Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,3,Mod(127,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, 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("1792.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.8284633734\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.9710629824630784.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 4x^{10} + 12x^{8} + 25x^{6} + 48x^{4} + 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.4 | ||
Root | \(-0.746179 + 1.20134i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.127 |
Dual form | 1792.3.g.g.127.3 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.98472 | −0.994906 | −0.497453 | − | 0.867491i | \(-0.665731\pi\) | ||||
−0.497453 | + | 0.867491i | \(0.665731\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.80536i | 1.36107i | 0.732715 | + | 0.680536i | \(0.238253\pi\) | ||||
−0.732715 | + | 0.680536i | \(0.761747\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0914622 | −0.0101625 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.3426 | 1.30388 | 0.651938 | − | 0.758272i | \(-0.273956\pi\) | ||||
0.651938 | + | 0.758272i | \(0.273956\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.62243i | 0.355572i | 0.984069 | + | 0.177786i | \(0.0568934\pi\) | ||||
−0.984069 | + | 0.177786i | \(0.943107\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 20.3121i | − 1.35414i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.6107 | 0.682983 | 0.341492 | − | 0.939885i | \(-0.389068\pi\) | ||||
0.341492 | + | 0.939885i | \(0.389068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.4428 | 1.18120 | 0.590601 | − | 0.806964i | \(-0.298891\pi\) | ||||
0.590601 | + | 0.806964i | \(0.298891\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 7.89682i | − 0.376039i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.853941i | 0.0371279i | 0.999828 | + | 0.0185639i | \(0.00590943\pi\) | ||||
−0.999828 | + | 0.0185639i | \(0.994091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.3129 | −0.852516 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.1354 | 1.00502 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 42.8321i | − 1.47697i | −0.674270 | − | 0.738485i | \(-0.735541\pi\) | ||||
0.674270 | − | 0.738485i | \(-0.264459\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.54982i | 0.0499943i | 0.999688 | + | 0.0249972i | \(0.00795767\pi\) | ||||
−0.999688 | + | 0.0249972i | \(0.992042\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −42.8087 | −1.29723 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −18.0053 | −0.514437 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 45.0151i | − 1.21662i | −0.793698 | − | 0.608312i | \(-0.791847\pi\) | ||||
0.793698 | − | 0.608312i | \(-0.208153\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 13.7967i | − 0.353760i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 36.6492 | 0.893883 | 0.446942 | − | 0.894563i | \(-0.352513\pi\) | ||||
0.446942 | + | 0.894563i | \(0.352513\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.9894 | 0.650916 | 0.325458 | − | 0.945557i | \(-0.394482\pi\) | ||||
0.325458 | + | 0.945557i | \(0.394482\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 0.622433i | − 0.0138318i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 42.1740i | − 0.897318i | −0.893703 | − | 0.448659i | \(-0.851902\pi\) | ||||
0.893703 | − | 0.448659i | \(-0.148098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −34.6547 | −0.679504 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 43.4044i | − 0.818950i | −0.912321 | − | 0.409475i | \(-0.865712\pi\) | ||||
0.912321 | − | 0.409475i | \(-0.134288\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 97.6068i | 1.77467i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −66.9856 | −1.17519 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 53.9979 | 0.915219 | 0.457609 | − | 0.889153i | \(-0.348706\pi\) | ||||
0.457609 | + | 0.889153i | \(0.348706\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 15.9498i | − 0.261472i | −0.991417 | − | 0.130736i | \(-0.958266\pi\) | ||||
0.991417 | − | 0.130736i | \(-0.0417340\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 0.241986i | − 0.00384105i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −31.4573 | −0.483959 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 91.9453 | 1.37232 | 0.686159 | − | 0.727452i | \(-0.259295\pi\) | ||||
0.686159 | + | 0.727452i | \(0.259295\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 2.54877i | − 0.0369387i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3585i | 0.230401i | 0.993342 | + | 0.115201i | \(0.0367511\pi\) | ||||
−0.993342 | + | 0.115201i | \(0.963249\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.58728 | −0.131333 | −0.0656663 | − | 0.997842i | \(-0.520917\pi\) | ||||
−0.0656663 | + | 0.997842i | \(0.520917\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 63.6130 | 0.848173 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 37.9470i | 0.492819i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 56.9826i | 0.721299i | 0.932701 | + | 0.360649i | \(0.117445\pi\) | ||||
−0.932701 | + | 0.360649i | \(0.882555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −80.1685 | −0.989734 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.3077 | 0.172381 | 0.0861907 | − | 0.996279i | \(-0.472531\pi\) | ||||
0.0861907 | + | 0.996279i | \(0.472531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 79.0151i | 0.929589i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 127.842i | 1.46945i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −100.136 | −1.12512 | −0.562562 | − | 0.826755i | \(-0.690184\pi\) | ||||
−0.562562 | + | 0.826755i | \(0.690184\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.2298 | −0.134394 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.62579i | − 0.0497396i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 152.732i | 1.60770i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 68.2834 | 0.703952 | 0.351976 | − | 0.936009i | \(-0.385510\pi\) | ||||
0.351976 | + | 0.936009i | \(0.385510\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.31181 | −0.0132506 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 28.1628i | 0.278840i | 0.990233 | + | 0.139420i | \(0.0445238\pi\) | ||||
−0.990233 | + | 0.139420i | \(0.955476\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 160.243i | − 1.55575i | −0.628416 | − | 0.777877i | \(-0.716297\pi\) | ||||
0.628416 | − | 0.777877i | \(-0.283703\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 53.7407 | 0.511816 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −118.923 | −1.11143 | −0.555713 | − | 0.831374i | \(-0.687555\pi\) | ||||
−0.555713 | + | 0.831374i | \(0.687555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 98.2666i | − 0.901529i | −0.892643 | − | 0.450764i | \(-0.851151\pi\) | ||||
