Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,2,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.8202346151\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.68772992.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} + 17x^{2} - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.854088\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.15704 | −1.82272 | −0.911360 | − | 0.411610i | \(-0.864967\pi\) | ||||
−0.911360 | + | 0.411610i | \(0.864967\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.42586 | −0.637663 | −0.318832 | − | 0.947811i | \(-0.603290\pi\) | ||||
−0.318832 | + | 0.947811i | \(0.603290\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.70818 | −0.645630 | −0.322815 | − | 0.946462i | \(-0.604629\pi\) | ||||
−0.322815 | + | 0.946462i | \(0.604629\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.96693 | 2.32231 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.15704 | −0.951885 | −0.475942 | − | 0.879477i | \(-0.657893\pi\) | ||||
−0.475942 | + | 0.879477i | \(0.657893\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.42586 | −0.395462 | −0.197731 | − | 0.980256i | \(-0.563357\pi\) | ||||
−0.197731 | + | 0.980256i | \(0.563357\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.50150 | 1.16228 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.39279 | −0.822871 | −0.411436 | − | 0.911439i | \(-0.634973\pi\) | ||||
−0.411436 | + | 0.911439i | \(0.634973\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.363721 | −0.0834433 | −0.0417216 | − | 0.999129i | \(-0.513284\pi\) | ||||
−0.0417216 | + | 0.999129i | \(0.513284\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.39279 | 1.17680 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.29482 | −1.52108 | −0.760538 | − | 0.649294i | \(-0.775065\pi\) | ||||
−0.760538 | + | 0.649294i | \(0.775065\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.96693 | −0.593385 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −12.5238 | −2.41020 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.44887 | −0.260224 | −0.130112 | − | 0.991499i | \(-0.541534\pi\) | ||||
−0.130112 | + | 0.991499i | \(0.541534\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.96693 | 1.73502 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.43562 | 0.411694 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.851718 | 0.140021 | 0.0700107 | − | 0.997546i | \(-0.477697\pi\) | ||||
0.0700107 | + | 0.997546i | \(0.477697\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.50150 | 0.720817 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.54107 | 1.33389 | 0.666945 | − | 0.745107i | \(-0.267601\pi\) | ||||
0.666945 | + | 0.745107i | \(0.267601\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.57340 | −1.00243 | −0.501217 | − | 0.865322i | \(-0.667114\pi\) | ||||
−0.501217 | + | 0.865322i | \(0.667114\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.93385 | −1.48085 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.1793 | −1.63067 | −0.815335 | − | 0.578990i | \(-0.803447\pi\) | ||||
−0.815335 | + | 0.578990i | \(0.803447\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.08214 | −0.583162 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.7112 | 1.49986 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.3597 | −1.83510 | −0.917549 | − | 0.397623i | \(-0.869835\pi\) | ||||
−0.917549 | + | 0.397623i | \(0.869835\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.50150 | 0.606982 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.14828 | 0.152094 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.7112 | 1.39448 | 0.697238 | − | 0.716840i | \(-0.254412\pi\) | ||||
0.697238 | + | 0.716840i | \(0.254412\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.39279 | −0.434402 | −0.217201 | − | 0.976127i | \(-0.569693\pi\) | ||||
−0.217201 | + | 0.976127i | \(0.569693\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.9007 | −1.49935 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.03307 | 0.252172 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.6282 | 1.54278 | 0.771389 | − | 0.636364i | \(-0.219562\pi\) | ||||
0.771389 | + | 0.636364i | \(0.219562\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 23.0301 | 2.77250 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.58665 | 0.663013 | 0.331506 | − | 0.943453i | \(-0.392443\pi\) | ||||
0.331506 | + | 0.943453i | \(0.392443\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.9339 | 1.63083 | 0.815417 | − | 0.578874i | \(-0.196508\pi\) | ||||
0.815417 | + | 0.578874i | \(0.196508\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.36672 | 1.08158 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.39279 | 0.614565 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.86522 | −0.547380 | −0.273690 | − | 0.961818i | \(-0.588244\pi\) | ||||
−0.273690 | + | 0.961818i | \(0.588244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 18.6373 | 2.07081 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.33335 | 0.585412 | 0.292706 | − | 0.956203i | \(-0.405444\pi\) | ||||
