Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.a (trivial) |
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: | yes |
Analytic conductor: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.86081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −5.97021 | −1.14897 | −0.574484 | − | 0.818516i | \(-0.694797\pi\) | ||||
−0.574484 | + | 0.818516i | \(0.694797\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.4882 | 1.11698 | 0.558491 | − | 0.829511i | \(-0.311381\pi\) | ||||
0.558491 | + | 0.829511i | \(0.311381\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 28.6773 | 1.54843 | 0.774213 | − | 0.632925i | \(-0.218146\pi\) | ||||
0.774213 | + | 0.632925i | \(0.218146\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.64344 | 0.320127 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.2099 | −0.499134 | −0.249567 | − | 0.968358i | \(-0.580288\pi\) | ||||
−0.249567 | + | 0.968358i | \(0.580288\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37.9978 | −0.810668 | −0.405334 | − | 0.914169i | \(-0.632845\pi\) | ||||
−0.405334 | + | 0.914169i | \(0.632845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −74.5574 | −1.28338 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.95162 | −0.0563769 | −0.0281885 | − | 0.999603i | \(-0.508974\pi\) | ||||
−0.0281885 | + | 0.999603i | \(0.508974\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −36.8211 | −0.444597 | −0.222298 | − | 0.974979i | \(-0.571356\pi\) | ||||
−0.222298 | + | 0.974979i | \(0.571356\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −171.209 | −1.77909 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −42.7480 | −0.387547 | −0.193773 | − | 0.981046i | \(-0.562073\pi\) | ||||
−0.193773 | + | 0.981046i | \(0.562073\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 30.9561 | 0.247649 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 109.593 | 0.781152 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 160.731 | 0.931231 | 0.465616 | − | 0.884987i | \(-0.345833\pi\) | ||||
0.465616 | + | 0.884987i | \(0.345833\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 108.717 | 0.573489 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 358.129 | 1.72957 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −313.040 | −1.39090 | −0.695451 | − | 0.718573i | \(-0.744796\pi\) | ||||
−0.695451 | + | 0.718573i | \(0.744796\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 226.855 | 0.931432 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 496.787 | 1.89232 | 0.946159 | − | 0.323703i | \(-0.104928\pi\) | ||||
0.946159 | + | 0.323703i | \(0.104928\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −139.195 | −0.493653 | −0.246827 | − | 0.969060i | \(-0.579388\pi\) | ||||
−0.246827 | + | 0.969060i | \(0.579388\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 107.941 | 0.357577 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 417.656 | 1.29620 | 0.648100 | − | 0.761556i | \(-0.275564\pi\) | ||||
0.648100 | + | 0.761556i | \(0.275564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 479.386 | 1.39763 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 23.5920 | 0.0647753 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 137.116 | 0.355365 | 0.177683 | − | 0.984088i | \(-0.443140\pi\) | ||||
0.177683 | + | 0.984088i | \(0.443140\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −227.409 | −0.557524 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 219.830 | 0.510827 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 190.033 | 0.419326 | 0.209663 | − | 0.977774i | \(-0.432763\pi\) | ||||
0.209663 | + | 0.977774i | \(0.432763\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −161.072 | −0.338084 | −0.169042 | − | 0.985609i | \(-0.554067\pi\) | ||||
−0.169042 | + | 0.985609i | \(0.554067\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 247.870 | 0.495694 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −474.525 | −0.905502 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 125.259 | 0.228400 | 0.114200 | − | 0.993458i | \(-0.463570\pi\) | ||||
0.114200 | + | 0.993458i | \(0.463570\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 255.215 | 0.445279 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 165.110 | 0.275984 | 0.137992 | − | 0.990433i | \(-0.455935\pi\) | ||||
0.137992 | + | 0.990433i | \(0.455935\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −938.243 | −1.50429 | −0.752144 | − | 0.658999i | \(-0.770980\pi\) | ||||
−0.752144 | + | 0.658999i | \(0.770980\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −184.815 | −0.284541 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −522.209 | −0.772873 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1315.60 | 1.87363 | 0.936816 | − | 0.349821i | \(-0.113758\pi\) | ||||
0.936816 | + | 0.349821i | \(0.113758\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −887.664 | −1.21765 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 505.294 | 0.668231 | 0.334116 | − | 0.942532i | \(-0.391562\pi\) | ||||
0.334116 | + | 0.942532i | \(0.391562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −49.3487 | −0.0629720 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −173.136 | −0.213358 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −769.587 | −0.916584 | −0.458292 | − | 0.888802i | \(-0.651539\pi\) | ||||
−0.458292 | + | 0.888802i | \(0.651539\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1089.67 | −1.25526 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −959.599 | −1.06996 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −459.830 | −0.496606 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1333.29 | 1.39561 | 0.697807 | − | 0.716286i | \(-0.254159\pi\) | ||||
0.697807 | + | 0.716286i | \(0.254159\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −157.396 | −0.159787 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −51.3094 | −0.0505493 | −0.0252746 | − | 0.999681i | \(-0.508046\pi\) | ||||
−0.0252746 | + | 0.999681i | \(0.508046\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1062.26 | −1.01619 | −0.508097 | − | 0.861300i | \(-0.669651\pi\) | ||||
−0.508097 | + | 0.861300i | \(0.669651\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2138.10 | −1.98721 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1414.85 | 1.27831 | 0.639155 | − | 0.769078i | \(-0.279284\pi\) | ||||
0.639155 | + | 0.769078i | \(0.279284\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −495.330 | −0.435266 | −0.217633 | − | 0.976031i | \(-0.569834\pi\) | ||||
