Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(865,1728)]
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([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.865");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.d (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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.592240896.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 7x^{6} + 40x^{4} - 63x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 865.1 | ||
Root | \(-1.99426 - 1.15139i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.865 |
Dual form | 1728.4.d.f.865.6 |
$q$-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 | ||||||||
\(5\) | − 12.4900i | − 1.11714i | −0.829458 | − | 0.558570i | \(-0.811350\pi\) | ||||
0.829458 | − | 0.558570i | \(-0.188650\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.1244 | −0.654654 | −0.327327 | − | 0.944911i | \(-0.606148\pi\) | ||||
−0.327327 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21.6333i | 0.592972i | 0.955037 | + | 0.296486i | \(0.0958147\pi\) | ||||
−0.955037 | + | 0.296486i | \(0.904185\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 15.5885i | − 0.332574i | −0.986077 | − | 0.166287i | \(-0.946822\pi\) | ||||
0.986077 | − | 0.166287i | \(-0.0531778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 64.8999 | 0.925914 | 0.462957 | − | 0.886381i | \(-0.346788\pi\) | ||||
0.462957 | + | 0.886381i | \(0.346788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 49.0000i | 0.591651i | 0.955242 | + | 0.295826i | \(0.0955947\pi\) | ||||
−0.955242 | + | 0.295826i | \(0.904405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −62.4500 | −0.566162 | −0.283081 | − | 0.959096i | \(-0.591356\pi\) | ||||
−0.283081 | + | 0.959096i | \(0.591356\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −31.0000 | −0.248000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 24.9800i | 0.159954i | 0.996797 | + | 0.0799770i | \(0.0254847\pi\) | ||||
−0.996797 | + | 0.0799770i | \(0.974515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −24.2487 | −0.140490 | −0.0702451 | − | 0.997530i | \(-0.522378\pi\) | ||||
−0.0702451 | + | 0.997530i | \(0.522378\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 151.433i | 0.731339i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 102.191i | − 0.454057i | −0.973888 | − | 0.227028i | \(-0.927099\pi\) | ||||
0.973888 | − | 0.227028i | \(-0.0729010\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 346.133 | 1.31846 | 0.659230 | − | 0.751941i | \(-0.270882\pi\) | ||||
0.659230 | + | 0.751941i | \(0.270882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 260.000i | 0.922084i | 0.887378 | + | 0.461042i | \(0.152524\pi\) | ||||
−0.887378 | + | 0.461042i | \(0.847476\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −362.210 | −1.12412 | −0.562061 | − | 0.827096i | \(-0.689991\pi\) | ||||
−0.562061 | + | 0.827096i | \(0.689991\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −196.000 | −0.571429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 574.540i | 1.48904i | 0.667600 | + | 0.744520i | \(0.267322\pi\) | ||||
−0.667600 | + | 0.744520i | \(0.732678\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 270.200 | 0.662432 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 324.500i | 0.716038i | 0.933714 | + | 0.358019i | \(0.116548\pi\) | ||||
−0.933714 | + | 0.358019i | \(0.883452\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 174.937i | − 0.367187i | −0.983002 | − | 0.183593i | \(-0.941227\pi\) | ||||
0.983002 | − | 0.183593i | \(-0.0587730\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −194.700 | −0.371531 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 241.000i | − 0.439445i | −0.975562 | − | 0.219723i | \(-0.929485\pi\) | ||||
0.975562 | − | 0.219723i | \(-0.0705152\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 249.800 | 0.417546 | 0.208773 | − | 0.977964i | \(-0.433053\pi\) | ||||
0.208773 | + | 0.977964i | \(0.433053\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 353.000 | 0.565966 | 0.282983 | − | 0.959125i | \(-0.408676\pi\) | ||||
0.282983 | + | 0.959125i | \(0.408676\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 262.290i | − 0.388191i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.19615 | 0.00740016 | 0.00370008 | − | 0.999993i | \(-0.498822\pi\) | ||||
0.00370008 | + | 0.999993i | \(0.498822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1038.40i | 1.37324i | 0.727016 | + | 0.686621i | \(0.240907\pi\) | ||||
−0.727016 | + | 0.686621i | \(0.759093\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 810.600i | − 1.03438i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 800.432 | 0.953322 | 0.476661 | − | 0.879087i | \(-0.341847\pi\) | ||||
0.476661 | + | 0.879087i | \(0.341847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 189.000i | 0.217721i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 612.010 | 0.660957 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1111.00 | 1.16294 | 0.581469 | − | 0.813569i | \(-0.302478\pi\) | ||||
0.581469 | + | 0.813569i | \(0.302478\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 24.9800i | − 0.0246099i | −0.999924 | − | 0.0123050i | \(-0.996083\pi\) | ||||