0.292706 | + | 0.956203i | \(0.405444\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.83763 | 0.524715 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.15704 | 0.338471 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.3266 | −1.62462 | −0.812310 | − | 0.583226i | \(-0.801790\pi\) | ||||
−0.812310 | + | 0.583226i | \(0.801790\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.43562 | 0.255322 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.57414 | 0.474316 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.518614 | 0.0532087 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.2445 | 1.44631 | 0.723155 | − | 0.690686i | \(-0.242691\pi\) | ||||
0.723155 | + | 0.690686i | \(0.242691\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −21.9949 | −2.21057 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.851718 | 0.0847491 | 0.0423745 | − | 0.999102i | \(-0.486508\pi\) | ||||
0.0423745 | + | 0.999102i | \(0.486508\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.31409 | 0.622146 | 0.311073 | − | 0.950386i | \(-0.399312\pi\) | ||||
0.311073 | + | 0.950386i | \(0.399312\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.68935 | −0.750404 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.12453 | −0.495407 | −0.247703 | − | 0.968836i | \(-0.579676\pi\) | ||||
−0.247703 | + | 0.968836i | \(0.579676\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.6563 | 1.88273 | 0.941365 | − | 0.337390i | \(-0.109544\pi\) | ||||
0.941365 | + | 0.337390i | \(0.109544\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.68891 | −0.255220 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.4014 | 0.969934 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.93385 | −0.918385 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.79547 | 0.531270 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.03307 | −0.0939157 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −26.9645 | −2.43131 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3597 | 1.01604 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.46898 | −0.574029 | −0.287015 | − | 0.957926i | \(-0.592663\pi\) | ||||
−0.287015 | + | 0.957926i | \(0.592663\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.7525 | 1.82716 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9534 | 1.30648 | 0.653241 | − | 0.757150i | \(-0.273409\pi\) | ||||
0.653241 | + | 0.757150i | \(0.273409\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.621299 | 0.0538735 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.8571 | 1.53690 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.14828 | 0.268976 | 0.134488 | − | 0.990915i | \(-0.457061\pi\) | ||||
0.134488 | + | 0.990915i | \(0.457061\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.33335 | 0.452369 | 0.226185 | − | 0.974084i | \(-0.427375\pi\) | ||||
0.226185 | + | 0.974084i | \(0.427375\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 35.2936 | 2.97225 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.50150 | 0.376434 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.42586 | 0.118411 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.8875 | 1.06294 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.2114 | −1.65578 | −0.827892 | − | 0.560887i | \(-0.810460\pi\) | ||||
−0.827892 | + | 0.560887i | \(0.810460\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.43562 | 0.198208 | 0.0991039 | − | 0.995077i | \(-0.468402\pi\) | ||||
0.0991039 | + | 0.995077i | \(0.468402\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −23.6373 | −1.91096 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.06588 | 0.165936 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.32664 | −0.584729 | −0.292365 | − | 0.956307i | \(-0.594442\pi\) | ||||
−0.292365 | + | 0.956307i | \(0.594442\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 42.1772 | 3.34487 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.4608 | 0.982052 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.8875 | −1.00943 | −0.504713 | − | 0.863287i | \(-0.668402\pi\) | ||||
−0.504713 | + | 0.863287i | \(0.668402\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.2114 | −1.10636 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.6312 | 1.67387 | 0.836935 | − | 0.547302i | \(-0.184345\pi\) | ||||
0.836935 | + | 0.547302i | \(0.184345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9669 | −0.843610 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.53402 | −0.193781 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.0821 | −0.842559 | −0.421280 | − | 0.906931i | \(-0.638419\pi\) | ||||
−0.421280 | + | 0.906931i | \(0.638419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.06803 | 0.383107 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −33.8156 | −2.54174 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.04153 | 0.526309 | 0.263154 | − | 0.964754i | \(-0.415237\pi\) | ||||
0.263154 | + | 0.964754i | \(0.415237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.2114 | 1.20499 | 0.602493 | − | 0.798124i | \(-0.294174\pi\) | ||||
