Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(1567,1728)]
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, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1567");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.b (of order \(2\), degree \(1\), 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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.116304318664704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + x^{10} + 6x^{9} - 9x^{8} - 2x^{7} + 18x^{6} - 4x^{5} - 36x^{4} + 48x^{3} + 16x^{2} - 64x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.6 | ||
Root | \(0.828615 + 1.14604i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1567 |
Dual form | 1728.3.b.j.1567.7 |
$q$-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 | ||||||||
\(5\) | − 2.64040i | − 0.528081i | −0.964512 | − | 0.264040i | \(-0.914945\pi\) | ||||
0.964512 | − | 0.264040i | \(-0.0850552\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.30833i | 1.18690i | 0.804870 | + | 0.593452i | \(0.202235\pi\) | ||||
−0.804870 | + | 0.593452i | \(0.797765\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.7629 | −1.70572 | −0.852859 | − | 0.522141i | \(-0.825133\pi\) | ||||
−0.852859 | + | 0.522141i | \(0.825133\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 22.3117i | 1.71628i | 0.513415 | + | 0.858141i | \(0.328380\pi\) | ||||
−0.513415 | + | 0.858141i | \(0.671620\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −23.4983 | −1.38225 | −0.691126 | − | 0.722734i | \(-0.742885\pi\) | ||||
−0.691126 | + | 0.722734i | \(0.742885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.93333 | −0.522807 | −0.261403 | − | 0.965230i | \(-0.584185\pi\) | ||||
−0.261403 | + | 0.965230i | \(0.584185\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 32.3517i | − 1.40659i | −0.710896 | − | 0.703297i | \(-0.751710\pi\) | ||||
0.710896 | − | 0.703297i | \(-0.248290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.0283 | 0.721131 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.45525i | 0.291560i | 0.989317 | + | 0.145780i | \(0.0465692\pi\) | ||||
−0.989317 | + | 0.145780i | \(0.953431\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 46.9532i | − 1.51462i | −0.653055 | − | 0.757310i | \(-0.726513\pi\) | ||||
0.653055 | − | 0.757310i | \(-0.273487\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 21.9373 | 0.626781 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 28.3219i | − 0.765457i | −0.923861 | − | 0.382728i | \(-0.874984\pi\) | ||||
0.923861 | − | 0.382728i | \(-0.125016\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 77.7915 | 1.89735 | 0.948677 | − | 0.316246i | \(-0.102422\pi\) | ||||
0.948677 | + | 0.316246i | \(0.102422\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 58.4797 | 1.35999 | 0.679997 | − | 0.733215i | \(-0.261981\pi\) | ||||
0.679997 | + | 0.733215i | \(0.261981\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 54.2933i | − 1.15518i | −0.816329 | − | 0.577588i | \(-0.803994\pi\) | ||||
0.816329 | − | 0.577588i | \(-0.196006\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −20.0283 | −0.408740 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.81484i | 0.109714i | 0.998494 | + | 0.0548570i | \(0.0174703\pi\) | ||||
−0.998494 | + | 0.0548570i | \(0.982530\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 49.5416i | 0.900757i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −47.5795 | −0.806432 | −0.403216 | − | 0.915105i | \(-0.632108\pi\) | ||||
−0.403216 | + | 0.915105i | \(0.632108\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 27.7128i | − 0.454308i | −0.973859 | − | 0.227154i | \(-0.927058\pi\) | ||||
0.973859 | − | 0.227154i | \(-0.0729421\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 58.9118 | 0.906335 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 50.6336 | 0.755725 | 0.377862 | − | 0.925862i | \(-0.376659\pi\) | ||||
0.377862 | + | 0.925862i | \(0.376659\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.34824i | 0.103496i | 0.998660 | + | 0.0517482i | \(0.0164793\pi\) | ||||
−0.998660 | + | 0.0517482i | \(0.983521\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −29.4383 | −0.403265 | −0.201632 | − | 0.979461i | \(-0.564625\pi\) | ||||
−0.201632 | + | 0.979461i | \(0.564625\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 155.888i | − 2.02452i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 43.2050i | − 0.546899i | −0.961886 | − | 0.273450i | \(-0.911835\pi\) | ||||
0.961886 | − | 0.273450i | \(-0.0881647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.7858 | −0.129950 | −0.0649748 | − | 0.997887i | \(-0.520697\pi\) | ||||
−0.0649748 | + | 0.997887i | \(0.520697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 62.0450i | 0.729941i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 136.703 | 1.53599 | 0.767996 | − | 0.640454i | \(-0.221254\pi\) | ||||
0.767996 | + | 0.640454i | \(0.221254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −185.372 | −2.03706 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26.2280i | 0.276084i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −54.6465 | −0.563366 | −0.281683 | − | 0.959508i | \(-0.590893\pi\) | ||||
