Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(865,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.865");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 170x^{12} + 7609x^{8} + 59868x^{4} + 104976 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 865.5 | ||
Root | \(-2.23276 + 2.23276i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.865 |
Dual form | 1728.4.d.i.865.11 |
$q$-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 | ||||||||
\(5\) | − 10.1512i | − 0.907949i | −0.891015 | − | 0.453974i | \(-0.850006\pi\) | ||||
0.891015 | − | 0.453974i | \(-0.149994\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −33.8599 | −1.82826 | −0.914131 | − | 0.405419i | \(-0.867126\pi\) | ||||
−0.914131 | + | 0.405419i | \(0.867126\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.5846i | 0.372354i | 0.982516 | + | 0.186177i | \(0.0596098\pi\) | ||||
−0.982516 | + | 0.186177i | \(0.940390\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.9227i | 0.979743i | 0.871795 | + | 0.489871i | \(0.162956\pi\) | ||||
−0.871795 | + | 0.489871i | \(0.837044\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −131.190 | −1.87166 | −0.935828 | − | 0.352456i | \(-0.885347\pi\) | ||||
−0.935828 | + | 0.352456i | \(0.885347\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.89999i | − 0.0953886i | −0.998862 | − | 0.0476943i | \(-0.984813\pi\) | ||||
0.998862 | − | 0.0476943i | \(-0.0151873\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −28.2430 | −0.256047 | −0.128023 | − | 0.991771i | \(-0.540863\pi\) | ||||
−0.128023 | + | 0.991771i | \(0.540863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 21.9537 | 0.175629 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 238.102i | − 1.52463i | −0.647204 | − | 0.762317i | \(-0.724062\pi\) | ||||
0.647204 | − | 0.762317i | \(-0.275938\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −67.2350 | −0.389541 | −0.194770 | − | 0.980849i | \(-0.562396\pi\) | ||||
−0.194770 | + | 0.980849i | \(0.562396\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 343.718i | 1.65997i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 80.2173i | − 0.356423i | −0.983992 | − | 0.178211i | \(-0.942969\pi\) | ||||
0.983992 | − | 0.178211i | \(-0.0570311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −299.356 | −1.14028 | −0.570140 | − | 0.821547i | \(-0.693111\pi\) | ||||
−0.570140 | + | 0.821547i | \(0.693111\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 378.069i | 1.34081i | 0.741994 | + | 0.670407i | \(0.233880\pi\) | ||||
−0.741994 | + | 0.670407i | \(0.766120\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −367.377 | −1.14016 | −0.570079 | − | 0.821590i | \(-0.693088\pi\) | ||||
−0.570079 | + | 0.821590i | \(0.693088\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 803.492 | 2.34254 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 28.5042i | − 0.0738746i | −0.999318 | − | 0.0369373i | \(-0.988240\pi\) | ||||
0.999318 | − | 0.0369373i | \(-0.0117602\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 137.899 | 0.338079 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 597.359i | 1.31813i | 0.752087 | + | 0.659063i | \(0.229047\pi\) | ||||
−0.752087 | + | 0.659063i | \(0.770953\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 142.614i | 0.299342i | 0.988736 | + | 0.149671i | \(0.0478214\pi\) | ||||
−0.988736 | + | 0.149671i | \(0.952179\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 466.169 | 0.889556 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 656.298i | 1.19671i | 0.801231 | + | 0.598355i | \(0.204179\pi\) | ||||
−0.801231 | + | 0.598355i | \(0.795821\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 982.700 | 1.64261 | 0.821303 | − | 0.570493i | \(-0.193248\pi\) | ||||
0.821303 | + | 0.570493i | \(0.193248\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −900.999 | −1.44457 | −0.722287 | − | 0.691593i | \(-0.756909\pi\) | ||||
−0.722287 | + | 0.691593i | \(0.756909\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 459.971i | − 0.680761i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −381.751 | −0.543675 | −0.271837 | − | 0.962343i | \(-0.587631\pi\) | ||||
−0.271837 | + | 0.962343i | \(0.587631\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 650.106i | − 0.859740i | −0.902891 | − | 0.429870i | \(-0.858559\pi\) | ||||
0.902891 | − | 0.429870i | \(-0.141441\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1331.73i | 1.69937i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1233.60 | 1.46923 | 0.734615 | − | 0.678484i | \(-0.237363\pi\) | ||||
0.734615 | + | 0.678484i | \(0.237363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1554.94i | − 1.79123i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −80.1942 | −0.0866079 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −25.6927 | −0.0268938 | −0.0134469 | − | 0.999910i | \(-0.504280\pi\) | ||||
−0.0134469 | + | 0.999910i | \(0.504280\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 556.136i | 0.547897i | 0.961744 | + | 0.273949i | \(0.0883299\pi\) | ||||
−0.961744 | + | 0.273949i | \(0.911670\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −855.126 | −0.818039 | −0.409020 | − | 0.912526i | \(-0.634129\pi\) | ||||
