Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(703,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.703");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.207360000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.5 | ||
Root | \(0.437016 - 0.756934i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.703 |
Dual form | 1728.3.g.l.703.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.08036 | 0.216073 | 0.108036 | − | 0.994147i | \(-0.465544\pi\) | ||||
0.108036 | + | 0.994147i | \(0.465544\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 6.01392i | − 0.859131i | −0.903036 | − | 0.429565i | \(-0.858667\pi\) | ||||
0.903036 | − | 0.429565i | \(-0.141333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.7247i | 1.61133i | 0.592369 | + | 0.805667i | \(0.298193\pi\) | ||||
−0.592369 | + | 0.805667i | \(0.701807\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.4164 | −0.955108 | −0.477554 | − | 0.878602i | \(-0.658477\pi\) | ||||
−0.477554 | + | 0.878602i | \(0.658477\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.3786 | 1.55168 | 0.775841 | − | 0.630929i | \(-0.217326\pi\) | ||||
0.775841 | + | 0.630929i | \(0.217326\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.19615i | 0.273482i | 0.990607 | + | 0.136741i | \(0.0436628\pi\) | ||||
−0.990607 | + | 0.136741i | \(0.956337\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 29.8356i | − 1.29720i | −0.761129 | − | 0.648600i | \(-0.775355\pi\) | ||||
0.761129 | − | 0.648600i | \(-0.224645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.8328 | −0.953313 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.32145 | 0.149016 | 0.0745078 | − | 0.997220i | \(-0.476261\pi\) | ||||
0.0745078 | + | 0.997220i | \(0.476261\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.8403i | 1.44646i | 0.690607 | + | 0.723230i | \(0.257343\pi\) | ||||
−0.690607 | + | 0.723230i | \(0.742657\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 6.49721i | − 0.185635i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 20.4164 | 0.551795 | 0.275897 | − | 0.961187i | \(-0.411025\pi\) | ||||
0.275897 | + | 0.961187i | \(0.411025\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −59.2393 | −1.44486 | −0.722431 | − | 0.691443i | \(-0.756975\pi\) | ||||
−0.722431 | + | 0.691443i | \(0.756975\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.1491i | 0.445328i | 0.974895 | + | 0.222664i | \(0.0714752\pi\) | ||||
−0.974895 | + | 0.222664i | \(0.928525\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 41.0631i | 0.873683i | 0.899539 | + | 0.436841i | \(0.143903\pi\) | ||||
−0.899539 | + | 0.436841i | \(0.856097\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.8328 | 0.261894 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −70.0430 | −1.32157 | −0.660783 | − | 0.750577i | \(-0.729776\pi\) | ||||
−0.660783 | + | 0.750577i | \(0.729776\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.1491i | 0.348165i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 28.9521i | − 0.490714i | −0.969433 | − | 0.245357i | \(-0.921095\pi\) | ||||
0.969433 | − | 0.245357i | \(-0.0789052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −18.4164 | −0.301908 | −0.150954 | − | 0.988541i | \(-0.548235\pi\) | ||||
−0.150954 | + | 0.988541i | \(0.548235\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.4142 | −0.206373 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 94.8767i | 1.41607i | 0.706177 | + | 0.708035i | \(0.250418\pi\) | ||||
−0.706177 | + | 0.708035i | \(0.749582\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 83.8931i | 1.18159i | 0.806821 | + | 0.590797i | \(0.201186\pi\) | ||||
−0.806821 | + | 0.590797i | \(0.798814\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 55.8328 | 0.764833 | 0.382417 | − | 0.923990i | \(-0.375092\pi\) | ||||
0.382417 | + | 0.923990i | \(0.375092\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 106.595 | 1.38435 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 41.0410i | 0.519507i | 0.965675 | + | 0.259753i | \(0.0836413\pi\) | ||||
−0.965675 | + | 0.259753i | \(0.916359\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 35.4493i | − 0.427101i | −0.976932 | − | 0.213550i | \(-0.931497\pi\) | ||||
0.976932 | − | 0.213550i | \(-0.0685027\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.4984 | 0.335276 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 26.3786 | 0.296389 | 0.148194 | − | 0.988958i | \(-0.452654\pi\) | ||||
0.148194 | + | 0.988958i | \(0.452654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 74.6712i | 0.820563i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.61373i | 0.0590919i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 76.3313 | 0.786920 | 0.393460 | − | 0.919342i | \(-0.371278\pi\) | ||||
0.393460 | + | 0.919342i | \(0.371278\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 72.2037 | 0.714888 | 0.357444 | − | 0.933935i | \(-0.383648\pi\) | ||||
0.357444 | + | 0.933935i | \(0.383648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 57.9754i | 0.562868i | 0.959581 | + | 0.281434i | \(0.0908101\pi\) | ||||
−0.959581 | + | 0.281434i | \(0.909190\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 64.4015i | − 0.601883i | −0.953643 | − | 0.300942i | \(-0.902699\pi\) | ||||