0.602493 | + | 0.798124i | \(0.294174\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.7112 | 0.791793 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.21443 | −0.0892866 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.7112 | 0.783279 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21.3928 | 1.55610 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.7193 | −0.992696 | −0.496348 | − | 0.868124i | \(-0.665326\pi\) | ||||
−0.496348 | + | 0.868124i | \(0.665326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.62320 | −0.692693 | −0.346347 | − | 0.938107i | \(-0.612578\pi\) | ||||
−0.346347 | + | 0.938107i | \(0.612578\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.41850 | −0.459638 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.7034 | −0.833835 | −0.416918 | − | 0.908944i | \(-0.636890\pi\) | ||||
−0.416918 | + | 0.908944i | \(0.636890\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.7142 | −1.39750 | −0.698750 | − | 0.715366i | \(-0.746260\pi\) | ||||
−0.698750 | + | 0.715366i | \(0.746260\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −39.8677 | −2.81205 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.70818 | 0.119890 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.1784 | −0.850573 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −50.8225 | −3.53241 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.14828 | 0.0794284 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2016 | 1.32189 | 0.660945 | − | 0.750434i | \(-0.270156\pi\) | ||||
0.660945 | + | 0.750434i | \(0.270156\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17.6373 | −1.20849 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.37273 | 0.639215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.47492 | 0.168009 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −43.9898 | −2.97255 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.83763 | 0.325414 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.1468 | 0.880374 | 0.440187 | − | 0.897906i | \(-0.354912\pi\) | ||||
0.440187 | + | 0.897906i | \(0.354912\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.6704 | −1.37802 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.5259 | 1.03049 | 0.515246 | − | 0.857043i | \(-0.327701\pi\) | ||||
0.515246 | + | 0.857043i | \(0.327701\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.16237 | 0.605466 | 0.302733 | − | 0.953075i | \(-0.402101\pi\) | ||||
0.302733 | + | 0.953075i | \(0.402101\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.0253 | −1.12018 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.96693 | −0.521931 | −0.260965 | − | 0.965348i | \(-0.584041\pi\) | ||||
−0.260965 | + | 0.965348i | \(0.584041\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.9401 | 1.03982 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.3597 | 0.997721 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3779 | 1.38282 | 0.691410 | − | 0.722463i | \(-0.256990\pi\) | ||||
0.691410 | + | 0.722463i | \(0.256990\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.96693 | 0.255532 | 0.127766 | − | 0.991804i | \(-0.459219\pi\) | ||||
0.127766 | + | 0.991804i | \(0.459219\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.2675 | −1.36431 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.82055 | 0.371861 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.518614 | 0.0329986 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.8376 | −1.06704 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.9585 | −1.70161 | −0.850803 | − | 0.525485i | \(-0.823884\pi\) | ||||
−0.850803 | + | 0.525485i | \(0.823884\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.0301 | 1.44789 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.2726 | −0.956409 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.3077 | 1.70340 | 0.851702 | − | 0.524026i | \(-0.175571\pi\) | ||||
0.851702 | + | 0.524026i | \(0.175571\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.45488 | −0.0904020 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.96693 | −0.431242 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.38383 | 0.331981 | 0.165991 | − | 0.986127i | \(-0.446918\pi\) | ||||
0.165991 | + | 0.986127i | \(0.446918\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.0491 | 1.17017 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 48.3869 | 2.96123 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.98592 | −0.486910 | −0.243455 | − | 0.969912i | \(-0.578281\pi\) | ||||
−0.243455 | + | 0.969912i | \(0.578281\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3911 | −1.23867 | −0.619337 | − | 0.785126i | \(-0.712598\pi\) | ||||
−0.619337 | + | 0.785126i | \(0.712598\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.68935 | −0.465381 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.36672 | 0.564834 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.8677 | 1.07357 | 0.536783 | − | 0.843720i | \(-0.319639\pi\) | ||||
0.536783 | + | 0.843720i | \(0.319639\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.0942 | −0.604322 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.522079 | 0.0311446 | 0.0155723 | − | 0.999879i | \(-0.495043\pi\) | ||||
