Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(449,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.7 | ||
Root | \(-0.437016 - 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.449 |
Dual form | 900.3.b.b.449.2 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.4868i | 1.92669i | 0.268265 | + | 0.963345i | \(0.413550\pi\) | ||||
−0.268265 | + | 0.963345i | \(0.586450\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 17.6590i | − 1.60537i | −0.596405 | − | 0.802684i | \(-0.703405\pi\) | ||||
0.596405 | − | 0.802684i | \(-0.296595\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 7.48683i | − 0.575910i | −0.957644 | − | 0.287955i | \(-0.907025\pi\) | ||||
0.957644 | − | 0.287955i | \(-0.0929754\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.9706 | 0.998268 | 0.499134 | − | 0.866525i | \(-0.333651\pi\) | ||||
0.499134 | + | 0.866525i | \(0.333651\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.9737 | 0.577561 | 0.288781 | − | 0.957395i | \(-0.406750\pi\) | ||||
0.288781 | + | 0.957395i | \(0.406750\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 21.9017 | 0.952247 | 0.476124 | − | 0.879378i | \(-0.342041\pi\) | ||||
0.476124 | + | 0.879378i | \(0.342041\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 47.3575i | 1.63302i | 0.577332 | + | 0.816509i | \(0.304094\pi\) | ||||
−0.577332 | + | 0.816509i | \(0.695906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −16.9737 | −0.547538 | −0.273769 | − | 0.961796i | \(-0.588270\pi\) | ||||
−0.273769 | + | 0.961796i | \(0.588270\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.53950i | 0.149716i | 0.997194 | + | 0.0748581i | \(0.0238504\pi\) | ||||
−0.997194 | + | 0.0748581i | \(0.976150\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 66.3936i | 1.61935i | 0.586875 | + | 0.809677i | \(0.300358\pi\) | ||||
−0.586875 | + | 0.809677i | \(0.699642\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 38.9737i | 0.906364i | 0.891418 | + | 0.453182i | \(0.149711\pi\) | ||||
−0.891418 | + | 0.453182i | \(0.850289\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 32.5642 | 0.692854 | 0.346427 | − | 0.938077i | \(-0.387395\pi\) | ||||
0.346427 | + | 0.938077i | \(0.387395\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −132.895 | −2.71214 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.2392 | −0.212061 | −0.106030 | − | 0.994363i | \(-0.533814\pi\) | ||||
−0.106030 | + | 0.994363i | \(0.533814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 31.8757i | 0.540266i | 0.962823 | + | 0.270133i | \(0.0870676\pi\) | ||||
−0.962823 | + | 0.270133i | \(0.912932\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 46.9210 | 0.769197 | 0.384598 | − | 0.923084i | \(-0.374340\pi\) | ||||
0.384598 | + | 0.923084i | \(0.374340\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 76.0000i | 1.13433i | 0.823605 | + | 0.567164i | \(0.191960\pi\) | ||||
−0.823605 | + | 0.567164i | \(0.808040\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 77.7445i | − 1.09499i | −0.836808 | − | 0.547497i | \(-0.815581\pi\) | ||||
0.836808 | − | 0.547497i | \(-0.184419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 94.9210i | 1.30029i | 0.759811 | + | 0.650144i | \(0.225291\pi\) | ||||
−0.759811 | + | 0.650144i | \(0.774709\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 238.165 | 3.09305 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.92100 | 0.0876076 | 0.0438038 | − | 0.999040i | \(-0.486052\pi\) | ||||
0.0438038 | + | 0.999040i | \(0.486052\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 62.1509 | 0.748806 | 0.374403 | − | 0.927266i | \(-0.377848\pi\) | ||||
0.374403 | + | 0.927266i | \(0.377848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 62.2626i | 0.699580i | 0.936828 | + | 0.349790i | \(0.113747\pi\) | ||||
−0.936828 | + | 0.349790i | \(0.886253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 100.974 | 1.10960 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 124.974i | 1.28839i | 0.764862 | + | 0.644194i | \(0.222807\pi\) | ||||
−0.764862 | + | 0.644194i | \(0.777193\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 112.262i | − 1.11151i | −0.831347 | − | 0.555754i | \(-0.812429\pi\) | ||||
0.831347 | − | 0.555754i | \(-0.187571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 170.302i | − 1.65342i | −0.562627 | − | 0.826711i | \(-0.690209\pi\) | ||||
0.562627 | − | 0.826711i | \(-0.309791\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 93.3381 | 0.872319 | 0.436159 | − | 0.899869i | \(-0.356338\pi\) | ||||
0.436159 | + | 0.899869i | \(0.356338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 68.8683 | 0.631820 | 0.315910 | − | 0.948789i | \(-0.397690\pi\) | ||||