0.999924 | − | 0.0123050i | \(-0.00391689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1557.11 | 1.48958 | 0.744791 | − | 0.667298i | \(-0.232549\pi\) | ||||
0.744791 | + | 0.667298i | \(0.232549\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1752.30i | − 1.58319i | −0.611048 | − | 0.791594i | \(-0.709252\pi\) | ||||
0.611048 | − | 0.791594i | \(-0.290748\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 69.2820i | 0.0608809i | 0.999537 | + | 0.0304404i | \(0.00969099\pi\) | ||||
−0.999537 | + | 0.0304404i | \(0.990309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −281.233 | −0.234125 | −0.117063 | − | 0.993125i | \(-0.537348\pi\) | ||||
−0.117063 | + | 0.993125i | \(0.537348\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 780.000i | 0.632482i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −786.870 | −0.606153 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 863.000 | 0.648385 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1174.06i | − 0.840089i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1125.83 | 0.786626 | 0.393313 | − | 0.919405i | \(-0.371329\pi\) | ||||
0.393313 | + | 0.919405i | \(0.371329\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1341.27i | − 0.894556i | −0.894395 | − | 0.447278i | \(-0.852393\pi\) | ||||
0.894395 | − | 0.447278i | \(-0.147607\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 594.093i | − 0.387327i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3093.56 | −1.92920 | −0.964602 | − | 0.263710i | \(-0.915054\pi\) | ||||
−0.964602 | + | 0.263710i | \(0.915054\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 233.000i | − 0.142178i | −0.997470 | − | 0.0710892i | \(-0.977352\pi\) | ||||
0.997470 | − | 0.0710892i | \(-0.0226475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 337.230 | 0.197207 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 312.000 | 0.178691 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1199.04i | 0.659256i | 0.944111 | + | 0.329628i | \(0.106923\pi\) | ||||
−0.944111 | + | 0.329628i | \(0.893077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2149.48 | 1.15842 | 0.579211 | − | 0.815177i | \(-0.303361\pi\) | ||||
0.579211 | + | 0.815177i | \(0.303361\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 302.866i | 0.156947i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3062.27i | − 1.55666i | −0.627856 | − | 0.778329i | \(-0.716067\pi\) | ||||
0.627856 | − | 0.778329i | \(-0.283933\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 757.166 | 0.370640 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2095.00i | 1.00671i | 0.864081 | + | 0.503353i | \(0.167900\pi\) | ||||
−0.864081 | + | 0.503353i | \(0.832100\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 287.270 | 0.133111 | 0.0665557 | − | 0.997783i | \(-0.478799\pi\) | ||||
0.0665557 | + | 0.997783i | \(0.478799\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1954.00 | 0.889395 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 4246.60i | − 1.86626i | −0.359540 | − | 0.933130i | \(-0.617066\pi\) | ||||
0.359540 | − | 0.933130i | \(-0.382934\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 375.855 | 0.162354 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2682.53i | − 1.12012i | −0.828452 | − | 0.560061i | \(-0.810778\pi\) | ||||
0.828452 | − | 0.560061i | \(-0.189222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2277.65i | − 0.935338i | −0.883904 | − | 0.467669i | \(-0.845094\pi\) | ||||
0.883904 | − | 0.467669i | \(-0.154906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1276.37 | −0.507244 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1404.00i | 0.549041i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 736.910 | 0.279167 | 0.139584 | − | 0.990210i | \(-0.455424\pi\) | ||||
0.139584 | + | 0.990210i | \(0.455424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −37.0000 | −0.0137996 | −0.00689979 | − | 0.999976i | \(-0.502196\pi\) | ||||
−0.00689979 | + | 0.999976i | \(0.502196\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3035.07i | 1.09766i | 0.835933 | + | 0.548832i | \(0.184927\pi\) | ||||
−0.835933 | + | 0.548832i | \(0.815073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4286.83 | 1.52706 | 0.763530 | − | 0.645772i | \(-0.223464\pi\) | ||||
0.763530 | + | 0.645772i | \(0.223464\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 302.866i | − 0.104715i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 4323.20i | − 1.47290i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1060.03 | −0.350832 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1829.00i | 0.596747i | 0.954449 | + | 0.298373i | \(0.0964440\pi\) | ||||
−0.954449 | + | 0.298373i | \(0.903556\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3247.40 | 1.03010 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 294.000 | 0.0919724 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1011.69i | − 0.307935i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1687.02 | 0.506597 | 0.253298 | − | 0.967388i | \(-0.418485\pi\) | ||||