0.953643 | − | 0.300942i | \(-0.0973009\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 43.1672 | 0.396029 | 0.198015 | − | 0.980199i | \(-0.436551\pi\) | ||||
0.198015 | + | 0.980199i | \(0.436551\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 81.2965 | 0.719438 | 0.359719 | − | 0.933061i | \(-0.382873\pi\) | ||||
0.359719 | + | 0.933061i | \(0.382873\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 32.2333i | − 0.280290i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 158.639i | − 1.33310i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −193.164 | −1.59640 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −52.7572 | −0.422057 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 191.968i | 1.51156i | 0.654826 | + | 0.755780i | \(0.272742\pi\) | ||||
−0.654826 | + | 0.755780i | \(0.727258\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 141.797i | 1.08242i | 0.840887 | + | 0.541211i | \(0.182034\pi\) | ||||
−0.840887 | + | 0.541211i | \(0.817966\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 31.2492 | 0.234957 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 87.7787 | 0.640720 | 0.320360 | − | 0.947296i | \(-0.396196\pi\) | ||||
0.320360 | + | 0.947296i | \(0.396196\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 183.501i | 1.32015i | 0.751200 | + | 0.660075i | \(0.229476\pi\) | ||||
−0.751200 | + | 0.660075i | \(0.770524\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 220.077i | − 1.53900i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.66874 | 0.0321982 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −153.950 | −1.03322 | −0.516611 | − | 0.856220i | \(-0.672807\pi\) | ||||
−0.516611 | + | 0.856220i | \(0.672807\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 185.375i | 1.22765i | 0.789442 | + | 0.613825i | \(0.210370\pi\) | ||||
−0.789442 | + | 0.613825i | \(0.789630\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 48.4438i | 0.312540i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −196.164 | −1.24945 | −0.624726 | − | 0.780844i | \(-0.714789\pi\) | ||||
−0.624726 | + | 0.780844i | \(0.714789\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −179.429 | −1.11447 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 129.325i | 0.793403i | 0.917948 | + | 0.396701i | \(0.129845\pi\) | ||||
−0.917948 | + | 0.396701i | \(0.870155\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 137.951i | 0.826052i | 0.910719 | + | 0.413026i | \(0.135528\pi\) | ||||
−0.910719 | + | 0.413026i | \(0.864472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.8328 | −0.0877681 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −160.432 | −0.927354 | −0.463677 | − | 0.886004i | \(-0.653470\pi\) | ||||
−0.463677 | + | 0.886004i | \(0.653470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 143.329i | 0.819020i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 201.469i | 1.12552i | 0.826619 | + | 0.562762i | \(0.190261\pi\) | ||||
−0.826619 | + | 0.562762i | \(0.809739\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 48.2523 | 0.266587 | 0.133294 | − | 0.991077i | \(-0.457445\pi\) | ||||
0.133294 | + | 0.991077i | \(0.457445\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.0571 | 0.119228 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 467.552i | 2.50028i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 147.411i | 0.771786i | 0.922544 | + | 0.385893i | \(0.126107\pi\) | ||||
−0.922544 | + | 0.385893i | \(0.873893\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.1641 | 0.130384 | 0.0651919 | − | 0.997873i | \(-0.479234\pi\) | ||||
0.0651919 | + | 0.997873i | \(0.479234\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 385.506 | 1.95688 | 0.978441 | − | 0.206528i | \(-0.0662165\pi\) | ||||
0.978441 | + | 0.206528i | \(0.0662165\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 121.386i | − 0.609978i | −0.952356 | − | 0.304989i | \(-0.901347\pi\) | ||||
0.952356 | − | 0.304989i | \(-0.0986528\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 25.9888i | − 0.128024i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −64.0000 | −0.312195 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −92.1001 | −0.440670 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 261.631i | − 1.23996i | −0.784619 | − | 0.619978i | \(-0.787141\pi\) | ||||
0.784619 | − | 0.619978i | \(-0.212859\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.6880i | 0.0962231i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 269.666 | 1.24270 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −327.527 | −1.48202 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 70.0542i | 0.314144i | 0.987587 | + | 0.157072i | \(0.0502056\pi\) | ||||
−0.987587 | + | 0.157072i | \(0.949794\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 298.356i | − 1.31434i | −0.753740 | − | 0.657172i | \(-0.771752\pi\) | ||||
0.753740 | − | 0.657172i | \(-0.228248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −259.666 | −1.13391 | −0.566956 | − | 0.823748i | \(-0.691879\pi\) | ||||
−0.566956 | + | 0.823748i | \(0.691879\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.38192 | −0.0316821 | −0.0158410 | − | 0.999875i | \(-0.505043\pi\) | ||||