−0.217633 | + | 0.976031i | \(0.569834\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1868.91 | 1.59810 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −603.969 | −0.502802 | −0.251401 | − | 0.967883i | \(-0.580891\pi\) | ||||
−0.251401 | + | 0.967883i | \(0.580891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −533.848 | −0.432883 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −328.432 | −0.259517 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −113.322 | −0.0872956 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −999.401 | −0.750865 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2965.92 | −2.17421 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1174.44 | −0.840363 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1282.23 | 0.895902 | 0.447951 | − | 0.894058i | \(-0.352154\pi\) | ||||
0.447951 | + | 0.894058i | \(0.352154\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 831.026 | 0.567192 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2446.25 | 1.63152 | 0.815762 | − | 0.578388i | \(-0.196318\pi\) | ||||
0.815762 | + | 0.578388i | \(0.196318\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1055.93 | −0.688425 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1368.62 | 0.872533 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1259.91 | 0.785703 | 0.392852 | − | 0.919602i | \(-0.371489\pi\) | ||||
0.392852 | + | 0.919602i | \(0.371489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −822.786 | −0.502070 | −0.251035 | − | 0.967978i | \(-0.580771\pi\) | ||||
−0.251035 | + | 0.967978i | \(0.580771\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2493.49 | −1.48929 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 691.934 | 0.404632 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 362.159 | 0.207418 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2862.03 | −1.60583 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 477.366 | 0.262466 | 0.131233 | − | 0.991352i | \(-0.458106\pi\) | ||||
0.131233 | + | 0.991352i | \(0.458106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1740.92 | 0.938240 | 0.469120 | − | 0.883135i | \(-0.344571\pi\) | ||||
0.469120 | + | 0.883135i | \(0.344571\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −34.1556 | −0.0180478 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2007.25 | 1.04017 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1372.90 | 0.697892 | 0.348946 | − | 0.937143i | \(-0.386540\pi\) | ||||
0.348946 | + | 0.937143i | \(0.386540\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −818.613 | −0.408304 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1225.90 | −0.600088 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3688.03 | 1.77220 | 0.886100 | − | 0.463495i | \(-0.153405\pi\) | ||||
0.886100 | + | 0.463495i | \(0.153405\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1357.68 | 0.640577 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4059.56 | −1.88107 | −0.940534 | − | 0.339701i | \(-0.889674\pi\) | ||||
−0.940534 | + | 0.339701i | \(0.889674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −753.169 | −0.342817 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −318.261 | −0.142328 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2811.92 | −1.23576 | −0.617879 | − | 0.786274i | \(-0.712008\pi\) | ||||
−0.617879 | + | 0.786274i | \(0.712008\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 887.737 | 0.383466 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1134.54 | −0.481792 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 163.787 | 0.0683913 | 0.0341956 | − | 0.999415i | \(-0.489113\pi\) | ||||
0.0341956 | + | 0.999415i | \(0.489113\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3540.42 | 1.45391 | 0.726954 | − | 0.686686i | \(-0.240935\pi\) | ||||
0.726954 | + | 0.686686i | \(0.240935\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 961.632 | 0.388447 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3909.31 | −1.55361 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 71.9584 | 0.0281397 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3142.82 | 1.20956 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2163.65 | −0.819665 | −0.409833 | − | 0.912161i | \(-0.634413\pi\) | ||||
−0.409833 | + | 0.912161i | \(0.634413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4632.75 | 1.72784 | 0.863919 | − | 0.503630i | \(-0.168003\pi\) | ||||
0.863919 | + | 0.503630i | \(0.168003\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2833.02 | 1.04039 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1239.91 | 0.448427 | 0.224214 | − | 0.974540i | \(-0.428019\pi\) | ||||
0.224214 | + | 0.974540i | \(0.428019\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4651.45 | −1.65695 | −0.828474 | − | 0.560028i | \(-0.810790\pi\) | ||||
−0.828474 | + | 0.560028i | \(0.810790\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −747.820 | −0.262424 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 831.641 | 0.287536 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6203.99 | 2.11369 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −369.490 | −0.124064 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 670.506 | 0.221913 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3516.90 | 1.14746 | 0.573728 | − | 0.819046i | \(-0.305497\pi\) | ||||
0.573728 | + | 0.819046i | \(0.305497\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −985.739 | −0.317097 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1738.30 | −0.551402 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4609.33 | 1.44194 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5601.51 | 1.72838 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 150.153 | 0.0457030 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3480.17 | −1.04506 | −0.522532 | − | 0.852620i | \(-0.675012\pi\) | ||||
−0.522532 | + | 0.852620i | \(0.675012\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 267.567 | 0.0792792 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1259.51 | 0.368266 | 0.184133 | − | 0.982901i | \(-0.441052\pi\) | ||||
0.184133 | + | 0.982901i | \(0.441052\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 274.295 | 0.0791524 | 0.0395762 | − | 0.999217i | \(-0.487399\pi\) | ||||
0.0395762 | + | 0.999217i | \(0.487399\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3117.70 | 0.888006 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6517.70 | 1.83257 | 0.916285 | − | 0.400526i | \(-0.131173\pi\) | ||||