0.0155723 | + | 0.999879i | \(0.495043\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.56738 | −0.390390 | −0.195195 | − | 0.980764i | \(-0.562534\pi\) | ||||
−0.195195 | + | 0.980764i | \(0.562534\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.63729 | −0.0969846 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.5896 | −0.861199 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.48901 | −0.322883 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −44.9705 | −2.63622 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.7856 | −1.91535 | −0.957677 | − | 0.287846i | \(-0.907061\pi\) | ||||
−0.957677 | + | 0.287846i | \(0.907061\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.2726 | −0.889206 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 39.5381 | 2.29423 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.4014 | 0.601528 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.2285 | 0.647201 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.68891 | −0.154474 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.83763 | 0.277002 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.05478 | 0.345565 | 0.172782 | − | 0.984960i | \(-0.444724\pi\) | ||||
0.172782 | + | 0.984960i | \(0.444724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.9339 | −1.13400 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.88664 | −0.390505 | −0.195253 | − | 0.980753i | \(-0.562553\pi\) | ||||
−0.195253 | + | 0.980753i | \(0.562553\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.26349 | −0.127940 | −0.0639701 | − | 0.997952i | \(-0.520376\pi\) | ||||
−0.0639701 | + | 0.997952i | \(0.520376\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.9688 | 0.956082 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.3928 | −1.08921 | −0.544604 | − | 0.838694i | \(-0.683320\pi\) | ||||
−0.544604 | + | 0.838694i | \(0.683320\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.15704 | 0.176761 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.1784 | 0.902988 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.23403 | 0.0686631 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.23042 | 0.234661 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −62.0557 | −3.43169 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.0962 | 1.05281 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.8948 | −1.53324 | −0.766618 | − | 0.642104i | \(-0.778062\pi\) | ||||
−0.766618 | + | 0.642104i | \(0.778062\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.93385 | 0.325173 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.0060 | −0.983773 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.0962 | −0.931290 | −0.465645 | − | 0.884971i | \(-0.654178\pi\) | ||||
−0.465645 | + | 0.884971i | \(0.654178\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.31409 | −0.342934 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.57414 | 0.247704 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.9302 | 1.02214 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −32.8376 | −1.76792 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.8370 | 0.689126 | 0.344563 | − | 0.938763i | \(-0.388027\pi\) | ||||
0.344563 | + | 0.938763i | \(0.388027\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.12929 | 0.167507 | 0.0837536 | − | 0.996486i | \(-0.473309\pi\) | ||||
0.0837536 | + | 0.996486i | \(0.473309\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.8571 | 0.953142 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.2746 | −1.34523 | −0.672615 | − | 0.739993i | \(-0.734829\pi\) | ||||
−0.672615 | + | 0.739993i | \(0.734829\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.96577 | −0.422779 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.2966 | −0.968357 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.6030 | 1.56238 | 0.781192 | − | 0.624291i | \(-0.214612\pi\) | ||||
0.781192 | + | 0.624291i | \(0.214612\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8677 | −0.993037 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.26146 | 0.171182 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.8677 | −1.03992 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.4142 | 1.79641 | 0.898204 | − | 0.439578i | \(-0.144872\pi\) | ||||
0.898204 | + | 0.439578i | \(0.144872\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 59.5050 | 3.09771 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.8207 | 1.18479 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.35971 | −0.277515 | −0.138758 | − | 0.990326i | \(-0.544311\pi\) | ||||
−0.138758 | + | 0.990326i | \(0.544311\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −35.8631 | −1.85196 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.42586 | 0.0734355 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0972 | 0.980955 | 0.490478 | − | 0.871454i | \(-0.336822\pi\) | ||||
0.490478 | + | 0.871454i | \(0.336822\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.4229 | 1.04629 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.0638 | −0.769724 | −0.384862 | − | 0.922974i | \(-0.625751\pi\) | ||||