−0.281683 | + | 0.959508i | \(0.590893\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 123.165i | − 1.21946i | −0.792611 | − | 0.609728i | \(-0.791279\pi\) | ||||
0.792611 | − | 0.609728i | \(-0.208721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 82.0848i | 0.796940i | 0.917181 | + | 0.398470i | \(0.130459\pi\) | ||||
−0.917181 | + | 0.398470i | \(0.869541\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −180.466 | −1.68660 | −0.843299 | − | 0.537445i | \(-0.819390\pi\) | ||||
−0.843299 | + | 0.537445i | \(0.819390\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 22.2137i | 0.203796i | 0.994795 | + | 0.101898i | \(0.0324915\pi\) | ||||
−0.994795 | + | 0.101898i | \(0.967509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 139.381 | 1.23346 | 0.616732 | − | 0.787173i | \(-0.288456\pi\) | ||||
0.616732 | + | 0.787173i | \(0.288456\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −85.4215 | −0.742795 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 195.231i | − 1.64060i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 231.046 | 1.90947 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 113.612i | − 0.908896i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 80.3083i | 0.632349i | 0.948701 | + | 0.316175i | \(0.102399\pi\) | ||||
−0.948701 | + | 0.316175i | \(0.897601\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 55.7583 | 0.425636 | 0.212818 | − | 0.977092i | \(-0.431736\pi\) | ||||
0.212818 | + | 0.977092i | \(0.431736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 82.5293i | − 0.620521i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.28641 | −0.0312877 | −0.0156438 | − | 0.999878i | \(-0.504980\pi\) | ||||
−0.0156438 | + | 0.999878i | \(0.504980\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.84615 | −0.0564471 | −0.0282236 | − | 0.999602i | \(-0.508985\pi\) | ||||
−0.0282236 | + | 0.999602i | \(0.508985\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 418.631i | − 2.92749i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.3253 | 0.153967 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 269.056i | 1.80574i | 0.429912 | + | 0.902871i | \(0.358545\pi\) | ||||
−0.429912 | + | 0.902871i | \(0.641455\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 179.626i | − 1.18958i | −0.803881 | − | 0.594789i | \(-0.797235\pi\) | ||||
0.803881 | − | 0.594789i | \(-0.202765\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −123.976 | −0.799842 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 145.890i | − 0.929238i | −0.885511 | − | 0.464619i | \(-0.846191\pi\) | ||||
0.885511 | − | 0.464619i | \(-0.153809\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 268.788 | 1.66949 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 100.496 | 0.616540 | 0.308270 | − | 0.951299i | \(-0.400250\pi\) | ||||
0.308270 | + | 0.951299i | \(0.400250\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 154.410i | − 0.924611i | −0.886721 | − | 0.462306i | \(-0.847022\pi\) | ||||
0.886721 | − | 0.462306i | \(-0.152978\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −328.810 | −1.94562 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 57.6442i | 0.333203i | 0.986024 | + | 0.166602i | \(0.0532794\pi\) | ||||
−0.986024 | + | 0.166602i | \(0.946721\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 149.785i | 0.855913i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −83.2753 | −0.465225 | −0.232613 | − | 0.972569i | \(-0.574727\pi\) | ||||
−0.232613 | + | 0.972569i | \(0.574727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 227.811i | 1.25862i | 0.777153 | + | 0.629311i | \(0.216663\pi\) | ||||
−0.777153 | + | 0.629311i | \(0.783337\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −74.7813 | −0.404223 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 440.896 | 2.35773 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 28.0652i | − 0.146938i | −0.997297 | − | 0.0734692i | \(-0.976593\pi\) | ||||
0.997297 | − | 0.0734692i | \(-0.0234071\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −310.951 | −1.61115 | −0.805573 | − | 0.592496i | \(-0.798142\pi\) | ||||
−0.805573 | + | 0.592496i | \(0.798142\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 177.071i | − 0.898838i | −0.893321 | − | 0.449419i | \(-0.851631\pi\) | ||||
0.893321 | − | 0.449419i | \(-0.148369\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 183.708i | − 0.923156i | −0.887100 | − | 0.461578i | \(-0.847283\pi\) | ||||
0.887100 | − | 0.461578i | \(-0.152717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −70.2489 | −0.346054 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 205.401i | − 1.00196i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 186.378 | 0.891761 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −198.513 | −0.940821 | −0.470411 | − | 0.882448i | \(-0.655894\pi\) | ||||
−0.470411 | + | 0.882448i | \(0.655894\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 154.410i | − 0.718186i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 390.103 | 1.79771 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 524.286i | − 2.37233i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2.68500i | − 0.0120403i | −0.999982 | − | 0.00602017i | \(-0.998084\pi\) | ||||