0.253298 | + | 0.967388i | \(0.418485\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3461.33i | 1.01206i | 0.862517 | + | 0.506028i | \(0.168887\pi\) | ||||
−0.862517 | + | 0.506028i | \(0.831113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4579.54i | − 1.32151i | −0.750604 | − | 0.660753i | \(-0.770237\pi\) | ||||
0.750604 | − | 0.660753i | \(-0.229763\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2293.13 | 0.644755 | 0.322378 | − | 0.946611i | \(-0.395518\pi\) | ||||
0.322378 | + | 0.946611i | \(0.395518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4524.00i | 1.25580i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −724.420 | −0.196062 | −0.0980310 | − | 0.995183i | \(-0.531254\pi\) | ||||
−0.0980310 | + | 0.995183i | \(0.531254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −379.000 | −0.101301 | −0.0506505 | − | 0.998716i | \(-0.516129\pi\) | ||||
−0.0506505 | + | 0.998716i | \(0.516129\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2448.04i | 0.638365i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 763.834 | 0.196768 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3201.73i | 0.805145i | 0.915388 | + | 0.402572i | \(0.131884\pi\) | ||||
−0.915388 | + | 0.402572i | \(0.868116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1351.00i | − 0.335718i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2293.13 | 0.556582 | 0.278291 | − | 0.960497i | \(-0.410232\pi\) | ||||
0.278291 | + | 0.960497i | \(0.410232\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1239.00i | 0.297250i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −824.340 | −0.193274 | −0.0966368 | − | 0.995320i | \(-0.530809\pi\) | ||||
−0.0966368 | + | 0.995320i | \(0.530809\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7176.00 | 1.66346 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 262.290i | 0.0594502i | 0.999558 | + | 0.0297251i | \(0.00946318\pi\) | ||||
−0.999558 | + | 0.0297251i | \(0.990537\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8197.80 | 1.83757 | 0.918784 | − | 0.394762i | \(-0.129173\pi\) | ||||
0.918784 | + | 0.394762i | \(0.129173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 670.633i | − 0.147057i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2438.73i | − 0.528985i | −0.964388 | − | 0.264493i | \(-0.914796\pi\) | ||||
0.964388 | − | 0.264493i | \(-0.0852045\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2639.26 | 0.560303 | 0.280152 | − | 0.959956i | \(-0.409615\pi\) | ||||
0.280152 | + | 0.959956i | \(0.409615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3292.00i | 0.691481i | 0.938330 | + | 0.345740i | \(0.112372\pi\) | ||||
−0.938330 | + | 0.345740i | \(0.887628\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4196.64 | −0.863135 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −701.000 | −0.142683 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3085.03i | 0.615117i | 0.951529 | + | 0.307559i | \(0.0995120\pi\) | ||||
−0.951529 | + | 0.307559i | \(0.900488\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4053.00 | 0.799914 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 973.499i | 0.188291i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3152.33i | − 0.603646i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2184.96 | −0.410199 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2372.00i | 0.440968i | 0.975391 | + | 0.220484i | \(0.0707637\pi\) | ||||
−0.975391 | + | 0.220484i | \(0.929236\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8705.53 | −1.58728 | −0.793642 | − | 0.608385i | \(-0.791818\pi\) | ||||
−0.793642 | + | 0.608385i | \(0.791818\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3337.00 | 0.602615 | 0.301307 | − | 0.953527i | \(-0.402577\pi\) | ||||
0.301307 | + | 0.953527i | \(0.402577\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1798.56i | 0.318666i | 0.987225 | + | 0.159333i | \(0.0509344\pi\) | ||||
−0.987225 | + | 0.159333i | \(0.949066\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −540.400 | −0.0948482 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3180.10i | 0.547818i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 483.242i | 0.0824783i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4391.56 | 0.735911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2057.00i | − 0.341580i | −0.985307 | − | 0.170790i | \(-0.945368\pi\) | ||||
0.985307 | − | 0.170790i | \(-0.0546320\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3010.09 | −0.490922 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6271.00 | 1.01366 | 0.506830 | − | 0.862046i | \(-0.330817\pi\) | ||||
0.506830 | + | 0.862046i | \(0.330817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 524.580i | − 0.0833067i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6535.03 | 1.02874 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5581.39i | 0.863472i | 0.902000 | + | 0.431736i | \(0.142099\pi\) | ||||
−0.902000 | + | 0.431736i | \(0.857901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 11034.9i | − 1.69251i | −0.532782 | − | 0.846253i | \(-0.678853\pi\) | ||||
0.532782 | − | 0.846253i | \(-0.321147\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8436.99 | 1.27211 | 0.636056 | − | 0.771643i | \(-0.280565\pi\) | ||||
