Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(1,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 552.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.42864 | −1.98055 | −0.990274 | − | 0.139132i | \(-0.955569\pi\) | ||||
−0.990274 | + | 0.139132i | \(0.955569\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.622216 | 0.235175 | 0.117588 | − | 0.993063i | \(-0.462484\pi\) | ||||
0.117588 | + | 0.993063i | \(0.462484\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.80642 | 1.75070 | 0.875351 | − | 0.483487i | \(-0.160630\pi\) | ||||
0.875351 | + | 0.483487i | \(0.160630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.42864 | −1.14347 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.37778 | 0.334162 | 0.167081 | − | 0.985943i | \(-0.446566\pi\) | ||||
0.167081 | + | 0.985943i | \(0.446566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.42864 | 1.47483 | 0.737416 | − | 0.675439i | \(-0.236046\pi\) | ||||
0.737416 | + | 0.675439i | \(0.236046\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.622216 | 0.135779 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.6128 | 2.92257 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.755569 | −0.140306 | −0.0701528 | − | 0.997536i | \(-0.522349\pi\) | ||||
−0.0701528 | + | 0.997536i | \(0.522349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.24443 | −0.223506 | −0.111753 | − | 0.993736i | \(-0.535647\pi\) | ||||
−0.111753 | + | 0.993736i | \(0.535647\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.80642 | 1.01077 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.75557 | −0.465776 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.05086 | 1.48795 | 0.743976 | − | 0.668207i | \(-0.232938\pi\) | ||||
0.743976 | + | 0.668207i | \(0.232938\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.61285 | −1.50127 | −0.750637 | − | 0.660715i | \(-0.770253\pi\) | ||||
−0.750637 | + | 0.660715i | \(0.770253\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.18421 | −0.790584 | −0.395292 | − | 0.918555i | \(-0.629357\pi\) | ||||
−0.395292 | + | 0.918555i | \(0.629357\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.42864 | −0.660183 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.24443 | −0.764979 | −0.382489 | − | 0.923960i | \(-0.624933\pi\) | ||||
−0.382489 | + | 0.923960i | \(0.624933\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.61285 | −0.944693 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.37778 | 0.192928 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0415 | 1.65403 | 0.827013 | − | 0.562183i | \(-0.190038\pi\) | ||||
0.827013 | + | 0.562183i | \(0.190038\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −25.7146 | −3.46735 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.42864 | 0.851494 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.8573 | −1.67388 | −0.836938 | − | 0.547298i | \(-0.815656\pi\) | ||||
−0.836938 | + | 0.547298i | \(0.815656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.94914 | 0.377599 | 0.188800 | − | 0.982016i | \(-0.439540\pi\) | ||||
0.188800 | + | 0.982016i | \(0.439540\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.622216 | 0.0783918 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.85728 | −1.09861 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.18421 | 0.633352 | 0.316676 | − | 0.948534i | \(-0.397433\pi\) | ||||
0.316676 | + | 0.948534i | \(0.397433\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.10171 | 0.724140 | 0.362070 | − | 0.932151i | \(-0.382070\pi\) | ||||
0.362070 | + | 0.932151i | \(0.382070\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.6128 | 1.68735 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.61285 | 0.411722 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.62222 | −0.970075 | −0.485038 | − | 0.874493i | \(-0.661194\pi\) | ||||
−0.485038 | + | 0.874493i | \(0.661194\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.9081 | 1.30709 | 0.653544 | − | 0.756889i | \(-0.273282\pi\) | ||||
0.653544 | + | 0.756889i | \(0.273282\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.10171 | −0.661823 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.755569 | −0.0810055 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.23506 | 0.660915 | 0.330458 | − | 0.943821i | \(-0.392797\pi\) | ||||
0.330458 | + | 0.943821i | \(0.392797\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.24443 | 0.130452 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.24443 | −0.129042 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −28.4701 | −2.92097 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.85728 | −0.290113 | −0.145056 | − | 0.989423i | \(-0.546336\pi\) | ||||
−0.145056 | + | 0.989423i | \(0.546336\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.80642 | 0.583568 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.7146 | 1.56366 | 0.781828 | − | 0.623494i | \(-0.214287\pi\) | ||||
0.781828 | + | 0.623494i | \(0.214287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.47949 | 0.539911 | 0.269955 | − | 0.962873i | \(-0.412991\pi\) | ||||
0.269955 | + | 0.962873i | \(0.412991\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.75557 | −0.268916 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.295286 | −0.0285464 | −0.0142732 | − | 0.999898i | \(-0.504543\pi\) | ||||
−0.0142732 | + | 0.999898i | \(0.504543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.31756 | −0.892461 | −0.446230 | − | 0.894918i | \(-0.647234\pi\) | ||||
−0.446230 | + | 0.894918i | \(0.647234\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.05086 | 0.859069 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.4795 | −1.07990 | −0.539950 | − | 0.841697i | \(-0.681557\pi\) | ||||
−0.539950 | + | 0.841697i | \(0.681557\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.42864 | 0.412973 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.857279 | 0.0785866 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.7146 | 2.06496 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.61285 | −0.866761 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −42.5718 | −3.80774 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.47013 | 0.751602 | 0.375801 | − | 0.926700i | \(-0.377368\pi\) | ||||