0.999982 | − | 0.00602017i | \(-0.00191629\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −337.120 | −1.48511 | −0.742555 | − | 0.669786i | \(-0.766386\pi\) | ||||
−0.742555 | + | 0.669786i | \(0.766386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 46.9618i | − 0.205073i | −0.994729 | − | 0.102537i | \(-0.967304\pi\) | ||||
0.994729 | − | 0.102537i | \(-0.0326959\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −86.6965 | −0.372088 | −0.186044 | − | 0.982541i | \(-0.559567\pi\) | ||||
−0.186044 | + | 0.982541i | \(0.559567\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −143.356 | −0.610026 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 149.408i | − 0.625138i | −0.949895 | − | 0.312569i | \(-0.898811\pi\) | ||||
0.949895 | − | 0.312569i | \(-0.101189\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 338.559 | 1.40481 | 0.702405 | − | 0.711778i | \(-0.252110\pi\) | ||||
0.702405 | + | 0.711778i | \(0.252110\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 52.8827i | 0.215848i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 221.629i | − 0.897284i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 117.462 | 0.467976 | 0.233988 | − | 0.972239i | \(-0.424822\pi\) | ||||
0.233988 | + | 0.972239i | \(0.424822\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 607.011i | 2.39925i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 79.7319 | 0.310241 | 0.155120 | − | 0.987896i | \(-0.450423\pi\) | ||||
0.155120 | + | 0.987896i | \(0.450423\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 235.308 | 0.908524 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 70.1112i | 0.266582i | 0.991077 | + | 0.133291i | \(0.0425546\pi\) | ||||
−0.991077 | + | 0.133291i | \(0.957445\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.3535 | 0.0579379 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 128.891i | − 0.479147i | −0.970878 | − | 0.239574i | \(-0.922992\pi\) | ||||
0.970878 | − | 0.239574i | \(-0.0770077\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 334.953i | 1.23599i | 0.786182 | + | 0.617995i | \(0.212055\pi\) | ||||
−0.786182 | + | 0.617995i | \(0.787945\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −338.262 | −1.23005 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 490.465i | − 1.77063i | −0.464991 | − | 0.885315i | \(-0.653942\pi\) | ||||
0.464991 | − | 0.885315i | \(-0.346058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 496.474 | 1.76681 | 0.883406 | − | 0.468608i | \(-0.155244\pi\) | ||||
0.883406 | + | 0.468608i | \(0.155244\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −323.319 | −1.14247 | −0.571235 | − | 0.820787i | \(-0.693535\pi\) | ||||
−0.571235 | + | 0.820787i | \(0.693535\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 646.317i | 2.25198i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 263.170 | 0.910621 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 238.720i | 0.814742i | 0.913263 | + | 0.407371i | \(0.133554\pi\) | ||||
−0.913263 | + | 0.407371i | \(0.866446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 125.629i | 0.425861i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 721.819 | 2.41411 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 485.868i | 1.61418i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −73.1730 | −0.239912 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −196.695 | −0.640699 | −0.320349 | − | 0.947299i | \(-0.603800\pi\) | ||||
−0.320349 | + | 0.947299i | \(0.603800\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 20.0012i | − 0.0643126i | −0.999483 | − | 0.0321563i | \(-0.989763\pi\) | ||||
0.999483 | − | 0.0321563i | \(-0.0102374\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −341.608 | −1.09140 | −0.545700 | − | 0.837981i | \(-0.683736\pi\) | ||||
−0.545700 | + | 0.837981i | \(0.683736\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 481.401i | − 1.51861i | −0.650732 | − | 0.759307i | \(-0.725538\pi\) | ||||
0.650732 | − | 0.759307i | \(-0.274462\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 158.645i | − 0.497319i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 233.416 | 0.722651 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 402.240i | 1.23766i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 451.086 | 1.37108 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 91.4065 | 0.276152 | 0.138076 | − | 0.990422i | \(-0.455908\pi\) | ||||
0.138076 | + | 0.990422i | \(0.455908\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 133.693i | − 0.399084i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −194.220 | −0.576320 | −0.288160 | − | 0.957582i | \(-0.593044\pi\) | ||||
−0.288160 | + | 0.957582i | \(0.593044\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 880.979i | 2.58352i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 240.707i | 0.701768i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 68.5829 | 0.197645 | 0.0988226 | − | 0.995105i | \(-0.468492\pi\) | ||||
0.0988226 | + | 0.995105i | \(0.468492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 536.933i | − 1.53849i | −0.638955 | − | 0.769244i | \(-0.720633\pi\) | ||||