0.916285 | + | 0.400526i | \(0.131173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5215.79 | 1.44783 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7854.43 | −2.15274 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6052.89 | 1.63820 | 0.819098 | − | 0.573654i | \(-0.194474\pi\) | ||||
0.819098 | + | 0.573654i | \(0.194474\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2265.19 | 0.605452 | 0.302726 | − | 0.953078i | \(-0.402103\pi\) | ||||
0.302726 | + | 0.953078i | \(0.402103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2340.54 | 0.617884 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5986.68 | 1.56112 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1399.12 | 0.360420 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3016.71 | −0.767777 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6653.27 | 1.67311 | 0.836555 | − | 0.547882i | \(-0.184566\pi\) | ||||
0.836555 | + | 0.547882i | \(0.184566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 778.435 | 0.193438 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 294.622 | 0.0723528 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3144.58 | −0.763244 | −0.381622 | − | 0.924319i | \(-0.624634\pi\) | ||||
−0.381622 | + | 0.924319i | \(0.624634\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8977.12 | −2.15371 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 250.660 | 0.0594462 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2409.66 | −0.564965 | −0.282483 | − | 0.959272i | \(-0.591158\pi\) | ||||
−0.282483 | + | 0.959272i | \(0.591158\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1712.34 | 0.396937 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4594.60 | 1.05313 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4542.85 | 1.02968 | 0.514838 | − | 0.857288i | \(-0.327852\pi\) | ||||
0.514838 | + | 0.857288i | \(0.327852\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6519.35 | 1.46134 | 0.730668 | − | 0.682733i | \(-0.239209\pi\) | ||||
0.730668 | + | 0.682733i | \(0.239209\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6505.58 | 1.44225 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −563.706 | −0.123610 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7440.91 | 1.61401 | 0.807005 | − | 0.590544i | \(-0.201087\pi\) | ||||
0.807005 | + | 0.590544i | \(0.201087\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1389.27 | 0.298113 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 272.086 | 0.0577625 | 0.0288813 | − | 0.999583i | \(-0.490806\pi\) | ||||
0.0288813 | + | 0.999583i | \(0.490806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1716.92 | −0.360636 | −0.180318 | − | 0.983608i | \(-0.557713\pi\) | ||||
−0.180318 | + | 0.983608i | \(0.557713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2745.29 | 0.570585 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14246.5 | 2.93012 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4897.38 | −0.996822 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7960.00 | −1.60352 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5903.51 | −1.17709 | −0.588544 | − | 0.808465i | \(-0.700299\pi\) | ||||
−0.588544 | + | 0.808465i | \(0.700299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2373.18 | 0.468379 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1995.66 | −0.389900 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1624.33 | 0.314172 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3991.74 | −0.764386 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 306.328 | 0.0580795 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2011.50 | −0.377633 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3769.05 | −0.700688 | −0.350344 | − | 0.936621i | \(-0.613935\pi\) | ||||
−0.350344 | + | 0.936621i | \(0.613935\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6341.94 | 1.16757 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3141.76 | −0.572839 | −0.286419 | − | 0.958104i | \(-0.592465\pi\) | ||||
−0.286419 | + | 0.958104i | \(0.592465\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1743.33 | −0.314820 | −0.157410 | − | 0.987533i | \(-0.550314\pi\) | ||||
−0.157410 | + | 0.987533i | \(0.550314\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3095.46 | 0.553681 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1836.62 | 0.325410 | 0.162705 | − | 0.986675i | \(-0.447978\pi\) | ||||
0.162705 | + | 0.986675i | \(0.447978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −528.086 | −0.0926869 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8446.99 | −1.46874 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 145.503 | 0.0250650 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1176.26 | −0.200761 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2957.23 | 0.500107 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11977.2 | 2.00707 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −106.340 | −0.0176585 | −0.00882924 | − | 0.999961i | \(-0.502810\pi\) | ||||
−0.00882924 | + | 0.999961i | \(0.502810\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2705.74 | −0.445266 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1564.26 | 0.255118 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 347.401 | 0.0561547 | 0.0280774 | − | 0.999606i | \(-0.491062\pi\) | ||||
0.0280774 | + | 0.999606i | \(0.491062\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3605.82 | 0.577703 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2926.89 | −0.464809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3911.17 | 0.615694 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3187.18 | 0.497369 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4319.94 | −0.668319 | −0.334159 | − | 0.942517i | \(-0.608452\pi\) | ||||
−0.334159 | + | 0.942517i | \(0.608452\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9732.19 | 1.49270 | 0.746350 | − | 0.665554i | \(-0.231805\pi\) | ||||
0.746350 | + | 0.665554i | \(0.231805\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4164.27 | −0.633255 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8396.92 | 1.26607 | 0.633035 | − | 0.774123i | \(-0.281809\pi\) | ||||
0.633035 | + | 0.774123i | \(0.281809\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2061.93 | 0.308270 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 676.554 | 0.100300 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1306.89 | −0.192130 | −0.0960652 | − | 0.995375i | \(-0.530626\pi\) | ||||