−0.409020 | + | 0.912526i | \(0.634129\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1423.76i | − 1.28636i | −0.765716 | − | 0.643179i | \(-0.777615\pi\) | ||||
0.765716 | − | 0.643179i | \(-0.222385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1772.20i | − 1.55730i | −0.627460 | − | 0.778649i | \(-0.715905\pi\) | ||||
0.627460 | − | 0.778649i | \(-0.284095\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 348.197 | 0.289873 | 0.144936 | − | 0.989441i | \(-0.453702\pi\) | ||||
0.144936 | + | 0.989441i | \(0.453702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 286.700i | 0.232477i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4442.07 | 3.42188 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1146.46 | 0.861352 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1491.75i | − 1.06741i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1541.87 | 1.07731 | 0.538657 | − | 0.842525i | \(-0.318932\pi\) | ||||
0.538657 | + | 0.842525i | \(0.318932\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 190.595i | 0.127117i | 0.997978 | + | 0.0635585i | \(0.0202449\pi\) | ||||
−0.997978 | + | 0.0635585i | \(0.979755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 267.493i | 0.174395i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2328.41 | 1.45204 | 0.726020 | − | 0.687674i | \(-0.241368\pi\) | ||||
0.726020 | + | 0.687674i | \(0.241368\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1310.45i | 0.799645i | 0.916593 | + | 0.399822i | \(0.130928\pi\) | ||||
−0.916593 | + | 0.399822i | \(0.869072\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −623.839 | −0.364812 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2417.01 | −1.38429 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2479.21i | − 1.36312i | −0.731763 | − | 0.681559i | \(-0.761302\pi\) | ||||
0.731763 | − | 0.681559i | \(-0.238698\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2277.83 | 1.22760 | 0.613799 | − | 0.789462i | \(-0.289640\pi\) | ||||
0.613799 | + | 0.789462i | \(0.289640\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 682.514i | 0.353683i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2918.51i | − 1.48358i | −0.670631 | − | 0.741791i | \(-0.733977\pi\) | ||||
0.670631 | − | 0.741791i | \(-0.266023\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 956.306 | 0.468121 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3451.21i | − 1.65840i | −0.558949 | − | 0.829202i | \(-0.688795\pi\) | ||||
0.558949 | − | 0.829202i | \(-0.311205\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2215.29 | 1.02649 | 0.513246 | − | 0.858241i | \(-0.328443\pi\) | ||||
0.513246 | + | 0.858241i | \(0.328443\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 88.1083 | 0.0401039 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 379.191i | − 0.166644i | −0.996523 | − | 0.0833218i | \(-0.973447\pi\) | ||||
0.996523 | − | 0.0833218i | \(-0.0265529\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −743.349 | −0.321097 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4053.71i | 1.69267i | 0.532648 | + | 0.846337i | \(0.321197\pi\) | ||||
−0.532648 | + | 0.846337i | \(0.678803\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 660.485i | − 0.271235i | −0.990761 | − | 0.135617i | \(-0.956698\pi\) | ||||
0.990761 | − | 0.135617i | \(-0.0433018\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −814.299 | −0.323613 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1782.15i | − 0.696920i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −583.007 | −0.220863 | −0.110432 | − | 0.993884i | \(-0.535223\pi\) | ||||
−0.110432 | + | 0.993884i | \(0.535223\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2720.37 | −1.01459 | −0.507296 | − | 0.861772i | \(-0.669355\pi\) | ||||
−0.507296 | + | 0.861772i | \(0.669355\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3698.56i | − 1.33762i | −0.743432 | − | 0.668812i | \(-0.766803\pi\) | ||||
0.743432 | − | 0.668812i | \(-0.233197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2153.47 | −0.767112 | −0.383556 | − | 0.923518i | \(-0.625301\pi\) | ||||
−0.383556 | + | 0.923518i | \(0.625301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8062.10i | 2.78743i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3038.81i | 1.03532i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 107.318 | 0.0355183 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 469.208i | 0.153088i | 0.997066 | + | 0.0765442i | \(0.0243886\pi\) | ||||
−0.997066 | + | 0.0765442i | \(0.975611\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3837.84 | 1.21739 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2276.57 | 0.712182 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 6024.58i | − 1.83374i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 201.276 | 0.0604416 | 0.0302208 | − | 0.999543i | \(-0.490379\pi\) | ||||
0.0302208 | + | 0.999543i | \(0.490379\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2071.91i | 0.605804i | 0.953022 | + | 0.302902i | \(0.0979555\pi\) | ||||