0.315910 | + | 0.948789i | \(0.397690\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 110.309 | 0.976183 | 0.488091 | − | 0.872793i | \(-0.337693\pi\) | ||||
0.488091 | + | 0.872793i | \(0.337693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 228.879i | 1.92335i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −190.842 | −1.57721 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 65.3815i | 0.514815i | 0.966303 | + | 0.257407i | \(0.0828683\pi\) | ||||
−0.966303 | + | 0.257407i | \(0.917132\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 47.2458i | 0.360655i | 0.983607 | + | 0.180328i | \(0.0577158\pi\) | ||||
−0.983607 | + | 0.180328i | \(0.942284\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 148.000i | 1.11278i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −216.039 | −1.57693 | −0.788465 | − | 0.615079i | \(-0.789124\pi\) | ||||
−0.788465 | + | 0.615079i | \(0.789124\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −211.842 | −1.52404 | −0.762022 | − | 0.647552i | \(-0.775793\pi\) | ||||
−0.762022 | + | 0.647552i | \(0.775793\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −132.210 | −0.924548 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 92.5379i | − 0.621060i | −0.950564 | − | 0.310530i | \(-0.899494\pi\) | ||||
0.950564 | − | 0.310530i | \(-0.100506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −123.842 | −0.820146 | −0.410073 | − | 0.912053i | \(-0.634497\pi\) | ||||
−0.410073 | + | 0.912053i | \(0.634497\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 31.4868i | 0.200553i | 0.994960 | + | 0.100277i | \(0.0319727\pi\) | ||||
−0.994960 | + | 0.100277i | \(0.968027\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 295.384i | 1.83469i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 101.132i | − 0.620440i | −0.950665 | − | 0.310220i | \(-0.899597\pi\) | ||||
0.950665 | − | 0.310220i | \(-0.100403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −147.804 | −0.885054 | −0.442527 | − | 0.896755i | \(-0.645918\pi\) | ||||
−0.442527 | + | 0.896755i | \(0.645918\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 112.947 | 0.668327 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 332.079 | 1.91953 | 0.959767 | − | 0.280797i | \(-0.0905986\pi\) | ||||
0.959767 | + | 0.280797i | \(0.0905986\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 45.8688i | − 0.256250i | −0.991758 | − | 0.128125i | \(-0.959104\pi\) | ||||
0.991758 | − | 0.128125i | \(-0.0408959\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 132.868 | 0.734079 | 0.367040 | − | 0.930205i | \(-0.380371\pi\) | ||||
0.367040 | + | 0.930205i | \(0.380371\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 299.684i | − 1.60259i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 163.974i | − 0.858504i | −0.903185 | − | 0.429252i | \(-0.858777\pi\) | ||||
0.903185 | − | 0.429252i | \(-0.141223\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 110.000i | 0.569948i | 0.958535 | + | 0.284974i | \(0.0919850\pi\) | ||||
−0.958535 | + | 0.284974i | \(0.908015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 211.108 | 1.07162 | 0.535808 | − | 0.844340i | \(-0.320007\pi\) | ||||
0.535808 | + | 0.844340i | \(0.320007\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.1053 | 0.0909816 | 0.0454908 | − | 0.998965i | \(-0.485515\pi\) | ||||
0.0454908 | + | 0.998965i | \(0.485515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −638.703 | −3.14632 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 193.785i | − 0.927199i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 341.579 | 1.61886 | 0.809428 | − | 0.587219i | \(-0.199777\pi\) | ||||
0.809428 | + | 0.587219i | \(0.199777\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 228.921i | − 1.05494i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 127.056i | − 0.574913i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 59.3288i | 0.266049i | 0.991113 | + | 0.133024i | \(0.0424688\pi\) | ||||
−0.991113 | + | 0.133024i | \(0.957531\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 115.593 | 0.509221 | 0.254610 | − | 0.967044i | \(-0.418053\pi\) | ||||
0.254610 | + | 0.967044i | \(0.418053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 253.895 | 1.10871 | 0.554355 | − | 0.832280i | \(-0.312965\pi\) | ||||
0.554355 | + | 0.832280i | \(0.312965\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 206.401 | 0.885840 | 0.442920 | − | 0.896561i | \(-0.353943\pi\) | ||||
0.442920 | + | 0.896561i | \(0.353943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 346.296i | − 1.44894i | −0.689308 | − | 0.724469i | \(-0.742085\pi\) | ||||