−0.0960652 | + | 0.995375i | \(0.530626\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5503.21 | −0.802334 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5966.64 | 0.862720 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11717.0 | −1.68026 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9859.59 | 1.40236 | 0.701181 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701181 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4293.95 | 0.605783 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3932.12 | 0.550257 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3393.01 | 0.471001 | 0.235500 | − | 0.971874i | \(-0.424327\pi\) | ||||
0.235500 | + | 0.971874i | \(0.424327\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7011.67 | 0.965550 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1101.94 | −0.150537 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2030.82 | −0.275240 | −0.137620 | − | 0.990485i | \(-0.543945\pi\) | ||||
−0.137620 | + | 0.990485i | \(0.543945\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7655.19 | −1.02936 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.81248 | −0.000642052 0 | −0.000321026 | − | 1.00000i | \(-0.500102\pi\) | ||||
−0.000321026 | 1.00000i | \(0.500102\pi\) | ||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6521.47 | −0.863285 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1203.13 | −0.158032 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9031.93 | −1.17722 | −0.588608 | − | 0.808418i | \(-0.700324\pi\) | ||||
−0.588608 | + | 0.808418i | \(0.700324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 168.924 | 0.0218487 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14604.6 | −1.87457 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16429.6 | 2.09281 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1443.16 | 0.182443 | 0.0912217 | − | 0.995831i | \(-0.470923\pi\) | ||||
0.0912217 | + | 0.995831i | \(0.470923\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6304.11 | 0.790979 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9877.59 | −1.23008 | −0.615042 | − | 0.788495i | \(-0.710861\pi\) | ||||
−0.615042 | + | 0.788495i | \(0.710861\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6107.43 | −0.754920 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11085.4 | −1.36009 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5700.41 | 0.694247 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14530.7 | 1.75672 | 0.878358 | − | 0.478003i | \(-0.158639\pi\) | ||||
0.878358 | + | 0.478003i | \(0.158639\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7521.93 | −0.902748 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5449.63 | 0.649295 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6310.23 | 0.746403 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4912.21 | 0.576863 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3312.84 | 0.386259 | 0.193130 | − | 0.981173i | \(-0.438136\pi\) | ||||
0.193130 | + | 0.981173i | \(0.438136\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6708.67 | 0.776629 | 0.388314 | − | 0.921527i | \(-0.373057\pi\) | ||||
0.388314 | + | 0.921527i | \(0.373057\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3609.98 | 0.414949 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −122.327 | −0.0139617 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4619.09 | −0.523498 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4130.99 | −0.464909 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14687.7 | 1.64148 | 0.820742 | − | 0.571299i | \(-0.193560\pi\) | ||||
0.820742 | + | 0.571299i | \(0.193560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 759.822 | 0.0843296 | 0.0421648 | − | 0.999111i | \(-0.486575\pi\) | ||||
0.0421648 | + | 0.999111i | \(0.486575\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2162.17 | −0.238317 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1574.03 | 0.172302 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4803.78 | −0.522260 | −0.261130 | − | 0.965304i | \(-0.584095\pi\) | ||||
−0.261130 | + | 0.965304i | \(0.584095\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4143.54 | 0.447418 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10123.3 | 1.08572 | 0.542858 | − | 0.839824i | \(-0.317342\pi\) | ||||
0.542858 | + | 0.839824i | \(0.317342\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9610.78 | −1.02381 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2849.98 | −0.301565 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −636.749 | −0.0669266 | −0.0334633 | − | 0.999440i | \(-0.510654\pi\) | ||||
−0.0334633 | + | 0.999440i | \(0.510654\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9046.41 | −0.944521 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10393.7 | −1.07801 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13608.1 | −1.40210 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12598.2 | 1.28954 | 0.644770 | − | 0.764376i | \(-0.276953\pi\) | ||||
0.644770 | + | 0.764376i | \(0.276953\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −433.068 | −0.0440389 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15728.3 | −1.58902 | −0.794512 | − | 0.607249i | \(-0.792273\pi\) | ||||
−0.794512 | + | 0.607249i | \(0.792273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5504.55 | −0.552523 | −0.276262 | − | 0.961083i | \(-0.589096\pi\) | ||||
−0.276262 | + | 0.961083i | \(0.589096\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11983.7 | −1.19512 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14851.2 | 1.47159 | 0.735796 | − | 0.677203i | \(-0.236808\pi\) | ||||
0.735796 | + | 0.677203i | \(0.236808\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3592.07 | 0.353660 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8196.48 | −0.801855 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2534.73 | 0.246399 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1139.84 | −0.110104 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1185.16 | 0.113762 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5778.20 | −0.551175 | −0.275587 | − | 0.961276i | \(-0.588872\pi\) | ||||
−0.275587 | + | 0.961276i | \(0.588872\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11894.8 | 1.12756 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7318.86 | 0.689482 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16650.4 | 1.55888 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12639.2 | 1.17605 | 0.588027 | − | 0.808841i | \(-0.299905\pi\) | ||||