0.638955 | − | 0.769244i | \(-0.279367\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −486.832 | −1.37913 | −0.689563 | − | 0.724226i | \(-0.742197\pi\) | ||||
−0.689563 | + | 0.724226i | \(0.742197\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.4023 | 0.0546544 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.1271i | 0.0867049i | 0.999060 | + | 0.0433525i | \(0.0138038\pi\) | ||||
−0.999060 | + | 0.0433525i | \(0.986196\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −262.329 | −0.726673 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 77.7291i | 0.212956i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 656.463i | − 1.78873i | −0.447340 | − | 0.894364i | \(-0.647629\pi\) | ||||
0.447340 | − | 0.894364i | \(-0.352371\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −48.3116 | −0.130220 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 285.162i | − 0.764508i | −0.924057 | − | 0.382254i | \(-0.875148\pi\) | ||||
0.924057 | − | 0.382254i | \(-0.124852\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −188.651 | −0.500399 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −96.1985 | −0.253822 | −0.126911 | − | 0.991914i | \(-0.540506\pi\) | ||||
−0.126911 | + | 0.991914i | \(0.540506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 542.017i | − 1.41519i | −0.706619 | − | 0.707594i | \(-0.749780\pi\) | ||||
0.706619 | − | 0.707594i | \(-0.250220\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −411.608 | −1.06911 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 251.966i | 0.647729i | 0.946104 | + | 0.323864i | \(0.104982\pi\) | ||||
−0.946104 | + | 0.323864i | \(0.895018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 760.209i | 1.94427i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −114.079 | −0.288807 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 534.951i | − 1.34748i | −0.738966 | − | 0.673742i | \(-0.764686\pi\) | ||||
0.738966 | − | 0.673742i | \(-0.235314\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −586.919 | −1.46364 | −0.731819 | − | 0.681499i | \(-0.761328\pi\) | ||||
−0.731819 | + | 0.681499i | \(0.761328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1047.60 | 2.59951 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 531.401i | 1.30565i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 364.507 | 0.891214 | 0.445607 | − | 0.895229i | \(-0.352988\pi\) | ||||
0.445607 | + | 0.895229i | \(0.352988\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 395.306i | − 0.957157i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.4789i | 0.0686239i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 181.773 | 0.433827 | 0.216913 | − | 0.976191i | \(-0.430401\pi\) | ||||
0.216913 | + | 0.976191i | \(0.430401\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 168.535i | − 0.400320i | −0.979763 | − | 0.200160i | \(-0.935854\pi\) | ||||
0.979763 | − | 0.200160i | \(-0.0641462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −423.633 | −0.996785 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 230.247 | 0.539220 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 373.929i | 0.867585i | 0.901013 | + | 0.433792i | \(0.142825\pi\) | ||||
−0.901013 | + | 0.433792i | \(0.857175\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 483.636 | 1.11694 | 0.558471 | − | 0.829524i | \(-0.311388\pi\) | ||||
0.558471 | + | 0.829524i | \(0.311388\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 321.360i | 0.735377i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 449.117i | − 1.02305i | −0.859270 | − | 0.511523i | \(-0.829081\pi\) | ||||
0.859270 | − | 0.511523i | \(-0.170919\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −361.663 | −0.816396 | −0.408198 | − | 0.912893i | \(-0.633843\pi\) | ||||
−0.408198 | + | 0.912893i | \(0.633843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 360.952i | − 0.811128i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −589.191 | −1.31223 | −0.656115 | − | 0.754661i | \(-0.727801\pi\) | ||||
−0.656115 | + | 0.754661i | \(0.727801\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1459.59 | −3.23635 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 489.458i | 1.07573i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −452.703 | −0.990597 | −0.495299 | − | 0.868723i | \(-0.664941\pi\) | ||||
−0.495299 | + | 0.868723i | \(0.664941\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 290.060i | − 0.629197i | −0.949225 | − | 0.314598i | \(-0.898130\pi\) | ||||
0.949225 | − | 0.314598i | \(-0.101870\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 389.267i | − 0.840749i | −0.907351 | − | 0.420374i | \(-0.861899\pi\) | ||||
0.907351 | − | 0.420374i | \(-0.138101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −175.827 | −0.376504 | −0.188252 | − | 0.982121i | \(-0.560282\pi\) | ||||
−0.188252 | + | 0.982121i | \(0.560282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 420.680i | 0.896972i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1097.25 | −2.31976 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −179.081 | −0.377012 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 321.473i | 0.671134i | 0.942016 | + | 0.335567i | \(0.108928\pi\) | ||||
