Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [180,3,Mod(161,180)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(180, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("180.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 180.g (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: | \(4.90464475849\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(1.58114 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 180.161 |
Dual form | 180.3.g.a.161.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(91\) | \(101\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.4868 | −1.92669 | −0.963345 | − | 0.268265i | \(-0.913550\pi\) | ||||
−0.963345 | + | 0.268265i | \(0.913550\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.6590i | 1.60537i | 0.596405 | + | 0.802684i | \(0.296595\pi\) | ||||
−0.596405 | + | 0.802684i | \(0.703405\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.48683 | −0.575910 | −0.287955 | − | 0.957644i | \(-0.592975\pi\) | ||||
−0.287955 | + | 0.957644i | \(0.592975\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 16.9706i | − 0.998268i | −0.866525 | − | 0.499134i | \(-0.833651\pi\) | ||||
0.866525 | − | 0.499134i | \(-0.166349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.9737 | −0.577561 | −0.288781 | − | 0.957395i | \(-0.593250\pi\) | ||||
−0.288781 | + | 0.957395i | \(0.593250\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 21.9017i | 0.952247i | 0.879378 | + | 0.476124i | \(0.157959\pi\) | ||||
−0.879378 | + | 0.476124i | \(0.842041\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 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 | ||||||||
\(35\) | − 30.1575i | − 0.861642i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.53950 | −0.149716 | −0.0748581 | − | 0.997194i | \(-0.523850\pi\) | ||||
−0.0748581 | + | 0.997194i | \(0.523850\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 66.3936i | − 1.61935i | −0.586875 | − | 0.809677i | \(-0.699642\pi\) | ||||
0.586875 | − | 0.809677i | \(-0.300358\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 38.9737 | 0.906364 | 0.453182 | − | 0.891418i | \(-0.350289\pi\) | ||||
0.453182 | + | 0.891418i | \(0.350289\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 32.5642i | − 0.692854i | −0.938077 | − | 0.346427i | \(-0.887395\pi\) | ||||
0.938077 | − | 0.346427i | \(-0.112605\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 132.895 | 2.71214 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.2392i | − 0.212061i | −0.994363 | − | 0.106030i | \(-0.966186\pi\) | ||||
0.994363 | − | 0.106030i | \(-0.0338141\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −39.4868 | −0.717942 | ||||||||
\(56\) | 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 | ||||||||
\(65\) | − 16.7411i | − 0.257555i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −76.0000 | −1.13433 | −0.567164 | − | 0.823605i | \(-0.691960\pi\) | ||||
−0.567164 | + | 0.823605i | \(0.691960\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 77.7445i | 1.09499i | 0.836808 | + | 0.547497i | \(0.184419\pi\) | ||||
−0.836808 | + | 0.547497i | \(0.815581\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 94.9210 | 1.30029 | 0.650144 | − | 0.759811i | \(-0.274709\pi\) | ||||
0.650144 | + | 0.759811i | \(0.274709\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 238.165i | − 3.09305i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.92100 | −0.0876076 | −0.0438038 | − | 0.999040i | \(-0.513948\pi\) | ||||
−0.0438038 | + | 0.999040i | \(0.513948\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 62.1509i | 0.748806i | 0.927266 | + | 0.374403i | \(0.122152\pi\) | ||||
−0.927266 | + | 0.374403i | \(0.877848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 37.9473 | 0.446439 | ||||||||
\(86\) | 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 | ||||||||
\(95\) | − 24.5379i | − 0.258293i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −124.974 | −1.28839 | −0.644194 | − | 0.764862i | \(-0.722807\pi\) | ||||
−0.644194 | + | 0.764862i | \(0.722807\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 112.262i | 1.11151i | 0.831347 | + | 0.555754i | \(0.187571\pi\) | ||||
−0.831347 | + | 0.555754i | \(0.812429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −170.302 | −1.65342 | −0.826711 | − | 0.562627i | \(-0.809791\pi\) | ||||