0.689308 | − | 0.724469i | \(-0.257915\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −182.053 | −0.755405 | −0.377703 | − | 0.925927i | \(-0.623286\pi\) | ||||
−0.377703 | + | 0.925927i | \(0.623286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 82.1580i | − 0.332623i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 140.807i | − 0.560985i | −0.959856 | − | 0.280493i | \(-0.909502\pi\) | ||||
0.959856 | − | 0.280493i | \(-0.0904979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 386.763i | − 1.52871i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −292.630 | −1.13864 | −0.569320 | − | 0.822116i | \(-0.692793\pi\) | ||||
−0.569320 | + | 0.822116i | \(0.692793\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −74.7103 | −0.288457 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −270.952 | −1.03024 | −0.515118 | − | 0.857119i | \(-0.672252\pi\) | ||||
−0.515118 | + | 0.857119i | \(0.672252\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 275.083i | − 1.02261i | −0.859398 | − | 0.511307i | \(-0.829162\pi\) | ||||
0.859398 | − | 0.511307i | \(-0.170838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 248.158 | 0.915712 | 0.457856 | − | 0.889026i | \(-0.348617\pi\) | ||||
0.457856 | + | 0.889026i | \(0.348617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 342.039i | 1.23480i | 0.786650 | + | 0.617399i | \(0.211814\pi\) | ||||
−0.786650 | + | 0.617399i | \(0.788186\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 352.139i | 1.25316i | 0.779355 | + | 0.626582i | \(0.215547\pi\) | ||||
−0.779355 | + | 0.626582i | \(0.784453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 249.631i | 0.882089i | 0.897485 | + | 0.441045i | \(0.145392\pi\) | ||||
−0.897485 | + | 0.441045i | \(0.854608\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −895.439 | −3.12000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.00346021 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 37.4953 | 0.127970 | 0.0639851 | − | 0.997951i | \(-0.479619\pi\) | ||||
0.0639851 | + | 0.997951i | \(0.479619\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 163.974i | − 0.548409i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −525.631 | −1.74628 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 457.842i | − 1.49134i | −0.666314 | − | 0.745671i | \(-0.732129\pi\) | ||||
0.666314 | − | 0.745671i | \(-0.267871\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 8.48528i | − 0.0272839i | −0.999907 | − | 0.0136419i | \(-0.995658\pi\) | ||||
0.999907 | − | 0.0136419i | \(-0.00434250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.57866i | − 0.00504363i | −0.999997 | − | 0.00252181i | \(-0.999197\pi\) | ||||
0.999997 | − | 0.00252181i | \(-0.000802719\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −529.195 | −1.66938 | −0.834692 | − | 0.550717i | \(-0.814354\pi\) | ||||
−0.834692 | + | 0.550717i | \(0.814354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 836.289 | 2.62160 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 186.229 | 0.576561 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 439.187i | 1.33492i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −390.763 | −1.18055 | −0.590276 | − | 0.807201i | \(-0.700981\pi\) | ||||
−0.590276 | + | 0.807201i | \(0.700981\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 414.710i | − 1.23059i | −0.788295 | − | 0.615297i | \(-0.789036\pi\) | ||||
0.788295 | − | 0.615297i | \(-0.210964\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 299.739i | 0.878999i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1131.47i | − 3.29876i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −128.656 | −0.370767 | −0.185384 | − | 0.982666i | \(-0.559353\pi\) | ||||
−0.185384 | + | 0.982666i | \(0.559353\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 37.0790 | 0.106244 | 0.0531218 | − | 0.998588i | \(-0.483083\pi\) | ||||
0.0531218 | + | 0.998588i | \(0.483083\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −190.584 | −0.539897 | −0.269949 | − | 0.962875i | \(-0.587007\pi\) | ||||
−0.269949 | + | 0.962875i | \(0.587007\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 254.782i | − 0.709699i | −0.934923 | − | 0.354849i | \(-0.884532\pi\) | ||||
0.934923 | − | 0.354849i | \(-0.115468\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −240.579 | −0.666423 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 300.460i | − 0.818693i | −0.912379 | − | 0.409347i | \(-0.865757\pi\) | ||||
0.912379 | − | 0.409347i | \(-0.134243\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 151.582i | − 0.408576i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 704.092i | 1.88765i | 0.330452 | + | 0.943823i | \(0.392799\pi\) | ||||
