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 | 1567.11 | ||
Root | \(0.742163 - 1.20382i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1567 |
Dual form | 1728.3.b.i.1567.2 |
$q$-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 | ||||||||
\(5\) | 8.36964i | 1.67393i | 0.547259 | + | 0.836964i | \(0.315671\pi\) | ||||
−0.547259 | + | 0.836964i | \(0.684329\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.43910i | − 0.348442i | −0.984707 | − | 0.174221i | \(-0.944259\pi\) | ||||
0.984707 | − | 0.174221i | \(-0.0557408\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.41295 | −0.219359 | −0.109679 | − | 0.993967i | \(-0.534982\pi\) | ||||
−0.109679 | + | 0.993967i | \(0.534982\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.8843i | 1.60648i | 0.595654 | + | 0.803241i | \(0.296893\pi\) | ||||
−0.595654 | + | 0.803241i | \(0.703107\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.1793 | −0.775256 | −0.387628 | − | 0.921816i | \(-0.626705\pi\) | ||||
−0.387628 | + | 0.921816i | \(0.626705\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −32.7976 | −1.72619 | −0.863096 | − | 0.505040i | \(-0.831478\pi\) | ||||
−0.863096 | + | 0.505040i | \(0.831478\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 33.8139i | − 1.47017i | −0.677975 | − | 0.735085i | \(-0.737142\pi\) | ||||
0.677975 | − | 0.735085i | \(-0.262858\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −45.0508 | −1.80203 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 34.7407i | − 1.19795i | −0.800766 | − | 0.598977i | \(-0.795574\pi\) | ||||
0.800766 | − | 0.598977i | \(-0.204426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 33.7335i | − 1.08818i | −0.839027 | − | 0.544089i | \(-0.816875\pi\) | ||||
0.839027 | − | 0.544089i | \(-0.183125\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 20.4143 | 0.583267 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.8546i | 0.833909i | 0.908927 | + | 0.416954i | \(0.136903\pi\) | ||||
−0.908927 | + | 0.416954i | \(0.863097\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 35.1659 | 0.857705 | 0.428852 | − | 0.903375i | \(-0.358918\pi\) | ||||
0.428852 | + | 0.903375i | \(0.358918\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −27.9121 | −0.649119 | −0.324560 | − | 0.945865i | \(-0.605216\pi\) | ||||
−0.324560 | + | 0.945865i | \(0.605216\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 21.9865i | 0.467799i | 0.972261 | + | 0.233899i | \(0.0751486\pi\) | ||||
−0.972261 | + | 0.233899i | \(0.924851\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 43.0508 | 0.878588 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 26.3710i | − 0.497567i | −0.968559 | − | 0.248783i | \(-0.919969\pi\) | ||||
0.968559 | − | 0.248783i | \(-0.0800307\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 20.1955i | − 0.367191i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 93.3081 | 1.58149 | 0.790747 | − | 0.612143i | \(-0.209693\pi\) | ||||
0.790747 | + | 0.612143i | \(0.209693\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27.7128i | 0.454308i | 0.973859 | + | 0.227154i | \(0.0729421\pi\) | ||||
−0.973859 | + | 0.227154i | \(0.927058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −174.794 | −2.68913 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.97035 | 0.148811 | 0.0744056 | − | 0.997228i | \(-0.476294\pi\) | ||||
0.0744056 | + | 0.997228i | \(0.476294\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 64.5448i | − 0.909081i | −0.890726 | − | 0.454541i | \(-0.849803\pi\) | ||||
0.890726 | − | 0.454541i | \(-0.150197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −45.5636 | −0.624159 | −0.312079 | − | 0.950056i | \(-0.601025\pi\) | ||||
−0.312079 | + | 0.950056i | \(0.601025\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.88541i | 0.0764339i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 82.8072i | 1.04819i | 0.851659 | + | 0.524096i | \(0.175597\pi\) | ||||
−0.851659 | + | 0.524096i | \(0.824403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −59.4956 | −0.716815 | −0.358407 | − | 0.933565i | \(-0.616680\pi\) | ||||
−0.358407 | + | 0.933565i | \(0.616680\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 110.306i | − 1.29772i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −139.628 | −1.56885 | −0.784426 | − | 0.620222i | \(-0.787042\pi\) | ||||
−0.784426 | + | 0.620222i | \(0.787042\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 50.9387 | 0.559766 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 274.504i | − 2.88952i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 150.716 | 1.55377 | 0.776887 | − | 0.629641i | \(-0.216798\pi\) | ||||
0.776887 | + | 0.629641i | \(0.216798\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 74.0246i | − 0.732916i | −0.930435 | − | 0.366458i | \(-0.880570\pi\) | ||||
0.930435 | − | 0.366458i | \(-0.119430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 107.152i | 1.04031i | 0.854070 | + | 0.520157i | \(0.174127\pi\) | ||||
−0.854070 | + | 0.520157i | \(0.825873\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −34.6694 | −0.324013 | −0.162007 | − | 0.986790i | \(-0.551797\pi\) | ||||