0.375801 | + | 0.926700i | \(0.377368\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.18421 | −0.456444 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.61285 | −0.665138 | −0.332569 | − | 0.943079i | \(-0.607915\pi\) | ||||
−0.332569 | + | 0.943079i | \(0.607915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.42864 | −0.381157 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.37778 | −0.459455 | −0.229728 | − | 0.973255i | \(-0.573784\pi\) | ||||
−0.229728 | + | 0.973255i | \(0.573784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.24443 | −0.441661 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.6128 | 0.971115 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.34614 | 0.277882 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.61285 | −0.545418 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.2859 | 1.08842 | 0.544212 | − | 0.838947i | \(-0.316829\pi\) | ||||
0.544212 | + | 0.838947i | \(0.316829\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.48886 | −0.202541 | −0.101270 | − | 0.994859i | \(-0.532291\pi\) | ||||
−0.101270 | + | 0.994859i | \(0.532291\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.37778 | 0.111387 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.51114 | 0.442665 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.1526 | −0.890072 | −0.445036 | − | 0.895513i | \(-0.646809\pi\) | ||||
−0.445036 | + | 0.895513i | \(0.646809\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.0415 | 0.954952 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.622216 | −0.0490375 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.85728 | −0.693756 | −0.346878 | − | 0.937910i | \(-0.612758\pi\) | ||||
−0.346878 | + | 0.937910i | \(0.612758\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −25.7146 | −2.00188 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.89829 | 0.146894 | 0.0734470 | − | 0.997299i | \(-0.476600\pi\) | ||||
0.0734470 | + | 0.997299i | \(0.476600\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.42864 | 0.491610 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.7556 | −1.27390 | −0.636951 | − | 0.770904i | \(-0.719805\pi\) | ||||
−0.636951 | + | 0.770904i | \(0.719805\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.09234 | 0.687316 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.8573 | −0.966412 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.9590 | −1.41706 | −0.708531 | − | 0.705680i | \(-0.750642\pi\) | ||||
−0.708531 | + | 0.705680i | \(0.750642\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.70471 | 0.126710 | 0.0633552 | − | 0.997991i | \(-0.479820\pi\) | ||||
0.0633552 | + | 0.997991i | \(0.479820\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.94914 | 0.218007 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −40.0830 | −2.94696 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | 0.585018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.622216 | 0.0452595 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3684 | −0.750232 | −0.375116 | − | 0.926978i | \(-0.622397\pi\) | ||||
−0.375116 | + | 0.926978i | \(0.622397\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.61285 | 0.116095 | 0.0580477 | − | 0.998314i | \(-0.481512\pi\) | ||||
0.0580477 | + | 0.998314i | \(0.481512\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.85728 | −0.634283 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.34614 | 0.380897 | 0.190448 | − | 0.981697i | \(-0.439006\pi\) | ||||
0.190448 | + | 0.981697i | \(0.439006\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.3590 | −1.51410 | −0.757051 | − | 0.653355i | \(-0.773361\pi\) | ||||
−0.757051 | + | 0.653355i | \(0.773361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.18421 | 0.365666 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.470127 | −0.0329964 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 42.5718 | 2.97335 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37.3274 | 2.58199 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.36842 | −0.438420 | −0.219210 | − | 0.975678i | \(-0.570348\pi\) | ||||
−0.219210 | + | 0.975678i | \(0.570348\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.10171 | 0.418082 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.9590 | 1.56579 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.774305 | −0.0525632 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.75557 | 0.185360 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.22570 | −0.483868 | −0.241934 | − | 0.970293i | \(-0.577782\pi\) | ||||
−0.241934 | + | 0.970293i | \(0.577782\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.6128 | 0.974190 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.0509 | 0.998960 | 0.499480 | − | 0.866325i | \(-0.333524\pi\) | ||||
0.499480 | + | 0.866325i | \(0.333524\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.29529 | −0.416004 | −0.208002 | − | 0.978128i | \(-0.566696\pi\) | ||||
−0.208002 | + | 0.978128i | \(0.566696\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.61285 | 0.237708 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.7146 | 1.81564 | 0.907821 | − | 0.419359i | \(-0.137745\pi\) | ||||
0.907821 | + | 0.419359i | \(0.137745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.2257 | 1.51508 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.62222 | −0.560073 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2257 | 0.984868 | 0.492434 | − | 0.870350i | \(-0.336107\pi\) | ||||
0.492434 | + | 0.870350i | \(0.336107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.14272 | 0.331272 | 0.165636 | − | 0.986187i | \(-0.447032\pi\) | ||||
0.165636 | + | 0.986187i | \(0.447032\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 29.2859 | 1.87101 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.8573 | 0.818089 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.9081 | 0.754647 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4380 | 0.721961 | 0.360980 | − | 0.932573i | \(-0.382442\pi\) | ||||
