | − | 0.567739i | \(-0.807818\pi\) | ||||
0.823209 | − | 0.567739i | \(-0.192182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7289.58 | 0.327671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19058.4 | −0.853448 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5639.39i | 0.250637i | 0.992117 | + | 0.125318i | \(0.0399952\pi\) | ||||
−0.992117 | + | 0.125318i | \(0.960005\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7762.31i | 0.343693i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11189.2 | −0.491729 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1731.33 | 0.0758030 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34032.0i | 1.47899i | 0.673163 | + | 0.739494i | \(0.264935\pi\) | ||||
−0.673163 | + | 0.739494i | \(0.735065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20119.5i | 0.871137i | 0.900156 | + | 0.435569i | \(0.143453\pi\) | ||||
−0.900156 | + | 0.435569i | \(0.856547\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6038.49 | 0.259532 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35430.0 | 1.51718 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 9057.81i | − 0.385042i | −0.981293 | − | 0.192521i | \(-0.938334\pi\) | ||||
0.981293 | − | 0.192521i | \(-0.0616664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 26277.7i | − 1.11298i | −0.830853 | − | 0.556491i | \(-0.812147\pi\) | ||||
0.830853 | − | 0.556491i | \(-0.187853\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21737.7 | 0.914018 | 0.457009 | − | 0.889462i | \(-0.348921\pi\) | ||||
0.457009 | + | 0.889462i | \(0.348921\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27552.6 | −1.15433 | −0.577167 | − | 0.816626i | \(-0.695842\pi\) | ||||
−0.577167 | + | 0.816626i | \(0.695842\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 31062.3i | − 1.29201i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 8485.65i | − 0.351686i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12231.7 | −0.503320 | −0.251660 | − | 0.967816i | \(-0.580977\pi\) | ||||
−0.251660 | + | 0.967816i | \(0.580977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22785.1 | 0.934236 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4612.48i | 0.187780i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6829.56i | 0.277056i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9511.00 | −0.383117 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2257.34 | 0.0906093 | 0.0453046 | − | 0.998973i | \(-0.485574\pi\) | ||||
0.0453046 | + | 0.998973i | \(0.485574\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24908.2i | 0.992820i | 0.868088 | + | 0.496410i | \(0.165349\pi\) | ||||
−0.868088 | + | 0.496410i | \(0.834651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11850.7i | 0.470710i | 0.971909 | + | 0.235355i | \(0.0756253\pi\) | ||||
−0.971909 | + | 0.235355i | \(0.924375\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43145.0 | 1.70182 | 0.850910 | − | 0.525311i | \(-0.176051\pi\) | ||||
0.850910 | + | 0.525311i | \(0.176051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3707.13 | 0.145718 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 6452.01i | − 0.251864i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10618.3i | 0.413072i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11133.1 | 0.430133 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14333.4 | 0.551886 | 0.275943 | − | 0.961174i | \(-0.411010\pi\) | ||||
0.275943 | + | 0.961174i | \(0.411010\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5066.51i | 0.193752i | 0.995296 | + | 0.0968758i | \(0.0308850\pi\) | ||||
−0.995296 | + | 0.0968758i | \(0.969115\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 7046.42i | − 0.268551i | −0.990944 | − | 0.134276i | \(-0.957129\pi\) | ||||
0.990944 | − | 0.134276i | \(-0.0428708\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −52122.7 | −1.97307 | −0.986534 | − | 0.163559i | \(-0.947703\pi\) | ||||
−0.986534 | + | 0.163559i | \(0.947703\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6664.41 | −0.251425 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7256.67i | 0.271932i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 16987.4i | − 0.634444i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11714.7 | 0.434602 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18578.7 | −0.686955 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 7908.56i | − 0.290486i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 41205.1i | − 1.50848i | −0.656599 | − | 0.754240i | \(-0.728006\pi\) | ||||