−0.384862 | + | 0.922974i | \(0.625751\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.68935 | −0.391886 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −45.7964 | −2.32796 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.06615 | −0.104758 | −0.0523789 | − | 0.998627i | \(-0.516680\pi\) | ||||
−0.0523789 | + | 0.998627i | \(0.516680\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.7498 | 1.25165 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −47.2084 | −2.38135 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.93712 | 0.349044 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.87071 | −0.244454 | −0.122227 | − | 0.992502i | \(-0.539004\pi\) | ||||
−0.122227 | + | 0.992502i | \(0.539004\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.96147 | −0.0981962 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.56006 | −0.227718 | −0.113859 | − | 0.993497i | \(-0.536321\pi\) | ||||
−0.113859 | + | 0.993497i | \(0.536321\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.06588 | 0.102909 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −26.5741 | −1.32048 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.68891 | −0.133284 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.40687 | −0.0695652 | −0.0347826 | − | 0.999395i | \(-0.511074\pi\) | ||||
−0.0347826 | + | 0.999395i | \(0.511074\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.93927 | −0.490268 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.2966 | −0.900315 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.60461 | −0.373296 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.8376 | −0.824542 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.4266 | −1.33988 | −0.669940 | − | 0.742416i | \(-0.733680\pi\) | ||||
−0.669940 | + | 0.742416i | \(0.733680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.0962 | 1.41806 | 0.709032 | − | 0.705177i | \(-0.249132\pi\) | ||||
0.709032 | + | 0.705177i | \(0.249132\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −77.8854 | −3.78692 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.0661 | 0.488280 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.79547 | 0.280463 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.2114 | −0.686134 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.8845 | 1.05414 | 0.527069 | − | 0.849823i | \(-0.323291\pi\) | ||||
0.527069 | + | 0.849823i | \(0.323291\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.23042 | 0.395529 | 0.197764 | − | 0.980250i | \(-0.436632\pi\) | ||||
0.197764 | + | 0.980250i | \(0.436632\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.50150 | −0.215830 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.65328 | 0.126924 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.8610 | 1.56837 | 0.784184 | − | 0.620528i | \(-0.213082\pi\) | ||||
0.784184 | + | 0.620528i | \(0.213082\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −28.4399 | −1.35428 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.4763 | −1.02037 | −0.510184 | − | 0.860065i | \(-0.670423\pi\) | ||||
−0.510184 | + | 0.860065i | \(0.670423\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.8536 | 1.03596 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 63.8084 | 3.01803 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.4890 | −1.06132 | −0.530661 | − | 0.847584i | \(-0.678056\pi\) | ||||
−0.530661 | + | 0.847584i | \(0.678056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.9645 | −1.26971 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.68935 | −0.361277 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.47285 | −0.162810 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.8677 | 1.21004 | 0.605020 | − | 0.796210i | \(-0.293165\pi\) | ||||
0.605020 | + | 0.796210i | \(0.293165\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 42.4904 | 1.98328 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.296565 | −0.0138124 | −0.00690620 | − | 0.999976i | \(-0.502198\pi\) | ||||
−0.00690620 | + | 0.999976i | \(0.502198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.1956 | 0.892093 | 0.446047 | − | 0.895010i | \(-0.352832\pi\) | ||||
0.446047 | + | 0.895010i | \(0.352832\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.52208 | −0.302454 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.9512 | −0.553036 | −0.276518 | − | 0.961009i | \(-0.589181\pi\) | ||||
−0.276518 | + | 0.961009i | \(0.589181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.5711 | −0.996063 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.1305 | 1.06580 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.7525 | 0.954201 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.07913 | 0.0495140 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −93.0761 | −4.26166 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.7052 | 1.22019 | 0.610096 | − | 0.792327i | \(-0.291131\pi\) | ||||