0.360980 | + | 0.932573i | \(0.382442\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.80642 | −0.365047 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.10171 | −0.382104 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.10171 | −0.255858 | −0.127929 | − | 0.991783i | \(-0.540833\pi\) | ||||
−0.127929 | + | 0.991783i | \(0.540833\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.63158 | 0.349930 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.755569 | −0.0467685 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.4701 | −1.50889 | −0.754446 | − | 0.656362i | \(-0.772095\pi\) | ||||
−0.754446 | + | 0.656362i | \(0.772095\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −53.3274 | −3.27588 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.23506 | 0.381580 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8573 | −0.905864 | −0.452932 | − | 0.891545i | \(-0.649622\pi\) | ||||
−0.452932 | + | 0.891545i | \(0.649622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.2444 | −1.04752 | −0.523762 | − | 0.851864i | \(-0.675472\pi\) | ||||
−0.523762 | + | 0.851864i | \(0.675472\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.24443 | 0.0753164 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 84.8484 | 5.11655 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.5906 | 0.876663 | 0.438331 | − | 0.898813i | \(-0.355570\pi\) | ||||
0.438331 | + | 0.898813i | \(0.355570\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.24443 | −0.0745022 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.00937 | 0.418144 | 0.209072 | − | 0.977900i | \(-0.432956\pi\) | ||||
0.209072 | + | 0.977900i | \(0.432956\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.08250 | 0.421011 | 0.210505 | − | 0.977593i | \(-0.432489\pi\) | ||||
0.210505 | + | 0.977593i | \(0.432489\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −28.4701 | −1.68642 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.98126 | −0.353063 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1017 | −0.888336 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.85728 | −0.167497 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.67307 | −0.331424 | −0.165712 | − | 0.986174i | \(-0.552992\pi\) | ||||
−0.165712 | + | 0.986174i | \(0.552992\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 56.9403 | 3.31519 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.80642 | 0.336923 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.22570 | −0.185926 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.7146 | 0.902778 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.0607 | −0.747853 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.0607 | −1.65858 | −0.829291 | − | 0.558817i | \(-0.811255\pi\) | ||||
−0.829291 | + | 0.558817i | \(0.811255\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.47949 | 0.311718 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.3684 | 0.814758 | 0.407379 | − | 0.913259i | \(-0.366443\pi\) | ||||
0.407379 | + | 0.913259i | \(0.366443\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.8163 | −1.68532 | −0.842658 | − | 0.538450i | \(-0.819010\pi\) | ||||
−0.842658 | + | 0.538450i | \(0.819010\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.75557 | −0.155259 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.7556 | 1.16575 | 0.582874 | − | 0.812562i | \(-0.301928\pi\) | ||||
0.582874 | + | 0.812562i | \(0.301928\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.38715 | −0.245633 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.295286 | −0.0164813 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.85728 | 0.492832 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.2257 | 1.62115 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.31756 | −0.515262 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.26317 | −0.179904 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.85728 | −0.486840 | −0.243420 | − | 0.969921i | \(-0.578269\pi\) | ||||
−0.243420 | + | 0.969921i | \(0.578269\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.05086 | 0.495984 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.9590 | −1.25438 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.9813 | −1.08845 | −0.544224 | − | 0.838940i | \(-0.683176\pi\) | ||||
−0.544224 | + | 0.838940i | \(0.683176\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.4795 | −0.623481 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.22570 | −0.391293 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.47013 | −0.457344 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.42864 | 0.238430 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.73329 | 0.200414 | 0.100207 | − | 0.994967i | \(-0.468050\pi\) | ||||
0.100207 | + | 0.994967i | \(0.468050\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.10171 | −0.219560 | −0.109780 | − | 0.993956i | \(-0.535015\pi\) | ||||
−0.109780 | + | 0.993956i | \(0.535015\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.73329 | 0.305152 | 0.152576 | − | 0.988292i | \(-0.451243\pi\) | ||||
0.152576 | + | 0.988292i | \(0.451243\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.0223 | −1.43419 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.857279 | 0.0453720 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.8573 | −1.10081 | −0.550403 | − | 0.834899i | \(-0.685526\pi\) | ||||
−0.550403 | + | 0.834899i | \(0.685526\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.3274 | 1.17513 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.7146 | 1.19221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.85728 | −0.463611 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.8479 | −0.827254 | −0.413627 | − | 0.910446i | \(-0.635738\pi\) | ||||
−0.413627 | + | 0.910446i | \(0.635738\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.61285 | −0.500425 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.49240 | 0.388986 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.0509 | 1.29708 | 0.648542 | − | 0.761179i | \(-0.275379\pi\) | ||||