−0.826711 | + | 0.562627i | \(0.809791\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 93.3381i | − 0.872319i | −0.899869 | − | 0.436159i | \(-0.856338\pi\) | ||||
0.899869 | − | 0.436159i | \(-0.143662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −68.8683 | −0.631820 | −0.315910 | − | 0.948789i | \(-0.602310\pi\) | ||||
−0.315910 | + | 0.948789i | \(0.602310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 110.309i | 0.976183i | 0.872793 | + | 0.488091i | \(0.162307\pi\) | ||||
−0.872793 | + | 0.488091i | \(0.837693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −48.9737 | −0.425858 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | − 11.1803i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −65.3815 | −0.514815 | −0.257407 | − | 0.966303i | \(-0.582868\pi\) | ||||
−0.257407 | + | 0.966303i | \(0.582868\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 47.2458i | − 0.360655i | −0.983607 | − | 0.180328i | \(-0.942284\pi\) | ||||
0.983607 | − | 0.180328i | \(-0.0577158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 148.000 | 1.11278 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 216.039i | 1.57693i | 0.615079 | + | 0.788465i | \(0.289124\pi\) | ||||
−0.615079 | + | 0.788465i | \(0.710876\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 211.842 | 1.52404 | 0.762022 | − | 0.647552i | \(-0.224207\pi\) | ||||
0.762022 | + | 0.647552i | \(0.224207\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 132.210i | − 0.924548i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −105.895 | −0.730308 | ||||||||
\(146\) | 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 | ||||||||
\(155\) | − 37.9543i | − 0.244866i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31.4868 | −0.200553 | −0.100277 | − | 0.994960i | \(-0.531973\pi\) | ||||
−0.100277 | + | 0.994960i | \(0.531973\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 295.384i | − 1.83469i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −101.132 | −0.620440 | −0.310220 | − | 0.950665i | \(-0.600403\pi\) | ||||
−0.310220 | + | 0.950665i | \(0.600403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 147.804i | 0.885054i | 0.896755 | + | 0.442527i | \(0.145918\pi\) | ||||
−0.896755 | + | 0.442527i | \(0.854082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −112.947 | −0.668327 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 332.079i | 1.91953i | 0.280797 | + | 0.959767i | \(0.409401\pi\) | ||||
−0.280797 | + | 0.959767i | \(0.590599\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 67.4342 | 0.385338 | ||||||||
\(176\) | 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 | ||||||||
\(185\) | − 12.3867i | − 0.0669551i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 299.684 | 1.60259 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 163.974i | 0.858504i | 0.903185 | + | 0.429252i | \(0.141223\pi\) | ||||
−0.903185 | + | 0.429252i | \(0.858777\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 110.000 | 0.569948 | 0.284974 | − | 0.958535i | \(-0.408015\pi\) | ||||
0.284974 | + | 0.958535i | \(0.408015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 211.108i | − 1.07162i | −0.844340 | − | 0.535808i | \(-0.820007\pi\) | ||||
0.844340 | − | 0.535808i | \(-0.179993\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1053 | −0.0909816 | −0.0454908 | − | 0.998965i | \(-0.514485\pi\) | ||||
−0.0454908 | + | 0.998965i | \(0.514485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 638.703i | − 3.14632i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 148.460 | 0.724198 | ||||||||
\(206\) | 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 | ||||||||
\(215\) | 87.1478i | 0.405338i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 228.921 | 1.05494 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 127.056i | 0.574913i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 59.3288 | 0.266049 | 0.133024 | − | 0.991113i | \(-0.457531\pi\) | ||||
0.133024 | + | 0.991113i | \(0.457531\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 115.593i | − 0.509221i | −0.967044 | − | 0.254610i | \(-0.918053\pi\) | ||||
0.967044 | − | 0.254610i | \(-0.0819472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −253.895 | −1.10871 | −0.554355 | − | 0.832280i | \(-0.687035\pi\) | ||||
−0.554355 | + | 0.832280i | \(0.687035\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 206.401i | 0.885840i | 0.896561 | + | 0.442920i | \(0.146057\pi\) | ||||