0.610096 | + | 0.792327i | \(0.291131\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.21443 | −0.0553732 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −39.3394 | −1.79001 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.3106 | −0.922259 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.9200 | −0.494832 | −0.247416 | − | 0.968909i | \(-0.579582\pi\) | ||||
−0.247416 | + | 0.968909i | \(0.579582\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.6864 | 1.83990 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −43.5217 | −1.96410 | −0.982052 | − | 0.188608i | \(-0.939602\pi\) | ||||
−0.982052 | + | 0.188608i | \(0.939602\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.39279 | 0.152803 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 31.3616 | 1.40960 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.54297 | −0.428061 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.60591 | 0.206189 | 0.103094 | − | 0.994672i | \(-0.467126\pi\) | ||||
0.103094 | + | 0.994672i | \(0.467126\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −68.2906 | −3.05100 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.1853 | −1.30131 | −0.650654 | − | 0.759374i | \(-0.725505\pi\) | ||||
−0.650654 | + | 0.759374i | \(0.725505\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.21443 | −0.0540414 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 34.6231 | 1.53766 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.80456 | 0.212958 | 0.106479 | − | 0.994315i | \(-0.466042\pi\) | ||||
0.106479 | + | 0.994315i | \(0.466042\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.8015 | −1.05291 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.55515 | 0.201115 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.00300 | −0.396719 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.2936 | 1.55221 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34.9868 | 1.53575 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.18136 | 0.402242 | 0.201121 | − | 0.979566i | \(-0.435541\pi\) | ||||
0.201121 | + | 0.979566i | \(0.435541\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.93927 | −0.434614 | −0.217307 | − | 0.976103i | \(-0.569727\pi\) | ||||
−0.217307 | + | 0.976103i | \(0.569727\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.0000 | −0.698297 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.91570 | 0.214131 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.2144 | 1.31367 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 74.6240 | 3.23840 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.1784 | −0.527503 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.30685 | 0.315903 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.2304 | −0.959313 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.8875 | 0.555103 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.5871 | −1.57300 | −0.786502 | − | 0.617588i | \(-0.788110\pi\) | ||||
−0.786502 | + | 0.617588i | \(0.788110\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −51.1802 | −2.19635 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.0271 | −1.20055 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.253293 | −0.0108300 | −0.00541500 | − | 0.999985i | \(-0.501724\pi\) | ||||
−0.00541500 | + | 0.999985i | \(0.501724\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.6373 | −1.00881 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.363721 | 0.0154950 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.31065 | 0.353405 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.83401 | 0.162744 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.2144 | −0.475171 | −0.237585 | − | 0.971367i | \(-0.576356\pi\) | ||||
−0.237585 | + | 0.971367i | \(0.576356\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.37273 | 0.396424 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.8156 | −1.42770 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.3676 | 0.647666 | 0.323833 | − | 0.946114i | \(-0.395028\pi\) | ||||
0.323833 | + | 0.946114i | \(0.395028\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.85172 | −0.119973 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −31.8358 | −1.33698 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.1423 | 1.55709 | 0.778543 | − | 0.627592i | \(-0.215959\pi\) | ||||
0.778543 | + | 0.627592i | \(0.215959\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.68891 | 0.112527 | 0.0562637 | − | 0.998416i | \(-0.482081\pi\) | ||||
0.0562637 | + | 0.998416i | \(0.482081\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 43.3126 | 1.80941 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.6432 | 0.902584 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.2605 | 0.635303 | 0.317651 | − | 0.948208i | \(-0.397106\pi\) | ||||
0.317651 | + | 0.948208i | \(0.397106\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30.3809 | 1.26259 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.11031 | −0.377959 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.1772 | 1.74680 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.1643 | 0.585621 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.7942 | −1.02337 | −0.511684 | − | 0.859174i | \(-0.670978\pi\) | ||||