0.892643 | − | 0.450764i | \(-0.148849\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 134.357i | 1.21043i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 96.9977 | 0.858387 | 0.429193 | − | 0.903213i | \(-0.358798\pi\) | ||||
0.429193 | + | 0.903213i | \(0.358798\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.81138 | −0.0505337 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 0.422778i | − 0.00361349i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 30.7191i | 0.258143i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 84.7112 | 0.700092 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −109.388 | −0.889330 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 25.0921i | 0.200737i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 71.8712i | 0.565915i | 0.959132 | + | 0.282958i | \(0.0913156\pi\) | ||||
−0.959132 | + | 0.282958i | \(0.908684\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −83.5404 | −0.647600 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 209.837 | 1.60181 | 0.800906 | − | 0.598791i | \(-0.204352\pi\) | ||||
0.800906 | + | 0.598791i | \(0.204352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 59.3782i | 0.446453i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 184.666i | 1.36790i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.1650 | 0.132591 | 0.0662954 | − | 0.997800i | \(-0.478882\pi\) | ||||
0.0662954 | + | 0.997800i | \(0.478882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 134.084 | 0.964635 | 0.482318 | − | 0.875996i | \(-0.339795\pi\) | ||||
0.482318 | + | 0.875996i | \(0.339795\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 125.877i | 0.892747i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 66.2979i | 0.463621i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 291.488 | 2.01026 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.8930 | 0.142129 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.7618i | 0.139341i | 0.997570 | + | 0.0696706i | \(0.0221948\pi\) | ||||
−0.997570 | + | 0.0696706i | \(0.977805\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 93.1090i | 0.616616i | 0.951287 | + | 0.308308i | \(0.0997628\pi\) | ||||
−0.951287 | + | 0.308308i | \(0.900237\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.06194 | −0.00694080 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.5471 | −0.0680458 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 159.337i | 1.01489i | 0.861685 | + | 0.507444i | \(0.169410\pi\) | ||||
−0.861685 | + | 0.507444i | \(0.830590\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 129.550i | 0.814778i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.25932 | −0.0140330 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 45.8277 | 0.281152 | 0.140576 | − | 0.990070i | \(-0.455105\pi\) | ||||
0.140576 | + | 0.990070i | \(0.455105\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 291.329i | − 1.76563i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 15.5845i | − 0.0933203i | −0.998911 | − | 0.0466602i | \(-0.985142\pi\) | ||||
0.998911 | − | 0.0466602i | \(-0.0148578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 147.633 | 0.873569 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.05267 | −0.0120039 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 266.021i | − 1.53770i | −0.639432 | − | 0.768848i | \(-0.720830\pi\) | ||||
0.639432 | − | 0.768848i | \(-0.279170\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 56.3886i | − 0.322221i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −161.168 | −0.910556 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 44.5059 | 0.248636 | 0.124318 | − | 0.992242i | \(-0.460326\pi\) | ||||
0.124318 | + | 0.992242i | \(0.460326\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 168.111i | 0.928787i | 0.885629 | + | 0.464394i | \(0.153728\pi\) | ||||
−0.885629 | + | 0.464394i | \(0.846272\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 47.6056i | 0.260140i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 306.344 | 1.65591 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 166.528 | 0.890525 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 71.7936i | 0.379861i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 353.607i | 1.85134i | 0.378328 | + | 0.925672i | \(0.376499\pi\) | ||||
−0.378328 | + | 0.925672i | \(0.623501\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −348.574 | −1.80608 | −0.903042 | − | 0.429553i | \(-0.858671\pi\) | ||||
−0.903042 | + | 0.429553i | \(0.858671\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 93.8912 | 0.481493 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.9314i | 0.136707i | 0.997661 | + | 0.0683537i | \(0.0217746\pi\) | ||||
−0.997661 | + | 0.0683537i | \(0.978225\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 231.560i | − 1.16362i | −0.813326 | − | 0.581809i | \(-0.802345\pi\) | ||||
0.813326 | − | 0.581809i | \(-0.197655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −274.431 | −1.36533 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 113.323 | 0.558242 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 249.411i | 1.21664i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 0.0781034i | 0 0.000377311i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 321.890 | 1.54014 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 79.6903 | 0.377679 | 0.188840 | − | 0.982008i | \(-0.439527\pi\) | ||||
0.188840 | + | 0.982008i | \(0.439527\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 48.8254i | − 0.229227i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 190.478i | 0.885943i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.10045 | −0.0188961 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 28.6153 | 0.130664 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 53.6698i | 0.242850i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 264.367i | − 1.18550i | −0.805386 | − | 0.592750i | \(-0.798042\pi\) | ||||
0.805386 | − | 0.592750i | \(-0.201958\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.94932 | 0.00866367 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 431.324 | 1.90011 | 0.950053 | − | 0.312088i | \(-0.101028\pi\) | ||||
0.950053 | + | 0.312088i | \(0.101028\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 424.901i | 1.85546i | 0.373247 | + | 0.927732i | \(0.378244\pi\) | ||||
−0.373247 | + | 0.927732i | \(0.621756\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 113.261i | − 0.490308i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −218.828 | −0.939176 | −0.469588 | − | 0.882886i | \(-0.655597\pi\) | ||||
−0.469588 | + | 0.882886i | \(0.655597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 287.009 | 1.22131 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 170.077i | − 0.717625i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 90.1656i | 0.377262i | 0.982048 | + | 0.188631i | \(0.0604050\pi\) | ||||