0.636056 | + | 0.771643i | \(0.280565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 3120.00i | − 0.466457i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4259.09 | 0.626145 | 0.313073 | − | 0.949729i | \(-0.398642\pi\) | ||||
0.313073 | + | 0.949729i | \(0.398642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4458.00 | 0.649949 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4408.97i | − 0.632263i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5901.10 | 0.839332 | 0.419666 | − | 0.907679i | \(-0.362147\pi\) | ||||
0.419666 | + | 0.907679i | \(0.362147\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 6965.93i | − 0.974805i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 8651.59i | − 1.20097i | −0.799635 | − | 0.600486i | \(-0.794974\pi\) | ||||
0.799635 | − | 0.600486i | \(-0.205026\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 389.400 | 0.0531965 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 335.000i | 0.0454032i | 0.999742 | + | 0.0227016i | \(0.00722676\pi\) | ||||
−0.999742 | + | 0.0227016i | \(0.992773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14413.5 | 1.92296 | 0.961479 | − | 0.274877i | \(-0.0886372\pi\) | ||||
0.961479 | + | 0.274877i | \(0.0886372\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3276.00 | −0.433663 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1211.53i | 0.157910i | 0.996878 | + | 0.0789550i | \(0.0251583\pi\) | ||||
−0.996878 | + | 0.0789550i | \(0.974842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4053.00 | −0.524217 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 64.8999i | − 0.00826701i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13856.4i | 1.75172i | 0.482565 | + | 0.875860i | \(0.339705\pi\) | ||||
−0.482565 | + | 0.875860i | \(0.660295\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6360.19 | −0.792052 | −0.396026 | − | 0.918239i | \(-0.629611\pi\) | ||||
−0.396026 | + | 0.918239i | \(0.629611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 378.000i | 0.0467234i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2210.73 | 0.269243 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9389.00 | 1.13510 | 0.567550 | − | 0.823339i | \(-0.307891\pi\) | ||||
0.567550 | + | 0.823339i | \(0.307891\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3934.35i | − 0.468757i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12969.6 | 1.53410 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2358.03i | 0.274934i | 0.990506 | + | 0.137467i | \(0.0438961\pi\) | ||||
−0.990506 | + | 0.137467i | \(0.956104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1945.09i | 0.225173i | 0.993642 | + | 0.112587i | \(0.0359136\pi\) | ||||
−0.993642 | + | 0.112587i | \(0.964086\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2011.90 | −0.229627 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2121.00i | 0.240380i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16424.3 | −1.83558 | −0.917788 | − | 0.397072i | \(-0.870026\pi\) | ||||
−0.917788 | + | 0.397072i | \(0.870026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15662.0 | −1.73826 | −0.869131 | − | 0.494581i | \(-0.835321\pi\) | ||||
−0.869131 | + | 0.494581i | \(0.835321\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3060.05i | − 0.334970i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5996.36 | −0.651915 | −0.325957 | − | 0.945384i | \(-0.605687\pi\) | ||||
−0.325957 | + | 0.945384i | \(0.605687\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 7831.26i | − 0.839897i | −0.907548 | − | 0.419948i | \(-0.862048\pi\) | ||||
0.907548 | − | 0.419948i | \(-0.137952\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 9997.40i | − 1.06499i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11573.8 | −1.21649 | −0.608243 | − | 0.793751i | \(-0.708125\pi\) | ||||
−0.608243 | + | 0.793751i | \(0.708125\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7488.00i | 0.781810i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2360.61 | 0.243224 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5066.00 | 0.518550 | 0.259275 | − | 0.965803i | \(-0.416516\pi\) | ||||
0.259275 | + | 0.965803i | \(0.416516\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13376.8i | 1.35145i | 0.737153 | + | 0.675726i | \(0.236170\pi\) | ||||
−0.737153 | + | 0.675726i | \(0.763830\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6157.44 | −0.618057 | −0.309029 | − | 0.951053i | \(-0.600004\pi\) | ||||
−0.309029 | + | 0.951053i | \(0.600004\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6122.23i | 0.606644i | 0.952888 | + | 0.303322i | \(0.0980958\pi\) | ||||
−0.952888 | + | 0.303322i | \(0.901904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2921.97i | 0.287684i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5624.66 | −0.546770 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1519.00i | − 0.146729i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17610.9 | 1.67988 | 0.839940 | − | 0.542680i | \(-0.182590\pi\) | ||||