−0.162007 | + | 0.986790i | \(0.551797\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 197.530i | − 1.81220i | −0.423060 | − | 0.906102i | \(-0.639044\pi\) | ||||
0.423060 | − | 0.906102i | \(-0.360956\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 52.7803 | 0.467082 | 0.233541 | − | 0.972347i | \(-0.424969\pi\) | ||||
0.233541 | + | 0.972347i | \(0.424969\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 283.010 | 2.46096 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 32.1457i | 0.270132i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −115.178 | −0.951882 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 167.818i | − 1.34254i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 74.4391i | − 0.586135i | −0.956092 | − | 0.293067i | \(-0.905324\pi\) | ||||
0.956092 | − | 0.293067i | \(-0.0946760\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 159.377 | 1.21662 | 0.608309 | − | 0.793700i | \(-0.291848\pi\) | ||||
0.608309 | + | 0.793700i | \(0.291848\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 79.9966i | 0.601478i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −218.704 | −1.59638 | −0.798189 | − | 0.602406i | \(-0.794209\pi\) | ||||
−0.798189 | + | 0.602406i | \(0.794209\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 37.8825 | 0.272536 | 0.136268 | − | 0.990672i | \(-0.456489\pi\) | ||||
0.136268 | + | 0.990672i | \(0.456489\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 50.3926i | − 0.352396i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 290.767 | 2.00529 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 52.1967i | 0.350314i | 0.984541 | + | 0.175157i | \(0.0560432\pi\) | ||||
−0.984541 | + | 0.175157i | \(0.943957\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 38.9569i | − 0.257993i | −0.991645 | − | 0.128996i | \(-0.958824\pi\) | ||||
0.991645 | − | 0.128996i | \(-0.0411756\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 282.337 | 1.82153 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 21.8278i | − 0.139031i | −0.997581 | − | 0.0695154i | \(-0.977855\pi\) | ||||
0.997581 | − | 0.0695154i | \(-0.0221453\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −82.4754 | −0.512270 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −262.870 | −1.61270 | −0.806350 | − | 0.591438i | \(-0.798560\pi\) | ||||
−0.806350 | + | 0.591438i | \(0.798560\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 233.614i | − 1.39889i | −0.714687 | − | 0.699444i | \(-0.753431\pi\) | ||||
0.714687 | − | 0.699444i | \(-0.246569\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −267.153 | −1.58079 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 293.868i | − 1.69866i | −0.527864 | − | 0.849329i | \(-0.677007\pi\) | ||||
0.527864 | − | 0.849329i | \(-0.322993\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 109.883i | 0.627904i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 305.165 | 1.70483 | 0.852415 | − | 0.522866i | \(-0.175137\pi\) | ||||
0.852415 | + | 0.522866i | \(0.175137\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 55.0270i | − 0.304017i | −0.988379 | − | 0.152008i | \(-0.951426\pi\) | ||||
0.988379 | − | 0.152008i | \(-0.0485740\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −258.242 | −1.39590 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.8011 | 0.170059 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 252.518i | − 1.32208i | −0.750349 | − | 0.661041i | \(-0.770115\pi\) | ||||
0.750349 | − | 0.661041i | \(-0.229885\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 66.1013 | 0.342494 | 0.171247 | − | 0.985228i | \(-0.445220\pi\) | ||||
0.171247 | + | 0.985228i | \(0.445220\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 152.421i | 0.773710i | 0.922141 | + | 0.386855i | \(0.126439\pi\) | ||||
−0.922141 | + | 0.386855i | \(0.873561\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 36.9774i | 0.185816i | 0.995675 | + | 0.0929081i | \(0.0296163\pi\) | ||||
−0.995675 | + | 0.0929081i | \(0.970384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −84.7359 | −0.417418 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 294.326i | 1.43573i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 79.1390 | 0.378655 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −277.237 | −1.31392 | −0.656960 | − | 0.753926i | \(-0.728158\pi\) | ||||
−0.656960 | + | 0.753926i | \(0.728158\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 233.614i | − 1.08658i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −82.2793 | −0.379167 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 275.241i | − 1.24543i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 45.6907i | − 0.204891i | −0.994739 | − | 0.102446i | \(-0.967333\pi\) | ||||
0.994739 | − | 0.102446i | \(-0.0326668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −399.744 | −1.76099 | −0.880493 | − | 0.474060i | \(-0.842788\pi\) | ||||
−0.880493 | + | 0.474060i | \(0.842788\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 189.213i | 0.826258i | 0.910672 | + | 0.413129i | \(0.135564\pi\) | ||||