−0.942016 | + | 0.335567i | \(0.891072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 631.909 | 1.31374 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 144.289i | 0.297503i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 244.014i | 0.501055i | 0.968109 | + | 0.250528i | \(0.0806041\pi\) | ||||
−0.968109 | + | 0.250528i | \(0.919396\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 239.563 | 0.487909 | 0.243955 | − | 0.969787i | \(-0.421555\pi\) | ||||
0.243955 | + | 0.969787i | \(0.421555\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 198.684i | − 0.403010i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −61.0516 | −0.122840 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 134.164 | 0.268865 | 0.134433 | − | 0.990923i | \(-0.457079\pi\) | ||||
0.134433 | + | 0.990923i | \(0.457079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 214.317i | − 0.426078i | −0.977044 | − | 0.213039i | \(-0.931664\pi\) | ||||
0.977044 | − | 0.213039i | \(-0.0683362\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −325.206 | −0.643971 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 453.973i | 0.891892i | 0.895060 | + | 0.445946i | \(0.147133\pi\) | ||||
−0.895060 | + | 0.445946i | \(0.852867\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 244.583i | − 0.478637i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 216.737 | 0.420849 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1018.70i | 1.97040i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 97.5418 | 0.187220 | 0.0936102 | − | 0.995609i | \(-0.470159\pi\) | ||||
0.0936102 | + | 0.995609i | \(0.470159\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −476.762 | −0.911590 | −0.455795 | − | 0.890085i | \(-0.650645\pi\) | ||||
−0.455795 | + | 0.890085i | \(0.650645\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1103.32i | 2.09359i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −517.630 | −0.978507 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1735.66i | 3.25639i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 476.503i | 0.890660i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 375.788 | 0.697195 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 987.446i | 1.82522i | 0.408826 | + | 0.912612i | \(0.365938\pi\) | ||||
−0.408826 | + | 0.912612i | \(0.634062\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 58.6532 | 0.107621 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 396.486 | 0.724837 | 0.362418 | − | 0.932016i | \(-0.381951\pi\) | ||||
0.362418 | + | 0.932016i | \(0.381951\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 83.9888i | − 0.152430i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 358.961 | 0.649117 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 488.922i | − 0.877778i | −0.898541 | − | 0.438889i | \(-0.855372\pi\) | ||||
0.898541 | − | 0.438889i | \(-0.144628\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1304.78i | 2.33413i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 417.788 | 0.742075 | 0.371037 | − | 0.928618i | \(-0.379002\pi\) | ||||
0.371037 | + | 0.928618i | \(0.379002\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 368.023i | − 0.651369i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −493.590 | −0.867469 | −0.433735 | − | 0.901041i | \(-0.642804\pi\) | ||||
−0.433735 | + | 0.901041i | \(0.642804\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 687.730 | 1.20443 | 0.602215 | − | 0.798334i | \(-0.294285\pi\) | ||||
0.602215 | + | 0.798334i | \(0.294285\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 583.244i | − 1.01434i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 206.939 | 0.358647 | 0.179324 | − | 0.983790i | \(-0.442609\pi\) | ||||
0.179324 | + | 0.983790i | \(0.442609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 89.6120i | − 0.154238i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 109.103i | − 0.187141i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 879.623 | 1.49851 | 0.749253 | − | 0.662284i | \(-0.230413\pi\) | ||||
0.749253 | + | 0.662284i | \(0.230413\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 466.402i | 0.791854i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 444.195 | 0.749064 | 0.374532 | − | 0.927214i | \(-0.377803\pi\) | ||||
0.374532 | + | 0.927214i | \(0.377803\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −515.490 | −0.866369 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1025.55i | 1.71211i | 0.516888 | + | 0.856053i | \(0.327090\pi\) | ||||
−0.516888 | + | 0.856053i | \(0.672910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.5617 | −0.0308846 | −0.0154423 | − | 0.999881i | \(-0.504916\pi\) | ||||
−0.0154423 | + | 0.999881i | \(0.504916\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 610.055i | − 1.00836i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 648.184i | − 1.06785i | −0.845533 | − | 0.533924i | \(-0.820717\pi\) | ||||
0.845533 | − | 0.533924i | \(-0.179283\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1211.37 | 1.98261 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 616.049i | − 1.00497i | −0.864585 | − | 0.502487i | \(-0.832418\pi\) | ||||