−0.896561 | + | 0.442920i | \(0.853943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 72.8157 | 0.309854 | ||||||||
\(236\) | 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 | ||||||||
\(245\) | 297.162i | 1.21290i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 82.1580 | 0.332623 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 140.807i | 0.560985i | 0.959856 | + | 0.280493i | \(0.0904979\pi\) | ||||
−0.959856 | + | 0.280493i | \(0.909502\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −386.763 | −1.52871 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 292.630i | 1.13864i | 0.822116 | + | 0.569320i | \(0.192793\pi\) | ||||
−0.822116 | + | 0.569320i | \(0.807207\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 74.7103 | 0.288457 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 270.952i | − 1.03024i | −0.857119 | − | 0.515118i | \(-0.827748\pi\) | ||||
0.857119 | − | 0.515118i | \(-0.172252\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.1317 | 0.0948365 | ||||||||
\(266\) | 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 | ||||||||
\(275\) | − 88.2952i | − 0.321074i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −342.039 | −1.23480 | −0.617399 | − | 0.786650i | \(-0.711814\pi\) | ||||
−0.617399 | + | 0.786650i | \(0.711814\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 352.139i | − 1.25316i | −0.779355 | − | 0.626582i | \(-0.784453\pi\) | ||||
0.779355 | − | 0.626582i | \(-0.215547\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 249.631 | 0.882089 | 0.441045 | − | 0.897485i | \(-0.354608\pi\) | ||||
0.441045 | + | 0.897485i | \(0.354608\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 895.439i | 3.12000i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.00346021 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 37.4953i | 0.127970i | 0.997951 | + | 0.0639851i | \(0.0203810\pi\) | ||||
−0.997951 | + | 0.0639851i | \(0.979619\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −71.2762 | −0.241614 | ||||||||
\(296\) | 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 | ||||||||
\(305\) | 104.919i | 0.343995i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 457.842 | 1.49134 | 0.745671 | − | 0.666314i | \(-0.232129\pi\) | ||||
0.745671 | + | 0.666314i | \(0.232129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.48528i | 0.0272839i | 0.999907 | + | 0.0136419i | \(0.00434250\pi\) | ||||
−0.999907 | + | 0.0136419i | \(0.995658\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.57866 | −0.00504363 | −0.00252181 | − | 0.999997i | \(-0.500803\pi\) | ||||
−0.00252181 | + | 0.999997i | \(0.500803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 529.195i | 1.66938i | 0.550717 | + | 0.834692i | \(0.314354\pi\) | ||||
−0.550717 | + | 0.834692i | \(0.685646\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −836.289 | −2.62160 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 186.229i | 0.576561i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 37.4342 | 0.115182 | ||||||||
\(326\) | 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 | ||||||||
\(335\) | − 169.941i | − 0.507287i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 414.710 | 1.23059 | 0.615297 | − | 0.788295i | \(-0.289036\pi\) | ||||
0.615297 | + | 0.788295i | \(0.289036\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 299.739i | − 0.878999i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1131.47 | −3.29876 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 128.656i | 0.370767i | 0.982666 | + | 0.185384i | \(0.0593528\pi\) | ||||
−0.982666 | + | 0.185384i | \(0.940647\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −37.0790 | −0.106244 | −0.0531218 | − | 0.998588i | \(-0.516917\pi\) | ||||
−0.0531218 | + | 0.998588i | \(0.516917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 190.584i | − 0.539897i | −0.962875 | − | 0.269949i | \(-0.912993\pi\) | ||||
0.962875 | − | 0.269949i | \(-0.0870067\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −173.842 | −0.489696 | ||||||||
\(356\) | 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 | ||||||||
\(365\) | 212.250i | 0.581506i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 300.460 | 0.818693 | 0.409347 | − | 0.912379i | \(-0.365757\pi\) | ||||
0.409347 | + | 0.912379i | \(0.365757\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 151.582i | 0.408576i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 704.092 | 1.88765 | 0.943823 | − | 0.330452i | \(-0.107201\pi\) | ||||