−0.953022 | + | 0.302902i | \(0.902045\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4791.50i | 1.38267i | 0.722534 | + | 0.691335i | \(0.242977\pi\) | ||||
−0.722534 | + | 0.691335i | \(0.757023\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −420.018 | −0.118096 | −0.0590478 | − | 0.998255i | \(-0.518806\pi\) | ||||
−0.0590478 | + | 0.998255i | \(0.518806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3729.31i | 1.03521i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 213.131 | 0.0576832 | 0.0288416 | − | 0.999584i | \(-0.490818\pi\) | ||||
0.0288416 | + | 0.999584i | \(0.490818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1184.91 | −0.316707 | −0.158354 | − | 0.987382i | \(-0.550619\pi\) | ||||
−0.158354 | + | 0.987382i | \(0.550619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 8156.38i | − 2.12691i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 362.789 | 0.0934563 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 435.785i | 0.109588i | 0.998498 | + | 0.0547938i | \(0.0174501\pi\) | ||||
−0.998498 | + | 0.0547938i | \(0.982550\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 383.669i | − 0.0953402i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2774.42 | −0.673398 | −0.336699 | − | 0.941612i | \(-0.609311\pi\) | ||||
−0.336699 | + | 0.941612i | \(0.609311\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2716.15i | 0.651634i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2037.84 | 0.477789 | 0.238895 | − | 0.971046i | \(-0.423215\pi\) | ||||
0.238895 | + | 0.971046i | \(0.423215\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −289.351 | −0.0670744 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2124.72i | 0.481586i | 0.970576 | + | 0.240793i | \(0.0774076\pi\) | ||||
−0.970576 | + | 0.240793i | \(0.922592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3347.92 | −0.750449 | −0.375225 | − | 0.926934i | \(-0.622434\pi\) | ||||
−0.375225 | + | 0.926934i | \(0.622434\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 298.231i | 0.0653964i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 400.152i | 0.0867971i | 0.999058 | + | 0.0433986i | \(0.0138185\pi\) | ||||
−0.999058 | + | 0.0433986i | \(0.986181\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6250.69 | 1.32699 | 0.663496 | − | 0.748179i | \(-0.269072\pi\) | ||||
0.663496 | + | 0.748179i | \(0.269072\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5019.04i | − 1.05424i | −0.849790 | − | 0.527122i | \(-0.823271\pi\) | ||||
0.849790 | − | 0.527122i | \(-0.176729\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10136.2 | 2.08473 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12297.7 | 2.50310 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3328.32i | − 0.663626i | −0.943345 | − | 0.331813i | \(-0.892340\pi\) | ||||
0.943345 | − | 0.331813i | \(-0.107660\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6063.89 | 1.19679 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1297.00i | − 0.250860i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 12801.4i | − 2.45136i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1447.70 | 0.271787 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7458.88i | 1.38665i | 0.720626 | + | 0.693324i | \(0.243854\pi\) | ||||
−0.720626 | + | 0.693324i | \(0.756146\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7654.03 | 1.39556 | 0.697781 | − | 0.716311i | \(-0.254171\pi\) | ||||
0.697781 | + | 0.716311i | \(0.254171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4667.07 | −0.842805 | −0.421403 | − | 0.906874i | \(-0.638462\pi\) | ||||
−0.421403 | + | 0.906874i | \(0.638462\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6817.04i | − 1.20783i | −0.797048 | − | 0.603916i | \(-0.793606\pi\) | ||||
0.797048 | − | 0.603916i | \(-0.206394\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3234.51 | 0.567704 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1036.40i | 0.178535i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1008.17i | 0.172072i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12439.3 | 2.08451 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9883.48i | 1.64122i | 0.571486 | + | 0.820612i | \(0.306367\pi\) | ||||
−0.571486 | + | 0.820612i | \(0.693633\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6662.20 | 1.08655 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2441.10 | 0.394585 | 0.197292 | − | 0.980345i | \(-0.436785\pi\) | ||||
0.197292 | + | 0.980345i | \(0.436785\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 913.357i | − 0.145047i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15592.2 | −2.45452 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8251.95i | − 1.27662i | −0.769778 | − | 0.638311i | \(-0.779633\pi\) | ||||
0.769778 | − | 0.638311i | \(-0.220367\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10034.7i | 1.53910i | 0.638587 | + | 0.769550i | \(0.279519\pi\) | ||||
−0.638587 | + | 0.769550i | \(0.720481\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 815.263 | 0.122924 | 0.0614618 | − | 0.998109i | \(-0.480424\pi\) | ||||
