Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(1025,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.e (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.7 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1025 |
Dual form | 1728.3.e.u.1025.1 |
$q$-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 | ||||||||
\(5\) | 6.61037i | 1.32207i | 0.750354 | + | 0.661037i | \(0.229883\pi\) | ||||
−0.750354 | + | 0.661037i | \(0.770117\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.43879 | −1.34840 | −0.674200 | − | 0.738549i | \(-0.735511\pi\) | ||||
−0.674200 | + | 0.738549i | \(0.735511\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.6969i | 1.60881i | 0.594080 | + | 0.804406i | \(0.297516\pi\) | ||||
−0.594080 | + | 0.804406i | \(0.702484\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.6969 | −1.59207 | −0.796036 | − | 0.605249i | \(-0.793073\pi\) | ||||
−0.796036 | + | 0.605249i | \(0.793073\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.0492i | 0.944068i | 0.881580 | + | 0.472034i | \(0.156480\pi\) | ||||
−0.881580 | + | 0.472034i | \(0.843520\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.2993 | −0.647333 | −0.323667 | − | 0.946171i | \(-0.604916\pi\) | ||||
−0.323667 | + | 0.946171i | \(0.604916\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 26.6969i | − 1.16074i | −0.814354 | − | 0.580368i | \(-0.802909\pi\) | ||||
0.814354 | − | 0.580368i | \(-0.197091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18.6969 | −0.747878 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.921404i | 0.0317725i | 0.999874 | + | 0.0158863i | \(0.00505697\pi\) | ||||
−0.999874 | + | 0.0158863i | \(0.994943\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −53.7722 | −1.73459 | −0.867294 | − | 0.497796i | \(-0.834143\pi\) | ||||
−0.867294 | + | 0.497796i | \(0.834143\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 62.3939i | − 1.78268i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 64.0908 | 1.73218 | 0.866092 | − | 0.499884i | \(-0.166624\pi\) | ||||
0.866092 | + | 0.499884i | \(0.166624\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 19.7990i | 0.482902i | 0.970413 | + | 0.241451i | \(0.0776233\pi\) | ||||
−0.970413 | + | 0.241451i | \(0.922377\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 69.7893 | 1.62301 | 0.811503 | − | 0.584348i | \(-0.198650\pi\) | ||||
0.811503 | + | 0.584348i | \(0.198650\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 0.606123i | − 0.0128962i | −0.999979 | − | 0.00644812i | \(-0.997947\pi\) | ||||
0.999979 | − | 0.00644812i | \(-0.00205251\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40.0908 | 0.818180 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 45.3512i | 0.855682i | 0.903854 | + | 0.427841i | \(0.140726\pi\) | ||||
−0.903854 | + | 0.427841i | \(0.859274\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −116.983 | −2.12697 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 71.3939i | − 1.21007i | −0.796201 | − | 0.605033i | \(-0.793160\pi\) | ||||
0.796201 | − | 0.605033i | \(-0.206840\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | 0.0655738 | 0.0327869 | − | 0.999462i | \(-0.489562\pi\) | ||||
0.0327869 | + | 0.999462i | \(0.489562\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 136.814i | − 2.10484i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.43545 | 0.110977 | 0.0554884 | − | 0.998459i | \(-0.482328\pi\) | ||||
0.0554884 | + | 0.998459i | \(0.482328\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 27.3031i | − 0.384550i | −0.981341 | − | 0.192275i | \(-0.938413\pi\) | ||||
0.981341 | − | 0.192275i | \(-0.0615866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.30306 | 0.0863433 | 0.0431717 | − | 0.999068i | \(-0.486254\pi\) | ||||
0.0431717 | + | 0.999068i | \(0.486254\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 167.038i | − 2.16932i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 42.6191 | 0.539482 | 0.269741 | − | 0.962933i | \(-0.413062\pi\) | ||||
0.269741 | + | 0.962933i | \(0.413062\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 72.3031i | − 0.871121i | −0.900159 | − | 0.435561i | \(-0.856550\pi\) | ||||
0.900159 | − | 0.435561i | \(-0.143450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −106.091 | −1.24813 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 126.486i | 1.42119i | 0.703599 | + | 0.710597i | \(0.251575\pi\) | ||||
−0.703599 | + | 0.710597i | \(0.748425\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 195.354 | 2.14675 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 81.3031i | − 0.855822i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 27.0000 | 0.278351 | 0.139175 | − | 0.990268i | \(-0.455555\pi\) | ||||
0.139175 | + | 0.990268i | \(0.455555\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 33.7806i | 0.334461i | 0.985918 | + | 0.167231i | \(0.0534824\pi\) | ||||
−0.985918 | + | 0.167231i | \(0.946518\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −95.2451 | −0.924710 | −0.462355 | − | 0.886695i | \(-0.652995\pi\) | ||||