−0.330452 | + | 0.943823i | \(0.607201\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 354.558 | 0.940472 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −333.789 | −0.880711 | −0.440355 | − | 0.897824i | \(-0.645148\pi\) | ||||
−0.440355 | + | 0.897824i | \(0.645148\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 260.996 | 0.681453 | 0.340726 | − | 0.940163i | \(-0.389327\pi\) | ||||
0.340726 | + | 0.940163i | \(0.389327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 35.8949i | − 0.0922747i | −0.998935 | − | 0.0461373i | \(-0.985309\pi\) | ||||
0.998935 | − | 0.0461373i | \(-0.0146912\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 371.684 | 0.950598 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 90.3552i | 0.227595i | 0.993504 | + | 0.113797i | \(0.0363015\pi\) | ||||
−0.993504 | + | 0.113797i | \(0.963699\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 43.6917i | − 0.108957i | −0.998515 | − | 0.0544784i | \(-0.982650\pi\) | ||||
0.998515 | − | 0.0544784i | \(-0.0173496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 127.079i | 0.315333i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 97.8223 | 0.240350 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 260.053 | 0.635826 | 0.317913 | − | 0.948120i | \(-0.397018\pi\) | ||||
0.317913 | + | 0.948120i | \(0.397018\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −429.902 | −1.04092 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 263.285i | − 0.628366i | −0.949362 | − | 0.314183i | \(-0.898269\pi\) | ||||
0.949362 | − | 0.314183i | \(-0.101731\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 367.210 | 0.872233 | 0.436116 | − | 0.899890i | \(-0.356354\pi\) | ||||
0.436116 | + | 0.899890i | \(0.356354\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 632.816i | 1.48200i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 690.768i | − 1.60271i | −0.598189 | − | 0.801355i | \(-0.704113\pi\) | ||||
0.598189 | − | 0.801355i | \(-0.295887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 117.500i | − 0.271363i | −0.990752 | − | 0.135682i | \(-0.956678\pi\) | ||||
0.990752 | − | 0.135682i | \(-0.0433224\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 240.342 | 0.549981 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −50.0000 | −0.113895 | −0.0569476 | − | 0.998377i | \(-0.518137\pi\) | ||||
−0.0569476 | + | 0.998377i | \(0.518137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −526.794 | −1.18915 | −0.594576 | − | 0.804040i | \(-0.702680\pi\) | ||||
−0.594576 | + | 0.804040i | \(0.702680\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 321.882i | − 0.716887i | −0.933552 | − | 0.358443i | \(-0.883308\pi\) | ||||
0.933552 | − | 0.358443i | \(-0.116692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1172.45 | 2.59966 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 433.079i | 0.947656i | 0.880617 | + | 0.473828i | \(0.157128\pi\) | ||||
−0.880617 | + | 0.473828i | \(0.842872\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 486.768i | 1.05590i | 0.849277 | + | 0.527948i | \(0.177039\pi\) | ||||
−0.849277 | + | 0.527948i | \(0.822961\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 423.223i | 0.914090i | 0.889444 | + | 0.457045i | \(0.151092\pi\) | ||||
−0.889444 | + | 0.457045i | \(0.848908\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 295.831 | 0.633472 | 0.316736 | − | 0.948514i | \(-0.397413\pi\) | ||||
0.316736 | + | 0.948514i | \(0.397413\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1025.00 | −2.18550 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 688.238 | 1.45505 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 266.728i | − 0.556843i | −0.960459 | − | 0.278421i | \(-0.910189\pi\) | ||||
0.960459 | − | 0.278421i | \(-0.0898112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.4733 | 0.0862231 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 247.750i | − 0.508727i | −0.967109 | − | 0.254364i | \(-0.918134\pi\) | ||||
0.967109 | − | 0.254364i | \(-0.0818660\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 170.394i | − 0.347035i | −0.984831 | − | 0.173517i | \(-0.944487\pi\) | ||||
0.984831 | − | 0.173517i | \(-0.0555133\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 803.684i | 1.63019i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1048.53 | 2.10971 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −47.3950 | −0.0949800 | −0.0474900 | − | 0.998872i | \(-0.515122\pi\) | ||||
−0.0474900 | + | 0.998872i | \(0.515122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −321.064 | −0.638298 | −0.319149 | − | 0.947705i | \(-0.603397\pi\) | ||||