0.943823 | + | 0.330452i | \(0.107201\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 354.558i | − 0.940472i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 333.789 | 0.880711 | 0.440355 | − | 0.897824i | \(-0.354852\pi\) | ||||
0.440355 | + | 0.897824i | \(0.354852\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 260.996i | 0.681453i | 0.940163 | + | 0.340726i | \(0.110673\pi\) | ||||
−0.940163 | + | 0.340726i | \(0.889327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 532.552 | 1.38325 | ||||||||
\(386\) | 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 | ||||||||
\(395\) | − 15.4758i | − 0.0391793i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −90.3552 | −0.227595 | −0.113797 | − | 0.993504i | \(-0.536301\pi\) | ||||
−0.113797 | + | 0.993504i | \(0.536301\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 43.6917i | 0.108957i | 0.998515 | + | 0.0544784i | \(0.0173496\pi\) | ||||
−0.998515 | + | 0.0544784i | \(0.982650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 127.079 | 0.315333 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 97.8223i | − 0.240350i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −260.053 | −0.635826 | −0.317913 | − | 0.948120i | \(-0.602982\pi\) | ||||
−0.317913 | + | 0.948120i | \(0.602982\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 429.902i | − 1.04092i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −138.974 | −0.334876 | ||||||||
\(416\) | 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 | ||||||||
\(425\) | 84.8528i | 0.199654i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −632.816 | −1.48200 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 690.768i | 1.60271i | 0.598189 | + | 0.801355i | \(0.295887\pi\) | ||||
−0.598189 | + | 0.801355i | \(0.704113\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −117.500 | −0.271363 | −0.135682 | − | 0.990752i | \(-0.543322\pi\) | ||||
−0.135682 | + | 0.990752i | \(0.543322\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 240.342i | − 0.549981i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 50.0000 | 0.113895 | 0.0569476 | − | 0.998377i | \(-0.481863\pi\) | ||||
0.0569476 | + | 0.998377i | \(0.481863\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 526.794i | − 1.18915i | −0.804040 | − | 0.594576i | \(-0.797320\pi\) | ||||
0.804040 | − | 0.594576i | \(-0.202680\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −139.223 | −0.312862 | ||||||||
\(446\) | 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 | ||||||||
\(455\) | 225.784i | 0.496229i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −433.079 | −0.947656 | −0.473828 | − | 0.880617i | \(-0.657128\pi\) | ||||
−0.473828 | + | 0.880617i | \(0.657128\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 486.768i | − 1.05590i | −0.849277 | − | 0.527948i | \(-0.822961\pi\) | ||||
0.849277 | − | 0.527948i | \(-0.177039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 423.223 | 0.914090 | 0.457045 | − | 0.889444i | \(-0.348908\pi\) | ||||
0.457045 | + | 0.889444i | \(0.348908\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 295.831i | − 0.633472i | −0.948514 | − | 0.316736i | \(-0.897413\pi\) | ||||
0.948514 | − | 0.316736i | \(-0.102587\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1025.00 | 2.18550 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 688.238i | 1.45505i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 54.8683 | 0.115512 | ||||||||
\(476\) | 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 | ||||||||
\(485\) | − 279.450i | − 0.576185i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 247.750 | 0.508727 | 0.254364 | − | 0.967109i | \(-0.418134\pi\) | ||||
0.254364 | + | 0.967109i | \(0.418134\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 170.394i | 0.347035i | 0.984831 | + | 0.173517i | \(0.0555133\pi\) | ||||
−0.984831 | + | 0.173517i | \(0.944487\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 803.684 | 1.63019 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1048.53i | − 2.10971i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 47.3950 | 0.0949800 | 0.0474900 | − | 0.998872i | \(-0.484878\pi\) | ||||
0.0474900 | + | 0.998872i | \(0.484878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 321.064i | − 0.638298i | −0.947705 | − | 0.319149i | \(-0.896603\pi\) | ||||