−0.462355 | + | 0.886695i | \(0.652995\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 96.5755i | 0.902575i | 0.892379 | + | 0.451287i | \(0.149035\pi\) | ||||
−0.892379 | + | 0.451287i | \(0.850965\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −90.8786 | −0.833748 | −0.416874 | − | 0.908964i | \(-0.636874\pi\) | ||||
−0.416874 | + | 0.908964i | \(0.636874\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 50.1829i | − 0.444097i | −0.975036 | − | 0.222048i | \(-0.928726\pi\) | ||||
0.975036 | − | 0.222048i | \(-0.0712743\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 176.477 | 1.53458 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 151.485i | − 1.27298i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −192.182 | −1.58828 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 41.6655i | 0.333324i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 134.146 | 1.05627 | 0.528136 | − | 0.849160i | \(-0.322891\pi\) | ||||
0.528136 | + | 0.849160i | \(0.322891\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 46.8184i | − 0.357392i | −0.983904 | − | 0.178696i | \(-0.942812\pi\) | ||||
0.983904 | − | 0.178696i | \(-0.0571879\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 116.091 | 0.872863 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 182.926i | − 1.33523i | −0.744507 | − | 0.667614i | \(-0.767315\pi\) | ||||
0.744507 | − | 0.667614i | \(-0.232685\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 137.864 | 0.991829 | 0.495914 | − | 0.868371i | \(-0.334833\pi\) | ||||
0.495914 | + | 0.868371i | \(0.334833\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 366.272i | − 2.56135i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.09082 | −0.0420056 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 43.6368i | 0.292864i | 0.989221 | + | 0.146432i | \(0.0467790\pi\) | ||||
−0.989221 | + | 0.146432i | \(0.953221\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −84.0920 | −0.556900 | −0.278450 | − | 0.960451i | \(-0.589821\pi\) | ||||
−0.278450 | + | 0.960451i | \(0.589821\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 355.454i | − 2.29325i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 236.545 | 1.50666 | 0.753328 | − | 0.657645i | \(-0.228447\pi\) | ||||
0.753328 | + | 0.657645i | \(0.228447\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 251.987i | 1.56514i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −282.307 | −1.73194 | −0.865971 | − | 0.500094i | \(-0.833299\pi\) | ||||
−0.865971 | + | 0.500094i | \(0.833299\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 70.1816i | 0.420249i | 0.977675 | + | 0.210125i | \(0.0673870\pi\) | ||||
−0.977675 | + | 0.210125i | \(0.932613\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 259.363 | 1.53469 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 338.586i | 1.95715i | 0.205901 | + | 0.978573i | \(0.433987\pi\) | ||||
−0.205901 | + | 0.978573i | \(0.566013\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 176.477 | 1.00844 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 348.576i | − 1.94735i | −0.227942 | − | 0.973675i | \(-0.573200\pi\) | ||||
0.227942 | − | 0.973675i | \(-0.426800\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.1816 | −0.0894013 | −0.0447006 | − | 0.999000i | \(-0.514233\pi\) | ||||
−0.0447006 | + | 0.999000i | \(0.514233\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 423.664i | 2.29007i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −284.021 | −1.51883 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 171.303i | − 0.896875i | −0.893814 | − | 0.448437i | \(-0.851981\pi\) | ||||
0.893814 | − | 0.448437i | \(-0.148019\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −241.091 | −1.24918 | −0.624588 | − | 0.780955i | \(-0.714733\pi\) | ||||
−0.624588 | + | 0.780955i | \(0.714733\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 182.165i | − 0.924698i | −0.886698 | − | 0.462349i | \(-0.847007\pi\) | ||||
0.886698 | − | 0.462349i | \(-0.152993\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −70.0782 | −0.352152 | −0.176076 | − | 0.984377i | \(-0.556340\pi\) | ||||
−0.176076 | + | 0.984377i | \(0.556340\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.69694i | − 0.0428421i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −130.879 | −0.638432 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 217.660i | − 1.04144i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −102.681 | −0.486638 | −0.243319 | − | 0.969946i | \(-0.578236\pi\) | ||||
−0.243319 | + | 0.969946i | \(0.578236\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 461.333i | 2.14573i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 507.545 | 2.33892 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 332.168i | − 1.50302i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −205.082 | −0.919650 | −0.459825 | − | 0.888010i | \(-0.652088\pi\) | ||||
−0.459825 | + | 0.888010i | \(0.652088\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 103.757i | 0.457080i | 0.973535 | + | 0.228540i | \(0.0733952\pi\) | ||||
−0.973535 | + | 0.228540i | \(0.926605\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −435.576 | −1.90208 | −0.951038 | − | 0.309073i | \(-0.899981\pi\) | ||||