−0.910672 | + | 0.413129i | \(0.864436\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −57.0895 | −0.245019 | −0.122510 | − | 0.992467i | \(-0.539094\pi\) | ||||
−0.122510 | + | 0.992467i | \(0.539094\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −184.019 | −0.783061 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 309.733i | 1.29595i | 0.761660 | + | 0.647977i | \(0.224385\pi\) | ||||
−0.761660 | + | 0.647977i | \(0.775615\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −400.843 | −1.66325 | −0.831624 | − | 0.555340i | \(-0.812588\pi\) | ||||
−0.831624 | + | 0.555340i | \(0.812588\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 360.320i | 1.47069i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 684.955i | − 2.77310i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −264.779 | −1.05490 | −0.527448 | − | 0.849587i | \(-0.676851\pi\) | ||||
−0.527448 | + | 0.849587i | \(0.676851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 81.5912i | 0.322495i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −354.023 | −1.37752 | −0.688760 | − | 0.724990i | \(-0.741845\pi\) | ||||
−0.688760 | + | 0.724990i | \(0.741845\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 75.2574 | 0.290569 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 386.105i | − 1.46808i | −0.679106 | − | 0.734041i | \(-0.737632\pi\) | ||||
0.679106 | − | 0.734041i | \(-0.262368\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 220.716 | 0.832891 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 167.021i | − 0.620896i | −0.950590 | − | 0.310448i | \(-0.899521\pi\) | ||||
0.950590 | − | 0.310448i | \(-0.100479\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 254.266i | − 0.938253i | −0.883131 | − | 0.469126i | \(-0.844569\pi\) | ||||
0.883131 | − | 0.469126i | \(-0.155431\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 108.705 | 0.395292 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 414.204i | 1.49532i | 0.664082 | + | 0.747660i | \(0.268823\pi\) | ||||
−0.664082 | + | 0.747660i | \(0.731177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 53.6902 | 0.191068 | 0.0955341 | − | 0.995426i | \(-0.469544\pi\) | ||||
0.0955341 | + | 0.995426i | \(0.469544\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −183.530 | −0.648517 | −0.324259 | − | 0.945969i | \(-0.605115\pi\) | ||||
−0.324259 | + | 0.945969i | \(0.605115\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 85.7730i | − 0.298861i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −115.305 | −0.398979 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 165.240i | − 0.563959i | −0.959420 | − | 0.281980i | \(-0.909009\pi\) | ||||
0.959420 | − | 0.281980i | \(-0.0909911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 780.955i | 2.64730i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 706.179 | 2.36180 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 68.0804i | 0.226181i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −231.946 | −0.760479 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −168.765 | −0.549723 | −0.274861 | − | 0.961484i | \(-0.588632\pi\) | ||||
−0.274861 | + | 0.961484i | \(0.588632\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 444.989i | 1.43083i | 0.698699 | + | 0.715416i | \(0.253763\pi\) | ||||
−0.698699 | + | 0.715416i | \(0.746237\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.7413 | 0.0662660 | 0.0331330 | − | 0.999451i | \(-0.489452\pi\) | ||||
0.0331330 | + | 0.999451i | \(0.489452\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 69.1362i | 0.218095i | 0.994037 | + | 0.109048i | \(0.0347801\pi\) | ||||
−0.994037 | + | 0.109048i | \(0.965220\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 83.8274i | 0.262782i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 432.252 | 1.33824 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 940.853i | − 2.89493i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 53.6273 | 0.163001 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 386.180 | 1.16671 | 0.583353 | − | 0.812219i | \(-0.301740\pi\) | ||||
0.583353 | + | 0.812219i | \(0.301740\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 83.4482i | 0.249099i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −211.767 | −0.628389 | −0.314194 | − | 0.949359i | \(-0.601734\pi\) | ||||
−0.314194 | + | 0.949359i | \(0.601734\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 81.3972i | 0.238701i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 224.521i | − 0.654580i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −540.291 | −1.55704 | −0.778518 | − | 0.627623i | \(-0.784028\pi\) | ||||
−0.778518 | + | 0.627623i | \(0.784028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 183.767i | 0.526553i | 0.964720 | + | 0.263276i | \(0.0848031\pi\) | ||||
−0.964720 | + | 0.263276i | \(0.915197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 549.830 | 1.55759 | 0.778796 | − | 0.627277i | \(-0.215831\pi\) | ||||
0.778796 | + | 0.627277i | \(0.215831\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 540.216 | 1.52174 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 406.677i | 1.13281i | 0.824129 | + | 0.566403i | \(0.191665\pi\) | ||||