−0.0158410 | + | 0.999875i | \(0.505043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 44.3630i | 0.188779i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 82.1262i | 0.343624i | 0.985130 | + | 0.171812i | \(0.0549622\pi\) | ||||
−0.985130 | + | 0.171812i | \(0.945038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −415.827 | −1.72542 | −0.862711 | − | 0.505698i | \(-0.831235\pi\) | ||||
−0.862711 | + | 0.505698i | \(0.831235\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.8641 | 0.0565882 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 64.5175i | − 0.261205i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 140.030i | − 0.557890i | −0.960307 | − | 0.278945i | \(-0.910015\pi\) | ||||
0.960307 | − | 0.278945i | \(-0.0899847\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 528.827 | 2.09022 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 66.9825 | 0.260632 | 0.130316 | − | 0.991472i | \(-0.458401\pi\) | ||||
0.130316 | + | 0.991472i | \(0.458401\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 122.783i | − 0.474064i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 37.2163i | − 0.141507i | −0.997494 | − | 0.0707534i | \(-0.977460\pi\) | ||||
0.997494 | − | 0.0707534i | \(-0.0225404\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −75.6718 | −0.285554 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 279.092 | 1.03752 | 0.518758 | − | 0.854921i | \(-0.326395\pi\) | ||||
0.518758 | + | 0.854921i | \(0.326395\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 406.305i | 1.49928i | 0.661845 | + | 0.749641i | \(0.269774\pi\) | ||||
−0.661845 | + | 0.749641i | \(0.730226\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 422.429i | − 1.53611i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.83282 | −0.0174470 | −0.00872349 | − | 0.999962i | \(-0.502777\pi\) | ||||
−0.00872349 | + | 0.999962i | \(0.502777\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.32145 | −0.0153788 | −0.00768942 | − | 0.999970i | \(-0.502448\pi\) | ||||
−0.00768942 | + | 0.999970i | \(0.502448\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 44.3630i | 0.156760i | 0.996924 | + | 0.0783799i | \(0.0249747\pi\) | ||||
−0.996924 | + | 0.0783799i | \(0.975025\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 356.260i | 1.24133i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 406.830 | 1.40772 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 388.927 | 1.32740 | 0.663699 | − | 0.748000i | \(-0.268986\pi\) | ||||
0.663699 | + | 0.748000i | \(0.268986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 31.2788i | − 0.106030i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 370.451i | 1.23897i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 115.161 | 0.382595 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.8964 | −0.0652341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 96.6999i | 0.314983i | 0.987520 | + | 0.157492i | \(0.0503407\pi\) | ||||
−0.987520 | + | 0.157492i | \(0.949659\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 136.184i | − 0.437890i | −0.975737 | − | 0.218945i | \(-0.929739\pi\) | ||||
0.975737 | − | 0.218945i | \(-0.0702615\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 282.161 | 0.901473 | 0.450736 | − | 0.892657i | \(-0.351161\pi\) | ||||
0.450736 | + | 0.892657i | \(0.351161\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 275.489 | 0.869051 | 0.434526 | − | 0.900659i | \(-0.356916\pi\) | ||||
0.434526 | + | 0.900659i | \(0.356916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 76.5963i | 0.240114i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 137.067i | 0.424356i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 295.918 | 0.910517 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 246.950 | 0.750608 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 55.5221i | 0.167741i | 0.996477 | + | 0.0838703i | \(0.0267281\pi\) | ||||
−0.996477 | + | 0.0838703i | \(0.973272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 102.501i | 0.305974i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −430.659 | −1.27792 | −0.638961 | − | 0.769239i | \(-0.720635\pi\) | ||||
−0.638961 | + | 0.769239i | \(0.720635\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −794.779 | −2.33073 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 371.857i | − 1.08413i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 135.871i | 0.391559i | 0.980648 | + | 0.195779i | \(0.0627236\pi\) | ||||
−0.980648 | + | 0.195779i | \(0.937276\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −288.082 | −0.825450 | −0.412725 | − | 0.910856i | \(-0.635423\pi\) | ||||
−0.412725 | + | 0.910856i | \(0.635423\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 198.964 | 0.563638 | 0.281819 | − | 0.959468i | \(-0.409062\pi\) | ||||
0.281819 | + | 0.959468i | \(0.409062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 90.6350i | 0.255310i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 324.658i | − 0.904339i | −0.891932 | − | 0.452170i | \(-0.850650\pi\) | ||||