0.839940 | + | 0.542680i | \(0.182590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1593.00 | −0.151007 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 13876.4i | − 1.29916i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4442.71 | 0.413385 | 0.206692 | − | 0.978406i | \(-0.433730\pi\) | ||||
0.206692 | + | 0.978406i | \(0.433730\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 9367.22i | − 0.860971i | −0.902597 | − | 0.430486i | \(-0.858342\pi\) | ||||
0.902597 | − | 0.430486i | \(-0.141658\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1621.20i | 0.148104i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3028.66 | −0.273348 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 6088.00i | − 0.546165i | −0.961991 | − | 0.273082i | \(-0.911957\pi\) | ||||
0.961991 | − | 0.273082i | \(-0.0880432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3159.97 | 0.280111 | 0.140056 | − | 0.990144i | \(-0.455272\pi\) | ||||
0.140056 | + | 0.990144i | \(0.455272\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −312.000 | −0.0274927 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5632.99i | 0.490526i | 0.969457 | + | 0.245263i | \(0.0788743\pi\) | ||||
−0.969457 | + | 0.245263i | \(0.921126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4279.90 | −0.370512 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 19448.3i | − 1.66407i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 7835.80i | − 0.666573i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11963.2 | −1.00598 | −0.502992 | − | 0.864291i | \(-0.667768\pi\) | ||||
−0.502992 | + | 0.864291i | \(0.667768\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12611.0i | 1.05438i | 0.849748 | + | 0.527190i | \(0.176754\pi\) | ||||
−0.849748 | + | 0.527190i | \(0.823246\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1573.74 | −0.130082 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8267.00 | −0.679461 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5395.68i | − 0.438485i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21886.2 | −1.76864 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4240.13i | − 0.338841i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14873.1i | 1.18197i | 0.806683 | + | 0.590985i | \(0.201261\pi\) | ||||
−0.806683 | + | 0.590985i | \(0.798739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 865.332 | 0.0680124 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4291.00i | 0.335411i | 0.985837 | + | 0.167706i | \(0.0536358\pi\) | ||||
−0.985837 | + | 0.167706i | \(0.946364\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1224.02 | −0.0946370 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −63.0000 | −0.00484454 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8056.05i | 0.612829i | 0.951898 | + | 0.306414i | \(0.0991293\pi\) | ||||
−0.951898 | + | 0.306414i | \(0.900871\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4053.00 | 0.306661 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10124.4i | 0.757890i | 0.925419 | + | 0.378945i | \(0.123713\pi\) | ||||
−0.925419 | + | 0.378945i | \(0.876287\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3512.60i | 0.261551i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7723.09 | 0.569014 | 0.284507 | − | 0.958674i | \(-0.408170\pi\) | ||||
0.284507 | + | 0.958674i | \(0.408170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 21143.0i | − 1.54957i | −0.632222 | − | 0.774787i | \(-0.717857\pi\) | ||||
0.632222 | − | 0.774787i | \(-0.282143\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1935.95 | 0.140408 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20459.0 | −1.47612 | −0.738058 | − | 0.674737i | \(-0.764257\pi\) | ||||
−0.738058 | + | 0.674737i | \(0.764257\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 12589.9i | − 0.898998i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12429.2 | −0.882958 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 281.233i | − 0.0197747i | −0.999951 | − | 0.00988733i | \(-0.996853\pi\) | ||||
0.999951 | − | 0.00988733i | \(-0.00314729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1188.19i | − 0.0831212i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10297.5 | 0.713096 | 0.356548 | − | 0.934277i | \(-0.383954\pi\) | ||||
0.356548 | + | 0.934277i | \(0.383954\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9828.00i | 0.677158i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17261.2 | −1.17742 | −0.588708 | − | 0.808346i | \(-0.700363\pi\) | ||||
−0.588708 | + | 0.808346i | \(0.700363\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22646.0 | 1.53702 | 0.768510 | − | 0.639837i | \(-0.220998\pi\) | ||||
0.768510 | + | 0.639837i | \(0.220998\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 10778.9i | − 0.724336i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18510.4 | −1.23775 | −0.618876 | − | 0.785489i | \(-0.712412\pi\) | ||||
−0.618876 | + | 0.785489i | \(0.712412\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5646.29i | 0.373854i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22501.1i | 1.48256i | 0.671196 | + | 0.741280i | \(0.265781\pi\) | ||||
−0.671196 | + | 0.741280i | \(0.734219\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4651.16 | −0.303482 | −0.151741 | − | 0.988420i | \(-0.548488\pi\) | ||||