−0.824129 | + | 0.566403i | \(0.808335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 714.686 | 1.97974 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 381.351i | − 1.04480i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 443.688i | 1.20896i | 0.796620 | + | 0.604480i | \(0.206619\pi\) | ||||
−0.796620 | + | 0.604480i | \(0.793381\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −64.3215 | −0.173373 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 98.5364i | − 0.264173i | −0.991238 | − | 0.132086i | \(-0.957832\pi\) | ||||
0.991238 | − | 0.132086i | \(-0.0421676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 725.534 | 1.92449 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −431.635 | −1.13888 | −0.569439 | − | 0.822033i | \(-0.692840\pi\) | ||||
−0.569439 | + | 0.822033i | \(0.692840\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 260.504i | 0.680167i | 0.940395 | + | 0.340083i | \(0.110455\pi\) | ||||
−0.940395 | + | 0.340083i | \(0.889545\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −49.2587 | −0.127945 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 360.413i | 0.926512i | 0.886224 | + | 0.463256i | \(0.153319\pi\) | ||||
−0.886224 | + | 0.463256i | \(0.846681\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 445.645i | 1.13976i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −693.066 | −1.75460 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 524.685i | − 1.32162i | −0.750551 | − | 0.660812i | \(-0.770212\pi\) | ||||
0.750551 | − | 0.660812i | \(-0.229788\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −469.300 | −1.17032 | −0.585162 | − | 0.810916i | \(-0.698969\pi\) | ||||
−0.585162 | + | 0.810916i | \(0.698969\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 704.500 | 1.74814 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 74.4505i | − 0.182925i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 493.509 | 1.20662 | 0.603311 | − | 0.797506i | \(-0.293848\pi\) | ||||
0.603311 | + | 0.797506i | \(0.293848\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 227.587i | − 0.551059i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 497.957i | − 1.19990i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −527.341 | −1.25857 | −0.629285 | − | 0.777175i | \(-0.716652\pi\) | ||||
−0.629285 | + | 0.777175i | \(0.716652\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 417.579i | 0.991875i | 0.868358 | + | 0.495937i | \(0.165175\pi\) | ||||
−0.868358 | + | 0.495937i | \(0.834825\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 593.740 | 1.39704 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 67.5942 | 0.158300 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 462.224i | − 1.07245i | −0.844076 | − | 0.536223i | \(-0.819851\pi\) | ||||
0.844076 | − | 0.536223i | \(-0.180149\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 58.2079 | 0.134429 | 0.0672147 | − | 0.997739i | \(-0.478589\pi\) | ||||
0.0672147 | + | 0.997739i | \(0.478589\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1109.02i | 2.53780i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 621.745i | − 1.41627i | −0.706075 | − | 0.708137i | \(-0.749536\pi\) | ||||
0.706075 | − | 0.708137i | \(-0.250464\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 127.815 | 0.288521 | 0.144261 | − | 0.989540i | \(-0.453920\pi\) | ||||
0.144261 | + | 0.989540i | \(0.453920\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1168.63i | − 2.62614i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 335.372 | 0.746932 | 0.373466 | − | 0.927644i | \(-0.378169\pi\) | ||||
0.373466 | + | 0.927644i | \(0.378169\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −84.8534 | −0.188145 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 426.339i | 0.937008i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −121.182 | −0.265169 | −0.132585 | − | 0.991172i | \(-0.542328\pi\) | ||||
−0.132585 | + | 0.991172i | \(0.542328\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 144.396i | − 0.313224i | −0.987660 | − | 0.156612i | \(-0.949943\pi\) | ||||
0.987660 | − | 0.156612i | \(-0.0500573\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 487.501i | 1.05292i | 0.850201 | + | 0.526459i | \(0.176480\pi\) | ||||
−0.850201 | + | 0.526459i | \(0.823520\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 298.591 | 0.639382 | 0.319691 | − | 0.947522i | \(-0.396421\pi\) | ||||
0.319691 | + | 0.947522i | \(0.396421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 24.3187i | − 0.0518521i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 67.3505 | 0.142390 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1477.56 | 3.11065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 86.7847i | 0.181179i | 0.995888 | + | 0.0905894i | \(0.0288751\pi\) | ||||
−0.995888 | + | 0.0905894i | \(0.971125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −644.376 | −1.33966 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1261.44i | 2.60090i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 781.377i | 1.60447i | 0.597009 | + | 0.802235i | \(0.296356\pi\) | ||||