0.648542 | + | 0.761179i | \(0.275379\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −42.5718 | −2.19840 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.51114 | −0.0778275 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.45091 | 0.485461 | 0.242730 | − | 0.970094i | \(-0.421957\pi\) | ||||
0.242730 | + | 0.970094i | \(0.421957\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.47013 | 0.433938 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.9813 | 1.94075 | 0.970376 | − | 0.241600i | \(-0.0776721\pi\) | ||||
0.970376 | + | 0.241600i | \(0.0776721\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0000 | −0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.18421 | −0.263528 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.0005 | −1.77459 | −0.887297 | − | 0.461198i | \(-0.847420\pi\) | ||||
−0.887297 | + | 0.461198i | \(0.847420\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.37778 | −0.0696776 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.61285 | −0.384017 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 38.1847 | 1.92128 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.4291 | 1.67776 | 0.838880 | − | 0.544317i | \(-0.183211\pi\) | ||||
0.838880 | + | 0.544317i | \(0.183211\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.00000 | 0.200250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.0701 | 1.60150 | 0.800751 | − | 0.598997i | \(-0.204434\pi\) | ||||
0.800751 | + | 0.598997i | \(0.204434\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.48886 | −0.123979 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.42864 | −0.220061 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 52.5531 | 2.60496 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.3274 | 0.560104 | 0.280052 | − | 0.959985i | \(-0.409648\pi\) | ||||
0.280052 | + | 0.959985i | \(0.409648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.37778 | −0.265267 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −52.7368 | −2.58875 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.3176 | −0.552899 | −0.276450 | − | 0.961028i | \(-0.589158\pi\) | ||||
−0.276450 | + | 0.961028i | \(0.589158\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.580728 | 0.0283030 | 0.0141515 | − | 0.999900i | \(-0.495495\pi\) | ||||
0.0141515 | + | 0.999900i | \(0.495495\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.24443 | −0.254993 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.1334 | 0.976611 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.83500 | 0.0888021 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.6128 | 0.560674 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.3497 | −1.55823 | −0.779115 | − | 0.626881i | \(-0.784331\pi\) | ||||
−0.779115 | + | 0.626881i | \(0.784331\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.61285 | 0.269736 | 0.134868 | − | 0.990864i | \(-0.456939\pi\) | ||||
0.134868 | + | 0.990864i | \(0.456939\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.34614 | 0.160435 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.42864 | −0.307524 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4889 | −0.500606 | −0.250303 | − | 0.968168i | \(-0.580530\pi\) | ||||
−0.250303 | + | 0.968168i | \(0.580530\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.61285 | −0.314898 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.9403 | −0.994901 | −0.497451 | − | 0.867492i | \(-0.665730\pi\) | ||||
−0.497451 | + | 0.867492i | \(0.665730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.6128 | −1.30897 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.2859 | 0.628402 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.87601 | −0.230113 | −0.115057 | − | 0.993359i | \(-0.536705\pi\) | ||||
−0.115057 | + | 0.993359i | \(0.536705\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −55.8163 | −2.62829 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.48886 | −0.116937 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.51114 | −0.258366 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.8573 | 1.06922 | 0.534609 | − | 0.845099i | \(-0.320459\pi\) | ||||
0.534609 | + | 0.845099i | \(0.320459\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.37778 | 0.0643095 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.5941 | 1.09889 | 0.549444 | − | 0.835531i | \(-0.314840\pi\) | ||||
0.549444 | + | 0.835531i | \(0.314840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.4889 | 0.487459 | 0.243729 | − | 0.969843i | \(-0.421629\pi\) | ||||
0.243729 | + | 0.969843i | \(0.421629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.51114 | 0.255573 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.0509 | −0.696471 | −0.348235 | − | 0.937407i | \(-0.613219\pi\) | ||||
−0.348235 | + | 0.937407i | \(0.613219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.22570 | 0.148949 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.1526 | −0.513883 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.1017 | −1.38408 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 93.9407 | 4.31030 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0415 | 0.551342 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.7146 | −1.54046 | −0.770229 | − | 0.637768i | \(-0.779858\pi\) | ||||
−0.770229 | + | 0.637768i | \(0.779858\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1017 | 0.825367 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.622216 | −0.0283118 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.6539 | 0.574582 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.2034 | −0.552990 | −0.276495 | − | 0.961015i | \(-0.589173\pi\) | ||||
−0.276495 | + | 0.961015i | \(0.589173\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.85728 | −0.400540 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.75557 | −0.304875 | −0.152437 | − | 0.988313i | \(-0.548712\pi\) | ||||
−0.152437 | + | 0.988313i | \(0.548712\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.04101 | −0.0468848 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −25.7146 | −1.15578 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.79658 | 0.170300 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.5941 | 1.68294 | 0.841472 | − | 0.540301i | \(-0.181690\pi\) | ||||