0.947705 | − | 0.319149i | \(-0.103397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −251.026 | −0.497082 | ||||||||
\(506\) | 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 | ||||||||
\(515\) | − 380.808i | − 0.739433i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 575.052 | 1.11229 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 79.4567i | 0.152508i | 0.997088 | + | 0.0762540i | \(0.0242960\pi\) | ||||
−0.997088 | + | 0.0762540i | \(0.975704\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −864.605 | −1.65316 | −0.826582 | − | 0.562816i | \(-0.809718\pi\) | ||||
−0.826582 | + | 0.562816i | \(0.809718\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 288.053i | 0.546589i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.3160 | 0.0932250 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 497.077i | 0.932603i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 208.710 | 0.390113 | ||||||||
\(536\) | 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 | ||||||||
\(545\) | − 153.994i | − 0.282558i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −559.079 | −1.02208 | −0.511041 | − | 0.859556i | \(-0.670740\pi\) | ||||
−0.511041 | + | 0.859556i | \(0.670740\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 519.686i | − 0.943168i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 93.3423 | 0.168793 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 310.308i | 0.557105i | 0.960421 | + | 0.278553i | \(0.0898547\pi\) | ||||
−0.960421 | + | 0.278553i | \(0.910145\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −291.789 | −0.521984 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 566.690i | 1.00655i | 0.864125 | + | 0.503277i | \(0.167872\pi\) | ||||
−0.864125 | + | 0.503277i | \(0.832128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −246.658 | −0.436562 | ||||||||
\(566\) | 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 | ||||||||
\(575\) | − 109.508i | − 0.190449i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 76.7630 | 0.133038 | 0.0665191 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665191 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 838.219i | − 1.44272i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 198.474 | 0.340436 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 684.554i | − 1.16619i | −0.812404 | − | 0.583095i | \(-0.801841\pi\) | ||||
0.812404 | − | 0.583095i | \(-0.198159\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 186.263 | 0.316237 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 592.146i | 0.998560i | 0.866441 | + | 0.499280i | \(0.166402\pi\) | ||||
−0.866441 | + | 0.499280i | \(0.833598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −511.789 | −0.860150 | ||||||||
\(596\) | 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 | ||||||||
\(605\) | − 426.736i | − 0.705348i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −799.828 | −1.31767 | −0.658837 | − | 0.752285i | \(-0.728951\pi\) | ||||
−0.658837 | + | 0.752285i | \(0.728951\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 243.802i | 0.399022i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −680.302 | −1.10979 | −0.554896 | − | 0.831920i | \(-0.687242\pi\) | ||||
−0.554896 | + | 0.831920i | \(0.687242\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 264.868i | − 0.429283i | −0.976693 | − | 0.214641i | \(-0.931142\pi\) | ||||
0.976693 | − | 0.214641i | \(-0.0688583\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 535.842 | 0.865658 | 0.432829 | − | 0.901476i | \(-0.357515\pi\) | ||||
0.432829 | + | 0.901476i | \(0.357515\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 839.726i | − 1.34787i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 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 | ||||||||
\(635\) | − 146.197i | − 0.230232i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −994.960 | −1.56195 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1246.33i | 1.94435i | 0.234248 | + | 0.972177i | \(0.424737\pi\) | ||||
−0.234248 | + | 0.972177i | \(0.575263\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 155.395 | 0.241672 | 0.120836 | − | 0.992672i | \(-0.461443\pi\) | ||||
0.120836 | + | 0.992672i | \(0.461443\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 142.649i | 0.220478i | 0.993905 | + | 0.110239i | \(0.0351617\pi\) | ||||