−0.982048 | + | 0.188631i | \(0.939595\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 375.944 | 1.55994 | 0.779968 | − | 0.625820i | \(-0.215236\pi\) | ||||
0.779968 | + | 0.625820i | \(0.215236\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.93877 | −0.0203242 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 47.6375i | − 0.194439i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 103.741i | 0.420002i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −42.7043 | −0.171503 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −319.525 | −1.27301 | −0.636503 | − | 0.771274i | \(-0.719620\pi\) | ||||
−0.636503 | + | 0.771274i | \(0.719620\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2478i | 0.0484101i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 235.838i | − 0.924854i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −167.466 | −0.651618 | −0.325809 | − | 0.945436i | \(-0.605637\pi\) | ||||
−0.325809 | + | 0.945436i | \(0.605637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 119.099 | 0.459840 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.91752i | 0.0150097i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 86.1276i | − 0.327481i | −0.986503 | − | 0.163741i | \(-0.947644\pi\) | ||||
0.986503 | − | 0.163741i | \(-0.0523560\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 295.382 | 1.11465 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 298.878 | 1.11939 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 269.343i | 1.00128i | 0.865657 | + | 0.500638i | \(0.166901\pi\) | ||||
−0.865657 | + | 0.500638i | \(0.833099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 318.318i | − 1.17460i | −0.809368 | − | 0.587302i | \(-0.800190\pi\) | ||||
0.809368 | − | 0.587302i | \(-0.199810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 36.5025 | 0.133709 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −305.683 | −1.11157 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 356.597i | − 1.28735i | −0.765298 | − | 0.643677i | \(-0.777408\pi\) | ||||
0.765298 | − | 0.643677i | \(-0.222592\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 0.141750i | 0 0.000508066i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −109.846 | −0.390911 | −0.195455 | − | 0.980713i | \(-0.562619\pi\) | ||||
−0.195455 | + | 0.980713i | \(0.562619\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 514.582 | 1.81831 | 0.909155 | − | 0.416457i | \(-0.136728\pi\) | ||||
0.909155 | + | 0.416457i | \(0.136728\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 455.861i | − 1.59951i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 96.9647i | 0.337856i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −154.191 | −0.533534 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −203.807 | −0.700366 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 133.002i | 0.453931i | 0.973903 | + | 0.226965i | \(0.0728804\pi\) | ||||
−0.973903 | + | 0.226965i | \(0.927120\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 367.475i | 1.24568i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 389.194 | 1.31042 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.94729 | −0.0132016 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 74.0530i | 0.246023i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 84.0581i | − 0.277420i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 108.544 | 0.355882 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −382.811 | −1.24694 | −0.623471 | − | 0.781847i | \(-0.714278\pi\) | ||||
−0.623471 | + | 0.781847i | \(0.714278\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 478.279i | 1.54783i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 196.374i | − 0.631426i | −0.948855 | − | 0.315713i | \(-0.897756\pi\) | ||||
0.948855 | − | 0.315713i | \(-0.102244\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −427.045 | −1.36436 | −0.682181 | − | 0.731183i | \(-0.738968\pi\) | ||||
−0.682181 | + | 0.731183i | \(0.738968\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.64680 | 0.00522795 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 111.049i | 0.350314i | 0.984541 | + | 0.175157i | \(0.0560433\pi\) | ||||
−0.984541 | + | 0.175157i | \(0.943957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 614.326i | − 1.92579i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 354.951 | 1.10577 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 260.577 | 0.806741 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 98.5174i | − 0.303131i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 293.298i | 0.896936i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 111.582 | 0.339154 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 119.629 | 0.361416 | 0.180708 | − | 0.983537i | \(-0.442161\pi\) | ||||
0.180708 | + | 0.983537i | \(0.442161\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.11718i | 0.0123639i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 625.721i | 1.86782i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −57.3636 | −0.170218 | −0.0851092 | − | 0.996372i | \(-0.527124\pi\) | ||||
−0.0851092 | + | 0.996372i | \(0.527124\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −289.511 | −0.854014 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.2286i | 0.0651864i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.5203i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.3453 | 0.0502763 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 268.774 | 0.774566 | 0.387283 | − | 0.921961i | \(-0.373414\pi\) | ||||
0.387283 | + | 0.921961i | \(0.373414\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 97.0498i | 0.278080i | 0.990287 | + | 0.139040i | \(0.0444016\pi\) | ||||
−0.990287 | + | 0.139040i | \(0.955598\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 125.432i | 0.357356i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −316.928 | −0.897813 | −0.448907 | − | 0.893579i | \(-0.648186\pi\) | ||||
−0.448907 | + | 0.893579i | \(0.648186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −111.325 | −0.313592 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 91.6877i | − 0.256828i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 590.194i | 1.64399i | 0.569492 | + | 0.821997i | \(0.307140\pi\) | ||||
−0.569492 | + | 0.821997i | \(0.692860\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 142.681 | 0.395239 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −252.839 | −0.696526 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 65.2449i | − 0.178753i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 175.544i | − 0.478321i | −0.970980 | − | 0.239160i | \(-0.923128\pi\) | ||||