−0.951038 | + | 0.309073i | \(0.899981\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 387.344i | − 1.66242i | −0.555959 | − | 0.831210i | \(-0.687649\pi\) | ||||
0.555959 | − | 0.831210i | \(-0.312351\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00670 | 0.0170498 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 225.303i | − 0.942691i | −0.881949 | − | 0.471345i | \(-0.843769\pi\) | ||||
0.881949 | − | 0.471345i | \(-0.156231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −127.757 | −0.530113 | −0.265056 | − | 0.964233i | \(-0.585391\pi\) | ||||
−0.265056 | + | 0.964233i | \(0.585391\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 265.015i | 1.08169i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 254.558 | 1.03060 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 54.0000i | 0.215139i | 0.994198 | + | 0.107570i | \(0.0343069\pi\) | ||||
−0.994198 | + | 0.107570i | \(0.965693\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 472.454 | 1.86741 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 181.941i | 0.707941i | 0.935257 | + | 0.353970i | \(0.115169\pi\) | ||||
−0.935257 | + | 0.353970i | \(0.884831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −604.940 | −2.33568 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 42.8786i | − 0.163036i | −0.996672 | − | 0.0815182i | \(-0.974023\pi\) | ||||
0.996672 | − | 0.0815182i | \(-0.0259769\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −299.788 | −1.13127 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 140.500i | − 0.522305i | −0.965298 | − | 0.261152i | \(-0.915898\pi\) | ||||
0.965298 | − | 0.261152i | \(-0.0841025\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 264.854 | 0.977323 | 0.488661 | − | 0.872474i | \(-0.337485\pi\) | ||||
0.488661 | + | 0.872474i | \(0.337485\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 330.879i | − 1.20319i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 91.8184 | 0.331474 | 0.165737 | − | 0.986170i | \(-0.447000\pi\) | ||||
0.165737 | + | 0.986170i | \(0.447000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 417.814i | − 1.48688i | −0.668801 | − | 0.743442i | \(-0.733192\pi\) | ||||
0.668801 | − | 0.743442i | \(-0.266808\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −389.851 | −1.37757 | −0.688783 | − | 0.724968i | \(-0.741855\pi\) | ||||
−0.688783 | + | 0.724968i | \(0.741855\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 186.879i | − 0.651145i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.4245 | 0.108735 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 108.145i | − 0.369095i | −0.982824 | − | 0.184547i | \(-0.940918\pi\) | ||||
0.982824 | − | 0.184547i | \(-0.0590819\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 471.940 | 1.59980 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 552.545i | 1.84798i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −658.727 | −2.18846 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.4415i | 0.0866933i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 52.3468 | 0.170511 | 0.0852554 | − | 0.996359i | \(-0.472829\pi\) | ||||
0.0852554 | + | 0.996359i | \(0.472829\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 412.999i | − 1.32797i | −0.747745 | − | 0.663985i | \(-0.768864\pi\) | ||||
0.747745 | − | 0.663985i | \(-0.231136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −447.636 | −1.43015 | −0.715073 | − | 0.699050i | \(-0.753607\pi\) | ||||
−0.715073 | + | 0.699050i | \(0.753607\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 422.582i | 1.33307i | 0.745476 | + | 0.666533i | \(0.232222\pi\) | ||||
−0.745476 | + | 0.666533i | \(0.767778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.3060 | −0.0511161 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 197.394i | − 0.611127i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 386.969 | 1.19068 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.72107i | 0.0173893i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −211.082 | −0.637711 | −0.318855 | − | 0.947803i | \(-0.603298\pi\) | ||||
−0.318855 | + | 0.947803i | \(0.603298\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 49.1510i | 0.146719i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −113.455 | −0.336662 | −0.168331 | − | 0.985731i | \(-0.553838\pi\) | ||||
−0.168331 | + | 0.985731i | \(0.553838\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 951.604i | − 2.79063i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 84.0920 | 0.245166 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 448.485i | 1.29246i | 0.763141 | + | 0.646232i | \(0.223656\pi\) | ||||
−0.763141 | + | 0.646232i | \(0.776344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 260.454 | 0.746287 | 0.373143 | − | 0.927774i | \(-0.378280\pi\) | ||||
0.373143 | + | 0.927774i | \(0.378280\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 541.129i | 1.53294i | 0.642279 | + | 0.766471i | \(0.277989\pi\) | ||||