0.891932 | − | 0.452170i | \(-0.149350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 334.000 | 0.925208 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 60.3197 | 0.165259 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 176.141i | 0.479948i | 0.970779 | + | 0.239974i | \(0.0771390\pi\) | ||||
−0.970779 | + | 0.239974i | \(0.922861\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 421.233i | 1.13540i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −596.580 | −1.59941 | −0.799706 | − | 0.600392i | \(-0.795011\pi\) | ||||
−0.799706 | + | 0.600392i | \(0.795011\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −53.6569 | −0.142326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 30.3082i | − 0.0799689i | −0.999200 | − | 0.0399844i | \(-0.987269\pi\) | ||||
0.999200 | − | 0.0399844i | \(-0.0127308\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 707.220i | − 1.84653i | −0.384167 | − | 0.923264i | \(-0.625511\pi\) | ||||
0.384167 | − | 0.923264i | \(-0.374489\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 115.161 | 0.299119 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −577.088 | −1.48352 | −0.741758 | − | 0.670668i | \(-0.766008\pi\) | ||||
−0.741758 | + | 0.670668i | \(0.766008\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 787.021i | − 2.01284i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 44.3392i | 0.112251i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.8266 | −0.0675733 | −0.0337867 | − | 0.999429i | \(-0.510757\pi\) | ||||
−0.0337867 | + | 0.999429i | \(0.510757\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −505.065 | −1.25951 | −0.629756 | − | 0.776793i | \(-0.716845\pi\) | ||||
−0.629756 | + | 0.776793i | \(0.716845\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 556.755i | − 1.38153i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 361.874i | 0.889126i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −683.328 | −1.67073 | −0.835364 | − | 0.549696i | \(-0.814743\pi\) | ||||
−0.835364 | + | 0.549696i | \(0.814743\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −174.116 | −0.421588 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 38.2982i | − 0.0922847i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 306.620i | 0.731791i | 0.930656 | + | 0.365895i | \(0.119237\pi\) | ||||
−0.930656 | + | 0.365895i | \(0.880763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5867 | 0.0441489 | 0.0220745 | − | 0.999756i | \(-0.492973\pi\) | ||||
0.0220745 | + | 0.999756i | \(0.492973\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −628.676 | −1.47924 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 110.755i | 0.259379i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 308.130i | − 0.714918i | −0.933929 | − | 0.357459i | \(-0.883643\pi\) | ||||
0.933929 | − | 0.357459i | \(-0.116357\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 174.839 | 0.403785 | 0.201893 | − | 0.979408i | \(-0.435291\pi\) | ||||
0.201893 | + | 0.979408i | \(0.435291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 155.030 | 0.354761 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 480.159i | − 1.09376i | −0.837212 | − | 0.546878i | \(-0.815816\pi\) | ||||
0.837212 | − | 0.546878i | \(-0.184184\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 555.962i | − 1.25499i | −0.778619 | − | 0.627497i | \(-0.784080\pi\) | ||||
0.778619 | − | 0.627497i | \(-0.215920\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.4984 | 0.0640415 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 801.711 | 1.78555 | 0.892774 | − | 0.450504i | \(-0.148756\pi\) | ||||
0.892774 | + | 0.450504i | \(0.148756\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1050.00i | − 2.32816i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 80.6720i | 0.177301i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −137.830 | −0.301597 | −0.150798 | − | 0.988565i | \(-0.548184\pi\) | ||||
−0.150798 | + | 0.988565i | \(0.548184\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 188.341 | 0.408549 | 0.204274 | − | 0.978914i | \(-0.434517\pi\) | ||||
0.204274 | + | 0.978914i | \(0.434517\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 548.425i | 1.18450i | 0.805753 | + | 0.592251i | \(0.201761\pi\) | ||||
−0.805753 | + | 0.592251i | \(0.798239\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 618.597i | − 1.32462i | −0.749231 | − | 0.662309i | \(-0.769577\pi\) | ||||
0.749231 | − | 0.662309i | \(-0.230423\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 570.580 | 1.21659 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −339.411 | −0.717571 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 123.839i | − 0.260714i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 770.425i | − 1.60840i | −0.594357 | − | 0.804202i | \(-0.702593\pi\) | ||||
0.594357 | − | 0.804202i | \(-0.297407\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −253.498 | −0.527024 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 82.4655 | 0.170032 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 549.208i | − 1.12774i | −0.825865 | − | 0.563868i | \(-0.809313\pi\) | ||||
0.825865 | − | 0.563868i | \(-0.190687\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 23.0256i | − 0.0468952i | −0.999725 | − | 0.0234476i | \(-0.992536\pi\) | ||||