0.970980 | − | 0.239160i | \(-0.0768722\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.35202 | −0.00908406 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 114.837 | 0.309534 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 554.016i | − 1.48530i | −0.669681 | − | 0.742649i | \(-0.733569\pi\) | ||||
0.669681 | − | 0.742649i | \(-0.266431\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 74.8928i | − 0.199714i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 197.989 | 0.525169 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −749.909 | −1.97865 | −0.989325 | − | 0.145723i | \(-0.953449\pi\) | ||||
−0.989325 | + | 0.145723i | \(0.953449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 214.515i | − 0.563032i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 246.230i | 0.642899i | 0.946927 | + | 0.321450i | \(0.104170\pi\) | ||||
−0.946927 | + | 0.321450i | \(0.895830\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −258.243 | −0.670762 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.55997 | −0.00661491 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 298.019i | − 0.766115i | −0.923724 | − | 0.383058i | \(-0.874871\pi\) | ||||
0.923724 | − | 0.383058i | \(-0.125129\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.91487i | 0.0253577i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −626.305 | −1.59365 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −387.787 | −0.981739 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 127.823i | 0.321971i | 0.986957 | + | 0.160986i | \(0.0514673\pi\) | ||||
−0.986957 | + | 0.160986i | \(0.948533\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 177.227i | − 0.444178i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −774.286 | −1.93089 | −0.965444 | − | 0.260609i | \(-0.916077\pi\) | ||||
−0.965444 | + | 0.260609i | \(0.916077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.16396 | −0.0177766 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 545.575i | − 1.34710i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 645.635i | − 1.58633i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −666.884 | −1.63052 | −0.815262 | − | 0.579093i | \(-0.803407\pi\) | ||||
−0.815262 | + | 0.579093i | \(0.803407\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −54.2172 | −0.131915 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 142.865i | 0.345920i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 97.3687i | 0.234623i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −400.204 | −0.959721 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −95.3634 | −0.227598 | −0.113799 | − | 0.993504i | \(-0.536302\pi\) | ||||
−0.113799 | + | 0.993504i | \(0.536302\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 279.158i | 0.663083i | 0.943441 | + | 0.331541i | \(0.107569\pi\) | ||||
−0.943441 | + | 0.331541i | \(0.892431\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.85732i | 0.00911897i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −247.458 | −0.582254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 42.1991 | 0.0988270 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 197.880i | − 0.461260i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 169.374i | − 0.392978i | −0.980506 | − | 0.196489i | \(-0.937046\pi\) | ||||
0.980506 | − | 0.196489i | \(-0.0629540\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −295.214 | −0.681787 | −0.340894 | − | 0.940102i | \(-0.610730\pi\) | ||||
−0.340894 | + | 0.940102i | \(0.610730\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −870.010 | −2.00002 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.1649i | 0.0438555i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 326.773i | − 0.744357i | −0.928161 | − | 0.372179i | \(-0.878611\pi\) | ||||
0.928161 | − | 0.372179i | \(-0.121389\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.640236 | 0.00145178 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −514.789 | −1.16205 | −0.581026 | − | 0.813885i | \(-0.697349\pi\) | ||||
−0.581026 | + | 0.813885i | \(0.697349\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 681.462i | − 1.53137i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 61.9682i | − 0.138631i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 602.217 | 1.34124 | 0.670620 | − | 0.741801i | \(-0.266028\pi\) | ||||
0.670620 | + | 0.741801i | \(0.266028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 525.646 | 1.16551 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 277.904i | − 0.613475i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 83.2282i | − 0.182919i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 264.634 | 0.579069 | 0.289534 | − | 0.957168i | \(-0.406500\pi\) | ||||
0.289534 | + | 0.957168i | \(0.406500\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 315.062 | 0.686409 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 434.788i | − 0.943140i | −0.881829 | − | 0.471570i | \(-0.843687\pi\) | ||||
0.881829 | − | 0.471570i | \(-0.156313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 193.258i | 0.417403i | 0.977979 | + | 0.208702i | \(0.0669237\pi\) | ||||
−0.977979 | + | 0.208702i | \(0.933076\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.4801 | 0.0676992 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −655.297 | −1.40320 | −0.701602 | − | 0.712569i | \(-0.747532\pi\) | ||||
−0.701602 | + | 0.712569i | \(0.747532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 243.264i | 0.518687i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 475.577i | − 1.00972i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 401.442 | 0.848714 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −478.322 | −1.00699 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.96986i | 0.00832256i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 102.660i | 0.214322i | 0.994242 | + | 0.107161i | \(0.0341761\pi\) | ||||
−0.994242 | + | 0.107161i | \(0.965824\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 208.079 | 0.432597 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.74342 | 0.0139615 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 464.693i | 0.958129i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 150.652i | − 0.309347i | −0.987966 | − | 0.154674i | \(-0.950567\pi\) | ||||
0.987966 | − | 0.154674i | \(-0.0494326\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −136.783 | −0.279720 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −118.795 | −0.241946 | −0.120973 | − | 0.992656i | \(-0.538601\pi\) | ||||
−0.120973 | + | 0.992656i | \(0.538601\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 497.312i | − 1.00875i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 8.92733i | − 0.0180350i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −43.2805 | −0.0870834 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −546.431 | −1.09505 | −0.547526 | − | 0.836789i | \(-0.684430\pi\) | ||||