−0.642279 | + | 0.766471i | \(0.722011\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 180.483 | 0.508403 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 314.908i | − 0.877181i | −0.898687 | − | 0.438591i | \(-0.855478\pi\) | ||||
0.898687 | − | 0.438591i | \(-0.144522\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −209.727 | −0.580960 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 41.6655i | 0.114152i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −227.677 | −0.620374 | −0.310187 | − | 0.950676i | \(-0.600392\pi\) | ||||
−0.310187 | + | 0.950676i | \(0.600392\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 428.060i | − 1.15380i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −165.546 | −0.443823 | −0.221911 | − | 0.975067i | \(-0.571230\pi\) | ||||
−0.221911 | + | 0.975067i | \(0.571230\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 19.0702i | − 0.0505842i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −124.708 | −0.329044 | −0.164522 | − | 0.986373i | \(-0.552608\pi\) | ||||
−0.164522 | + | 0.986373i | \(0.552608\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 382.454i | 0.998575i | 0.866436 | + | 0.499287i | \(0.166405\pi\) | ||||
−0.866436 | + | 0.499287i | \(0.833595\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1104.18 | 2.86800 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 215.057i | 0.552845i | 0.961036 | + | 0.276423i | \(0.0891489\pi\) | ||||
−0.961036 | + | 0.276423i | \(0.910851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 428.463 | 1.09581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 281.728i | 0.713234i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 241.909 | 0.609343 | 0.304672 | − | 0.952457i | \(-0.401453\pi\) | ||||
0.304672 | + | 0.952457i | \(0.401453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 325.183i | − 0.810929i | −0.914111 | − | 0.405464i | \(-0.867110\pi\) | ||||
0.914111 | − | 0.405464i | \(-0.132890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1112.92 | 2.76159 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1134.21i | 2.78676i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 419.302 | 1.02519 | 0.512594 | − | 0.858631i | \(-0.328685\pi\) | ||||
0.512594 | + | 0.858631i | \(0.328685\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 673.872i | 1.63165i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 477.950 | 1.15169 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 337.151i | − 0.804656i | −0.915496 | − | 0.402328i | \(-0.868201\pi\) | ||||
0.915496 | − | 0.402328i | \(-0.131799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 422.969 | 1.00468 | 0.502339 | − | 0.864671i | \(-0.332473\pi\) | ||||
0.502339 | + | 0.864671i | \(0.332473\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 300.070i | − 0.706047i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −37.7552 | −0.0884196 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 137.333i | 0.318637i | 0.987227 | + | 0.159319i | \(0.0509297\pi\) | ||||
−0.987227 | + | 0.159319i | \(0.949070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 523.545 | 1.20911 | 0.604555 | − | 0.796563i | \(-0.293351\pi\) | ||||
0.604555 | + | 0.796563i | \(0.293351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 328.354i | 0.751383i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 566.617 | 1.29070 | 0.645349 | − | 0.763888i | \(-0.276712\pi\) | ||||
0.645349 | + | 0.763888i | \(0.276712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 592.788i | 1.33812i | 0.743208 | + | 0.669061i | \(0.233303\pi\) | ||||
−0.743208 | + | 0.669061i | \(0.766697\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −836.120 | −1.87892 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 127.151i | 0.283187i | 0.989925 | + | 0.141593i | \(0.0452225\pi\) | ||||
−0.989925 | + | 0.141593i | \(0.954777\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −350.382 | −0.776899 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1291.36i | 2.83816i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −192.576 | −0.421391 | −0.210695 | − | 0.977552i | \(-0.567573\pi\) | ||||
−0.210695 | + | 0.977552i | \(0.567573\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 227.077i | 0.492575i | 0.969197 | + | 0.246287i | \(0.0792107\pi\) | ||||
−0.969197 | + | 0.246287i | \(0.920789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −638.399 | −1.37883 | −0.689416 | − | 0.724365i | \(-0.742133\pi\) | ||||
−0.689416 | + | 0.724365i | \(0.742133\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 604.423i | 1.29427i | 0.762376 | + | 0.647134i | \(0.224033\pi\) | ||||
−0.762376 | + | 0.647134i | \(0.775967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −70.1816 | −0.149641 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1235.06i | 2.61111i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 229.960 | 0.484126 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 368.302i | − 0.768898i | −0.923146 | − | 0.384449i | \(-0.874391\pi\) | ||||
0.923146 | − | 0.384449i | \(-0.125609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1326.48 | −2.75776 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 178.480i | 0.368000i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −536.865 | −1.10239 | −0.551196 | − | 0.834376i | \(-0.685828\pi\) | ||||