0.588027 | + | 0.808841i | \(0.299905\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22018.3 | −2.03620 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −363.554 | −0.0334154 | −0.0167077 | − | 0.999860i | \(-0.505318\pi\) | ||||
−0.0167077 | + | 0.999860i | \(0.505318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −114.597 | −0.0104689 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1965.60 | −0.178479 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4734.89 | 0.427342 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4327.18 | −0.388198 | −0.194099 | − | 0.980982i | \(-0.562178\pi\) | ||||
−0.194099 | + | 0.980982i | \(0.562178\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24236.4 | 2.16129 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21621.8 | −1.91664 | −0.958318 | − | 0.285704i | \(-0.907773\pi\) | ||||
−0.958318 | + | 0.285704i | \(0.907773\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −640.764 | −0.0564626 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4496.58 | 0.393886 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12903.3 | −1.12363 | −0.561817 | − | 0.827261i | \(-0.689898\pi\) | ||||
−0.561817 | + | 0.827261i | \(0.689898\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26906.2 | −2.32928 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4035.32 | −0.347297 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13265.8 | −1.13507 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7605.45 | −0.646977 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16787.7 | 1.41985 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5015.65 | −0.421765 | −0.210883 | − | 0.977511i | \(-0.567634\pi\) | ||||
−0.210883 | + | 0.977511i | \(0.567634\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10454.3 | −0.874059 | −0.437030 | − | 0.899447i | \(-0.643970\pi\) | ||||
−0.437030 | + | 0.899447i | \(0.643970\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5299.98 | −0.440591 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −635.148 | −0.0525000 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10339.6 | −0.849807 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1642.54 | 0.134238 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18876.8 | −1.53404 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17669.0 | 1.42785 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −977.845 | −0.0785794 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8729.54 | −0.697603 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16028.3 | −1.27377 | −0.636886 | − | 0.770958i | \(-0.719778\pi\) | ||||
−0.636886 | + | 0.770958i | \(0.719778\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21137.1 | −1.67049 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6185.80 | −0.486184 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7590.17 | −0.593295 | −0.296647 | − | 0.954987i | \(-0.595869\pi\) | ||||
−0.296647 | + | 0.954987i | \(0.595869\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1392.21 | −0.108230 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1067.81 | −0.0825595 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37727.9 | 2.90118 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 23339.4 | 1.78505 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15598.4 | 1.18658 | 0.593291 | − | 0.804988i | \(-0.297828\pi\) | ||||
0.593291 | + | 0.804988i | \(0.297828\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5289.11 | 0.400189 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −429.607 | −0.0323316 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18275.4 | −1.36806 | −0.684030 | − | 0.729454i | \(-0.739774\pi\) | ||||
−0.684030 | + | 0.729454i | \(0.739774\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7542.51 | −0.561621 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −25455.8 | −1.88544 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11103.6 | −0.818081 | −0.409040 | − | 0.912516i | \(-0.634136\pi\) | ||||
−0.409040 | + | 0.912516i | \(0.634136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12505.8 | 0.916550 | 0.458275 | − | 0.888810i | \(-0.348467\pi\) | ||||
0.458275 | + | 0.888810i | \(0.348467\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12917.4 | 0.941769 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1323.31 | −0.0959756 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16122.3 | 1.16322 | 0.581612 | − | 0.813466i | \(-0.302422\pi\) | ||||
0.581612 | + | 0.813466i | \(0.302422\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27658.5 | −1.98523 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14490.4 | 1.03471 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2496.87 | −0.177375 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4101.53 | −0.289876 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 82.7289 | 0.00581701 | 0.00290851 | − | 0.999996i | \(-0.499074\pi\) | ||||
0.00290851 | + | 0.999996i | \(0.499074\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5918.29 | −0.414022 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7402.55 | −0.515229 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5049.72 | −0.349692 | −0.174846 | − | 0.984596i | \(-0.555943\pi\) | ||||
−0.174846 | + | 0.984596i | \(0.555943\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1415.19 | −0.0975076 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27770.1 | 1.90378 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16393.1 | 1.11820 | 0.559101 | − | 0.829100i | \(-0.311147\pi\) | ||||
0.559101 | + | 0.829100i | \(0.311147\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22564.2 | 1.53147 | 0.765733 | − | 0.643158i | \(-0.222376\pi\) | ||||
0.765733 | + | 0.643158i | \(0.222376\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1082.67 | 0.0731170 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12480.8 | −0.838703 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10441.9 | 0.698230 | 0.349115 | − | 0.937080i | \(-0.386482\pi\) | ||||
0.349115 | + | 0.937080i | \(0.386482\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4965.07 | −0.330369 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15870.0 | −1.05079 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5153.31 | 0.339544 | 0.169772 | − | 0.985483i | \(-0.445697\pi\) | ||||