0.0614618 | + | 0.998109i | \(0.480424\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 9975.55i | − 1.49140i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7902.99 | −1.16185 | −0.580925 | − | 0.813957i | \(-0.697309\pi\) | ||||
−0.580925 | + | 0.813957i | \(0.697309\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6796.59 | 0.990901 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9146.20i | 1.31160i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 328.415 | 0.0467115 | 0.0233557 | − | 0.999727i | \(-0.492565\pi\) | ||||
0.0233557 | + | 0.999727i | \(0.492565\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 965.149i | 0.135062i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11569.9i | 1.60608i | 0.595924 | + | 0.803041i | \(0.296786\pi\) | ||||
−0.595924 | + | 0.803041i | \(0.703214\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10934.3 | 1.49375 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 26.9740i | − 0.00365584i | −0.999998 | − | 0.00182792i | \(-0.999418\pi\) | ||||
0.999998 | − | 0.00182792i | \(-0.000581845\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10627.4 | 1.41785 | 0.708924 | − | 0.705285i | \(-0.249181\pi\) | ||||
0.708924 | + | 0.705285i | \(0.249181\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4669.25 | −0.618096 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8604.92i | 1.12156i | 0.827965 | + | 0.560780i | \(0.189499\pi\) | ||||
−0.827965 | + | 0.560780i | \(0.810501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3705.19 | 0.479232 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3875.22i | 0.493629i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1354.63i | 0.171251i | 0.996327 | + | 0.0856256i | \(0.0272889\pi\) | ||||
−0.996327 | + | 0.0856256i | \(0.972711\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10242.5 | 1.27552 | 0.637762 | − | 0.770234i | \(-0.279861\pi\) | ||||
0.637762 | + | 0.770234i | \(0.279861\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3087.61i | − 0.381650i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1089.72 | 0.132716 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11355.2 | −1.37281 | −0.686406 | − | 0.727219i | \(-0.740813\pi\) | ||||
−0.686406 | + | 0.727219i | \(0.740813\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 20226.5i | − 2.40988i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6599.34 | −0.780600 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1194.81i | − 0.139309i | −0.997571 | − | 0.0696543i | \(-0.977810\pi\) | ||||
0.997571 | − | 0.0696543i | \(-0.0221896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6624.50i | − 0.766884i | −0.923565 | − | 0.383442i | \(-0.874739\pi\) | ||||
0.923565 | − | 0.383442i | \(-0.125261\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2880.10 | −0.328718 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4828.89i | − 0.547275i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12152.0 | 1.35810 | 0.679051 | − | 0.734091i | \(-0.262391\pi\) | ||||
0.679051 | + | 0.734091i | \(0.262391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −56.5109 | −0.00627192 | −0.00313596 | − | 0.999995i | \(-0.500998\pi\) | ||||
−0.00313596 | + | 0.999995i | \(0.500998\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 223.120i | 0.0244239i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10326.6 | 1.12269 | 0.561347 | − | 0.827581i | \(-0.310283\pi\) | ||||
0.561347 | + | 0.827581i | \(0.310283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16354.5i | 1.75401i | 0.480484 | + | 0.877004i | \(0.340461\pi\) | ||||
−0.480484 | + | 0.877004i | \(0.659539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 12522.5i | − 1.33399i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9058.38 | −0.952096 | −0.476048 | − | 0.879419i | \(-0.657931\pi\) | ||||
−0.476048 | + | 0.879419i | \(0.657931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 4066.62i | − 0.424589i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15784.4 | −1.62634 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9478.41 | −0.970200 | −0.485100 | − | 0.874459i | \(-0.661217\pi\) | ||||
−0.485100 | + | 0.874459i | \(0.661217\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4920.18i | 0.497084i | 0.968621 | + | 0.248542i | \(0.0799514\pi\) | ||||
−0.968621 | + | 0.248542i | \(0.920049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1311.62 | −0.131654 | −0.0658271 | − | 0.997831i | \(-0.520969\pi\) | ||||
−0.0658271 | + | 0.997831i | \(0.520969\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 5211.07i | − 0.516359i | −0.966097 | − | 0.258179i | \(-0.916877\pi\) | ||||
0.966097 | − | 0.258179i | \(-0.0831225\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 22222.2i | − 2.18790i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5135.90 | −0.499258 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 173.434i | − 0.0167530i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4097.70 | −0.390874 | −0.195437 | − | 0.980716i | \(-0.562613\pi\) | ||||