−0.319149 | + | 0.947705i | \(0.603397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 122.125i | 0.239931i | 0.992778 | + | 0.119965i | \(0.0382783\pi\) | ||||
−0.992778 | + | 0.119965i | \(0.961722\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1280.18 | −2.50525 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 575.052i | − 1.11229i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 79.4567i | − 0.152508i | −0.997088 | − | 0.0762540i | \(-0.975704\pi\) | ||||
0.997088 | − | 0.0762540i | \(-0.0242960\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 864.605i | − 1.65316i | −0.562816 | − | 0.826582i | \(-0.690282\pi\) | ||||
0.562816 | − | 0.826582i | \(-0.309718\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −288.053 | −0.546589 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.3160 | −0.0932250 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 497.077 | 0.932603 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2346.79i | 4.35398i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.6057 | 0.0621177 | 0.0310589 | − | 0.999518i | \(-0.490112\pi\) | ||||
0.0310589 | + | 0.999518i | \(0.490112\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 559.079i | 1.02208i | 0.859556 | + | 0.511041i | \(0.170740\pi\) | ||||
−0.859556 | + | 0.511041i | \(0.829260\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 519.686i | 0.943168i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 93.3423i | 0.168793i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −310.308 | −0.557105 | −0.278553 | − | 0.960421i | \(-0.589855\pi\) | ||||
−0.278553 | + | 0.960421i | \(0.589855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 291.789 | 0.521984 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 566.690 | 1.00655 | 0.503277 | − | 0.864125i | \(-0.332128\pi\) | ||||
0.503277 | + | 0.864125i | \(0.332128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 134.052i | − 0.235593i | −0.993038 | − | 0.117796i | \(-0.962417\pi\) | ||||
0.993038 | − | 0.117796i | \(-0.0375830\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −661.920 | −1.15923 | −0.579615 | − | 0.814890i | \(-0.696797\pi\) | ||||
−0.579615 | + | 0.814890i | \(0.696797\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 76.7630i | − 0.133038i | −0.997785 | − | 0.0665191i | \(-0.978811\pi\) | ||||
0.997785 | − | 0.0665191i | \(-0.0211893\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 838.219i | 1.44272i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 198.474i | 0.340436i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 684.554 | 1.16619 | 0.583095 | − | 0.812404i | \(-0.301841\pi\) | ||||
0.583095 | + | 0.812404i | \(0.301841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −186.263 | −0.316237 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 592.146 | 0.998560 | 0.499280 | − | 0.866441i | \(-0.333598\pi\) | ||||
0.499280 | + | 0.866441i | \(0.333598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1012.76i | 1.69075i | 0.534169 | + | 0.845377i | \(0.320624\pi\) | ||||
−0.534169 | + | 0.845377i | \(0.679376\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 323.579 | 0.538400 | 0.269200 | − | 0.963084i | \(-0.413241\pi\) | ||||
0.269200 | + | 0.963084i | \(0.413241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 799.828i | 1.31767i | 0.752285 | + | 0.658837i | \(0.228951\pi\) | ||||
−0.752285 | + | 0.658837i | \(0.771049\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 243.802i | − 0.399022i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 680.302i | − 1.10979i | −0.831920 | − | 0.554896i | \(-0.812758\pi\) | ||||
0.831920 | − | 0.554896i | \(-0.187242\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 264.868 | 0.429283 | 0.214641 | − | 0.976693i | \(-0.431142\pi\) | ||||
0.214641 | + | 0.976693i | \(0.431142\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −535.842 | −0.865658 | −0.432829 | − | 0.901476i | \(-0.642485\pi\) | ||||
−0.432829 | + | 0.901476i | \(0.642485\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −839.726 | −1.34787 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 94.0085i | 0.149457i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 307.026 | 0.486571 | 0.243286 | − | 0.969955i | \(-0.421775\pi\) | ||||
0.243286 | + | 0.969955i | \(0.421775\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 994.960i | 1.56195i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1246.33i | − 1.94435i | −0.234248 | − | 0.972177i | \(-0.575263\pi\) | ||||
0.234248 | − | 0.972177i | \(-0.424737\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 155.395i | 0.241672i | 0.992672 | + | 0.120836i | \(0.0385575\pi\) | ||||