0.841472 | + | 0.540301i | \(0.181690\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.89829 | 0.0848093 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.59057 | −0.383035 | −0.191517 | − | 0.981489i | \(-0.561341\pi\) | ||||
−0.191517 | + | 0.981489i | \(0.561341\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −69.5941 | −3.09690 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.77784 | −0.167450 | −0.0837250 | − | 0.996489i | \(-0.526682\pi\) | ||||
−0.0837250 | + | 0.996489i | \(0.526682\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.24443 | 0.0550504 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.42864 | 0.283831 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.2667 | −1.06932 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.4514 | −1.33925 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.7556 | −0.735488 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.8256 | 1.35050 | 0.675248 | − | 0.737591i | \(-0.264037\pi\) | ||||
0.675248 | + | 0.737591i | \(0.264037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.89877 | 0.301662 | 0.150831 | − | 0.988560i | \(-0.451805\pi\) | ||||
0.150831 | + | 0.988560i | \(0.451805\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.09234 | 0.396822 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.71456 | −0.0746873 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8573 | −0.557958 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.2257 | −0.832757 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.30772 | 0.0565375 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.9590 | −0.818141 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −38.3970 | −1.65388 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.5906 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728426\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728426\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.70471 | 0.0731563 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 41.2641 | 1.76756 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.3461 | −1.16924 | −0.584618 | − | 0.811308i | \(-0.698756\pi\) | ||||
−0.584618 | + | 0.811308i | \(0.698756\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.94914 | 0.125866 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.85728 | −0.206927 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.36488 | −0.228138 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −40.0830 | −1.70143 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.1432 | 1.44669 | 0.723347 | − | 0.690485i | \(-0.242603\pi\) | ||||
0.723347 | + | 0.690485i | \(0.242603\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.3684 | −0.438537 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.0509 | 1.30864 | 0.654319 | − | 0.756219i | \(-0.272955\pi\) | ||||
0.654319 | + | 0.756219i | \(0.272955\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 50.8385 | 2.13879 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.622216 | 0.0261306 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.8479 | −0.915912 | −0.457956 | − | 0.888975i | \(-0.651418\pi\) | ||||
−0.457956 | + | 0.888975i | \(0.651418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1619 | 0.760053 | 0.380027 | − | 0.924976i | \(-0.375915\pi\) | ||||
0.380027 | + | 0.924976i | \(0.375915\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.3684 | −0.433147 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.6128 | −0.609398 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.3274 | −1.63722 | −0.818611 | − | 0.574349i | \(-0.805255\pi\) | ||||
−0.818611 | + | 0.574349i | \(0.805255\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.61285 | 0.0670277 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.40943 | 0.307395 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 69.9180 | 2.89571 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.85728 | −0.366203 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.8385 | −1.60304 | −0.801519 | − | 0.597969i | \(-0.795975\pi\) | ||||
−0.801519 | + | 0.597969i | \(0.795975\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.34614 | 0.219911 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.6128 | 1.21605 | 0.608027 | − | 0.793916i | \(-0.291961\pi\) | ||||
0.608027 | + | 0.793916i | \(0.291961\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.79658 | −0.155645 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.3590 | −0.874168 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.0000 | −1.30748 | −0.653742 | − | 0.756717i | \(-0.726802\pi\) | ||||
−0.653742 | + | 0.756717i | \(0.726802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.672594 | 0.0274357 | 0.0137178 | − | 0.999906i | \(-0.495633\pi\) | ||||
0.0137178 | + | 0.999906i | \(0.495633\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.18421 | 0.211117 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −100.595 | −4.08975 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0000 | −0.974130 | −0.487065 | − | 0.873366i | \(-0.661933\pi\) | ||||
−0.487065 | + | 0.873366i | \(0.661933\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.470127 | −0.0190505 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.4889 | −0.424334 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.94914 | 0.119115 | 0.0595574 | − | 0.998225i | \(-0.481031\pi\) | ||||
0.0595574 | + | 0.998225i | \(0.481031\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 42.5718 | 1.71666 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.1753 | 1.57714 | 0.788569 | − | 0.614946i | \(-0.210822\pi\) | ||||
0.788569 | + | 0.614946i | \(0.210822\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.3689 | −0.939275 | −0.469638 | − | 0.882859i | \(-0.655615\pi\) | ||||