0.999725 | − | 0.0234476i | \(-0.00746429\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 113.994 | 0.231225 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 504.526 | 1.01514 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 626.809i | − 1.25613i | −0.778160 | − | 0.628065i | \(-0.783847\pi\) | ||||
0.778160 | − | 0.628065i | \(-0.216153\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 732.896i | 1.45705i | 0.685019 | + | 0.728525i | \(0.259794\pi\) | ||||
−0.685019 | + | 0.728525i | \(0.740206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 78.0062 | 0.154468 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 437.363 | 0.859259 | 0.429630 | − | 0.903005i | \(-0.358644\pi\) | ||||
0.429630 | + | 0.903005i | \(0.358644\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 335.774i | − 0.657092i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 62.6345i | 0.121620i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −727.830 | −1.40779 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 385.236 | 0.739417 | 0.369709 | − | 0.929148i | \(-0.379458\pi\) | ||||
0.369709 | + | 0.929148i | \(0.379458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 418.572i | 0.800328i | 0.916443 | + | 0.400164i | \(0.131047\pi\) | ||||
−0.916443 | + | 0.400164i | \(0.868953\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1182.82i | 2.24445i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −361.164 | −0.682730 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 735.540 | 1.38000 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 69.5770i | − 0.130050i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 227.457i | 0.421999i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.4257 | 0.0433008 | 0.0216504 | − | 0.999766i | \(-0.493108\pi\) | ||||
0.0216504 | + | 0.999766i | \(0.493108\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 46.6362 | 0.0855711 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 722.163i | − 1.32023i | −0.751167 | − | 0.660113i | \(-0.770509\pi\) | ||||
0.751167 | − | 0.660113i | \(-0.229491\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.4549i | 0.0407530i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 246.817 | 0.446324 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.34135 | −0.00420349 | −0.00210175 | − | 0.999998i | \(-0.500669\pi\) | ||||
−0.00210175 | + | 0.999998i | \(0.500669\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 237.763i | − 0.425336i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 359.794i | 0.639066i | 0.947575 | + | 0.319533i | \(0.103526\pi\) | ||||
−0.947575 | + | 0.319533i | \(0.896474\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 87.8297 | 0.155451 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.6354 | −0.0327512 | −0.0163756 | − | 0.999866i | \(-0.505213\pi\) | ||||
−0.0163756 | + | 0.999866i | \(0.505213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 284.528i | 0.498298i | 0.968465 | + | 0.249149i | \(0.0801509\pi\) | ||||
−0.968465 | + | 0.249149i | \(0.919849\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 711.067i | 1.23664i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 664.823 | 1.15221 | 0.576104 | − | 0.817377i | \(-0.304572\pi\) | ||||
0.576104 | + | 0.817377i | \(0.304572\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −213.189 | −0.366935 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1241.49i | − 2.12948i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 754.467i | − 1.28529i | −0.766162 | − | 0.642647i | \(-0.777836\pi\) | ||||
0.766162 | − | 0.642647i | \(-0.222164\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −232.997 | −0.395580 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −550.801 | −0.928838 | −0.464419 | − | 0.885615i | \(-0.653737\pi\) | ||||
−0.464419 | + | 0.885615i | \(0.653737\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 171.387i | − 0.288046i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.9888i | 0.0433871i | 0.999765 | + | 0.0216935i | \(0.00690581\pi\) | ||||
−0.999765 | + | 0.0216935i | \(0.993094\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 186.170 | 0.309768 | 0.154884 | − | 0.987933i | \(-0.450500\pi\) | ||||
0.154884 | + | 0.987933i | \(0.450500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −208.687 | −0.344938 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 99.5447i | 0.163994i | 0.996633 | + | 0.0819972i | \(0.0261299\pi\) | ||||
−0.996633 | + | 0.0819972i | \(0.973870\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 509.856i | − 0.834461i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 960.234 | 1.56645 | 0.783225 | − | 0.621739i | \(-0.213573\pi\) | ||||
0.783225 | + | 0.621739i | \(0.213573\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −354.625 | −0.574757 | −0.287378 | − | 0.957817i | \(-0.592784\pi\) | ||||
−0.287378 | + | 0.957817i | \(0.592784\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 360.647i | 0.582629i | 0.956627 | + | 0.291314i | \(0.0940926\pi\) | ||||
−0.956627 | + | 0.291314i | \(0.905907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 158.639i | − 0.254637i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 538.823 | 0.862118 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 538.556 | 0.856210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 82.7121i | − 0.131081i | −0.997850 | − | 0.0655405i | \(-0.979123\pi\) | ||||