−0.195437 | + | 0.980716i | \(0.562613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3683.79 | 0.349202 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 260.811i | 0.0244182i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10183.4 | 0.947545 | 0.473773 | − | 0.880647i | \(-0.342892\pi\) | ||||
0.473773 | + | 0.880647i | \(0.342892\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 10083.3i | − 0.926792i | −0.886151 | − | 0.463396i | \(-0.846631\pi\) | ||||
0.886151 | − | 0.463396i | \(-0.153369\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31236.5i | 2.85359i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −33274.1 | −3.00311 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8267.61i | 0.741702i | 0.928692 | + | 0.370851i | \(0.120934\pi\) | ||||
−0.928692 | + | 0.370851i | \(0.879066\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21173.2 | −1.87687 | −0.938435 | − | 0.345455i | \(-0.887725\pi\) | ||||
−0.938435 | + | 0.345455i | \(0.887725\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5645.44 | 0.497463 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 15391.3i | − 1.34029i | −0.742231 | − | 0.670145i | \(-0.766232\pi\) | ||||
0.742231 | − | 0.670145i | \(-0.233768\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30507.7 | 2.64106 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8680.53i | 0.742738i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 4990.66i | − 0.424543i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4749.37 | 0.399374 | 0.199687 | − | 0.979860i | \(-0.436007\pi\) | ||||
0.199687 | + | 0.979860i | \(0.436007\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 15205.4i | − 1.27129i | −0.771982 | − | 0.635644i | \(-0.780735\pi\) | ||||
0.771982 | − | 0.635644i | \(-0.219265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8820.53 | 0.729086 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11369.3 | −0.934440 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 13747.2i | − 1.11718i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14452.9 | −1.16795 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10915.1i | 0.872255i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 11241.2i | − 0.893339i | −0.894699 | − | 0.446669i | \(-0.852610\pi\) | ||||
0.894699 | − | 0.446669i | \(-0.147390\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17989.9 | −1.41395 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18724.2i | 1.46360i | 0.681521 | + | 0.731798i | \(0.261319\pi\) | ||||
−0.681521 | + | 0.731798i | \(0.738681\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1881.00 | −0.145433 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12926.0 | 0.993979 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23022.4i | 1.75133i | 0.482921 | + | 0.875664i | \(0.339576\pi\) | ||||
−0.482921 | + | 0.875664i | \(0.660424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17361.9 | −1.31365 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14064.1i | 1.05281i | 0.850234 | + | 0.526404i | \(0.176460\pi\) | ||||
−0.850234 | + | 0.526404i | \(0.823540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3534.61i | − 0.263190i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10365.8 | 0.763720 | 0.381860 | − | 0.924220i | \(-0.375284\pi\) | ||||
0.381860 | + | 0.924220i | \(0.375284\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5061.81i | 0.370981i | 0.982646 | + | 0.185491i | \(0.0593874\pi\) | ||||
−0.982646 | + | 0.185491i | \(0.940613\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −620.039 | −0.0449694 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16242.2 | −1.17187 | −0.585937 | − | 0.810357i | \(-0.699273\pi\) | ||||
−0.585937 | + | 0.810357i | \(0.699273\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22012.5i | 1.57183i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 387.217 | 0.0275075 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 10850.8i | − 0.762964i | −0.924376 | − | 0.381482i | \(-0.875414\pi\) | ||||
0.924376 | − | 0.381482i | \(-0.124586\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 531.156i | 0.0371577i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26700.0 | −1.84897 | −0.924484 | − | 0.381221i | \(-0.875504\pi\) | ||||
−0.924484 | + | 0.381221i | \(0.875504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 45092.2i | − 3.10689i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9801.85 | −0.668602 | −0.334301 | − | 0.942466i | \(-0.608500\pi\) | ||||
−0.334301 | + | 0.942466i | \(0.608500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12947.5 | 0.878767 | 0.439384 | − | 0.898300i | \(-0.355197\pi\) | ||||
0.439384 | + | 0.898300i | \(0.355197\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 11637.9i | − 0.782063i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10742.0 | −0.718294 | −0.359147 | − | 0.933281i | \(-0.616932\pi\) | ||||
−0.359147 | + | 0.933281i | \(0.616932\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 16870.9i | − 1.11706i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 16243.2i | − 1.07024i | −0.844777 | − | 0.535118i | \(-0.820267\pi\) | ||||
0.844777 | − | 0.535118i | \(-0.179733\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16310.9 | 1.06427 | 0.532134 | − | 0.846660i | \(-0.321390\pi\) | ||||