−0.597009 | + | 0.802235i | \(0.703644\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 158.487 | 0.322783 | 0.161392 | − | 0.986890i | \(-0.448402\pi\) | ||||
0.161392 | + | 0.986890i | \(0.448402\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 457.859i | 0.928721i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −157.431 | −0.316762 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −780.549 | −1.56423 | −0.782113 | − | 0.623137i | \(-0.785858\pi\) | ||||
−0.782113 | + | 0.623137i | \(0.785858\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 517.773i | 1.02937i | 0.857379 | + | 0.514685i | \(0.172091\pi\) | ||||
−0.857379 | + | 0.514685i | \(0.827909\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 619.559 | 1.22685 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 653.045i | − 1.28300i | −0.767124 | − | 0.641498i | \(-0.778313\pi\) | ||||
0.767124 | − | 0.641498i | \(-0.221687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 111.134i | 0.217483i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −896.827 | −1.74141 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 53.0523i | − 0.102616i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −310.175 | −0.595346 | −0.297673 | − | 0.954668i | \(-0.596210\pi\) | ||||
−0.297673 | + | 0.954668i | \(0.596210\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −779.063 | −1.48960 | −0.744802 | − | 0.667285i | \(-0.767456\pi\) | ||||
−0.744802 | + | 0.667285i | \(0.767456\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 444.586i | 0.843616i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −614.381 | −1.16140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 734.414i | 1.37789i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 290.170i | − 0.542374i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −103.879 | −0.192726 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 410.019i | 0.757892i | 0.925419 | + | 0.378946i | \(0.123713\pi\) | ||||
−0.925419 | + | 0.378946i | \(0.876287\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1653.26 | 3.03350 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −561.353 | −1.02624 | −0.513120 | − | 0.858317i | \(-0.671510\pi\) | ||||
−0.513120 | + | 0.858317i | \(0.671510\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1139.41i | 2.06790i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 201.975 | 0.365235 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 363.521i | − 0.652640i | −0.945259 | − | 0.326320i | \(-0.894191\pi\) | ||||
0.945259 | − | 0.326320i | \(-0.105809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 582.924i | − 1.04280i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 287.769 | 0.511134 | 0.255567 | − | 0.966791i | \(-0.417738\pi\) | ||||
0.255567 | + | 0.966791i | \(0.417738\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 441.752i | 0.781861i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 414.386 | 0.728270 | 0.364135 | − | 0.931346i | \(-0.381365\pi\) | ||||
0.364135 | + | 0.931346i | \(0.381365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −529.424 | −0.927188 | −0.463594 | − | 0.886048i | \(-0.653440\pi\) | ||||
−0.463594 | + | 0.886048i | \(0.653440\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1523.34i | 2.64930i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −409.148 | −0.709095 | −0.354548 | − | 0.935038i | \(-0.615365\pi\) | ||||
−0.354548 | + | 0.935038i | \(0.615365\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 145.116i | 0.249769i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 63.6319i | 0.109146i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −368.026 | −0.626961 | −0.313481 | − | 0.949595i | \(-0.601495\pi\) | ||||
−0.313481 | + | 0.949595i | \(0.601495\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1106.38i | 1.87840i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1055.08 | 1.77922 | 0.889612 | − | 0.456717i | \(-0.150975\pi\) | ||||
0.889612 | + | 0.456717i | \(0.150975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −269.048 | −0.452181 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 863.896i | − 1.44223i | −0.692815 | − | 0.721116i | \(-0.743630\pi\) | ||||
0.692815 | − | 0.721116i | \(-0.256370\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.43642 | −0.00405394 | −0.00202697 | − | 0.999998i | \(-0.500645\pi\) | ||||
−0.00202697 | + | 0.999998i | \(0.500645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 963.995i | − 1.59338i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 755.681i | − 1.24494i | −0.782642 | − | 0.622472i | \(-0.786128\pi\) | ||||
0.782642 | − | 0.622472i | \(-0.213872\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −459.173 | −0.751510 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 183.950i | 0.300082i | 0.988680 | + | 0.150041i | \(0.0479406\pi\) | ||||
−0.988680 | + | 0.150041i | \(0.952059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 502.269 | 0.814050 | 0.407025 | − | 0.913417i | \(-0.366566\pi\) | ||||