−0.151741 | + | 0.988420i | \(0.548488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 13067.0i | − 0.848477i | −0.905551 | − | 0.424238i | \(-0.860542\pi\) | ||||
0.905551 | − | 0.424238i | \(-0.139458\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9704.73 | −0.624096 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18539.0 | −1.18650 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 6632.19i | − 0.420418i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18250.6 | 1.15142 | 0.575710 | − | 0.817654i | \(-0.304726\pi\) | ||||
0.575710 | + | 0.817654i | \(0.304726\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 14061.6i | − 0.878771i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3055.34i | 0.190042i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20335.3 | 1.25304 | 0.626518 | − | 0.779407i | \(-0.284479\pi\) | ||||
0.626518 | + | 0.779407i | \(0.284479\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 23612.0i | − 1.44816i | −0.689716 | − | 0.724080i | \(-0.742265\pi\) | ||||
0.689716 | − | 0.724080i | \(-0.257735\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26029.2 | 1.58163 | 0.790813 | − | 0.612058i | \(-0.209658\pi\) | ||||
0.790813 | + | 0.612058i | \(0.209658\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7020.00 | −0.424590 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10341.7i | 0.619759i | 0.950776 | + | 0.309880i | \(0.100289\pi\) | ||||
−0.950776 | + | 0.309880i | \(0.899711\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16752.4 | −0.999344 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23580.3i | 1.39387i | 0.717136 | + | 0.696933i | \(0.245453\pi\) | ||||
−0.717136 | + | 0.696933i | \(0.754547\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 3230.27i | − 0.190080i | −0.995473 | − | 0.0950402i | \(-0.969702\pi\) | ||||
0.995473 | − | 0.0950402i | \(-0.0302980\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7420.22 | −0.432698 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1560.00i | − 0.0905599i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3784.47 | 0.217731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21911.0 | −1.25499 | −0.627494 | − | 0.778621i | \(-0.715919\pi\) | ||||
−0.627494 | + | 0.778621i | \(0.715919\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1711.13i | 0.0971404i | 0.998820 | + | 0.0485702i | \(0.0154665\pi\) | ||||
−0.998820 | + | 0.0485702i | \(0.984534\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13470.2 | −0.761321 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22888.0i | 1.28226i | 0.767431 | + | 0.641132i | \(0.221535\pi\) | ||||
−0.767431 | + | 0.641132i | \(0.778465\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38638.6i | 2.15519i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8956.19 | 0.495216 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 7796.00i | − 0.429195i | −0.976703 | − | 0.214598i | \(-0.931156\pi\) | ||||
0.976703 | − | 0.214598i | \(-0.0688440\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2910.17 | −0.158833 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22464.0 | 1.22078 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21994.9i | 1.18507i | 0.805544 | + | 0.592536i | \(0.201873\pi\) | ||||
−0.805544 | + | 0.592536i | \(0.798127\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5007.36 | 0.268643 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 302.866i | 0.0161110i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28043.6i | 1.48547i | 0.669583 | + | 0.742737i | \(0.266473\pi\) | ||||
−0.669583 | + | 0.742737i | \(0.733527\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1514.33 | 0.0795402 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 4212.00i | − 0.220308i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34622.3 | −1.79582 | −0.897909 | − | 0.440182i | \(-0.854914\pi\) | ||||
−0.897909 | + | 0.440182i | \(0.854914\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18879.0 | −0.975160 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 774.380i | − 0.0396686i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12834.5 | −0.654753 | −0.327376 | − | 0.944894i | \(-0.606164\pi\) | ||||
−0.327376 | + | 0.944894i | \(0.606164\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16874.0i | 0.853771i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 17223.5i | − 0.867892i | −0.900939 | − | 0.433946i | \(-0.857121\pi\) | ||||
0.900939 | − | 0.433946i | \(-0.142879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5213.63 | 0.260579 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 9964.00i | − 0.495983i | −0.968762 | − | 0.247992i | \(-0.920229\pi\) | ||||
0.968762 | − | 0.247992i | \(-0.0797706\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17323.6 | −0.855373 | −0.427687 | − | 0.903927i | \(-0.640671\pi\) | ||||
−0.427687 | + | 0.903927i | \(0.640671\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14976.0 | 0.736481 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21245.5i | 1.03644i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24028.7 | −1.16754 | −0.583769 | − | 0.811920i | \(-0.698423\pi\) | ||||