−0.469638 | + | 0.882859i | \(0.655615\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.87955 | 0.155431 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 115.471 | 4.61884 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 37.3274 | 1.49071 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.4701 | 0.497217 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.7239 | −0.904625 | −0.452313 | − | 0.891859i | \(-0.649401\pi\) | ||||
−0.452313 | + | 0.891859i | \(0.649401\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.36842 | −0.253122 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −37.5111 | −1.48858 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.2257 | −0.524021 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.10171 | 0.241380 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.5812 | 1.80035 | 0.900175 | − | 0.435529i | \(-0.143439\pi\) | ||||
0.900175 | + | 0.435529i | \(0.143439\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.8381 | 0.545720 | 0.272860 | − | 0.962054i | \(-0.412030\pi\) | ||||
0.272860 | + | 0.962054i | \(0.412030\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.9590 | 0.904009 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.5718 | 0.730134 | 0.365067 | − | 0.930981i | \(-0.381046\pi\) | ||||
0.365067 | + | 0.930981i | \(0.381046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −74.6548 | −2.93046 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.774305 | −0.0303474 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.0000 | −0.391330 | −0.195665 | − | 0.980671i | \(-0.562687\pi\) | ||||
−0.195665 | + | 0.980671i | \(0.562687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.7146 | 1.31734 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.2988 | −1.29714 | −0.648569 | − | 0.761156i | \(-0.724632\pi\) | ||||
−0.648569 | + | 0.761156i | \(0.724632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.68598 | 0.298950 | 0.149475 | − | 0.988766i | \(-0.452242\pi\) | ||||
0.149475 | + | 0.988766i | \(0.452242\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.75557 | 0.107017 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.7146 | −0.686941 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.755569 | 0.0292557 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.22570 | −0.279362 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.1240 | 0.661064 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.3274 | −1.20758 | −0.603791 | − | 0.797142i | \(-0.706344\pi\) | ||||
−0.603791 | + | 0.797142i | \(0.706344\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.6128 | 0.562449 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.89523 | −0.149706 | −0.0748529 | − | 0.997195i | \(-0.523849\pi\) | ||||
−0.0748529 | + | 0.997195i | \(0.523849\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.77784 | −0.0682274 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.0509 | 0.576750 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.8760 | −0.416159 | −0.208080 | − | 0.978112i | \(-0.566721\pi\) | ||||
−0.208080 | + | 0.978112i | \(0.566721\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.8163 | 0.909973 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.29529 | −0.240180 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.0830 | 0.917488 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.5718 | 0.402172 | 0.201086 | − | 0.979574i | \(-0.435553\pi\) | ||||
0.201086 | + | 0.979574i | \(0.435553\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.61285 | 0.137241 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.7146 | 0.671951 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.2444 | −0.501669 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.7146 | 1.04826 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.2065 | 0.687649 | 0.343825 | − | 0.939034i | \(-0.388277\pi\) | ||||
0.343825 | + | 0.939034i | \(0.388277\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.1847 | 2.19448 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.2257 | 0.874730 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.77784 | 0.367734 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.1338 | −0.643474 | −0.321737 | − | 0.946829i | \(-0.604267\pi\) | ||||
−0.321737 | + | 0.946829i | \(0.604267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.62222 | −0.323358 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.24443 | 0.0466043 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −51.4291 | −1.92334 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.2257 | 0.568614 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.34614 | 0.124790 | 0.0623950 | − | 0.998052i | \(-0.480126\pi\) | ||||
0.0623950 | + | 0.998052i | \(0.480126\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.40943 | 0.126974 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.14272 | 0.191260 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.0410 | −0.410053 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.09234 | −0.337216 | −0.168608 | − | 0.985683i | \(-0.553927\pi\) | ||||
−0.168608 | + | 0.985683i | \(0.553927\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.14272 | −0.264183 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.3595 | −1.49071 | −0.745357 | − | 0.666666i | \(-0.767721\pi\) | ||||
−0.745357 | + | 0.666666i | \(0.767721\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.2859 | 1.08023 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.1017 | 1.10881 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.9180 | 1.54198 | 0.770989 | − | 0.636849i | \(-0.219762\pi\) | ||||
0.770989 | + | 0.636849i | \(0.219762\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.8573 | 0.472324 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.9590 | 1.28252 | 0.641260 | − | 0.767323i | \(-0.278412\pi\) | ||||
0.641260 | + | 0.767323i | \(0.278412\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −58.8385 | −2.15568 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.9081 | 0.435696 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.183732 | −0.00671341 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.7462 | 0.939492 | 0.469746 | − | 0.882802i | \(-0.344345\pi\) | ||||