0.407025 | + | 0.913417i | \(0.366566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 222.995 | 0.360250 | 0.180125 | − | 0.983644i | \(-0.442350\pi\) | ||||
0.180125 | + | 0.983644i | \(0.442350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 340.566i | 0.546655i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 278.305 | 0.445288 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 406.644i | − 0.646492i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1058.12i | − 1.67689i | −0.544988 | − | 0.838444i | \(-0.683466\pi\) | ||||
0.544988 | − | 0.838444i | \(-0.316534\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 623.028 | 0.981147 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 899.085i | 1.41144i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −353.113 | −0.550878 | −0.275439 | − | 0.961319i | \(-0.588823\pi\) | ||||
−0.275439 | + | 0.961319i | \(0.588823\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 404.720 | 0.629424 | 0.314712 | − | 0.949187i | \(-0.398092\pi\) | ||||
0.314712 | + | 0.949187i | \(0.398092\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 257.672i | − 0.398257i | −0.979973 | − | 0.199129i | \(-0.936189\pi\) | ||||
0.979973 | − | 0.199129i | \(-0.0638111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −225.147 | −0.346914 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 841.878i | 1.28925i | 0.764500 | + | 0.644624i | \(0.222986\pi\) | ||||
−0.764500 | + | 0.644624i | \(0.777014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1333.93i | 2.03653i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −673.789 | −1.02244 | −0.511221 | − | 0.859449i | \(-0.670807\pi\) | ||||
−0.511221 | + | 0.859449i | \(0.670807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 116.970i | − 0.176959i | −0.996078 | − | 0.0884796i | \(-0.971799\pi\) | ||||
0.996078 | − | 0.0884796i | \(-0.0282008\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −669.543 | −1.00683 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1174.72 | −1.76120 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 66.8695i | − 0.0996565i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −772.635 | −1.14805 | −0.574023 | − | 0.818839i | \(-0.694618\pi\) | ||||
−0.574023 | + | 0.818839i | \(0.694618\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 172.800i | 0.255244i | 0.991823 | + | 0.127622i | \(0.0407344\pi\) | ||||
−0.991823 | + | 0.127622i | \(0.959266\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 367.611i | − 0.541400i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −808.636 | −1.18395 | −0.591974 | − | 0.805957i | \(-0.701651\pi\) | ||||
−0.591974 | + | 0.805957i | \(0.701651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1830.47i | − 2.67222i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 550.740 | 0.799332 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −315.802 | −0.457022 | −0.228511 | − | 0.973541i | \(-0.573386\pi\) | ||||
−0.228511 | + | 0.973541i | \(0.573386\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 317.063i | 0.456205i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −463.463 | −0.664940 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 276.941i | 0.395066i | 0.980296 | + | 0.197533i | \(0.0632929\pi\) | ||||
−0.980296 | + | 0.197533i | \(0.936707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1011.96i | − 1.43949i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −180.553 | −0.255379 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 512.419i | 0.722734i | 0.932424 | + | 0.361367i | \(0.117690\pi\) | ||||
−0.932424 | + | 0.361367i | \(0.882310\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1140.66 | −1.59981 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 421.768 | 0.589885 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 129.848i | 0.180595i | 0.995915 | + | 0.0902975i | \(0.0287818\pi\) | ||||
−0.995915 | + | 0.0902975i | \(0.971218\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 261.355 | 0.362490 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1565.10i | 2.15875i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 581.866i | 0.800366i | 0.916435 | + | 0.400183i | \(0.131053\pi\) | ||||
−0.916435 | + | 0.400183i | \(0.868947\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 367.864 | 0.503233 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 452.139i | 0.616834i | 0.951251 | + | 0.308417i | \(0.0997992\pi\) | ||||
−0.951251 | + | 0.308417i | \(0.900201\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.0579 | −0.0326430 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.9916 | 0.0581754 | 0.0290877 | − | 0.999577i | \(-0.490740\pi\) | ||||
0.0290877 | + | 0.999577i | \(0.490740\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 51.4541i | 0.0692518i | 0.999400 | + | 0.0346259i | \(0.0110240\pi\) | ||||
−0.999400 | + | 0.0346259i | \(0.988976\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −436.868 | −0.586399 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 84.5620i | 0.112900i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 390.652i | 0.520175i | 0.965585 | + | 0.260088i | \(0.0837514\pi\) | ||||