−0.547526 | + | 0.836789i | \(0.684430\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46.5153i | 0.0928449i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 520.718i | 1.03522i | 0.855615 | + | 0.517612i | \(0.173179\pi\) | ||||
−0.855615 | + | 0.517612i | \(0.826821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −191.658 | −0.379521 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −440.643 | −0.869119 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 601.427i | 1.18159i | 0.806823 | + | 0.590793i | \(0.201185\pi\) | ||||
−0.806823 | + | 0.590793i | \(0.798815\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 25.3656i | − 0.0496391i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 608.997 | 1.18713 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1090.51 | 2.11749 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 604.886i | − 1.16999i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 793.998i | 1.52986i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 582.268 | 1.11760 | 0.558798 | − | 0.829304i | \(-0.311263\pi\) | ||||
0.558798 | + | 0.829304i | \(0.311263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 143.593 | 0.274557 | 0.137278 | − | 0.990533i | \(-0.456165\pi\) | ||||
0.137278 | + | 0.990533i | \(0.456165\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 168.304i | 0.320579i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.9946i | 0.0341453i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.271 | 0.998622 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.93877 | −0.00930088 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 169.409i | 0.317840i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 809.311i | − 1.51273i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −132.838 | −0.247370 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −100.398 | −0.186268 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 833.097i | 1.53992i | 0.638092 | + | 0.769960i | \(0.279724\pi\) | ||||
−0.638092 | + | 0.769960i | \(0.720276\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 501.762i | − 0.924056i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 668.740 | 1.22705 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −356.858 | −0.652391 | −0.326196 | − | 0.945302i | \(-0.605767\pi\) | ||||
−0.326196 | + | 0.945302i | \(0.605767\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.45880i | 0.00265720i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 961.275i | − 1.74460i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −150.762 | −0.272625 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −914.349 | −1.64748 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 324.859i | 0.583230i | 0.956536 | + | 0.291615i | \(0.0941927\pi\) | ||||
−0.956536 | + | 0.291615i | \(0.905807\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 129.379i | 0.231447i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −497.040 | −0.885989 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −85.2531 | −0.151427 | −0.0757133 | − | 0.997130i | \(-0.524123\pi\) | ||||
−0.0757133 | + | 0.997130i | \(0.524123\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 660.104i | 1.16833i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 212.106i | − 0.374084i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.7512 | 0.0505293 | 0.0252647 | − | 0.999681i | \(-0.491957\pi\) | ||||
0.0252647 | + | 0.999681i | \(0.491957\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −677.532 | −1.18657 | −0.593286 | − | 0.804992i | \(-0.702170\pi\) | ||||
−0.593286 | + | 0.804992i | \(0.702170\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1055.42i | − 1.84191i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 18.2000i | − 0.0316521i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.6675 | −0.0358189 | −0.0179095 | − | 0.999840i | \(-0.505701\pi\) | ||||
−0.0179095 | + | 0.999840i | \(0.505701\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1040.40 | 1.79688 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.8545i | 0.0651541i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 622.533i | − 1.06781i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.87716 | 0.00491822 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 551.489 | 0.939504 | 0.469752 | − | 0.882798i | \(-0.344343\pi\) | ||||
0.469752 | + | 0.882798i | \(0.344343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.7825i | 0.0590534i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 80.3825i | − 0.136011i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.9313 | 0.0774558 | 0.0387279 | − | 0.999250i | \(-0.487669\pi\) | ||||
0.0387279 | + | 0.999250i | \(0.487669\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −209.054 | −0.351352 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 691.141i | 1.15769i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 662.449i | − 1.10593i | −0.833206 | − | 0.552963i | \(-0.813497\pi\) | ||||
0.833206 | − | 0.552963i | \(-0.186503\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 840.257 | 1.39810 | 0.699049 | − | 0.715074i | \(-0.253607\pi\) | ||||
0.699049 | + | 0.715074i | \(0.253607\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.40952 | −0.0139461 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 576.490i | 0.952876i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1024.92i | − 1.68850i | −0.535951 | − | 0.844249i | \(-0.680047\pi\) | ||||
0.535951 | − | 0.844249i | \(-0.319953\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −338.238 | −0.555399 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 194.946 | 0.319061 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 109.148i | 0.178055i | 0.996029 | + | 0.0890276i | \(0.0283759\pi\) | ||||
−0.996029 | + | 0.0890276i | \(0.971624\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 744.422i | − 1.21044i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −78.9177 | −0.127905 | −0.0639527 | − | 0.997953i | \(-0.520371\pi\) | ||||
−0.0639527 | + | 0.997953i | \(0.520371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 715.995 | 1.15670 | 0.578348 | − | 0.815790i | \(-0.303698\pi\) | ||||
0.578348 | + | 0.815790i | \(0.303698\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.1721i | 0.0373141i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 264.935i | − 0.425257i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −703.583 | −1.12573 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −960.749 | −1.53230 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 522.657i | − 0.830933i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 849.316i | − 1.34598i | −0.739650 | − | 0.672992i | \(-0.765009\pi\) | ||||