0.469746 | + | 0.882802i | \(0.344345\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.4380 | 0.416824 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.0223 | 0.401142 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.9304 | 1.48764 | 0.743821 | − | 0.668379i | \(-0.233012\pi\) | ||||
0.743821 | + | 0.668379i | \(0.233012\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.80642 | −0.210760 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.26671 | −0.0821680 | −0.0410840 | − | 0.999156i | \(-0.513081\pi\) | ||||
−0.0410840 | + | 0.999156i | \(0.513081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.79753 | −0.209885 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.10171 | −0.220608 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.7146 | −0.928499 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.6128 | −1.50060 | −0.750299 | − | 0.661099i | \(-0.770090\pi\) | ||||
−0.750299 | + | 0.661099i | \(0.770090\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.10171 | −0.147719 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.44738 | 0.0880260 | 0.0440130 | − | 0.999031i | \(-0.485986\pi\) | ||||
0.0440130 | + | 0.999031i | \(0.485986\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.1847 | −0.653213 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.63158 | 0.202032 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −61.7975 | −2.21413 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.4291 | 1.26775 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.755569 | −0.0270018 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 49.3907 | 1.76283 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.4099 | −1.29787 | −0.648936 | − | 0.760843i | \(-0.724786\pi\) | ||||
−0.648936 | + | 0.760843i | \(0.724786\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.4701 | −0.871160 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.14272 | −0.253966 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.89829 | 0.209454 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −53.3274 | −1.89133 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.428639 | 0.0151832 | 0.00759159 | − | 0.999971i | \(-0.497583\pi\) | ||||
0.00759159 | + | 0.999971i | \(0.497583\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.22570 | −0.255627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.23506 | 0.220305 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.6128 | 0.409808 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.75557 | 0.0971210 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.8573 | −0.523001 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.9813 | −1.26503 | −0.632517 | − | 0.774547i | \(-0.717978\pi\) | ||||
−0.632517 | + | 0.774547i | \(0.717978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.12045 | 0.144688 | 0.0723442 | − | 0.997380i | \(-0.476952\pi\) | ||||
0.0723442 | + | 0.997380i | \(0.476952\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.2444 | −0.604789 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.2257 | 1.37402 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.3274 | −1.16598 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.24443 | 0.0434839 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.4514 | −0.853359 | −0.426680 | − | 0.904403i | \(-0.640317\pi\) | ||||
−0.426680 | + | 0.904403i | \(0.640317\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2667 | −0.427590 | −0.213795 | − | 0.976878i | \(-0.568583\pi\) | ||||
−0.213795 | + | 0.976878i | \(0.568583\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 84.8484 | 2.95404 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.5022 | −0.747706 | −0.373853 | − | 0.927488i | \(-0.621964\pi\) | ||||
−0.373853 | + | 0.927488i | \(0.621964\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.38715 | −0.0829092 | −0.0414546 | − | 0.999140i | \(-0.513199\pi\) | ||||
−0.0414546 | + | 0.999140i | \(0.513199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5906 | 0.506141 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.11108 | −0.315680 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.40684 | −0.290931 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.24443 | −0.0430138 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.24443 | 0.0429625 | 0.0214813 | − | 0.999769i | \(-0.493162\pi\) | ||||
0.0214813 | + | 0.999769i | \(0.493162\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4291 | −0.980314 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.00937 | 0.241415 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39.8578 | 1.37115 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.1334 | 0.485628 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.08250 | 0.243071 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.05086 | −0.310259 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.0000 | 1.30110 | 0.650548 | − | 0.759465i | \(-0.274539\pi\) | ||||
0.650548 | + | 0.759465i | \(0.274539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −28.4701 | −0.973658 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.98126 | −0.203841 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.8573 | 1.39080 | 0.695399 | − | 0.718624i | \(-0.255228\pi\) | ||||
0.695399 | + | 0.718624i | \(0.255228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 74.2044 | 2.52302 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.1017 | −0.512881 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −50.0642 | −1.69831 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.3684 | 0.351320 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.85728 | −0.0967042 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.4889 | −0.895487 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.89829 | 0.266706 | 0.133353 | − | 0.991069i | \(-0.457426\pi\) | ||||
0.133353 | + | 0.991069i | \(0.457426\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.67307 | −0.191348 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.9906 | −1.65054 | −0.825268 | − | 0.564741i | \(-0.808976\pi\) | ||||