−0.992672 | + | 0.120836i | \(0.961443\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −142.649 | −0.220478 | −0.110239 | − | 0.993905i | \(-0.535162\pi\) | ||||
−0.110239 | + | 0.993905i | \(0.535162\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 562.894 | 0.867325 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 924.579 | 1.41589 | 0.707947 | − | 0.706266i | \(-0.249622\pi\) | ||||
0.707947 | + | 0.706266i | \(0.249622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 352.046i | − 0.534212i | −0.963667 | − | 0.267106i | \(-0.913933\pi\) | ||||
0.963667 | − | 0.267106i | \(-0.0860674\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −642.921 | −0.972649 | −0.486325 | − | 0.873778i | \(-0.661663\pi\) | ||||
−0.486325 | + | 0.873778i | \(0.661663\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1037.21i | 1.55504i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 828.580i | − 1.23484i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 982.605i | 1.46004i | 0.683427 | + | 0.730019i | \(0.260489\pi\) | ||||
−0.683427 | + | 0.730019i | \(0.739511\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 386.769 | 0.571298 | 0.285649 | − | 0.958334i | \(-0.407791\pi\) | ||||
0.285649 | + | 0.958334i | \(0.407791\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1685.50 | −2.48233 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 504.539 | 0.738710 | 0.369355 | − | 0.929288i | \(-0.379579\pi\) | ||||
0.369355 | + | 0.929288i | \(0.379579\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 84.1462i | 0.122128i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −271.079 | −0.392300 | −0.196150 | − | 0.980574i | \(-0.562844\pi\) | ||||
−0.196150 | + | 0.980574i | \(0.562844\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1126.74i | 1.61655i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 358.559i | − 0.511496i | −0.966743 | − | 0.255748i | \(-0.917678\pi\) | ||||
0.966743 | − | 0.255748i | \(-0.0823218\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 60.7886i | 0.0864703i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1514.06 | 2.14153 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 733.579 | 1.03467 | 0.517333 | − | 0.855784i | \(-0.326925\pi\) | ||||
0.517333 | + | 0.855784i | \(0.326925\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −371.752 | −0.521391 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1108.37i | − 1.54155i | −0.637110 | − | 0.770773i | \(-0.719870\pi\) | ||||
0.637110 | − | 0.770773i | \(-0.280130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2296.84 | 3.18563 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1265.04i | − 1.74008i | −0.492981 | − | 0.870040i | \(-0.664093\pi\) | ||||
0.492981 | − | 0.870040i | \(-0.335907\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 661.405i | 0.904795i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 586.749i | − 0.800477i | −0.916411 | − | 0.400238i | \(-0.868927\pi\) | ||||
0.916411 | − | 0.400238i | \(-0.131073\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1342.09 | 1.82101 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 215.973 | 0.292250 | 0.146125 | − | 0.989266i | \(-0.453320\pi\) | ||||
0.146125 | + | 0.989266i | \(0.453320\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −599.961 | −0.807484 | −0.403742 | − | 0.914873i | \(-0.632291\pi\) | ||||
−0.403742 | + | 0.914873i | \(0.632291\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1258.84i | 1.68069i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 813.657 | 1.08343 | 0.541716 | − | 0.840562i | \(-0.317775\pi\) | ||||
0.541716 | + | 0.840562i | \(0.317775\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1070.43i | − 1.41405i | −0.707190 | − | 0.707023i | \(-0.750038\pi\) | ||||
0.707190 | − | 0.707023i | \(-0.249962\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 654.892i | − 0.860567i | −0.902694 | − | 0.430284i | \(-0.858414\pi\) | ||||
0.902694 | − | 0.430284i | \(-0.141586\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 928.816i | 1.21732i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 238.648 | 0.311144 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −682.631 | −0.887686 | −0.443843 | − | 0.896105i | \(-0.646385\pi\) | ||||
−0.443843 | + | 0.896105i | \(0.646385\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −770.690 | −0.997012 | −0.498506 | − | 0.866886i | \(-0.666118\pi\) | ||||
−0.498506 | + | 0.866886i | \(0.666118\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 728.581i | 0.935277i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1372.89 | −1.75787 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 253.869i | 0.322578i | 0.986907 | + | 0.161289i | \(0.0515652\pi\) | ||||