0.169772 | + | 0.985483i | \(0.445697\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −37039.1 | −2.42856 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22893.5 | 1.49377 | 0.746886 | − | 0.664952i | \(-0.231548\pi\) | ||||
0.746886 | + | 0.664952i | \(0.231548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1872.55 | 0.121590 | 0.0607949 | − | 0.998150i | \(-0.480636\pi\) | ||||
0.0607949 | + | 0.998150i | \(0.480636\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4684.87 | −0.302733 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22069.6 | −1.41926 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18536.2 | −1.18632 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4003.07 | −0.254971 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1237.01 | 0.0784148 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12644.7 | −0.797745 | −0.398872 | − | 0.917006i | \(-0.630598\pi\) | ||||
−0.398872 | + | 0.917006i | \(0.630598\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20996.6 | −1.31839 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16012.8 | 1.00071 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18215.6 | −1.13301 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1427.11 | 0.0883502 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17232.7 | −1.06186 | −0.530929 | − | 0.847416i | \(-0.678157\pi\) | ||||
−0.530929 | + | 0.847416i | \(0.678157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4194.66 | 0.257265 | 0.128632 | − | 0.991692i | \(-0.458941\pi\) | ||||
0.128632 | + | 0.991692i | \(0.458941\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10378.0 | 0.633543 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29338.5 | 1.78271 | 0.891355 | − | 0.453305i | \(-0.149755\pi\) | ||||
0.891355 | + | 0.453305i | \(0.149755\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3460.48 | −0.209300 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27518.7 | −1.65675 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30988.6 | 1.85709 | 0.928543 | − | 0.371225i | \(-0.121062\pi\) | ||||
0.928543 | + | 0.371225i | \(0.121062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30549.3 | 1.82238 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8109.65 | −0.481564 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8159.70 | 0.482332 | 0.241166 | − | 0.970484i | \(-0.422470\pi\) | ||||
0.241166 | + | 0.970484i | \(0.422470\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24409.7 | −1.43635 | −0.718174 | − | 0.695864i | \(-0.755022\pi\) | ||||
−0.718174 | + | 0.695864i | \(0.755022\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −896.443 | −0.0525113 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13186.7 | −0.768959 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1239.69 | −0.0719657 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20777.3 | 1.20074 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2933.09 | 0.168749 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 371.652 | 0.0212870 | 0.0106435 | − | 0.999943i | \(-0.496612\pi\) | ||||
0.0106435 | + | 0.999943i | \(0.496612\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3392.56 | 0.193451 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8788.32 | −0.498911 | −0.249455 | − | 0.968386i | \(-0.580252\pi\) | ||||
−0.249455 | + | 0.968386i | \(0.580252\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38235.0 | 2.16101 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7519.51 | −0.423125 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8840.50 | 0.495274 | 0.247637 | − | 0.968853i | \(-0.420346\pi\) | ||||
0.247637 | + | 0.968853i | \(0.420346\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15734.0 | 0.877616 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1637.60 | −0.0909436 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5210.11 | −0.288083 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34252.5 | 1.88571 | 0.942856 | − | 0.333199i | \(-0.108128\pi\) | ||||
0.942856 | + | 0.333199i | \(0.108128\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4513.68 | −0.247418 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10275.1 | −0.560804 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1963.11 | −0.106683 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −38912.1 | −2.10556 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27978.5 | 1.50747 | 0.753733 | − | 0.657180i | \(-0.228251\pi\) | ||||
0.753733 | + | 0.657180i | \(0.228251\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11526.5 | 0.618391 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31139.3 | −1.66351 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1471.41 | −0.0782719 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 378.764 | 0.0200632 | 0.0100316 | − | 0.999950i | \(-0.496807\pi\) | ||||
0.0100316 | + | 0.999950i | \(0.496807\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11371.3 | 0.599801 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6870.94 | −0.360896 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8641.03 | 0.451967 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −36137.0 | −1.88223 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9369.50 | −0.485985 | −0.242993 | − | 0.970028i | \(-0.578129\pi\) | ||||
−0.242993 | + | 0.970028i | \(0.578129\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30462.8 | −1.57350 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13523.7 | −0.695645 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 897.728 | 0.0459873 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14672.0 | −0.748494 | −0.374247 | − | 0.927329i | \(-0.622099\pi\) | ||||
−0.374247 | + | 0.927329i | \(0.622099\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9993.38 | 0.507717 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 550.047 | 0.0278307 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9764.90 | 0.492053 | 0.246027 | − | 0.969263i | \(-0.420875\pi\) | ||||
0.246027 | + | 0.969263i | \(0.420875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −35741.8 | −1.79368 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2280.94 | −0.114002 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11150.5 | 0.555043 | 0.277521 | − | 0.960719i | \(-0.410487\pi\) | ||||
0.277521 | + | 0.960719i | \(0.410487\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8353.04 | −0.414111 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17461.6 | −0.862186 | −0.431093 | − | 0.902307i | \(-0.641872\pi\) | ||||