0.532134 | + | 0.846660i | \(0.321390\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 14103.9i | − 0.915808i | −0.889002 | − | 0.457904i | \(-0.848600\pi\) | ||||
0.889002 | − | 0.457904i | \(-0.151400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −41769.6 | −2.68614 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12398.8 | −0.793525 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10523.7i | 0.667101i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12131.1 | −0.765341 | −0.382670 | − | 0.923885i | \(-0.624996\pi\) | ||||
−0.382670 | + | 0.923885i | \(0.624996\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 15651.8i | − 0.978146i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36898.5i | 2.29509i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18764.5 | 1.15625 | 0.578124 | − | 0.815949i | \(-0.303785\pi\) | ||||
0.578124 | + | 0.815949i | \(0.303785\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30709.2i | 1.88344i | 0.336393 | + | 0.941722i | \(0.390793\pi\) | ||||
−0.336393 | + | 0.941722i | \(0.609207\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −164.430 | −0.00999133 | −0.00499567 | − | 0.999988i | \(-0.501590\pi\) | ||||
−0.00499567 | + | 0.999988i | \(0.501590\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8114.85 | −0.490810 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31130.3i | 1.86558i | 0.360425 | + | 0.932788i | \(0.382632\pi\) | ||||
−0.360425 | + | 0.932788i | \(0.617368\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1934.76 | 0.115416 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 9482.21i | − 0.560507i | −0.959926 | − | 0.280254i | \(-0.909581\pi\) | ||||
0.959926 | − | 0.280254i | \(-0.0904186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22841.2i | 1.34405i | 0.740527 | + | 0.672026i | \(0.234576\pi\) | ||||
−0.740527 | + | 0.672026i | \(0.765424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2715.37 | 0.158342 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6724.71i | 0.390378i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1937.35 | −0.111461 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2738.50 | −0.156852 | −0.0784261 | − | 0.996920i | \(-0.524989\pi\) | ||||
−0.0784261 | + | 0.996920i | \(0.524989\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19290.9i | 1.09514i | 0.836760 | + | 0.547570i | \(0.184447\pi\) | ||||
−0.836760 | + | 0.547570i | \(0.815553\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 869.951 | 0.0491688 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11873.0i | 0.665167i | 0.943074 | + | 0.332584i | \(0.107920\pi\) | ||||
−0.943074 | + | 0.332584i | \(0.892080\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 23636.1i | − 1.31838i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1308.99 | 0.0723781 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27541.3i | 1.51624i | 0.652117 | + | 0.758118i | \(0.273881\pi\) | ||||
−0.652117 | + | 0.758118i | \(0.726119\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13302.6 | 0.726036 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39272.4 | 2.13421 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21855.2i | 1.17754i | 0.808299 | + | 0.588772i | \(0.200388\pi\) | ||||
−0.808299 | + | 0.588772i | \(0.799612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −633.716 | −0.0339986 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 18830.7i | − 1.00170i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19143.2i | 1.01402i | 0.861941 | + | 0.507008i | \(0.169248\pi\) | ||||
−0.861941 | + | 0.507008i | \(0.830752\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1898.92 | 0.0997407 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6332.70i | 0.331230i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2602.05 | −0.134965 | −0.0674827 | − | 0.997720i | \(-0.521497\pi\) | ||||
−0.0674827 | + | 0.997720i | \(0.521497\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28954.5 | 1.49559 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 5227.21i | − 0.267771i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27517.5 | 1.40381 | 0.701903 | − | 0.712273i | \(-0.252334\pi\) | ||||
0.701903 | + | 0.712273i | \(0.252334\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 49598.7i | − 2.50954i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 7060.72i | − 0.355789i | −0.984050 | − | 0.177895i | \(-0.943071\pi\) | ||||
0.984050 | − | 0.177895i | \(-0.0569286\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8915.52 | −0.445600 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 7853.91i | − 0.390948i | −0.980709 | − | 0.195474i | \(-0.937375\pi\) | ||||
0.980709 | − | 0.195474i | \(-0.0626246\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2484.32 | −0.122666 | −0.0613329 | − | 0.998117i | \(-0.519535\pi\) | ||||
−0.0613329 | + | 0.998117i | \(0.519535\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25166.9 | −1.23764 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48208.4i | 2.35180i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27913.9 | −1.35632 | −0.678158 | − | 0.734916i | \(-0.737221\pi\) | ||||