−0.986907 | + | 0.161289i | \(0.948435\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1487.71i | 1.88080i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 351.290i | − 0.442988i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1055.86 | −1.32479 | −0.662396 | − | 0.749154i | \(-0.730460\pi\) | ||||
−0.662396 | + | 0.749154i | \(0.730460\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 552.632 | 0.691655 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1676.21 | 2.08744 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 506.698i | − 0.626326i | −0.949699 | − | 0.313163i | \(-0.898611\pi\) | ||||
0.949699 | − | 0.313163i | \(-0.101389\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 537.473 | 0.662729 | 0.331365 | − | 0.943503i | \(-0.392491\pi\) | ||||
0.331365 | + | 0.943503i | \(0.392491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 427.684i | 0.523481i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 257.219i | 0.313299i | 0.987654 | + | 0.156650i | \(0.0500694\pi\) | ||||
−0.987654 | + | 0.156650i | \(0.949931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 367.013i | − 0.445945i | −0.974825 | − | 0.222973i | \(-0.928424\pi\) | ||||
0.974825 | − | 0.222973i | \(-0.0715760\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −122.254 | −0.147829 | −0.0739144 | − | 0.997265i | \(-0.523549\pi\) | ||||
−0.0739144 | + | 0.997265i | \(0.523549\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −335.237 | −0.404387 | −0.202194 | − | 0.979346i | \(-0.564807\pi\) | ||||
−0.202194 | + | 0.979346i | \(0.564807\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2255.30 | −2.70744 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 774.021i | − 0.922552i | −0.887257 | − | 0.461276i | \(-0.847392\pi\) | ||||
0.887257 | − | 0.461276i | \(-0.152608\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1401.74 | −1.66675 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2573.85i | − 3.03879i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 121.324i | 0.142567i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 764.591i | 0.896356i | 0.893944 | + | 0.448178i | \(0.147927\pi\) | ||||
−0.893944 | + | 0.448178i | \(0.852073\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1516.15 | −1.76913 | −0.884567 | − | 0.466413i | \(-0.845546\pi\) | ||||
−0.884567 | + | 0.466413i | \(0.845546\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −433.684 | −0.504871 | −0.252435 | − | 0.967614i | \(-0.581232\pi\) | ||||
−0.252435 | + | 0.967614i | \(0.581232\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1255.50 | 1.45481 | 0.727407 | − | 0.686206i | \(-0.240725\pi\) | ||||
0.727407 | + | 0.686206i | \(0.240725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 122.218i | − 0.140642i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 568.999 | 0.653271 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1003.59i | − 1.14435i | −0.820133 | − | 0.572173i | \(-0.806100\pi\) | ||||
0.820133 | − | 0.572173i | \(-0.193900\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 737.214i | 0.836792i | 0.908265 | + | 0.418396i | \(0.137408\pi\) | ||||
−0.908265 | + | 0.418396i | \(0.862592\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 336.394i | 0.380968i | 0.981690 | + | 0.190484i | \(0.0610057\pi\) | ||||
−0.981690 | + | 0.190484i | \(0.938994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −793.132 | −0.894174 | −0.447087 | − | 0.894491i | \(-0.647539\pi\) | ||||
−0.447087 | + | 0.894491i | \(0.647539\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −881.789 | −0.991889 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 357.348 | 0.400166 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 803.831i | − 0.894139i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −190.736 | −0.211694 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1079.66i | 1.19036i | 0.803592 | + | 0.595180i | \(0.202919\pi\) | ||||
−0.803592 | + | 0.595180i | \(0.797081\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1473.69i | 1.61766i | 0.588045 | + | 0.808828i | \(0.299898\pi\) | ||||
−0.588045 | + | 0.808828i | \(0.700102\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1097.53i | − 1.20211i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −637.196 | −0.694871 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1602.92 | 1.74420 | 0.872101 | − | 0.489327i | \(-0.162757\pi\) | ||||
0.872101 | + | 0.489327i | \(0.162757\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −582.060 | −0.630618 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1033.98i | 1.11300i | 0.830848 | + | 0.556499i | \(0.187856\pi\) | ||||