0.739650 | − | 0.672992i | \(-0.234991\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −237.853 | −0.375755 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −489.109 | −0.770251 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 32.3570i | − 0.0507960i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 1.49618i | − 0.00234144i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 488.089 | 0.761450 | 0.380725 | − | 0.924688i | \(-0.375674\pi\) | ||||
0.380725 | + | 0.924688i | \(0.375674\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 257.106 | 0.399854 | 0.199927 | − | 0.979811i | \(-0.435930\pi\) | ||||
0.199927 | + | 0.979811i | \(0.435930\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 568.522i | − 0.881430i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 699.536i | 1.08120i | 0.841280 | + | 0.540600i | \(0.181803\pi\) | ||||
−0.841280 | + | 0.540600i | \(0.818197\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 774.472 | 1.19333 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.2387 | 0.0187998 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 277.629i | 0.425160i | 0.977144 | + | 0.212580i | \(0.0681866\pi\) | ||||
−0.977144 | + | 0.212580i | \(0.931813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1428.02i | 2.18018i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.876874 | 0.00133466 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 522.721 | 0.793204 | 0.396602 | − | 0.917991i | \(-0.370189\pi\) | ||||
0.396602 | + | 0.917991i | \(0.370189\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 515.922i | − 0.780518i | −0.920705 | − | 0.390259i | \(-0.872385\pi\) | ||||
0.920705 | − | 0.390259i | \(-0.127615\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 160.189i | − 0.241612i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −404.090 | −0.607654 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.5761 | 0.0548368 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 789.060i | 1.17946i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 228.762i | − 0.340927i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1231.64 | −1.83008 | −0.915041 | − | 0.403361i | \(-0.867842\pi\) | ||||
−0.915041 | + | 0.403361i | \(0.867842\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −578.335 | −0.856792 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 576.563i | 0.851645i | 0.904807 | + | 0.425822i | \(0.140015\pi\) | ||||
−0.904807 | + | 0.425822i | \(0.859985\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 180.661i | 0.266069i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1287.38 | −1.89043 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −161.395 | −0.236302 | −0.118151 | − | 0.992996i | \(-0.537697\pi\) | ||||
−0.118151 | + | 0.992996i | \(0.537697\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 123.619i | 0.180466i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 1268.21i | − 1.84601i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 200.634 | 0.291196 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 113.661 | 0.164488 | 0.0822442 | − | 0.996612i | \(-0.473791\pi\) | ||||
0.0822442 | + | 0.996612i | \(0.473791\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 3.47072i | − 0.00500826i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 912.491i | 1.31294i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 425.524 | 0.610507 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 653.140 | 0.934391 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 331.011i | 0.472198i | 0.971729 | + | 0.236099i | \(0.0758689\pi\) | ||||
−0.971729 | + | 0.236099i | \(0.924131\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1010.27i | − 1.43708i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −856.640 | −1.21509 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −74.5119 | −0.105392 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 591.351i | 0.834063i | 0.908892 | + | 0.417032i | \(0.136930\pi\) | ||||
−0.908892 | + | 0.417032i | \(0.863070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 5.21176i | − 0.00733018i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.32346 | −0.00185618 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −451.181 | −0.631022 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 269.119i | − 0.375340i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 483.600i | − 0.672600i | −0.941755 | − | 0.336300i | \(-0.890824\pi\) | ||||
0.941755 | − | 0.336300i | \(-0.109176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 423.962 | 0.588020 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1122.09 | −1.55199 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 912.877i | 1.25914i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 659.508i | 0.907163i | 0.891215 | + | 0.453582i | \(0.149854\pi\) | ||||
−0.891215 | + | 0.453582i | \(0.850146\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 736.257 | 1.00995 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 324.977 | 0.444565 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 211.776i | 0.288916i | 0.989511 | + | 0.144458i | \(0.0461439\pi\) | ||||
−0.989511 | + | 0.144458i | \(0.953856\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 142.184i | 0.193448i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1318.74 | 1.78933 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −246.912 | −0.334116 | −0.167058 | − | 0.985947i | \(-0.553427\pi\) | ||||
−0.167058 | + | 0.985947i | \(0.553427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 309.636i | − 0.417863i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 333.126i | − 0.448352i | −0.974549 | − | 0.224176i | \(-0.928031\pi\) | ||||
0.974549 | − | 0.224176i | \(-0.0719691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −141.292 | −0.189653 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.30861 | −0.00175182 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 314.640i | − 0.420080i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 609.916i | − 0.812139i | −0.913842 | − | 0.406069i | \(-0.866899\pi\) | ||||
0.913842 | − | 0.406069i | \(-0.133101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 953.691 | 1.26652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −633.640 | −0.839259 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 439.344i | − 0.580375i | −0.956970 | − | 0.290187i | \(-0.906282\pi\) | ||||
0.956970 | − | 0.290187i | \(-0.0937176\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 36.5561i | − 0.0481635i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 460.968 | 0.605740 | 0.302870 | − | 0.953032i | \(-0.402055\pi\) | ||||