−0.993905 | + | 0.110239i | \(0.964838\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −562.894 | −0.867325 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 924.579i | 1.41589i | 0.706266 | + | 0.707947i | \(0.250378\pi\) | ||||
−0.706266 | + | 0.707947i | \(0.749622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 105.645 | 0.161290 | ||||||||
\(656\) | 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 | ||||||||
\(665\) | 330.938i | 0.497651i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1037.21 | −1.55504 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 828.580i | 1.23484i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 982.605 | 1.46004 | 0.730019 | − | 0.683427i | \(-0.239511\pi\) | ||||
0.730019 | + | 0.683427i | \(0.239511\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 386.769i | − 0.571298i | −0.958334 | − | 0.285649i | \(-0.907791\pi\) | ||||
0.958334 | − | 0.285649i | \(-0.0922092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1685.50 | 2.48233 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 504.539i | 0.738710i | 0.929288 | + | 0.369355i | \(0.120421\pi\) | ||||
−0.929288 | + | 0.369355i | \(0.879579\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −483.079 | −0.705225 | ||||||||
\(686\) | 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 | ||||||||
\(695\) | 473.693i | 0.681573i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1126.74 | −1.61655 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 358.559i | 0.511496i | 0.966743 | + | 0.255748i | \(0.0823218\pi\) | ||||
−0.966743 | + | 0.255748i | \(0.917678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 60.7886 | 0.0864703 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1514.06i | − 2.14153i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −733.579 | −1.03467 | −0.517333 | − | 0.855784i | \(-0.673075\pi\) | ||||
−0.517333 | + | 0.855784i | \(0.673075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 371.752i | − 0.521391i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 295.631 | 0.413470 | ||||||||
\(716\) | 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 | ||||||||
\(725\) | − 236.788i | − 0.326604i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1265.04 | 1.74008 | 0.870040 | − | 0.492981i | \(-0.164093\pi\) | ||||
0.870040 | + | 0.492981i | \(0.164093\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 661.405i | − 0.904795i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −586.749 | −0.800477 | −0.400238 | − | 0.916411i | \(-0.631073\pi\) | ||||
−0.400238 | + | 0.916411i | \(0.631073\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1342.09i | − 1.82101i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −215.973 | −0.292250 | −0.146125 | − | 0.989266i | \(-0.546680\pi\) | ||||
−0.146125 | + | 0.989266i | \(0.546680\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 599.961i | − 0.807484i | −0.914873 | − | 0.403742i | \(-0.867709\pi\) | ||||
0.914873 | − | 0.403742i | \(-0.132291\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 206.921 | 0.277746 | ||||||||
\(746\) | 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 | ||||||||
\(755\) | − 276.919i | − 0.366780i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1070.43 | 1.41405 | 0.707023 | − | 0.707190i | \(-0.250038\pi\) | ||||
0.707023 | + | 0.707190i | \(0.250038\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 654.892i | 0.860567i | 0.902694 | + | 0.430284i | \(0.141586\pi\) | ||||
−0.902694 | + | 0.430284i | \(0.858414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 928.816 | 1.21732 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 238.648i | − 0.311144i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 682.631 | 0.887686 | 0.443843 | − | 0.896105i | \(-0.353615\pi\) | ||||
0.443843 | + | 0.896105i | \(0.353615\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 770.690i | − 0.997012i | −0.866886 | − | 0.498506i | \(-0.833882\pi\) | ||||
0.866886 | − | 0.498506i | \(-0.166118\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 84.8683 | 0.109508 | ||||||||
\(776\) | 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 | ||||||||
\(785\) | − 70.4067i | − 0.0896901i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −253.869 | −0.322578 | −0.161289 | − | 0.986907i | \(-0.551565\pi\) | ||||
−0.161289 | + | 0.986907i | \(0.551565\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1487.71i | − 1.88080i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −351.290 | −0.442988 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1055.86i | 1.32479i | 0.749154 | + | 0.662396i | \(0.230460\pi\) | ||||