−0.551196 | + | 0.834376i | \(0.685828\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 405.606i | 0.826082i | 0.910712 | + | 0.413041i | \(0.135533\pi\) | ||||
−0.910712 | + | 0.413041i | \(0.864467\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.7878 | −0.0299954 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 257.708i | 0.518527i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 874.090 | 1.75168 | 0.875842 | − | 0.482598i | \(-0.160307\pi\) | ||||
0.875842 | + | 0.482598i | \(0.160307\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 586.515i | 1.16603i | 0.812460 | + | 0.583017i | \(0.198128\pi\) | ||||
−0.812460 | + | 0.583017i | \(0.801872\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −223.302 | −0.442182 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 541.096i | − 1.06306i | −0.847040 | − | 0.531529i | \(-0.821618\pi\) | ||||
0.847040 | − | 0.531529i | \(-0.178382\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −59.4933 | −0.116425 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 629.605i | − 1.22253i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7265 | 0.0207476 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 563.050i | − 1.08071i | −0.841437 | − | 0.540355i | \(-0.818290\pi\) | ||||
0.841437 | − | 0.540355i | \(-0.181710\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 353.232 | 0.675396 | 0.337698 | − | 0.941254i | \(-0.390352\pi\) | ||||
0.337698 | + | 0.941254i | \(0.390352\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 862.999i | − 1.63757i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −183.727 | −0.347309 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 409.778i | − 0.768815i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −638.399 | −1.19327 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 709.485i | 1.31630i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −122.302 | −0.226067 | −0.113033 | − | 0.993591i | \(-0.536057\pi\) | ||||
−0.113033 | + | 0.993591i | \(0.536057\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 600.741i | − 1.10228i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 189.055 | 0.345622 | 0.172811 | − | 0.984955i | \(-0.444715\pi\) | ||||
0.172811 | + | 0.984955i | \(0.444715\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 11.3326i | − 0.0205674i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −402.272 | −0.727437 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 522.883i | − 0.938749i | −0.882999 | − | 0.469375i | \(-0.844479\pi\) | ||||
0.882999 | − | 0.469375i | \(-0.155521\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1444.42 | −2.58394 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 743.574i | 1.32074i | 0.750942 | + | 0.660368i | \(0.229600\pi\) | ||||
−0.750942 | + | 0.660368i | \(0.770400\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 331.728 | 0.587128 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 317.984i | 0.558848i | 0.960168 | + | 0.279424i | \(0.0901435\pi\) | ||||
−0.960168 | + | 0.279424i | \(0.909857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1032.27 | −1.80782 | −0.903911 | − | 0.427720i | \(-0.859317\pi\) | ||||
−0.903911 | + | 0.427720i | \(0.859317\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 499.151i | 0.868089i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 374.545 | 0.649125 | 0.324562 | − | 0.945864i | \(-0.394783\pi\) | ||||
0.324562 | + | 0.945864i | \(0.394783\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 682.454i | 1.17462i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −802.577 | −1.37663 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 338.455i | 0.576585i | 0.957542 | + | 0.288292i | \(0.0930875\pi\) | ||||
−0.957542 | + | 0.288292i | \(0.906913\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 661.362 | 1.12286 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 134.371i | 0.226596i | 0.993561 | + | 0.113298i | \(0.0361414\pi\) | ||||
−0.993561 | + | 0.113298i | \(0.963859\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1001.37 | 1.68297 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 615.031i | 1.02676i | 0.858161 | + | 0.513381i | \(0.171607\pi\) | ||||
−0.858161 | + | 0.513381i | \(0.828393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 373.817 | 0.621992 | 0.310996 | − | 0.950411i | \(-0.399337\pi\) | ||||
0.310996 | + | 0.950411i | \(0.399337\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1270.39i | − 2.09982i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −471.082 | −0.776083 | −0.388042 | − | 0.921642i | \(-0.626848\pi\) | ||||
−0.388042 | + | 0.921642i | \(0.626848\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.5449i | 0.0205317i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −210.727 | −0.343763 | −0.171881 | − | 0.985118i | \(-0.554985\pi\) | ||||
−0.171881 | + | 0.985118i | \(0.554985\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1037.73i | − 1.68190i | −0.541114 | − | 0.840949i | \(-0.681997\pi\) | ||||