−0.431093 | + | 0.902307i | \(0.641872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5961.47 | 0.293169 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4367.48 | 0.213919 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40574.2 | 1.97937 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12692.5 | −0.616717 | −0.308358 | − | 0.951270i | \(-0.599780\pi\) | ||||
−0.308358 | + | 0.951270i | \(0.599780\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −39721.5 | −1.92235 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21741.0 | 1.04800 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35923.3 | −1.72477 | −0.862387 | − | 0.506250i | \(-0.831031\pi\) | ||||
−0.862387 | + | 0.506250i | \(0.831031\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4647.42 | −0.222254 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27302.4 | −1.30054 | −0.650270 | − | 0.759703i | \(-0.725344\pi\) | ||||
−0.650270 | + | 0.759703i | \(0.725344\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14204.7 | −0.673978 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −426.543 | −0.0201591 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7220.84 | −0.339934 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17941.0 | 0.841314 | 0.420657 | − | 0.907220i | \(-0.361800\pi\) | ||||
0.420657 | + | 0.907220i | \(0.361800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18773.8 | 0.876943 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6566.84 | −0.305553 | −0.152777 | − | 0.988261i | \(-0.548822\pi\) | ||||
−0.152777 | + | 0.988261i | \(0.548822\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4975.61 | 0.230619 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 53595.3 | 2.47455 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18292.2 | −0.841318 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3006.62 | −0.137753 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3178.18 | 0.145056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17145.1 | 0.779533 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28734.0 | −1.30147 | −0.650736 | − | 0.759304i | \(-0.725539\pi\) | ||||
−0.650736 | + | 0.759304i | \(0.725539\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14386.2 | 0.649127 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17320.2 | −0.778552 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6120.36 | 0.274074 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10223.0 | −0.456068 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22553.9 | 1.00238 | 0.501192 | − | 0.865336i | \(-0.332895\pi\) | ||||
0.501192 | + | 0.865336i | \(0.332895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1650.42 | −0.0730757 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6651.88 | −0.293424 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17085.3 | 0.750841 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15309.3 | −0.670288 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27121.8 | −1.18306 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24921.7 | 1.08307 | 0.541533 | − | 0.840680i | \(-0.317844\pi\) | ||||
0.541533 | + | 0.840680i | \(0.317844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41652.2 | 1.80346 | 0.901730 | − | 0.432300i | \(-0.142298\pi\) | ||||
0.901730 | + | 0.432300i | \(0.142298\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −38921.9 | −1.67903 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 46057.0 | 1.97952 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5125.32 | 0.219477 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9418.52 | −0.401843 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10969.1 | 0.466288 | 0.233144 | − | 0.972442i | \(-0.425099\pi\) | ||||
0.233144 | + | 0.972442i | \(0.425099\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16669.2 | −0.706015 | −0.353008 | − | 0.935620i | \(-0.614841\pi\) | ||||
−0.353008 | + | 0.935620i | \(0.614841\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3365.45 | 0.142024 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9424.07 | −0.396260 | −0.198130 | − | 0.980176i | \(-0.563487\pi\) | ||||
−0.198130 | + | 0.980176i | \(0.563487\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23359.5 | 0.978658 | 0.489329 | − | 0.872099i | \(-0.337242\pi\) | ||||
0.489329 | + | 0.872099i | \(0.337242\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −44423.8 | −1.85445 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1894.35 | −0.0787938 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −50696.8 | −2.10112 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17614.9 | 0.727433 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9260.03 | 0.381039 | 0.190520 | − | 0.981683i | \(-0.438983\pi\) | ||||
0.190520 | + | 0.981683i | \(0.438983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1624.41 | −0.0663673 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9405.76 | −0.382921 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28660.1 | −1.16266 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10250.4 | 0.414359 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13381.8 | 0.539040 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43938.1 | 1.76367 | 0.881836 | − | 0.471556i | \(-0.156307\pi\) | ||||
0.881836 | + | 0.471556i | \(0.156307\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3974.52 | −0.158977 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44540.6 | 1.77535 | 0.887676 | − | 0.460469i | \(-0.152319\pi\) | ||||
0.887676 | + | 0.460469i | \(0.152319\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5126.48 | −0.203624 | −0.101812 | − | 0.994804i | \(-0.532464\pi\) | ||||
−0.101812 | + | 0.994804i | \(0.532464\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −85054.5 | −3.36661 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29711.0 | −1.17193 | −0.585964 | − | 0.810337i | \(-0.699284\pi\) | ||||
−0.585964 | + | 0.810337i | \(0.699284\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35115.9 | −1.38032 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29238.4 | 1.14532 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23956.9 | −0.935194 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4759.55 | −0.185156 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11524.2 | 0.446775 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −33679.8 | −1.30124 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24925.9 | 0.959735 | 0.479867 | − | 0.877341i | \(-0.340685\pi\) | ||||