0.997850 | − | 0.0655405i | \(-0.0208772\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 207.395i | 0.326607i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −159.337 | −0.250137 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −760.569 | −1.18653 | −0.593267 | − | 0.805005i | \(-0.702162\pi\) | ||||
−0.593267 | + | 0.805005i | \(0.702162\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 787.021i | − 1.22398i | −0.790864 | − | 0.611992i | \(-0.790369\pi\) | ||||
0.790864 | − | 0.611992i | \(-0.209631\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 978.962i | − 1.51308i | −0.653948 | − | 0.756539i | \(-0.726889\pi\) | ||||
0.653948 | − | 0.756539i | \(-0.273111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 513.167 | 0.790704 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −939.548 | −1.43882 | −0.719409 | − | 0.694587i | \(-0.755587\pi\) | ||||
−0.719409 | + | 0.694587i | \(0.755587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 153.193i | 0.233882i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 149.491i | 0.226845i | 0.993547 | + | 0.113423i | \(0.0361814\pi\) | ||||
−0.993547 | + | 0.113423i | \(0.963819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −337.420 | −0.510468 | −0.255234 | − | 0.966879i | \(-0.582153\pi\) | ||||
−0.255234 | + | 0.966879i | \(0.582153\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.7605 | 0.0507677 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 128.933i | − 0.193303i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 326.425i | − 0.486475i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −321.341 | −0.477475 | −0.238737 | − | 0.971084i | \(-0.576734\pi\) | ||||
−0.238737 | + | 0.971084i | \(0.576734\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −741.841 | −1.09578 | −0.547889 | − | 0.836551i | \(-0.684568\pi\) | ||||
−0.547889 | + | 0.836551i | \(0.684568\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 459.050i | − 0.676067i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1259.02i | 1.84337i | 0.387938 | + | 0.921686i | \(0.373188\pi\) | ||||
−0.387938 | + | 0.921686i | \(0.626812\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 94.8328 | 0.138442 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 869.682 | 1.26224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 222.770i | − 0.322387i | −0.986923 | − | 0.161194i | \(-0.948466\pi\) | ||||
0.986923 | − | 0.161194i | \(-0.0515344\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 198.248i | 0.285248i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1562.65 | −2.24197 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.34135 | −0.00334001 | −0.00167000 | − | 0.999999i | \(-0.500532\pi\) | ||||
−0.00167000 | + | 0.999999i | \(0.500532\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 106.087i | 0.150906i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 434.227i | − 0.614182i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 495.085 | 0.698287 | 0.349143 | − | 0.937069i | \(-0.386473\pi\) | ||||
0.349143 | + | 0.937069i | \(0.386473\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1337.84 | 1.87635 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 237.763i | − 0.332535i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 962.433i | − 1.33857i | −0.743005 | − | 0.669286i | \(-0.766600\pi\) | ||||
0.743005 | − | 0.669286i | \(-0.233400\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 348.659 | 0.483578 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −102.992 | −0.142058 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 544.625i | 0.749141i | 0.927198 | + | 0.374570i | \(0.122210\pi\) | ||||
−0.927198 | + | 0.374570i | \(0.877790\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 505.126i | 0.691006i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 146.170 | 0.199414 | 0.0997069 | − | 0.995017i | \(-0.468209\pi\) | ||||
0.0997069 | + | 0.995017i | \(0.468209\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1681.66 | −2.28176 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1172.87i | − 1.58710i | −0.608505 | − | 0.793550i | \(-0.708231\pi\) | ||||
0.608505 | − | 0.793550i | \(-0.291769\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 494.837i | − 0.665998i | −0.942927 | − | 0.332999i | \(-0.891939\pi\) | ||||
0.942927 | − | 0.332999i | \(-0.108061\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −166.322 | −0.223251 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −387.305 | −0.517096 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 927.250i | − 1.23469i | −0.786693 | − | 0.617344i | \(-0.788209\pi\) | ||||
0.786693 | − | 0.617344i | \(-0.211791\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 200.272i | 0.265261i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 757.748 | 1.00099 | 0.500494 | − | 0.865740i | \(-0.333152\pi\) | ||||
0.500494 | + | 0.865740i | \(0.333152\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 953.139 | 1.25248 | 0.626241 | − | 0.779629i | \(-0.284592\pi\) | ||||