0.541114 | − | 0.840949i | \(-0.318003\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 75.7896 | 0.122439 | 0.0612194 | − | 0.998124i | \(-0.480501\pi\) | ||||
0.0612194 | + | 0.998124i | \(0.480501\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1193.88i | − 1.91634i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −742.848 | −1.18856 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1028.60i | 1.63530i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 289.174 | 0.458279 | 0.229139 | − | 0.973394i | \(-0.426409\pi\) | ||||
0.229139 | + | 0.973394i | \(0.426409\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 886.757i | 1.39647i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −829.757 | −1.30260 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 985.234i | − 1.53703i | −0.639834 | − | 0.768513i | \(-0.720997\pi\) | ||||
0.639834 | − | 0.768513i | \(-0.279003\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −743.103 | −1.15568 | −0.577840 | − | 0.816150i | \(-0.696104\pi\) | ||||
−0.577840 | + | 0.816150i | \(0.696104\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 328.849i | 0.508267i | 0.967169 | + | 0.254134i | \(0.0817903\pi\) | ||||
−0.967169 | + | 0.254134i | \(0.918210\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1263.45 | 1.94677 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 205.865i | 0.315261i | 0.987498 | + | 0.157630i | \(0.0503854\pi\) | ||||
−0.987498 | + | 0.157630i | \(0.949615\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 309.487 | 0.472499 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 364.151i | 0.552581i | 0.961074 | + | 0.276291i | \(0.0891052\pi\) | ||||
−0.961074 | + | 0.276291i | \(0.910895\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −507.728 | −0.768120 | −0.384060 | − | 0.923308i | \(-0.625474\pi\) | ||||
−0.384060 | + | 0.923308i | \(0.625474\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 767.403i | 1.15399i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.5987 | 0.0368795 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 70.7878i | 0.105496i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 847.363 | 1.25908 | 0.629542 | − | 0.776967i | \(-0.283243\pi\) | ||||
0.629542 | + | 0.776967i | \(0.283243\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 902.076i | − 1.33246i | −0.745746 | − | 0.666230i | \(-0.767907\pi\) | ||||
0.745746 | − | 0.666230i | \(-0.232093\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −254.847 | −0.375328 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 754.604i | − 1.10484i | −0.833567 | − | 0.552419i | \(-0.813705\pi\) | ||||
0.833567 | − | 0.552419i | \(-0.186295\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1209.21 | 1.76527 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 938.630i | − 1.36231i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −420.450 | −0.608466 | −0.304233 | − | 0.952598i | \(-0.598400\pi\) | ||||
−0.304233 | + | 0.952598i | \(0.598400\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 911.333i | 1.31127i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −317.757 | −0.455893 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 423.953i | 0.604783i | 0.953184 | + | 0.302391i | \(0.0977850\pi\) | ||||
−0.953184 | + | 0.302391i | \(0.902215\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −788.274 | −1.12130 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 318.848i | − 0.450987i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.3020 | −0.0201721 | −0.0100861 | − | 0.999949i | \(-0.503211\pi\) | ||||
−0.0100861 | + | 0.999949i | \(0.503211\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1435.55i | 2.01340i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2421.19 | 3.38629 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 453.453i | 0.630672i | 0.948980 | + | 0.315336i | \(0.102117\pi\) | ||||
−0.948980 | + | 0.315336i | \(0.897883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 898.999 | 1.24688 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 17.2274i | − 0.0237620i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −818.324 | −1.12562 | −0.562809 | − | 0.826587i | \(-0.690279\pi\) | ||||
−0.562809 | + | 0.826587i | \(0.690279\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1120.06i | 1.53223i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −164.636 | −0.224605 | −0.112303 | − | 0.993674i | \(-0.535823\pi\) | ||||
−0.112303 | + | 0.993674i | \(0.535823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 131.585i | 0.178541i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −392.143 | −0.530641 | −0.265320 | − | 0.964160i | \(-0.585478\pi\) | ||||
−0.265320 | + | 0.964160i | \(0.585478\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1341.12i | 1.80501i | 0.430684 | + | 0.902503i | \(0.358272\pi\) | ||||
−0.430684 | + | 0.902503i | \(0.641728\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −288.455 | −0.387188 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 911.556i | − 1.21703i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 330.637 | 0.440262 | 0.220131 | − | 0.975470i | \(-0.429351\pi\) | ||||