−0.965585 | + | 0.260088i | \(0.916249\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 326.055 | 0.431862 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 310.240i | − 0.409828i | −0.978780 | − | 0.204914i | \(-0.934309\pi\) | ||||
0.978780 | − | 0.204914i | \(-0.0656915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 859.524 | 1.12947 | 0.564733 | − | 0.825273i | \(-0.308979\pi\) | ||||
0.564733 | + | 0.825273i | \(0.308979\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −481.795 | −0.631448 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1948.67i | 2.54064i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1408.40 | 1.83147 | 0.915733 | − | 0.401787i | \(-0.131611\pi\) | ||||
0.915733 | + | 0.401787i | \(0.131611\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1297.40i | 1.67839i | 0.543828 | + | 0.839197i | \(0.316975\pi\) | ||||
−0.543828 | + | 0.839197i | \(0.683025\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1519.72i | 1.96093i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1153.36 | −1.48056 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 155.743i | 0.199415i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 182.691 | 0.232727 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 390.371 | 0.496024 | 0.248012 | − | 0.968757i | \(-0.420223\pi\) | ||||
0.248012 | + | 0.968757i | \(0.420223\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 128.736i | − 0.162751i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −578.762 | −0.729838 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 480.484i | − 0.602866i | −0.953487 | − | 0.301433i | \(-0.902535\pi\) | ||||
0.953487 | − | 0.301433i | \(-0.0974649\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 289.768i | − 0.362664i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 109.942 | 0.136915 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 690.289i | − 0.857502i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1074.34 | 1.32798 | 0.663991 | − | 0.747741i | \(-0.268861\pi\) | ||||
0.663991 | + | 0.747741i | \(0.268861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 740.795 | 0.913434 | 0.456717 | − | 0.889612i | \(-0.349025\pi\) | ||||
0.456717 | + | 0.889612i | \(0.349025\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 2200.13i | − 2.69954i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 915.452 | 1.12050 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 216.891i | − 0.264180i | −0.991238 | − | 0.132090i | \(-0.957831\pi\) | ||||
0.991238 | − | 0.132090i | \(-0.0421687\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1368.30i | − 1.66257i | −0.555844 | − | 0.831287i | \(-0.687605\pi\) | ||||
0.555844 | − | 0.831287i | \(-0.312395\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 936.451 | 1.13235 | 0.566174 | − | 0.824286i | \(-0.308423\pi\) | ||||
0.566174 | + | 0.824286i | \(0.308423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.5189i | 0.0211325i | 0.999944 | + | 0.0105663i | \(0.00336341\pi\) | ||||
−0.999944 | + | 0.0105663i | \(0.996637\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −567.381 | −0.681130 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1955.27 | 2.34164 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 115.442i | − 0.137595i | −0.997631 | − | 0.0687976i | \(-0.978084\pi\) | ||||
0.997631 | − | 0.0687976i | \(-0.0219163\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −365.915 | −0.435095 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2235.97i | − 2.64612i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 280.929i | 0.331676i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1043.32 | 1.22599 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1273.82i | − 1.49335i | −0.665191 | − | 0.746673i | \(-0.731650\pi\) | ||||
0.665191 | − | 0.746673i | \(-0.268350\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 517.583 | 0.603947 | 0.301973 | − | 0.953316i | \(-0.402355\pi\) | ||||
0.301973 | + | 0.953316i | \(0.402355\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 354.668 | 0.412885 | 0.206443 | − | 0.978459i | \(-0.433811\pi\) | ||||
0.206443 | + | 0.978459i | \(0.433811\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1069.96i | − 1.23982i | −0.784673 | − | 0.619910i | \(-0.787169\pi\) | ||||
0.784673 | − | 0.619910i | \(-0.212831\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2459.57 | 2.84343 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 199.809i | − 0.229930i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 208.224i | 0.239063i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −409.324 | −0.467799 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 101.572i | − 0.115818i | −0.998322 | − | 0.0579088i | \(-0.981557\pi\) | ||||
0.998322 | − | 0.0579088i | \(-0.0184433\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −858.174 | −0.974091 | −0.487045 | − | 0.873377i | \(-0.661925\pi\) | ||||
−0.487045 | + | 0.873377i | \(0.661925\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 437.517 | 0.495489 | 0.247745 | − | 0.968825i | \(-0.420311\pi\) | ||||