−0.749154 | + | 0.662396i | \(0.769540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −552.632 | −0.691655 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1676.21i | 2.08744i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 660.500 | 0.820496 | ||||||||
\(806\) | 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 | ||||||||
\(815\) | − 226.137i | − 0.277469i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −427.684 | −0.523481 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 257.219i | − 0.313299i | −0.987654 | − | 0.156650i | \(-0.949931\pi\) | ||||
0.987654 | − | 0.156650i | \(-0.0500694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −367.013 | −0.445945 | −0.222973 | − | 0.974825i | \(-0.571576\pi\) | ||||
−0.222973 | + | 0.974825i | \(0.571576\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 122.254i | 0.147829i | 0.997265 | + | 0.0739144i | \(0.0235492\pi\) | ||||
−0.997265 | + | 0.0739144i | \(0.976451\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 335.237 | 0.404387 | 0.202194 | − | 0.979346i | \(-0.435193\pi\) | ||||
0.202194 | + | 0.979346i | \(0.435193\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 2255.30i | − 2.70744i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −330.500 | −0.395808 | ||||||||
\(836\) | 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 | ||||||||
\(845\) | − 252.558i | − 0.298885i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2573.85 | 3.03879 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 121.324i | − 0.142567i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 764.591 | 0.896356 | 0.448178 | − | 0.893944i | \(-0.352073\pi\) | ||||
0.448178 | + | 0.893944i | \(0.352073\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1516.15i | 1.76913i | 0.466413 | + | 0.884567i | \(0.345546\pi\) | ||||
−0.466413 | + | 0.884567i | \(0.654454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 433.684 | 0.504871 | 0.252435 | − | 0.967614i | \(-0.418768\pi\) | ||||
0.252435 | + | 0.967614i | \(0.418768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1255.50i | 1.45481i | 0.686206 | + | 0.727407i | \(0.259275\pi\) | ||||
−0.686206 | + | 0.727407i | \(0.740725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −742.552 | −0.858442 | ||||||||
\(866\) | 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 | ||||||||
\(875\) | 150.787i | 0.172328i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1003.59 | 1.14435 | 0.572173 | − | 0.820133i | \(-0.306100\pi\) | ||||
0.572173 | + | 0.820133i | \(0.306100\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 737.214i | − 0.836792i | −0.908265 | − | 0.418396i | \(-0.862592\pi\) | ||||
0.908265 | − | 0.418396i | \(-0.137408\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 336.394 | 0.380968 | 0.190484 | − | 0.981690i | \(-0.438994\pi\) | ||||
0.190484 | + | 0.981690i | \(0.438994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 793.132i | 0.894174i | 0.894491 | + | 0.447087i | \(0.147539\pi\) | ||||
−0.894491 | + | 0.447087i | \(0.852461\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 881.789 | 0.991889 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 357.348i | 0.400166i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 102.566 | 0.114599 | ||||||||
\(896\) | 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 | ||||||||
\(905\) | 297.103i | 0.328290i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1079.66 | −1.19036 | −0.595180 | − | 0.803592i | \(-0.702919\pi\) | ||||
−0.595180 | + | 0.803592i | \(0.702919\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1473.69i | − 1.61766i | −0.588045 | − | 0.808828i | \(-0.700102\pi\) | ||||
0.588045 | − | 0.808828i | \(-0.299898\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1097.53 | −1.20211 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 637.196i | 0.694871i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1602.92 | −1.74420 | −0.872101 | − | 0.489327i | \(-0.837243\pi\) | ||||
−0.872101 | + | 0.489327i | \(0.837243\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 582.060i | − 0.630618i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.6975 | 0.0299432 | ||||||||
\(926\) | 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 | ||||||||