0.220131 | + | 0.975470i | \(0.429351\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 555.879i | − 0.736263i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 70.1816 | 0.0927102 | 0.0463551 | − | 0.998925i | \(-0.485239\pi\) | ||||
0.0463551 | + | 0.998925i | \(0.485239\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 761.704i | − 1.00093i | −0.865758 | − | 0.500463i | \(-0.833163\pi\) | ||||
0.865758 | − | 0.500463i | \(-0.166837\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 857.784 | 1.12423 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1477.63i | 1.92651i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −853.272 | −1.10959 | −0.554794 | − | 0.831988i | \(-0.687203\pi\) | ||||
−0.554794 | + | 0.831988i | \(0.687203\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 487.925i | 0.631209i | 0.948891 | + | 0.315605i | \(0.102207\pi\) | ||||
−0.948891 | + | 0.315605i | \(0.897793\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1005.38 | 1.29726 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 243.514i | − 0.312599i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 483.181 | 0.618669 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1563.65i | 1.99191i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −492.532 | −0.625834 | −0.312917 | − | 0.949780i | \(-0.601306\pi\) | ||||
−0.312917 | + | 0.949780i | \(0.601306\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 473.666i | 0.598820i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −82.7878 | −0.104398 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 361.085i | 0.453055i | 0.974005 | + | 0.226528i | \(0.0727374\pi\) | ||||
−0.974005 | + | 0.226528i | \(0.927263\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.72777 | 0.0121749 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 111.545i | 0.138910i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1665.73 | −2.06922 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 579.548i | 0.716376i | 0.933649 | + | 0.358188i | \(0.116605\pi\) | ||||
−0.933649 | + | 0.358188i | \(0.883395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1406.37 | −1.73412 | −0.867059 | − | 0.498205i | \(-0.833993\pi\) | ||||
−0.867059 | + | 0.498205i | \(0.833993\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1866.15i | − 2.28975i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −858.361 | −1.05063 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 111.702i | − 0.136056i | −0.997683 | − | 0.0680280i | \(-0.978329\pi\) | ||||
0.997683 | − | 0.0680280i | \(-0.0216707\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 161.895 | 0.196713 | 0.0983564 | − | 0.995151i | \(-0.468641\pi\) | ||||
0.0983564 | + | 0.995151i | \(0.468641\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 592.788i | 0.716793i | 0.933569 | + | 0.358396i | \(0.116676\pi\) | ||||
−0.933569 | + | 0.358396i | \(0.883324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 950.363 | 1.14640 | 0.573199 | − | 0.819416i | \(-0.305702\pi\) | ||||
0.573199 | + | 0.819416i | \(0.305702\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 643.424i | 0.772418i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −463.926 | −0.555600 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 326.636i | 0.389316i | 0.980871 | + | 0.194658i | \(0.0623596\pi\) | ||||
−0.980871 | + | 0.194658i | \(0.937640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 840.151 | 0.998991 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1714.49i | 2.02898i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1813.96 | 2.14163 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1711.03i | − 2.01061i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 906.727 | 1.06299 | 0.531493 | − | 0.847063i | \(-0.321631\pi\) | ||||
0.531493 | + | 0.847063i | \(0.321631\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 715.483i | − 0.834869i | −0.908707 | − | 0.417435i | \(-0.862929\pi\) | ||||
0.908707 | − | 0.417435i | \(-0.137071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.7558 | −0.0579229 | −0.0289615 | − | 0.999581i | \(-0.509220\pi\) | ||||
−0.0289615 | + | 0.999581i | \(0.509220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1595.76i | − 1.84908i | −0.381086 | − | 0.924539i | \(-0.624450\pi\) | ||||
0.381086 | − | 0.924539i | \(-0.375550\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2238.18 | −2.58749 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 754.227i | 0.867925i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −153.891 | −0.176683 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 393.272i | − 0.449454i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 494.182 | 0.563491 | 0.281746 | − | 0.959489i | \(-0.409087\pi\) | ||||
0.281746 | + | 0.959489i | \(0.409087\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 728.383i | − 0.826768i | −0.910557 | − | 0.413384i | \(-0.864347\pi\) | ||||
0.910557 | − | 0.413384i | \(-0.135653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1378.34 | 1.56098 | 0.780489 | − | 0.625170i | \(-0.214970\pi\) | ||||