0.864585 | − | 0.502487i | \(-0.167582\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −321.805 | −0.521564 | −0.260782 | − | 0.965398i | \(-0.583980\pi\) | ||||
−0.260782 | + | 0.965398i | \(0.583980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 769.275 | 1.24277 | 0.621386 | − | 0.783505i | \(-0.286570\pi\) | ||||
0.621386 | + | 0.783505i | \(0.286570\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1135.78i | 1.82307i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 150.725 | 0.241160 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 665.516i | 1.05805i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 766.730i | − 1.21510i | −0.794280 | − | 0.607551i | \(-0.792152\pi\) | ||||
0.794280 | − | 0.607551i | \(-0.207848\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 212.046 | 0.333931 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 446.864i | − 0.701513i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 436.825 | 0.681474 | 0.340737 | − | 0.940159i | \(-0.389323\pi\) | ||||
0.340737 | + | 0.940159i | \(0.389323\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −276.284 | −0.429680 | −0.214840 | − | 0.976649i | \(-0.568923\pi\) | ||||
−0.214840 | + | 0.976649i | \(0.568923\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 795.622i | 1.22971i | 0.788640 | + | 0.614855i | \(0.210785\pi\) | ||||
−0.788640 | + | 0.614855i | \(0.789215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 892.729 | 1.37555 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 305.664i | − 0.468091i | −0.972226 | − | 0.234046i | \(-0.924804\pi\) | ||||
0.972226 | − | 0.234046i | \(-0.0751965\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 147.224i | − 0.224770i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 153.889 | 0.233519 | 0.116760 | − | 0.993160i | \(-0.462749\pi\) | ||||
0.116760 | + | 0.993160i | \(0.462749\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 38.0847i | − 0.0576167i | −0.999585 | − | 0.0288084i | \(-0.990829\pi\) | ||||
0.999585 | − | 0.0288084i | \(-0.00917126\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −217.911 | −0.327685 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 273.541 | 0.410107 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 519.973i | 0.774922i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 392.195 | 0.582757 | 0.291378 | − | 0.956608i | \(-0.405886\pi\) | ||||
0.291378 | + | 0.956608i | \(0.405886\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 917.262i | 1.35489i | 0.735573 | + | 0.677446i | \(0.236913\pi\) | ||||
−0.735573 | + | 0.677446i | \(0.763087\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 454.021i | − 0.668661i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1280.10 | −1.87424 | −0.937119 | − | 0.349010i | \(-0.886518\pi\) | ||||
−0.937119 | + | 0.349010i | \(0.886518\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.3179i | 0.0165224i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −129.739 | −0.188300 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1147.79 | 1.66106 | 0.830531 | − | 0.556972i | \(-0.188037\pi\) | ||||
0.830531 | + | 0.556972i | \(0.188037\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.7170i | 0.0298086i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1827.97 | −2.62262 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 450.531i | − 0.642697i | −0.946961 | − | 0.321349i | \(-0.895864\pi\) | ||||
0.946961 | − | 0.321349i | \(-0.104136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 281.331i | 0.400186i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1023.30 | 1.44738 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1071.57i | − 1.51139i | −0.654926 | − | 0.755693i | \(-0.727300\pi\) | ||||
0.654926 | − | 0.755693i | \(-0.272700\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1519.02 | −2.13046 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1105.36 | −1.54595 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 569.979i | 0.792739i | 0.918091 | + | 0.396370i | \(0.129730\pi\) | ||||
−0.918091 | + | 0.396370i | \(0.870270\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −681.987 | −0.945891 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 152.433i | 0.210253i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 699.311i | − 0.961914i | −0.876744 | − | 0.480957i | \(-0.840289\pi\) | ||||
0.876744 | − | 0.480957i | \(-0.159711\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1374.17 | −1.87985 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 175.235i | − 0.239065i | −0.992830 | − | 0.119533i | \(-0.961860\pi\) | ||||
0.992830 | − | 0.119533i | \(-0.0381396\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −950.032 | −1.28905 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 975.643 | 1.32022 | 0.660110 | − | 0.751169i | \(-0.270510\pi\) | ||||
0.660110 | + | 0.751169i | \(0.270510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 880.230i | − 1.18470i | −0.805682 | − | 0.592349i | \(-0.798201\pi\) | ||||
0.805682 | − | 0.592349i | \(-0.201799\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 710.415 | 0.953578 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1499.37i | − 2.00183i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 48.7538i | − 0.0649186i | −0.999473 | − | 0.0324593i | \(-0.989666\pi\) | ||||