\(935\) | 670.114i | 0.716699i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1258.05 | −1.34264 | −0.671319 | − | 0.741169i | \(-0.734272\pi\) | ||||
−0.671319 | + | 0.741169i | \(0.734272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 762.875i | 0.810707i | 0.914160 | + | 0.405353i | \(0.132852\pi\) | ||||
−0.914160 | + | 0.405353i | \(0.867148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1454.13 | 1.54203 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1023.55i | 1.08084i | 0.841396 | + | 0.540419i | \(0.181734\pi\) | ||||
−0.841396 | + | 0.540419i | \(0.818266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −710.658 | −0.748849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 63.7513i | − 0.0668954i | −0.999440 | − | 0.0334477i | \(-0.989351\pi\) | ||||
0.999440 | − | 0.0334477i | \(-0.0106487\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −366.658 | −0.383935 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | 245.967i | 0.254889i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −505.986 | −0.523254 | −0.261627 | − | 0.965169i | \(-0.584259\pi\) | ||||
−0.261627 | + | 0.965169i | \(0.584259\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1803.51i | 1.85738i | 0.370862 | + | 0.928688i | \(0.379062\pi\) | ||||
−0.370862 | + | 0.928688i | \(0.620938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2857.08 | −2.93636 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1844.54i | 1.88797i | 0.329994 | + | 0.943983i | \(0.392953\pi\) | ||||
−0.329994 | + | 0.943983i | \(0.607047\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1099.50 | −1.12308 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 592.146i | − 0.602386i | −0.953563 | − | 0.301193i | \(-0.902615\pi\) | ||||
0.953563 | − | 0.301193i | \(-0.0973849\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 472.053 | 0.479241 | ||||||||
\(986\) | 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 | ||||||||
\(995\) | − 40.4848i | − 0.0406882i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 899.670 | 0.902378 | 0.451189 | − | 0.892429i | \(-0.351000\pi\) | ||||
0.451189 | + | 0.892429i | \(0.351000\pi\) | |||||||
\(998\) | 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 | 180.3.g.a.161.3 | yes | 4 | |
3.2 | odd | 2 | inner | 180.3.g.a.161.1 | ✓ | 4 | |
4.3 | odd | 2 | 720.3.l.c.161.4 | 4 | |||
5.2 | odd | 4 | 900.3.b.b.449.2 | 8 | |||
5.3 | odd | 4 | 900.3.b.b.449.8 | 8 | |||
5.4 | even | 2 | 900.3.g.d.701.4 | 4 | |||
8.3 | odd | 2 | 2880.3.l.f.1601.2 | 4 | |||
8.5 | even | 2 | 2880.3.l.b.1601.1 | 4 | |||
9.2 | odd | 6 | 1620.3.o.f.701.4 | 8 | |||
9.4 | even | 3 | 1620.3.o.f.1241.4 | 8 | |||
9.5 | odd | 6 | 1620.3.o.f.1241.2 | 8 | |||
9.7 | even | 3 | 1620.3.o.f.701.2 | 8 | |||
12.11 | even | 2 | 720.3.l.c.161.2 | 4 | |||
15.2 | even | 4 | 900.3.b.b.449.1 | 8 | |||
15.8 | even | 4 | 900.3.b.b.449.7 | 8 | |||
15.14 | odd | 2 | 900.3.g.d.701.3 | 4 | |||
20.3 | even | 4 | 3600.3.c.k.449.1 | 8 | |||
20.7 | even | 4 | 3600.3.c.k.449.7 | 8 | |||
20.19 | odd | 2 | 3600.3.l.n.1601.1 | 4 | |||
24.5 | odd | 2 | 2880.3.l.b.1601.3 | 4 | |||
24.11 | even | 2 | 2880.3.l.f.1601.4 | 4 | |||
60.23 | odd | 4 | 3600.3.c.k.449.2 | 8 | |||
60.47 | odd | 4 | 3600.3.c.k.449.8 | 8 | |||
60.59 | even | 2 | 3600.3.l.n.1601.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.g.a.161.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
180.3.g.a.161.3 | yes | 4 | 1.1 | even | 1 | trivial | |
720.3.l.c.161.2 | 4 | 12.11 | even | 2 | |||
720.3.l.c.161.4 | 4 | 4.3 | odd | 2 | |||
900.3.b.b.449.1 | 8 | 15.2 | even | 4 | |||
900.3.b.b.449.2 | 8 | 5.2 | odd | 4 | |||
900.3.b.b.449.7 | 8 | 15.8 | even | 4 | |||
900.3.b.b.449.8 | 8 | 5.3 | odd | 4 | |||
900.3.g.d.701.3 | 4 | 15.14 | odd | 2 | |||
900.3.g.d.701.4 | 4 | 5.4 | even | 2 | |||
1620.3.o.f.701.2 | 8 | 9.7 | even | 3 | |||
1620.3.o.f.701.4 | 8 | 9.2 | odd | 6 | |||
1620.3.o.f.1241.2 | 8 | 9.5 | odd | 6 | |||
1620.3.o.f.1241.4 | 8 | 9.4 | even | 3 | |||
2880.3.l.b.1601.1 | 4 | 8.5 | even | 2 | |||
2880.3.l.b.1601.3 | 4 | 24.5 | odd | 2 | |||
2880.3.l.f.1601.2 | 4 | 8.3 | odd | 2 | |||
2880.3.l.f.1601.4 | 4 | 24.11 | even | 2 | |||
3600.3.c.k.449.1 | 8 | 20.3 | even | 4 | |||
3600.3.c.k.449.2 | 8 | 60.23 | odd | 4 | |||
3600.3.c.k.449.7 | 8 | 20.7 | even | 4 | |||
3600.3.c.k.449.8 | 8 | 60.47 | odd | 4 | |||
3600.3.l.n.1601.1 | 4 | 20.19 | odd | 2 | |||
3600.3.l.n.1601.2 | 4 | 60.59 | even | 2 |