0.780489 | + | 0.625170i | \(0.214970\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1329.00i | − 1.49831i | −0.662397 | − | 0.749153i | \(-0.730461\pi\) | ||||
0.662397 | − | 0.749153i | \(-0.269539\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1266.18 | −1.42428 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.45491i | 0.00834816i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2304.21 | 2.57454 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 49.5459i | − 0.0551123i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −727.848 | −0.807822 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 106.967i | − 0.118195i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −940.152 | −1.03655 | −0.518276 | − | 0.855214i | \(-0.673426\pi\) | ||||
−0.518276 | + | 0.855214i | \(0.673426\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 962.486i | − 1.05652i | −0.849084 | − | 0.528258i | \(-0.822845\pi\) | ||||
0.849084 | − | 0.528258i | \(-0.177155\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1279.54 | 1.40147 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 441.909i | 0.481907i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 441.610 | 0.480533 | 0.240267 | − | 0.970707i | \(-0.422765\pi\) | ||||
0.240267 | + | 0.970707i | \(0.422765\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 565.090i | 0.612232i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1198.30 | −1.29546 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 401.078i | − 0.431731i | −0.976423 | − | 0.215866i | \(-0.930743\pi\) | ||||
0.976423 | − | 0.215866i | \(-0.0692573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −493.090 | −0.529635 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1877.48i | − 2.00800i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 493.000 | 0.526147 | 0.263074 | − | 0.964776i | \(-0.415264\pi\) | ||||
0.263074 | + | 0.964776i | \(0.415264\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 556.439i | − 0.591328i | −0.955292 | − | 0.295664i | \(-0.904459\pi\) | ||||
0.955292 | − | 0.295664i | \(-0.0955408\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 528.572 | 0.560522 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1295.91i | − 1.36844i | −0.729278 | − | 0.684218i | \(-0.760144\pi\) | ||||
0.729278 | − | 0.684218i | \(-0.239856\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −130.454 | −0.137465 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 838.672i | − 0.880034i | −0.897990 | − | 0.440017i | \(-0.854972\pi\) | ||||
0.897990 | − | 0.440017i | \(-0.145028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1132.38 | 1.18573 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1726.60i | 1.80042i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1930.45 | 2.00880 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1593.70i | − 1.65150i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 96.6705 | 0.0999695 | 0.0499848 | − | 0.998750i | \(-0.484083\pi\) | ||||
0.0499848 | + | 0.998750i | \(0.484083\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1218.66i | 1.25506i | 0.778592 | + | 0.627531i | \(0.215934\pi\) | ||||
−0.778592 | + | 0.627531i | \(0.784066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1301.27 | −1.33738 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 315.692i | − 0.323124i | −0.986863 | − | 0.161562i | \(-0.948347\pi\) | ||||
0.986863 | − | 0.161562i | \(-0.0516532\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2238.42 | −2.28643 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.2429i | 0.0409388i | 0.999790 | + | 0.0204694i | \(0.00651607\pi\) | ||||
−0.999790 | + | 0.0204694i | \(0.993484\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1204.18 | 1.22252 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1863.16i | − 1.88388i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −173.635 | −0.175212 | −0.0876062 | − | 0.996155i | \(-0.527922\pi\) | ||||
−0.0876062 | + | 0.996155i | \(0.527922\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 463.243i | − 0.465571i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 818.454 | 0.820917 | 0.410458 | − | 0.911879i | \(-0.365369\pi\) | ||||
0.410458 | + | 0.911879i | \(0.365369\pi\) | |||||||
\(998\) | 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.e.u.1025.7 | 8 | ||
3.2 | odd | 2 | inner | 1728.3.e.u.1025.1 | 8 | ||
4.3 | odd | 2 | inner | 1728.3.e.u.1025.8 | 8 | ||
8.3 | odd | 2 | 864.3.e.f.161.2 | yes | 8 | ||
8.5 | even | 2 | 864.3.e.f.161.1 | ✓ | 8 | ||
12.11 | even | 2 | inner | 1728.3.e.u.1025.2 | 8 | ||
24.5 | odd | 2 | 864.3.e.f.161.7 | yes | 8 | ||
24.11 | even | 2 | 864.3.e.f.161.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.3.e.f.161.1 | ✓ | 8 | 8.5 | even | 2 | ||
864.3.e.f.161.2 | yes | 8 | 8.3 | odd | 2 | ||
864.3.e.f.161.7 | yes | 8 | 24.5 | odd | 2 | ||
864.3.e.f.161.8 | yes | 8 | 24.11 | even | 2 | ||
1728.3.e.u.1025.1 | 8 | 3.2 | odd | 2 | inner | ||
1728.3.e.u.1025.2 | 8 | 12.11 | even | 2 | inner | ||
1728.3.e.u.1025.7 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.e.u.1025.8 | 8 | 4.3 | odd | 2 | inner |