0.302870 | + | 0.953032i | \(0.402055\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 259.989 | 0.340746 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 7.22689i | − 0.00944692i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 249.602i | 0.325426i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1431.37 | 1.86134 | 0.930670 | − | 0.365859i | \(-0.119225\pi\) | ||||
0.930670 | + | 0.365859i | \(0.119225\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 499.838 | 0.648299 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 245.480i | − 0.317568i | −0.987313 | − | 0.158784i | \(-0.949243\pi\) | ||||
0.987313 | − | 0.158784i | \(-0.0507574\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 33.0312i | − 0.0426209i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −355.476 | −0.457498 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 822.513 | 1.05586 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 234.624i | 0.300414i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 1162.27i | − 1.48438i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1084.35 | −1.38134 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −579.993 | −0.736967 | −0.368483 | − | 0.929634i | \(-0.620123\pi\) | ||||
−0.368483 | + | 0.929634i | \(0.620123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 257.067i | 0.325813i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 256.632i | 0.324440i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 73.7268 | 0.0929720 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −881.632 | −1.10897 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1348.22i | − 1.69162i | −0.533484 | − | 0.845810i | \(-0.679118\pi\) | ||||
0.533484 | − | 0.845810i | \(-0.320882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 489.670i | − 0.612853i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.15867 | 0.0114340 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −137.507 | −0.171241 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 15.3755i | − 0.0190999i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 803.913i | − 0.996175i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 697.465 | 0.862132 | 0.431066 | − | 0.902320i | \(-0.358138\pi\) | ||||
0.431066 | + | 0.902320i | \(0.358138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −482.271 | −0.594662 | −0.297331 | − | 0.954774i | \(-0.596097\pi\) | ||||
−0.297331 | + | 0.954774i | \(0.596097\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 950.089i | 1.16862i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 311.874i | 0.382668i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 628.161 | 0.768863 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.11857 | 0.00136577 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 386.345i | 0.470579i | 0.971925 | + | 0.235289i | \(0.0756038\pi\) | ||||
−0.971925 | + | 0.235289i | \(0.924396\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 354.386i | 0.430603i | 0.976548 | + | 0.215301i | \(0.0690734\pi\) | ||||
−0.976548 | + | 0.215301i | \(0.930927\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 912.377 | 1.10591 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1260.47 | 1.52414 | 0.762072 | − | 0.647493i | \(-0.224182\pi\) | ||||
0.762072 | + | 0.647493i | \(0.224182\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1443.69i | − 1.74148i | −0.491746 | − | 0.870739i | \(-0.663641\pi\) | ||||
0.491746 | − | 0.870739i | \(-0.336359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1064.34i | 1.28080i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −81.2750 | −0.0975690 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 106.058 | 0.127016 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 42.0552i | 0.0502451i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.6511i | 0.0532194i | 0.999646 | + | 0.0266097i | \(0.00847114\pi\) | ||||
−0.999646 | + | 0.0266097i | \(0.991529\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −993.593 | −1.18144 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 327.859 | 0.388920 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1004.70i | 1.18899i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 224.125i | 0.264610i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1535.88 | −1.80905 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.4402 | 0.0451707 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 118.167i | 0.138531i | 0.997598 | + | 0.0692655i | \(0.0220656\pi\) | ||||
−0.997598 | + | 0.0692655i | \(0.977934\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 13.9692i | − 0.0163382i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 153.130 | 0.178682 | 0.0893408 | − | 0.996001i | \(-0.471524\pi\) | ||||
0.0893408 | + | 0.996001i | \(0.471524\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 136.656 | 0.159087 | 0.0795437 | − | 0.996831i | \(-0.474654\pi\) | ||||
0.0795437 | + | 0.996831i | \(0.474654\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 289.412i | − 0.336135i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1462.52i | 1.69470i | 0.531036 | + | 0.847349i | \(0.321803\pi\) | ||||
−0.531036 | + | 0.847349i | \(0.678197\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1810.37 | 2.09291 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 460.217 | 0.530816 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 817.281i | 0.940484i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 425.011i | 0.487957i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.24535 | −0.00715389 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −66.3874 | −0.0758713 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.8881i | 0.0340799i | 0.999855 | + | 0.0170399i | \(0.00542424\pi\) | ||||
−0.999855 | + | 0.0170399i | \(0.994576\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 396.972i | − 0.451618i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −497.832 | −0.565076 | −0.282538 | − | 0.959256i | \(-0.591176\pi\) | ||||
−0.282538 | + | 0.959256i | \(0.591176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1430.98 | −1.62059 | −0.810295 | − | 0.586022i | \(-0.800693\pi\) | ||||
−0.810295 | + | 0.586022i | \(0.800693\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1096.81i | − 1.23933i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1187.21i | 1.33846i | 0.743057 | + | 0.669228i | \(0.233375\pi\) | ||||
−0.743057 | + | 0.669228i | \(0.766625\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −190.153 | −0.213896 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1149.83 | −1.29049 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 946.504i | − 1.05991i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 302.879i | 0.338412i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.7815 | 0.0131344 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 66.3823 | 0.0738401 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 503.956i | − 0.559329i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 221.027i | − 0.244770i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1144.05 | −1.26415 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −818.659 | −0.902601 | −0.451301 | − | 0.892372i | \(-0.649040\pi\) | ||||