0.247745 | + | 0.968825i | \(0.420311\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 938.095i | 1.05760i | 0.848745 | + | 0.528802i | \(0.177359\pi\) | ||||
−0.848745 | + | 0.528802i | \(0.822641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −181.564 | −0.204234 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 721.107i | − 0.807510i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2554.12i | 2.85376i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1171.93 | −1.30359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 347.553i | 0.385741i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 460.556 | 0.508902 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 409.225 | 0.451185 | 0.225593 | − | 0.974222i | \(-0.427568\pi\) | ||||
0.225593 | + | 0.974222i | \(0.427568\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1544.02i | − 1.69486i | −0.530907 | − | 0.847430i | \(-0.678148\pi\) | ||||
0.530907 | − | 0.847430i | \(-0.321852\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 143.560 | 0.157240 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 388.736i | − 0.423921i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1204.58i | 1.31075i | 0.755305 | + | 0.655374i | \(0.227489\pi\) | ||||
−0.755305 | + | 0.655374i | \(0.772511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1347.97 | 1.46042 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1390.03i | − 1.50273i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1317.76 | −1.41847 | −0.709234 | − | 0.704973i | \(-0.750959\pi\) | ||||
−0.709234 | + | 0.704973i | \(0.750959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1411.97 | −1.51661 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 266.163i | 0.284667i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −649.172 | −0.692820 | −0.346410 | − | 0.938083i | \(-0.612599\pi\) | ||||
−0.346410 | + | 0.938083i | \(0.612599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1352.72i | − 1.43753i | −0.695252 | − | 0.718766i | \(-0.744707\pi\) | ||||
0.695252 | − | 0.718766i | \(-0.255293\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1189.10i | − 1.26097i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1194.59 | 1.26145 | 0.630723 | − | 0.776008i | \(-0.282758\pi\) | ||||
0.630723 | + | 0.776008i | \(0.282758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 951.562i | − 1.00270i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −681.561 | −0.715174 | −0.357587 | − | 0.933880i | \(-0.616400\pi\) | ||||
−0.357587 | + | 0.933880i | \(0.616400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2113.48 | 2.21307 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 533.440i | 0.556246i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −176.950 | −0.184131 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 553.244i | 0.573310i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1050.38i | − 1.08623i | −0.839658 | − | 0.543115i | \(-0.817245\pi\) | ||||
0.839658 | − | 0.543115i | \(-0.182755\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1307.27 | 1.34631 | 0.673157 | − | 0.739500i | \(-0.264938\pi\) | ||||
0.673157 | + | 0.739500i | \(0.264938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 92.3990i | − 0.0949630i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.7045 | 0.0170977 | 0.00854886 | − | 0.999963i | \(-0.497279\pi\) | ||||
0.00854886 | + | 0.999963i | \(0.497279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 336.914 | 0.344141 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 373.268i | − 0.379723i | −0.981811 | − | 0.189862i | \(-0.939196\pi\) | ||||
0.981811 | − | 0.189862i | \(-0.0608040\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1275.71 | −1.29513 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 943.819i | 0.954316i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1028.67i | − 1.03801i | −0.854772 | − | 0.519004i | \(-0.826303\pi\) | ||||
0.854772 | − | 0.519004i | \(-0.173697\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −309.487 | −0.311043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 968.595i | 0.971509i | 0.874095 | + | 0.485755i | \(0.161455\pi\) | ||||
−0.874095 | + | 0.485755i | \(0.838545\pi\) | |||||||
\(998\) | 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.i.1567.11 | yes | 12 | |
3.2 | odd | 2 | 1728.3.b.j.1567.1 | yes | 12 | ||
4.3 | odd | 2 | inner | 1728.3.b.i.1567.12 | yes | 12 | |
8.3 | odd | 2 | inner | 1728.3.b.i.1567.2 | yes | 12 | |
8.5 | even | 2 | inner | 1728.3.b.i.1567.1 | ✓ | 12 | |
12.11 | even | 2 | 1728.3.b.j.1567.2 | yes | 12 | ||
24.5 | odd | 2 | 1728.3.b.j.1567.11 | yes | 12 | ||
24.11 | even | 2 | 1728.3.b.j.1567.12 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.3.b.i.1567.1 | ✓ | 12 | 8.5 | even | 2 | inner | |
1728.3.b.i.1567.2 | yes | 12 | 8.3 | odd | 2 | inner | |
1728.3.b.i.1567.11 | yes | 12 | 1.1 | even | 1 | trivial | |
1728.3.b.i.1567.12 | yes | 12 | 4.3 | odd | 2 | inner | |
1728.3.b.j.1567.1 | yes | 12 | 3.2 | odd | 2 | ||
1728.3.b.j.1567.2 | yes | 12 | 12.11 | even | 2 | ||
1728.3.b.j.1567.11 | yes | 12 | 24.5 | odd | 2 | ||
1728.3.b.j.1567.12 | yes | 12 | 24.11 | even | 2 |