0.479867 | + | 0.877341i | \(0.340685\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35245.2 | 1.35244 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13514.7 | 0.516825 | 0.258413 | − | 0.966035i | \(-0.416801\pi\) | ||||
0.258413 | + | 0.966035i | \(0.416801\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21759.9 | 0.829309 | 0.414654 | − | 0.909979i | \(-0.363903\pi\) | ||||
0.414654 | + | 0.909979i | \(0.363903\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14168.4 | −0.538153 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15556.4 | 0.588877 | 0.294439 | − | 0.955670i | \(-0.404867\pi\) | ||||
0.294439 | + | 0.955670i | \(0.404867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36770.9 | 1.38724 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16164.2 | 0.607769 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15378.5 | −0.576286 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2045.42 | 0.0763919 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9697.60 | −0.360974 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4661.20 | 0.172925 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −541.831 | −0.0200344 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23831.5 | 0.878255 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 44213.6 | 1.62399 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36707.3 | −1.34382 | −0.671910 | − | 0.740633i | \(-0.734526\pi\) | ||||
−0.671910 | + | 0.740633i | \(0.734526\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −443.490 | −0.0161822 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21608.1 | 0.785849 | 0.392924 | − | 0.919571i | \(-0.371463\pi\) | ||||
0.392924 | + | 0.919571i | \(0.371463\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9201.33 | −0.333537 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12009.1 | 0.433889 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 70151.7 | 2.52630 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40069.5 | 1.43827 | 0.719135 | − | 0.694870i | \(-0.244538\pi\) | ||||
0.719135 | + | 0.694870i | \(0.244538\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22502.1 | 0.805068 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6273.79 | −0.223732 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9690.49 | −0.344456 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9181.61 | −0.325311 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18663.0 | −0.659112 | −0.329556 | − | 0.944136i | \(-0.606899\pi\) | ||||
−0.329556 | + | 0.944136i | \(0.606899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17651.5 | −0.621380 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18757.0 | 0.658173 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 898.633 | 0.0314315 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13742.0 | 0.479115 | 0.239557 | − | 0.970882i | \(-0.422998\pi\) | ||||
0.239557 | + | 0.970882i | \(0.422998\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10408.0 | 0.361718 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31953.9 | −1.10698 | −0.553489 | − | 0.832856i | \(-0.686704\pi\) | ||||
−0.553489 | + | 0.832856i | \(0.686704\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21236.6 | −0.733362 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 39248.2 | 1.35105 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11988.8 | 0.411386 | 0.205693 | − | 0.978617i | \(-0.434055\pi\) | ||||
0.205693 | + | 0.978617i | \(0.434055\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35651.1 | 1.21948 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10965.0 | −0.373886 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6567.87 | −0.223247 | −0.111623 | − | 0.993751i | \(-0.535605\pi\) | ||||
−0.111623 | + | 0.993751i | \(0.535605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27020.2 | −0.915552 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3152.78 | 0.106494 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36130.8 | 1.21660 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3956.49 | −0.132808 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12229.2 | 0.409222 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57854.9 | 1.92997 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40868.4 | −1.35909 | −0.679545 | − | 0.733634i | \(-0.737823\pi\) | ||||
−0.679545 | + | 0.733634i | \(0.737823\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −868.683 | −0.0287989 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53372.2 | −1.76395 | −0.881976 | − | 0.471295i | \(-0.843787\pi\) | ||||
−0.881976 | + | 0.471295i | \(0.843787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23595.3 | −0.777419 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7022.54 | 0.230668 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32609.8 | 1.06784 | 0.533920 | − | 0.845535i | \(-0.320718\pi\) | ||||
0.533920 | + | 0.845535i | \(0.320718\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14014.1 | 0.457499 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4281.36 | −0.139341 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23719.0 | −0.769602 | −0.384801 | − | 0.923000i | \(-0.625730\pi\) | ||||
−0.384801 | + | 0.923000i | \(0.625730\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15484.3 | 0.500885 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −71506.6 | −2.30606 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5950.33 | 0.191314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12328.2 | 0.395176 | 0.197588 | − | 0.980285i | \(-0.436689\pi\) | ||||
0.197588 | + | 0.980285i | \(0.436689\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 634.871 | 0.0202890 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −58088.4 | −1.85078 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55140.7 | −1.75158 | −0.875790 | − | 0.482693i | \(-0.839659\pi\) | ||||
−0.875790 | + | 0.482693i | \(0.839659\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −34306.8 | −1.08651 |
(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 | 1856.4.a.u.1.1 | 3 | ||
4.3 | odd | 2 | 1856.4.a.p.1.3 | 3 | |||
8.3 | odd | 2 | 232.4.a.b.1.1 | ✓ | 3 | ||
8.5 | even | 2 | 464.4.a.g.1.3 | 3 | |||
24.11 | even | 2 | 2088.4.a.b.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.b.1.1 | ✓ | 3 | 8.3 | odd | 2 | ||
464.4.a.g.1.3 | 3 | 8.5 | even | 2 | |||
1856.4.a.p.1.3 | 3 | 4.3 | odd | 2 | |||
1856.4.a.u.1.1 | 3 | 1.1 | even | 1 | trivial | ||
2088.4.a.b.1.3 | 3 | 24.11 | even | 2 |