0.656599 | − | 0.754240i | \(-0.271994\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34305.8 | 1.24764 | 0.623821 | − | 0.781567i | \(-0.285580\pi\) | ||||
0.623821 | + | 0.781567i | \(0.285580\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7990.37 | 0.289642 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17895.7i | 0.644458i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 43537.1i | − 1.56274i | −0.624068 | − | 0.781370i | \(-0.714521\pi\) | ||||
0.624068 | − | 0.781370i | \(-0.285479\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 51360.8 | 1.83160 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25750.9 | −0.915333 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 8764.21i | − 0.309520i | −0.987952 | − | 0.154760i | \(-0.950539\pi\) | ||||
0.987952 | − | 0.154760i | \(-0.0494605\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 29038.9i | − 1.02225i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16161.5 | 0.565281 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22745.0 | −0.793006 | −0.396503 | − | 0.918033i | \(-0.629776\pi\) | ||||
−0.396503 | + | 0.918033i | \(0.629776\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24740.5i | 0.857084i | 0.903522 | + | 0.428542i | \(0.140973\pi\) | ||||
−0.903522 | + | 0.428542i | \(0.859027\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12338.3i | 0.426078i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1886.69 | −0.0647405 | −0.0323703 | − | 0.999476i | \(-0.510306\pi\) | ||||
−0.0323703 | + | 0.999476i | \(0.510306\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25896.0 | 0.885796 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 36292.1i | − 1.23360i | −0.787122 | − | 0.616798i | \(-0.788430\pi\) | ||||
0.787122 | − | 0.616798i | \(-0.211570\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 20368.5i | − 0.690165i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16627.9 | 0.559900 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −55770.8 | −1.87207 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17008.7i | 0.567387i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12599.4i | 0.418996i | 0.977809 | + | 0.209498i | \(0.0671830\pi\) | ||||
−0.977809 | + | 0.209498i | \(0.932817\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41974.3 | −1.38725 | −0.693625 | − | 0.720336i | \(-0.743988\pi\) | ||||
−0.693625 | + | 0.720336i | \(0.743988\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 827.721 | 0.0272719 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 33488.8i | − 1.09662i | −0.836274 | − | 0.548312i | \(-0.815271\pi\) | ||||
0.836274 | − | 0.548312i | \(-0.184729\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 17472.1i | − 0.570387i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3461.54 | −0.112315 | −0.0561576 | − | 0.998422i | \(-0.517885\pi\) | ||||
−0.0561576 | + | 0.998422i | \(0.517885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14204.0 | 0.459470 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10856.5i | 0.349055i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 20067.6i | − 0.643256i | −0.946866 | − | 0.321628i | \(-0.895770\pi\) | ||||
0.946866 | − | 0.321628i | \(-0.104230\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3288.41 | 0.104774 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −821.726 | −0.0261026 | −0.0130513 | − | 0.999915i | \(-0.504154\pi\) | ||||
−0.0130513 | + | 0.999915i | \(0.504154\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.4.c.j.1727.9 | 12 | ||
3.2 | odd | 2 | inner | 1728.4.c.j.1727.3 | 12 | ||
4.3 | odd | 2 | inner | 1728.4.c.j.1727.10 | 12 | ||
8.3 | odd | 2 | 108.4.b.b.107.3 | ✓ | 12 | ||
8.5 | even | 2 | 108.4.b.b.107.9 | yes | 12 | ||
12.11 | even | 2 | inner | 1728.4.c.j.1727.4 | 12 | ||
24.5 | odd | 2 | 108.4.b.b.107.4 | yes | 12 | ||
24.11 | even | 2 | 108.4.b.b.107.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.b.b.107.3 | ✓ | 12 | 8.3 | odd | 2 | ||
108.4.b.b.107.4 | yes | 12 | 24.5 | odd | 2 | ||
108.4.b.b.107.9 | yes | 12 | 8.5 | even | 2 | ||
108.4.b.b.107.10 | yes | 12 | 24.11 | even | 2 | ||
1728.4.c.j.1727.3 | 12 | 3.2 | odd | 2 | inner | ||
1728.4.c.j.1727.4 | 12 | 12.11 | even | 2 | inner | ||
1728.4.c.j.1727.9 | 12 | 1.1 | even | 1 | trivial | ||
1728.4.c.j.1727.10 | 12 | 4.3 | odd | 2 | inner |