−0.678158 | + | 0.734916i | \(0.737221\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 23122.7i | − 1.11460i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 36850.4i | − 1.76929i | −0.466269 | − | 0.884643i | \(-0.654402\pi\) | ||||
0.466269 | − | 0.884643i | \(-0.345598\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24465.1 | 1.16539 | 0.582694 | − | 0.812691i | \(-0.301998\pi\) | ||||
0.582694 | + | 0.812691i | \(0.301998\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 60006.3i | 2.84715i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27432.3 | −1.29143 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38131.1 | 1.78809 | 0.894047 | − | 0.447974i | \(-0.147854\pi\) | ||||
0.894047 | + | 0.447974i | \(0.147854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13060.0i | 0.607680i | 0.952723 | + | 0.303840i | \(0.0982688\pi\) | ||||
−0.952723 | + | 0.303840i | \(0.901731\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1476.06 | −0.0684148 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2364.91i | 0.108770i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13349.5i | 0.611631i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29626.3 | −1.34702 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 18883.6i | − 0.855310i | −0.903942 | − | 0.427655i | \(-0.859340\pi\) | ||||
0.903942 | − | 0.427655i | \(-0.140660\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11789.9 | −0.529963 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6549.22 | −0.293278 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 6999.63i | − 0.311091i | −0.987829 | − | 0.155546i | \(-0.950286\pi\) | ||||
0.987829 | − | 0.155546i | \(-0.0497136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48196.1 | 2.13399 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 12239.7i | − 0.537894i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 9707.62i | − 0.425030i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24272.5 | 1.05485 | 0.527426 | − | 0.849601i | \(-0.323157\pi\) | ||||
0.527426 | + | 0.849601i | \(0.323157\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 22038.3i | − 0.954217i | −0.878845 | − | 0.477108i | \(-0.841685\pi\) | ||||
0.878845 | − | 0.477108i | \(-0.158315\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35033.9 | −1.50575 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2986.74 | 0.127898 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12819.5i | 0.544950i | 0.962163 | + | 0.272475i | \(0.0878422\pi\) | ||||
−0.962163 | + | 0.272475i | \(0.912158\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3627.33 | −0.153634 | −0.0768170 | − | 0.997045i | \(-0.524476\pi\) | ||||
−0.0768170 | + | 0.997045i | \(0.524476\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 40155.1i | − 1.68843i | −0.536007 | − | 0.844213i | \(-0.680068\pi\) | ||||
0.536007 | − | 0.844213i | \(-0.319932\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15348.4i | 0.643030i | 0.946904 | + | 0.321515i | \(0.104192\pi\) | ||||
−0.946904 | + | 0.321515i | \(0.895808\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −105410. | −4.38443 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 22487.8i | − 0.932002i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45000.1 | 1.85170 | 0.925850 | − | 0.377891i | \(-0.123351\pi\) | ||||
0.925850 | + | 0.377891i | \(0.123351\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −32303.4 | −1.32451 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 894.403i | − 0.0364123i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38819.0 | −1.57478 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2265.58i | 0.0912609i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22419.3i | 0.899910i | 0.893051 | + | 0.449955i | \(0.148560\pi\) | ||||
−0.893051 | + | 0.449955i | \(0.851440\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22129.7 | 0.882073 | 0.441037 | − | 0.897489i | \(-0.354611\pi\) | ||||
0.441037 | + | 0.897489i | \(0.354611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 16643.6i | − 0.661086i | −0.943791 | − | 0.330543i | \(-0.892768\pi\) | ||||
0.943791 | − | 0.330543i | \(-0.107232\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43612.7 | −1.72027 | −0.860135 | − | 0.510066i | \(-0.829621\pi\) | ||||
−0.860135 | + | 0.510066i | \(0.829621\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3849.23 | −0.151304 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 5185.91i | − 0.202440i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30139.0 | −1.17247 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 50510.6i | 1.95151i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24856.8i | 0.957075i | 0.878067 | + | 0.478537i | \(0.158833\pi\) | ||||
−0.878067 | + | 0.478537i | \(0.841167\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9284.63 | −0.355059 | −0.177530 | − | 0.984115i | \(-0.556811\pi\) | ||||
−0.177530 | + | 0.984115i | \(0.556811\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10002.7i | 0.381220i | 0.981666 | + | 0.190610i | \(0.0610465\pi\) | ||||