−0.830848 | + | 0.556499i | \(0.812144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1458.34 | −1.56642 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1258.05i | 1.34264i | 0.741169 | + | 0.671319i | \(0.234272\pi\) | ||||
−0.741169 | + | 0.671319i | \(0.765728\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 762.875i | − 0.810707i | −0.914160 | − | 0.405353i | \(-0.867148\pi\) | ||||
0.914160 | − | 0.405353i | \(-0.132852\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1454.13i | 1.54203i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1023.55 | −1.08084 | −0.540419 | − | 0.841396i | \(-0.681734\pi\) | ||||
−0.540419 | + | 0.841396i | \(0.681734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 710.658 | 0.748849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −63.7513 | −0.0668954 | −0.0334477 | − | 0.999440i | \(-0.510649\pi\) | ||||
−0.0334477 | + | 0.999440i | \(0.510649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2913.69i | − 3.03826i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −672.895 | −0.700203 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 505.986i | 0.523254i | 0.965169 | + | 0.261627i | \(0.0842590\pi\) | ||||
−0.965169 | + | 0.261627i | \(0.915741\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1803.51i | − 1.85738i | −0.370862 | − | 0.928688i | \(-0.620938\pi\) | ||||
0.370862 | − | 0.928688i | \(-0.379062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2857.08i | − 2.93636i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1844.54 | −1.88797 | −0.943983 | − | 0.329994i | \(-0.892953\pi\) | ||||
−0.943983 | + | 0.329994i | \(0.892953\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1099.50 | 1.12308 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −592.146 | −0.602386 | −0.301193 | − | 0.953563i | \(-0.597385\pi\) | ||||
−0.301193 | + | 0.953563i | \(0.597385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 853.589i | 0.863083i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 961.684 | 0.970418 | 0.485209 | − | 0.874398i | \(-0.338744\pi\) | ||||
0.485209 | + | 0.874398i | \(0.338744\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 899.670i | − 0.902378i | −0.892429 | − | 0.451189i | \(-0.851000\pi\) | ||||
0.892429 | − | 0.451189i | \(-0.149000\pi\) | |||||||
\(998\) | 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 | 900.3.b.b.449.7 | 8 | ||
3.2 | odd | 2 | inner | 900.3.b.b.449.8 | 8 | ||
4.3 | odd | 2 | 3600.3.c.k.449.2 | 8 | |||
5.2 | odd | 4 | 180.3.g.a.161.1 | ✓ | 4 | ||
5.3 | odd | 4 | 900.3.g.d.701.3 | 4 | |||
5.4 | even | 2 | inner | 900.3.b.b.449.1 | 8 | ||
12.11 | even | 2 | 3600.3.c.k.449.1 | 8 | |||
15.2 | even | 4 | 180.3.g.a.161.3 | yes | 4 | ||
15.8 | even | 4 | 900.3.g.d.701.4 | 4 | |||
15.14 | odd | 2 | inner | 900.3.b.b.449.2 | 8 | ||
20.3 | even | 4 | 3600.3.l.n.1601.2 | 4 | |||
20.7 | even | 4 | 720.3.l.c.161.2 | 4 | |||
20.19 | odd | 2 | 3600.3.c.k.449.8 | 8 | |||
40.27 | even | 4 | 2880.3.l.f.1601.4 | 4 | |||
40.37 | odd | 4 | 2880.3.l.b.1601.3 | 4 | |||
45.2 | even | 12 | 1620.3.o.f.701.2 | 8 | |||
45.7 | odd | 12 | 1620.3.o.f.701.4 | 8 | |||
45.22 | odd | 12 | 1620.3.o.f.1241.2 | 8 | |||
45.32 | even | 12 | 1620.3.o.f.1241.4 | 8 | |||
60.23 | odd | 4 | 3600.3.l.n.1601.1 | 4 | |||
60.47 | odd | 4 | 720.3.l.c.161.4 | 4 | |||
60.59 | even | 2 | 3600.3.c.k.449.7 | 8 | |||
120.77 | even | 4 | 2880.3.l.b.1601.1 | 4 | |||
120.107 | odd | 4 | 2880.3.l.f.1601.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.g.a.161.1 | ✓ | 4 | 5.2 | odd | 4 | ||
180.3.g.a.161.3 | yes | 4 | 15.2 | even | 4 | ||
720.3.l.c.161.2 | 4 | 20.7 | even | 4 | |||
720.3.l.c.161.4 | 4 | 60.47 | odd | 4 | |||
900.3.b.b.449.1 | 8 | 5.4 | even | 2 | inner | ||
900.3.b.b.449.2 | 8 | 15.14 | odd | 2 | inner | ||
900.3.b.b.449.7 | 8 | 1.1 | even | 1 | trivial | ||
900.3.b.b.449.8 | 8 | 3.2 | odd | 2 | inner | ||
900.3.g.d.701.3 | 4 | 5.3 | odd | 4 | |||
900.3.g.d.701.4 | 4 | 15.8 | even | 4 | |||
1620.3.o.f.701.2 | 8 | 45.2 | even | 12 | |||
1620.3.o.f.701.4 | 8 | 45.7 | odd | 12 | |||
1620.3.o.f.1241.2 | 8 | 45.22 | odd | 12 | |||
1620.3.o.f.1241.4 | 8 | 45.32 | even | 12 | |||
2880.3.l.b.1601.1 | 4 | 120.77 | even | 4 | |||
2880.3.l.b.1601.3 | 4 | 40.37 | odd | 4 | |||
2880.3.l.f.1601.2 | 4 | 120.107 | odd | 4 | |||
2880.3.l.f.1601.4 | 4 | 40.27 | even | 4 | |||
3600.3.c.k.449.1 | 8 | 12.11 | even | 2 | |||
3600.3.c.k.449.2 | 8 | 4.3 | odd | 2 | |||
3600.3.c.k.449.7 | 8 | 60.59 | even | 2 | |||
3600.3.c.k.449.8 | 8 | 20.19 | odd | 2 | |||
3600.3.l.n.1601.1 | 4 | 60.23 | odd | 4 | |||
3600.3.l.n.1601.2 | 4 | 20.3 | even | 4 |