−0.825268 | + | 0.564741i | \(0.808976\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.85728 | 0.298071 | 0.149036 | − | 0.988832i | \(-0.452383\pi\) | ||||
0.149036 | + | 0.988832i | \(0.452383\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 56.9403 | 1.91403 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.1624 | 1.71787 | 0.858933 | − | 0.512088i | \(-0.171128\pi\) | ||||
0.858933 | + | 0.512088i | \(0.171128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.27025 | 0.176758 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.80642 | 0.194523 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.7146 | −1.12821 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 83.9625 | 2.80656 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.940253 | 0.0313592 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.5906 | 0.552712 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.22570 | −0.107344 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.54956 | −0.250956 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0228 | 0.797662 | 0.398831 | − | 0.917024i | \(-0.369416\pi\) | ||||
0.398831 | + | 0.917024i | \(0.369416\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.7146 | 0.521219 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.8385 | −1.15425 | −0.577126 | − | 0.816655i | \(-0.695826\pi\) | ||||
−0.577126 | + | 0.816655i | \(0.695826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 69.1437 | 2.28832 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.0607 | −0.431773 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.73683 | −0.156424 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.6035 | 1.27341 | 0.636706 | − | 0.771107i | \(-0.280297\pi\) | ||||
0.636706 | + | 0.771107i | \(0.280297\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.0607 | −0.957583 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.2034 | 0.401680 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 132.259 | 4.34864 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.47949 | 0.179970 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.8163 | −0.978240 | −0.489120 | − | 0.872216i | \(-0.662682\pi\) | ||||
−0.489120 | + | 0.872216i | \(0.662682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.5116 | −1.39326 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.3684 | 0.470401 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.4291 | −1.15866 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.5111 | −1.16010 | −0.580049 | − | 0.814581i | \(-0.696967\pi\) | ||||
−0.580049 | + | 0.814581i | \(0.696967\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.8163 | −0.973017 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.2029 | −0.691196 | −0.345598 | − | 0.938383i | \(-0.612324\pi\) | ||||
−0.345598 | + | 0.938383i | \(0.612324\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.61285 | 0.313037 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.75557 | −0.0896387 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.2070 | −1.20906 | −0.604532 | − | 0.796581i | \(-0.706640\pi\) | ||||
−0.604532 | + | 0.796581i | \(0.706640\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.7556 | 0.673045 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.2958 | 1.27291 | 0.636457 | − | 0.771312i | \(-0.280399\pi\) | ||||
0.636457 | + | 0.771312i | \(0.280399\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.9180 | 1.48587 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.38715 | −0.141816 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.34614 | −0.108053 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4514 | −0.950045 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.295286 | −0.00951547 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.14272 | −0.229932 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.9367 | −0.769753 | −0.384876 | − | 0.922968i | \(-0.625756\pi\) | ||||
−0.384876 | + | 0.922968i | \(0.625756\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.85728 | 0.284537 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.8448 | −1.66378 | −0.831890 | − | 0.554940i | \(-0.812741\pi\) | ||||
−0.831890 | + | 0.554940i | \(0.812741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.48886 | −0.0797893 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29.2257 | 0.935971 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.1111 | 0.931346 | 0.465673 | − | 0.884957i | \(-0.345812\pi\) | ||||
0.465673 | + | 0.884957i | \(0.345812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.2034 | 1.15707 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.31756 | −0.297487 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.36488 | 0.0435328 | 0.0217664 | − | 0.999763i | \(-0.493071\pi\) | ||||
0.0217664 | + | 0.999763i | \(0.493071\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.6761 | −0.754384 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.26317 | −0.103868 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.18421 | 0.164848 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.3881 | 1.21944 | 0.609719 | − | 0.792618i | \(-0.291282\pi\) | ||||
0.609719 | + | 0.792618i | \(0.291282\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.85728 | −0.281077 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 94.5915 | 2.99875 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.3051 | 0.389707 | 0.194854 | − | 0.980832i | \(-0.437577\pi\) | ||||
0.194854 | + | 0.980832i | \(0.437577\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.05086 | 0.286356 |
(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 | 552.2.a.g.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 1656.2.a.n.1.3 | 3 | |||
4.3 | odd | 2 | 1104.2.a.o.1.1 | 3 | |||
8.3 | odd | 2 | 4416.2.a.bs.1.3 | 3 | |||
8.5 | even | 2 | 4416.2.a.bp.1.3 | 3 | |||
12.11 | even | 2 | 3312.2.a.bf.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.a.g.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1104.2.a.o.1.1 | 3 | 4.3 | odd | 2 | |||
1656.2.a.n.1.3 | 3 | 3.2 | odd | 2 | |||
3312.2.a.bf.1.3 | 3 | 12.11 | even | 2 | |||
4416.2.a.bp.1.3 | 3 | 8.5 | even | 2 | |||
4416.2.a.bs.1.3 | 3 | 8.3 | odd | 2 |