−0.981666 | + | 0.190610i | \(0.938953\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17532.9 | −0.663695 | −0.331848 | − | 0.943333i | \(-0.607672\pi\) | ||||
−0.331848 | + | 0.943333i | \(0.607672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52207.6 | −1.96961 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2902.28i | 0.108758i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41149.9 | 1.53686 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16008.8i | 0.593907i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3739.46i | 0.138268i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6704.70 | −0.246267 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6351.57i | 0.232525i | 0.993219 | + | 0.116263i | \(0.0370914\pi\) | ||||
−0.993219 | + | 0.116263i | \(0.962909\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4753.51 | −0.172877 | −0.0864384 | − | 0.996257i | \(-0.527549\pi\) | ||||
−0.0864384 | + | 0.996257i | \(0.527549\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8831.41 | 0.320128 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 6453.51i | − 0.232403i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41240.4 | −1.48030 | −0.740150 | − | 0.672442i | \(-0.765245\pi\) | ||||
−0.740150 | + | 0.672442i | \(0.765245\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45128.2i | 1.60933i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1761.06i | − 0.0625983i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33423.7 | −1.18040 | −0.590202 | − | 0.807255i | \(-0.700952\pi\) | ||||
−0.590202 | + | 0.807255i | \(0.700952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6347.58i | − 0.223452i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18090.9 | −0.632767 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52959.8 | 1.84645 | 0.923223 | − | 0.384264i | \(-0.125545\pi\) | ||||
0.923223 | + | 0.384264i | \(0.125545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27256.8i | 0.944258i | 0.881529 | + | 0.472129i | \(0.156514\pi\) | ||||
−0.881529 | + | 0.472129i | \(0.843486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8454.71 | 0.291965 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 3537.26i | − 0.121379i | −0.998157 | − | 0.0606893i | \(-0.980670\pi\) | ||||
0.998157 | − | 0.0606893i | \(-0.0193299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 41376.3i | − 1.41531i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23661.6 | −0.804275 | −0.402138 | − | 0.915579i | \(-0.631733\pi\) | ||||
−0.402138 | + | 0.915579i | \(0.631733\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5918.20i | 0.200532i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −78839.7 | −2.65471 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25270.5 | −0.848258 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27614.9i | 0.921198i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16800.1 | 0.558691 | 0.279345 | − | 0.960191i | \(-0.409883\pi\) | ||||
0.279345 | + | 0.960191i | \(0.409883\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 28036.7i | − 0.926611i | −0.886199 | − | 0.463306i | \(-0.846663\pi\) | ||||
0.886199 | − | 0.463306i | \(-0.153337\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 44371.6i | − 1.46196i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8961.37 | −0.293449 | −0.146724 | − | 0.989177i | \(-0.546873\pi\) | ||||
−0.146724 | + | 0.989177i | \(0.546873\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16757.9i | 0.547074i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33372.7 | −1.08283 | −0.541415 | − | 0.840755i | \(-0.682111\pi\) | ||||
−0.541415 | + | 0.840755i | \(0.682111\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37544.8 | −1.21449 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 10677.8i | − 0.343311i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39288.7 | −1.25938 | −0.629691 | − | 0.776846i | \(-0.716818\pi\) | ||||
−0.629691 | + | 0.776846i | \(0.716818\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21860.2i | 0.696499i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26951.7i | 0.856137i | 0.903746 | + | 0.428068i | \(0.140806\pi\) | ||||
−0.903746 | + | 0.428068i | \(0.859194\pi\) | |||||||
\(998\) | 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 | 1728.4.d.i.865.5 | ✓ | 16 | |
3.2 | odd | 2 | 1728.4.d.k.865.11 | yes | 16 | ||
4.3 | odd | 2 | inner | 1728.4.d.i.865.6 | yes | 16 | |
8.3 | odd | 2 | inner | 1728.4.d.i.865.12 | yes | 16 | |
8.5 | even | 2 | inner | 1728.4.d.i.865.11 | yes | 16 | |
12.11 | even | 2 | 1728.4.d.k.865.12 | yes | 16 | ||
24.5 | odd | 2 | 1728.4.d.k.865.5 | yes | 16 | ||
24.11 | even | 2 | 1728.4.d.k.865.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.4.d.i.865.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1728.4.d.i.865.6 | yes | 16 | 4.3 | odd | 2 | inner | |
1728.4.d.i.865.11 | yes | 16 | 8.5 | even | 2 | inner | |
1728.4.d.i.865.12 | yes | 16 | 8.3 | odd | 2 | inner | |
1728.4.d.k.865.5 | yes | 16 | 24.5 | odd | 2 | ||
1728.4.d.k.865.6 | yes | 16 | 24.11 | even | 2 | ||
1728.4.d.k.865.11 | yes | 16 | 3.2 | odd | 2 | ||
1728.4.d.k.865.12 | yes | 16 | 12.11 | even | 2 |