−0.583769 | + | 0.811920i | \(0.698423\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 26846.9i | − 1.29412i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38408.2i | 1.84408i | 0.387091 | + | 0.922041i | \(0.373480\pi\) | ||||
−0.387091 | + | 0.922041i | \(0.626520\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23169.3 | 1.10366 | 0.551830 | − | 0.833957i | \(-0.313930\pi\) | ||||
0.551830 | + | 0.833957i | \(0.313930\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 840.000i | − 0.0398559i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5058.45 | 0.238136 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8833.00 | −0.414208 | −0.207104 | − | 0.978319i | \(-0.566404\pi\) | ||||
−0.207104 | + | 0.978319i | \(0.566404\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12490.0i | 0.581156i | 0.956851 | + | 0.290578i | \(0.0938476\pi\) | ||||
−0.956851 | + | 0.290578i | \(0.906152\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 751.710 | 0.0348416 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16960.5i | 0.780069i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5404.00i | 0.247593i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38247.7 | −1.73900 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 39791.0i | − 1.80228i | −0.433526 | − | 0.901141i | \(-0.642731\pi\) | ||||
0.433526 | − | 0.901141i | \(-0.357269\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3409.77 | 0.153271 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2727.00 | −0.122117 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28052.5i | 1.24676i | 0.781917 | + | 0.623382i | \(0.214242\pi\) | ||||
−0.781917 | + | 0.623382i | \(0.785758\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23507.4 | −1.04084 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7636.56i | 0.335602i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 9457.00i | − 0.414056i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37815.0 | 1.64339 | 0.821697 | − | 0.569925i | \(-0.193028\pi\) | ||||
0.821697 | + | 0.569925i | \(0.193028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1460.00i | 0.0632152i | 0.999500 | + | 0.0316076i | \(0.0100627\pi\) | ||||
−0.999500 | + | 0.0316076i | \(0.989937\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26166.5 | 1.12463 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12740.0 | −0.545552 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 28714.5i | − 1.22064i | −0.792156 | − | 0.610319i | \(-0.791041\pi\) | ||||
0.792156 | − | 0.610319i | \(-0.208959\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34424.5 | −1.45804 | −0.729018 | − | 0.684495i | \(-0.760023\pi\) | ||||
−0.729018 | + | 0.684495i | \(0.760023\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 13131.4i | − 0.552145i | −0.961137 | − | 0.276073i | \(-0.910967\pi\) | ||||
0.961137 | − | 0.276073i | \(-0.0890330\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31982.3i | 1.33992i | 0.742398 | + | 0.669959i | \(0.233688\pi\) | ||||
−0.742398 | + | 0.669959i | \(0.766312\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12720.4 | −0.529094 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 3588.00i | − 0.148704i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1673.66 | −0.0688691 | −0.0344345 | − | 0.999407i | \(-0.510963\pi\) | ||||
−0.0344345 | + | 0.999407i | \(0.510963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23765.0 | 0.974415 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 24405.5i | − 0.993578i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10463.3 | −0.424467 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6381.83i | 0.257070i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 6663.20i | − 0.267460i | −0.991018 | − | 0.133730i | \(-0.957304\pi\) | ||||
0.991018 | − | 0.133730i | \(-0.0426955\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3980.53 | 0.158661 | 0.0793304 | − | 0.996848i | \(-0.474722\pi\) | ||||
0.0793304 | + | 0.996848i | \(0.474722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 511.000i | − 0.0202970i | −0.999949 | − | 0.0101485i | \(-0.996770\pi\) | ||||
0.999949 | − | 0.0101485i | \(-0.00323042\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21570.2 | 0.850821 | 0.425411 | − | 0.905000i | \(-0.360130\pi\) | ||||
0.425411 | + | 0.905000i | \(0.360130\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −53040.0 | −2.08487 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 112.410i | 0.00438809i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3756.82 | −0.146148 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14234.7i | 0.549967i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11474.8i | 0.441822i | 0.975294 | + | 0.220911i | \(0.0709030\pi\) | ||||
−0.975294 | + | 0.220911i | \(0.929097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28707.4 | 1.09782 | 0.548909 | − | 0.835882i | \(-0.315044\pi\) | ||||
0.548909 | + | 0.835882i | \(0.315044\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32443.0i | 1.23646i | 0.785997 | + | 0.618230i | \(0.212150\pi\) | ||||