0.999473 | − | 0.0324593i | \(-0.0103339\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −474.286 | −0.628194 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1194.56i | 1.57802i | 0.614382 | + | 0.789009i | \(0.289406\pi\) | ||||
−0.614382 | + | 0.789009i | \(0.710594\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1032.85 | 1.35722 | 0.678612 | − | 0.734497i | \(-0.262582\pi\) | ||||
0.678612 | + | 0.734497i | \(0.262582\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −184.559 | −0.241886 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1061.58i | − 1.38406i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −200.830 | −0.261157 | −0.130579 | − | 0.991438i | \(-0.541684\pi\) | ||||
−0.130579 | + | 0.991438i | \(0.541684\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 949.438i | 1.22825i | 0.789208 | + | 0.614126i | \(0.210491\pi\) | ||||
−0.789208 | + | 0.614126i | \(0.789509\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 846.486i | − 1.09224i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −772.729 | −0.991950 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 137.874i | − 0.176536i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −385.210 | −0.490713 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −646.331 | −0.821259 | −0.410630 | − | 0.911802i | \(-0.634691\pi\) | ||||
−0.410630 | + | 0.911802i | \(0.634691\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1158.03i | 1.46400i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 618.319 | 0.779721 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 37.5148i | − 0.0470700i | −0.999723 | − | 0.0235350i | \(-0.992508\pi\) | ||||
0.999723 | − | 0.0235350i | \(-0.00749211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1275.80i | 1.59674i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 552.348 | 0.687856 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 709.709i | − 0.881626i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −572.790 | −0.708023 | −0.354011 | − | 0.935241i | \(-0.615183\pi\) | ||||
−0.354011 | + | 0.935241i | \(0.615183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −486.350 | −0.599692 | −0.299846 | − | 0.953988i | \(-0.596935\pi\) | ||||
−0.299846 | + | 0.953988i | \(0.596935\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 265.350i | − 0.325583i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −580.898 | −0.711014 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 311.021i | − 0.378832i | −0.981897 | − | 0.189416i | \(-0.939341\pi\) | ||||
0.981897 | − | 0.189416i | \(-0.0606595\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 824.124i | 1.00137i | 0.865631 | + | 0.500683i | \(0.166918\pi\) | ||||
−0.865631 | + | 0.500683i | \(0.833082\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 918.441 | 1.11057 | 0.555285 | − | 0.831660i | \(-0.312609\pi\) | ||||
0.555285 | + | 0.831660i | \(0.312609\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 937.997i | 1.13148i | 0.824584 | + | 0.565740i | \(0.191409\pi\) | ||||
−0.824584 | + | 0.565740i | \(0.808591\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 470.630 | 0.564982 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −407.705 | −0.488269 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 612.844i | − 0.730446i | −0.930920 | − | 0.365223i | \(-0.880993\pi\) | ||||
0.930920 | − | 0.365223i | \(-0.119007\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 769.509 | 0.914993 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 868.191i | 1.02744i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1919.61i | 2.26636i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −916.261 | −1.07669 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 491.372i | 0.576051i | 0.957623 | + | 0.288026i | \(0.0929989\pi\) | ||||
−0.957623 | + | 0.288026i | \(0.907001\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 642.820 | 0.750082 | 0.375041 | − | 0.927008i | \(-0.377629\pi\) | ||||
0.375041 | + | 0.927008i | \(0.377629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −443.260 | −0.516018 | −0.258009 | − | 0.966142i | \(-0.583066\pi\) | ||||
−0.258009 | + | 0.966142i | \(0.583066\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 565.494i | − 0.655265i | −0.944805 | − | 0.327632i | \(-0.893749\pi\) | ||||
0.944805 | − | 0.327632i | \(-0.106251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 152.204 | 0.175958 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 810.652i | 0.932856i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1129.72i | 1.29704i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 943.925 | 1.07877 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 330.215i | 0.376528i | 0.982118 | + | 0.188264i | \(0.0602861\pi\) | ||||
−0.982118 | + | 0.188264i | \(0.939714\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −358.037 | −0.406398 | −0.203199 | − | 0.979137i | \(-0.565134\pi\) | ||||
−0.203199 | + | 0.979137i | \(0.565134\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −266.351 | −0.301643 | −0.150822 | − | 0.988561i | \(-0.548192\pi\) | ||||