0.626241 | + | 0.779629i | \(0.284592\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 259.604i | − 0.340241i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 359.482i | 0.468685i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 145.675 | 0.189434 | 0.0947171 | − | 0.995504i | \(-0.469805\pi\) | ||||
0.0947171 | + | 0.995504i | \(0.469805\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −60.1391 | −0.0777996 | −0.0388998 | − | 0.999243i | \(-0.512385\pi\) | ||||
−0.0388998 | + | 0.999243i | \(0.512385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1068.67i | − 1.37893i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 307.817i | − 0.395143i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1486.98 | −1.90394 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −211.928 | −0.269973 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 328.312i | − 0.417169i | −0.978004 | − | 0.208585i | \(-0.933114\pi\) | ||||
0.978004 | − | 0.208585i | \(-0.0668856\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 488.910i | − 0.618091i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 228.666 | 0.288355 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 446.725 | 0.560508 | 0.280254 | − | 0.959926i | \(-0.409581\pi\) | ||||
0.280254 | + | 0.959926i | \(0.409581\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1083.19i | 1.35568i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 989.618i | 1.23240i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −193.848 | −0.240805 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −793.341 | −0.980644 | −0.490322 | − | 0.871541i | \(-0.663121\pi\) | ||||
−0.490322 | + | 0.871541i | \(0.663121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 788.930i | 0.972787i | 0.873740 | + | 0.486394i | \(0.161688\pi\) | ||||
−0.873740 | + | 0.486394i | \(0.838312\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 139.718i | 0.171433i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −99.5016 | −0.121789 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1448.75 | 1.76462 | 0.882310 | − | 0.470668i | \(-0.155987\pi\) | ||||
0.882310 | + | 0.470668i | \(0.155987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 129.939i | − 0.157884i | −0.996879 | − | 0.0789421i | \(-0.974846\pi\) | ||||
0.996879 | − | 0.0789421i | \(-0.0251542\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 350.389i | − 0.423687i | −0.977304 | − | 0.211843i | \(-0.932053\pi\) | ||||
0.977304 | − | 0.211843i | \(-0.0679467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −167.748 | −0.202349 | −0.101175 | − | 0.994869i | \(-0.532260\pi\) | ||||
−0.101175 | + | 0.994869i | \(0.532260\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 338.512 | 0.406376 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 149.037i | 0.178487i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 661.684i | 0.788658i | 0.918969 | + | 0.394329i | \(0.129023\pi\) | ||||
−0.918969 | + | 0.394329i | \(0.870977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −822.325 | −0.977794 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.0248 | −0.0189643 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1161.67i | 1.37151i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 609.136i | − 0.715789i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.0789 | −0.0200222 | −0.0100111 | − | 0.999950i | \(-0.503187\pi\) | ||||
−0.0100111 | + | 0.999950i | \(0.503187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 422.419 | 0.492904 | 0.246452 | − | 0.969155i | \(-0.420735\pi\) | ||||
0.246452 | + | 0.969155i | \(0.420735\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1323.18i | 1.54037i | 0.637819 | + | 0.770186i | \(0.279837\pi\) | ||||
−0.637819 | + | 0.770186i | \(0.720163\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1455.50i | 1.68656i | 0.537473 | + | 0.843281i | \(0.319379\pi\) | ||||
−0.537473 | + | 0.843281i | \(0.680621\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −173.325 | −0.200376 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −727.439 | −0.837099 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1178.03i | − 1.35250i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 317.277i | 0.362602i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 753.085 | 0.858706 | 0.429353 | − | 0.903137i | \(-0.358742\pi\) | ||||
0.429353 | + | 0.903137i | \(0.358742\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 996.177 | 1.13073 | 0.565367 | − | 0.824839i | \(-0.308735\pi\) | ||||
0.565367 | + | 0.824839i | \(0.308735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 950.011i | 1.07589i | 0.842980 | + | 0.537945i | \(0.180799\pi\) | ||||
−0.842980 | + | 0.537945i | \(0.819201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 433.086i | − 0.488259i | −0.969743 | − | 0.244129i | \(-0.921498\pi\) | ||||
0.969743 | − | 0.244129i | \(-0.0785022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1154.48 | 1.29863 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −213.370 | −0.238936 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 217.659i | 0.243195i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 193.775i | 0.215545i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1847.63 | −2.05065 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 52.1300 | 0.0576022 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 685.704i | 0.756014i | 0.925803 | + | 0.378007i | \(0.123390\pi\) | ||||