−0.785997 | + | 0.618230i | \(0.787850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14238.6 | −0.538991 | −0.269496 | − | 0.963002i | \(-0.586857\pi\) | ||||
−0.269496 | + | 0.963002i | \(0.586857\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13650.0 | −0.514968 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 17748.3i | − 0.665088i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33504.8 | −1.25133 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 605.733i | − 0.0224720i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37287.6i | 1.37872i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28447.8 | −1.04490 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 18013.0i | − 0.659440i | −0.944079 | − | 0.329720i | \(-0.893046\pi\) | ||||
0.944079 | − | 0.329720i | \(-0.106954\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26029.2 | −0.946635 | −0.473317 | − | 0.880892i | \(-0.656944\pi\) | ||||
−0.473317 | + | 0.880892i | \(0.656944\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22464.0 | −0.814293 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16262.0i | 0.585625i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43782.8 | 1.57156 | 0.785778 | − | 0.618508i | \(-0.212263\pi\) | ||||
0.785778 | + | 0.618508i | \(0.212263\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3894.00i | − 0.138865i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3167.92i | 0.112606i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50405.6 | −1.78014 | −0.890072 | − | 0.455819i | \(-0.849346\pi\) | ||||
−0.890072 | + | 0.455819i | \(0.849346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 9604.00i | − 0.338086i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17536.0 | 0.613355 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11449.0 | 0.399170 | 0.199585 | − | 0.979880i | \(-0.436041\pi\) | ||||
0.199585 | + | 0.979880i | \(0.436041\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 43927.3i | − 1.52177i | −0.648884 | − | 0.760887i | \(-0.724764\pi\) | ||||
0.648884 | − | 0.760887i | \(-0.275236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21616.0 | −0.746462 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 15208.2i | − 0.521859i | −0.965358 | − | 0.260930i | \(-0.915971\pi\) | ||||
0.965358 | − | 0.260930i | \(-0.0840290\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 5502.73i | − 0.188226i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21828.0 | −0.741950 | −0.370975 | − | 0.928643i | \(-0.620976\pi\) | ||||
−0.370975 | + | 0.928643i | \(0.620976\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 9204.00i | − 0.311869i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37507.5 | 1.26296 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29203.0 | −0.980262 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 462.130i | 0.0154160i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31351.9 | −1.04261 | −0.521307 | − | 0.853369i | \(-0.674555\pi\) | ||||
−0.521307 | + | 0.853369i | \(0.674555\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 41038.4i | − 1.35632i | −0.734915 | − | 0.678159i | \(-0.762778\pi\) | ||||
0.734915 | − | 0.678159i | \(-0.237222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2824.97i | 0.0930776i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31325.0 | 1.02577 | 0.512885 | − | 0.858458i | \(-0.328577\pi\) | ||||
0.512885 | + | 0.858458i | \(0.328577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17316.0i | 0.565293i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29189.1 | −0.947089 | −0.473544 | − | 0.880770i | \(-0.657026\pi\) | ||||
−0.473544 | + | 0.880770i | \(0.657026\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37908.0 | 1.22624 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 16237.0i | − 0.522049i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17831.5 | 0.571579 | 0.285790 | − | 0.958292i | \(-0.407744\pi\) | ||||
0.285790 | + | 0.958292i | \(0.407744\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 53542.4i | − 1.70594i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 20535.2i | − 0.652313i | −0.945316 | − | 0.326157i | \(-0.894246\pi\) | ||||
0.945316 | − | 0.326157i | \(-0.105754\pi\) | |||||||
\(998\) | 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.d.f.865.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 1728.4.d.f.865.5 | yes | 8 | |
4.3 | odd | 2 | inner | 1728.4.d.f.865.3 | yes | 8 | |
8.3 | odd | 2 | inner | 1728.4.d.f.865.8 | yes | 8 | |
8.5 | even | 2 | inner | 1728.4.d.f.865.6 | yes | 8 | |
12.11 | even | 2 | inner | 1728.4.d.f.865.7 | yes | 8 | |
24.5 | odd | 2 | inner | 1728.4.d.f.865.2 | yes | 8 | |
24.11 | even | 2 | inner | 1728.4.d.f.865.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.4.d.f.865.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1728.4.d.f.865.2 | yes | 8 | 24.5 | odd | 2 | inner | |
1728.4.d.f.865.3 | yes | 8 | 4.3 | odd | 2 | inner | |
1728.4.d.f.865.4 | yes | 8 | 24.11 | even | 2 | inner | |
1728.4.d.f.865.5 | yes | 8 | 3.2 | odd | 2 | inner | |
1728.4.d.f.865.6 | yes | 8 | 8.5 | even | 2 | inner | |
1728.4.d.f.865.7 | yes | 8 | 12.11 | even | 2 | inner | |
1728.4.d.f.865.8 | yes | 8 | 8.3 | odd | 2 | inner |