−0.150822 | + | 0.988561i | \(0.548192\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1375.40i | − 1.55062i | −0.631581 | − | 0.775310i | \(-0.717594\pi\) | ||||
0.631581 | − | 0.775310i | \(-0.282406\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −667.228 | −0.750537 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 539.313i | 0.603934i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 219.880i | 0.245676i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 397.001 | 0.441603 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 136.639i | − 0.151652i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 601.512 | 0.664654 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −106.524 | −0.117446 | −0.0587230 | − | 0.998274i | \(-0.518703\pi\) | ||||
−0.0587230 | + | 0.998274i | \(0.518703\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 842.877i | − 0.925222i | −0.886561 | − | 0.462611i | \(-0.846913\pi\) | ||||
0.886561 | − | 0.462611i | \(-0.153087\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 202.373 | 0.221657 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 463.258i | 0.505189i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1388.07i | − 1.51041i | −0.655489 | − | 0.755205i | \(-0.727537\pi\) | ||||
0.655489 | − | 0.755205i | \(-0.272463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −163.951 | −0.177629 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 510.595i | − 0.551995i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −557.068 | −0.599643 | −0.299821 | − | 0.953995i | \(-0.596927\pi\) | ||||
−0.299821 | + | 0.953995i | \(0.596927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 198.947 | 0.213692 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1164.14i | − 1.24507i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 876.585 | 0.935523 | 0.467761 | − | 0.883855i | \(-0.345061\pi\) | ||||
0.467761 | + | 0.883855i | \(0.345061\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1290.14i | − 1.37103i | −0.728058 | − | 0.685515i | \(-0.759577\pi\) | ||||
0.728058 | − | 0.685515i | \(-0.240423\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2516.69i | − 2.66881i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −850.851 | −0.898470 | −0.449235 | − | 0.893414i | \(-0.648303\pi\) | ||||
−0.449235 | + | 0.893414i | \(0.648303\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 656.818i | − 0.692116i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 297.237 | 0.311896 | 0.155948 | − | 0.987765i | \(-0.450157\pi\) | ||||
0.155948 | + | 0.987765i | \(0.450157\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −74.1036 | −0.0775954 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 35.6129i | − 0.0371355i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1243.61 | −1.29408 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 821.037i | 0.850815i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 943.377i | 0.975570i | 0.872964 | + | 0.487785i | \(0.162195\pi\) | ||||
−0.872964 | + | 0.487785i | \(0.837805\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 709.360 | 0.730546 | 0.365273 | − | 0.930900i | \(-0.380976\pi\) | ||||
0.365273 | + | 0.930900i | \(0.380976\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 65.1884i | − 0.0669973i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −295.503 | −0.302459 | −0.151230 | − | 0.988499i | \(-0.548323\pi\) | ||||
−0.151230 | + | 0.988499i | \(0.548323\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2564.95 | −2.61997 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 559.879i | 0.569561i | 0.958593 | + | 0.284781i | \(0.0919208\pi\) | ||||
−0.958593 | + | 0.284781i | \(0.908079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −467.539 | −0.474659 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1891.92i | − 1.91296i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1327.50i | − 1.33955i | −0.742563 | − | 0.669776i | \(-0.766390\pi\) | ||||
0.742563 | − | 0.669776i | \(-0.233610\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −485.064 | −0.487501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 878.699i | 0.881343i | 0.897668 | + | 0.440672i | \(0.145260\pi\) | ||||
−0.897668 | + | 0.440672i | \(0.854740\pi\) | |||||||
\(998\) | 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 | 1728.3.b.j.1567.6 | yes | 12 | |
3.2 | odd | 2 | 1728.3.b.i.1567.8 | yes | 12 | ||
4.3 | odd | 2 | inner | 1728.3.b.j.1567.5 | yes | 12 | |
8.3 | odd | 2 | inner | 1728.3.b.j.1567.7 | yes | 12 | |
8.5 | even | 2 | inner | 1728.3.b.j.1567.8 | yes | 12 | |
12.11 | even | 2 | 1728.3.b.i.1567.7 | yes | 12 | ||
24.5 | odd | 2 | 1728.3.b.i.1567.6 | yes | 12 | ||
24.11 | even | 2 | 1728.3.b.i.1567.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.3.b.i.1567.5 | ✓ | 12 | 24.11 | even | 2 | ||
1728.3.b.i.1567.6 | yes | 12 | 24.5 | odd | 2 | ||
1728.3.b.i.1567.7 | yes | 12 | 12.11 | even | 2 | ||
1728.3.b.i.1567.8 | yes | 12 | 3.2 | odd | 2 | ||
1728.3.b.j.1567.5 | yes | 12 | 4.3 | odd | 2 | inner | |
1728.3.b.j.1567.6 | yes | 12 | 1.1 | even | 1 | trivial | |
1728.3.b.j.1567.7 | yes | 12 | 8.3 | odd | 2 | inner | |
1728.3.b.j.1567.8 | yes | 12 | 8.5 | even | 2 | inner |