−0.451301 | + | 0.892372i | \(0.649040\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 2.57584i | − 0.00283370i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 774.905i | 0.850610i | 0.905050 | + | 0.425305i | \(0.139833\pi\) | ||||
−0.905050 | + | 0.425305i | \(0.860167\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 205.210 | 0.224764 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −323.973 | −0.354069 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 555.177i | 0.605428i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1695.99i | 1.84547i | 0.385437 | + | 0.922734i | \(0.374051\pi\) | ||||
−0.385437 | + | 0.922734i | \(0.625949\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1142.58 | 1.24059 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −75.6160 | −0.0819241 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 959.401i | 1.03719i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.6562i | 0.0158103i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1173.31 | −1.26298 | −0.631491 | − | 0.775383i | \(-0.717557\pi\) | ||||
−0.631491 | + | 0.775383i | \(0.717557\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −157.100 | −0.168743 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 586.120i | 0.628210i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1133.28i | 1.21207i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 315.505 | 0.336719 | 0.168359 | − | 0.985726i | \(-0.446153\pi\) | ||||
0.168359 | + | 0.985726i | \(0.446153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1274.61 | 1.35741 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 423.505i | − 0.450058i | −0.974352 | − | 0.225029i | \(-0.927752\pi\) | ||||
0.974352 | − | 0.225029i | \(-0.0722477\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.2963i | 0.0331880i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −488.581 | −0.517017 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1147.28 | 1.21149 | 0.605743 | − | 0.795660i | \(-0.292876\pi\) | ||||
0.605743 | + | 0.795660i | \(0.292876\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 44.3166i | − 0.0466982i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 331.451i | − 0.348529i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −736.494 | −0.772816 | −0.386408 | − | 0.922328i | \(-0.626284\pi\) | ||||
−0.386408 | + | 0.922328i | \(0.626284\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2406.42 | −2.51981 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1833.59i | 1.91598i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 48.0599i | 0.0501146i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 958.598 | 0.997501 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.8769 | 0.0112948 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 2372.17i | − 2.45821i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1147.66i | 1.18682i | 0.804899 | + | 0.593411i | \(0.202219\pi\) | ||||
−0.804899 | + | 0.593411i | \(0.797781\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −777.750 | −0.802632 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1108.64 | 1.14175 | 0.570876 | − | 0.821036i | \(-0.306604\pi\) | ||||
0.570876 | + | 0.821036i | \(0.306604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 354.754i | 0.364598i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 294.047i | 0.301586i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 779.026 | 0.797366 | 0.398683 | − | 0.917089i | \(-0.369467\pi\) | ||||
0.398683 | + | 0.917089i | \(0.369467\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1436.21 | −1.46702 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.98769i | 0.00916176i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 79.5940i | − 0.0809705i | −0.999180 | − | 0.0404853i | \(-0.987110\pi\) | ||||
0.999180 | − | 0.0404853i | \(-0.0128904\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −183.277 | −0.186069 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −333.040 | −0.337427 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.9013i | 0.0241671i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 644.244i | 0.650095i | 0.945698 | + | 0.325047i | \(0.105380\pi\) | ||||
−0.945698 | + | 0.325047i | \(0.894620\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −357.057 | −0.359574 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1575.85 | 1.58377 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1739.99i | 1.74523i | 0.488409 | + | 0.872615i | \(0.337578\pi\) | ||||
−0.488409 | + | 0.872615i | \(0.662422\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 1221.50i | − 1.22273i |
(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 | 1792.3.g.g.127.4 | 12 | ||
4.3 | odd | 2 | inner | 1792.3.g.g.127.10 | 12 | ||
8.3 | odd | 2 | inner | 1792.3.g.g.127.3 | 12 | ||
8.5 | even | 2 | inner | 1792.3.g.g.127.9 | 12 | ||
16.3 | odd | 4 | 448.3.d.d.127.5 | 6 | |||
16.5 | even | 4 | 28.3.c.a.15.5 | ✓ | 6 | ||
16.11 | odd | 4 | 28.3.c.a.15.6 | yes | 6 | ||
16.13 | even | 4 | 448.3.d.d.127.2 | 6 | |||
48.5 | odd | 4 | 252.3.g.a.127.2 | 6 | |||
48.11 | even | 4 | 252.3.g.a.127.1 | 6 | |||
112.5 | odd | 12 | 196.3.g.j.67.1 | 12 | |||
112.11 | odd | 12 | 196.3.g.k.79.1 | 12 | |||
112.27 | even | 4 | 196.3.c.g.99.6 | 6 | |||
112.37 | even | 12 | 196.3.g.k.67.1 | 12 | |||
112.53 | even | 12 | 196.3.g.k.79.3 | 12 | |||
112.59 | even | 12 | 196.3.g.j.79.1 | 12 | |||
112.69 | odd | 4 | 196.3.c.g.99.5 | 6 | |||
112.75 | even | 12 | 196.3.g.j.67.3 | 12 | |||
112.101 | odd | 12 | 196.3.g.j.79.3 | 12 | |||
112.107 | odd | 12 | 196.3.g.k.67.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.3.c.a.15.5 | ✓ | 6 | 16.5 | even | 4 | ||
28.3.c.a.15.6 | yes | 6 | 16.11 | odd | 4 | ||
196.3.c.g.99.5 | 6 | 112.69 | odd | 4 | |||
196.3.c.g.99.6 | 6 | 112.27 | even | 4 | |||
196.3.g.j.67.1 | 12 | 112.5 | odd | 12 | |||
196.3.g.j.67.3 | 12 | 112.75 | even | 12 | |||
196.3.g.j.79.1 | 12 | 112.59 | even | 12 | |||
196.3.g.j.79.3 | 12 | 112.101 | odd | 12 | |||
196.3.g.k.67.1 | 12 | 112.37 | even | 12 | |||
196.3.g.k.67.3 | 12 | 112.107 | odd | 12 | |||
196.3.g.k.79.1 | 12 | 112.11 | odd | 12 | |||
196.3.g.k.79.3 | 12 | 112.53 | even | 12 | |||
252.3.g.a.127.1 | 6 | 48.11 | even | 4 | |||
252.3.g.a.127.2 | 6 | 48.5 | odd | 4 | |||
448.3.d.d.127.2 | 6 | 16.13 | even | 4 | |||
448.3.d.d.127.5 | 6 | 16.3 | odd | 4 | |||
1792.3.g.g.127.3 | 12 | 8.3 | odd | 2 | inner | ||
1792.3.g.g.127.4 | 12 | 1.1 | even | 1 | trivial | ||
1792.3.g.g.127.9 | 12 | 8.5 | even | 2 | inner | ||
1792.3.g.g.127.10 | 12 | 4.3 | odd | 2 | inner |