−0.925803 | + | 0.378007i | \(0.876610\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.0750i | 0.0395994i | 0.999804 | + | 0.0197997i | \(0.00630285\pi\) | ||||
−0.999804 | + | 0.0197997i | \(0.993697\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 628.328 | 0.688202 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 852.758 | 0.929943 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 953.775i | 1.03784i | 0.854823 | + | 0.518920i | \(0.173666\pi\) | ||||
−0.854823 | + | 0.518920i | \(0.826334\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1041.65i | − 1.12855i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −486.580 | −0.526033 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −149.629 | −0.161064 | −0.0805321 | − | 0.996752i | \(-0.525662\pi\) | ||||
−0.0805321 | + | 0.996752i | \(0.525662\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 66.6813i | 0.0716233i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 505.126i | 0.540241i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −661.158 | −0.705611 | −0.352806 | − | 0.935697i | \(-0.614772\pi\) | ||||
−0.352806 | + | 0.935697i | \(0.614772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 466.713 | 0.495976 | 0.247988 | − | 0.968763i | \(-0.420231\pi\) | ||||
0.247988 | + | 0.968763i | \(0.420231\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1767.44i | 1.87428i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1302.74i | − 1.37565i | −0.725879 | − | 0.687823i | \(-0.758567\pi\) | ||||
0.725879 | − | 0.687823i | \(-0.241433\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −693.243 | −0.730498 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.6959 | −0.0227659 | −0.0113829 | − | 0.999935i | \(-0.503623\pi\) | ||||
−0.0113829 | + | 0.999935i | \(0.503623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 159.258i | 0.166762i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 527.893i | − 0.550462i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1049.65 | −1.09225 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.1863 | 0.0281724 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 640.899i | − 0.662770i | −0.943496 | − | 0.331385i | \(-0.892484\pi\) | ||||
0.943496 | − | 0.331385i | \(-0.107516\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1396.09i | − 1.43779i | −0.695121 | − | 0.718893i | \(-0.744649\pi\) | ||||
0.695121 | − | 0.718893i | \(-0.255351\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1103.56 | 1.13418 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1009.95 | −1.03373 | −0.516864 | − | 0.856068i | \(-0.672901\pi\) | ||||
−0.516864 | + | 0.856068i | \(0.672901\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 467.552i | 0.477581i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 485.376i | − 0.493770i | −0.969045 | − | 0.246885i | \(-0.920593\pi\) | ||||
0.969045 | − | 0.246885i | \(-0.0794071\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 416.486 | 0.422828 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 571.325 | 0.577679 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 265.720i | − 0.268133i | −0.990972 | − | 0.134066i | \(-0.957196\pi\) | ||||
0.990972 | − | 0.134066i | \(-0.0428035\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 131.141i | − 0.131800i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1715.81 | 1.72097 | 0.860487 | − | 0.509472i | \(-0.170159\pi\) | ||||
0.860487 | + | 0.509472i | \(0.170159\pi\) | |||||||
\(998\) | 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.g.l.703.5 | 8 | ||
3.2 | odd | 2 | inner | 1728.3.g.l.703.3 | 8 | ||
4.3 | odd | 2 | inner | 1728.3.g.l.703.6 | 8 | ||
8.3 | odd | 2 | 108.3.d.d.55.1 | ✓ | 8 | ||
8.5 | even | 2 | 108.3.d.d.55.2 | yes | 8 | ||
12.11 | even | 2 | inner | 1728.3.g.l.703.4 | 8 | ||
24.5 | odd | 2 | 108.3.d.d.55.7 | yes | 8 | ||
24.11 | even | 2 | 108.3.d.d.55.8 | yes | 8 | ||
72.5 | odd | 6 | 324.3.f.o.55.2 | 8 | |||
72.11 | even | 6 | 324.3.f.o.271.2 | 8 | |||
72.13 | even | 6 | 324.3.f.o.55.3 | 8 | |||
72.29 | odd | 6 | 324.3.f.p.271.1 | 8 | |||
72.43 | odd | 6 | 324.3.f.o.271.3 | 8 | |||
72.59 | even | 6 | 324.3.f.p.55.2 | 8 | |||
72.61 | even | 6 | 324.3.f.p.271.4 | 8 | |||
72.67 | odd | 6 | 324.3.f.p.55.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.d.d.55.1 | ✓ | 8 | 8.3 | odd | 2 | ||
108.3.d.d.55.2 | yes | 8 | 8.5 | even | 2 | ||
108.3.d.d.55.7 | yes | 8 | 24.5 | odd | 2 | ||
108.3.d.d.55.8 | yes | 8 | 24.11 | even | 2 | ||
324.3.f.o.55.2 | 8 | 72.5 | odd | 6 | |||
324.3.f.o.55.3 | 8 | 72.13 | even | 6 | |||
324.3.f.o.271.2 | 8 | 72.11 | even | 6 | |||
324.3.f.o.271.3 | 8 | 72.43 | odd | 6 | |||
324.3.f.p.55.2 | 8 | 72.59 | even | 6 | |||
324.3.f.p.55.3 | 8 | 72.67 | odd | 6 | |||
324.3.f.p.271.1 | 8 | 72.29 | odd | 6 | |||
324.3.f.p.271.4 | 8 | 72.61 | even | 6 | |||
1728.3.g.l.703.3 | 8 | 3.2 | odd | 2 | inner | ||
1728.3.g.l.703.4 | 8 | 12.11 | even | 2 | inner | ||
1728.3.g.l.703.5 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.g.l.703.6 | 8 | 4.3 | odd | 2 | inner |