−0.511684 | + | 0.859174i | \(0.670978\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.526984 | 0.0217140 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.9483 | 1.51985 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.0491 | 1.02864 | 0.514321 | − | 0.857598i | \(-0.328044\pi\) | ||||
0.514321 | + | 0.857598i | \(0.328044\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.26353 | −0.338772 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 62.2385 | 2.54725 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.48610 | −0.101579 | −0.0507896 | − | 0.998709i | \(-0.516174\pi\) | ||||
−0.0507896 | + | 0.998709i | \(0.516174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.7555 | 0.561098 | 0.280549 | − | 0.959840i | \(-0.409483\pi\) | ||||
0.280549 | + | 0.959840i | \(0.409483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 87.9796 | 3.58281 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.47302 | 0.0598866 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.4729 | −1.52098 | −0.760489 | − | 0.649351i | \(-0.775041\pi\) | ||||
−0.760489 | + | 0.649351i | \(0.775041\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.39279 | −0.218527 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.9401 | 0.644868 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.44185 | 0.260184 | 0.130092 | − | 0.991502i | \(-0.458473\pi\) | ||||
0.130092 | + | 0.991502i | \(0.458473\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 38.4476 | 1.55036 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.4229 | −0.741676 | −0.370838 | − | 0.928697i | \(-0.620930\pi\) | ||||
−0.370838 | + | 0.928697i | \(0.620930\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.05348 | −0.363890 | −0.181945 | − | 0.983309i | \(-0.558239\pi\) | ||||
−0.181945 | + | 0.983309i | \(0.558239\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 91.3586 | 3.66610 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.1806 | 1.04890 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.36271 | −0.0545085 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.62518 | −0.144776 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.88969 | −0.115220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8742 | 0.552324 | 0.276162 | − | 0.961111i | \(-0.410937\pi\) | ||||
0.276162 | + | 0.961111i | \(0.410937\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −60.6202 | −2.40944 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.22385 | 0.366037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.82055 | 0.230619 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 38.9218 | 1.53972 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.8818 | 1.25926 | 0.629628 | − | 0.776897i | \(-0.283208\pi\) | ||||
0.629628 | + | 0.776897i | \(0.283208\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.35855 | 0.250757 | 0.125378 | − | 0.992109i | \(-0.459985\pi\) | ||||
0.125378 | + | 0.992109i | \(0.459985\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −29.5901 | −1.16511 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.6504 | −0.811853 | −0.405926 | − | 0.913906i | \(-0.633051\pi\) | ||||
−0.405926 | + | 0.913906i | \(0.633051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.8156 | −1.32738 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.81344 | −0.306233 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.2445 | 1.18356 | 0.591779 | − | 0.806100i | \(-0.298426\pi\) | ||||
0.591779 | + | 0.806100i | \(0.298426\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.3214 | −0.833096 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 97.0761 | 3.78730 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7202 | 0.768189 | 0.384095 | − | 0.923294i | \(-0.374514\pi\) | ||||
0.384095 | + | 0.923294i | \(0.374514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.0821 | 1.52012 | 0.760059 | − | 0.649854i | \(-0.225170\pi\) | ||||
0.760059 | + | 0.649854i | \(0.225170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.2726 | −0.593139 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.885885 | −0.0343531 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.29482 | 0.282457 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −41.5050 | −1.60468 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.7112 | 0.413500 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.2415 | 0.895894 | 0.447947 | − | 0.894060i | \(-0.352155\pi\) | ||||
0.447947 | + | 0.894060i | \(0.352155\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 37.1571 | 1.43018 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.67527 | −0.294984 | −0.147492 | − | 0.989063i | \(-0.547120\pi\) | ||||
−0.147492 | + | 0.989063i | \(0.547120\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.3321 | −0.933781 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −49.0160 | −1.87830 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.97780 | −0.305262 | −0.152631 | − | 0.988283i | \(-0.548775\pi\) | ||||
−0.152631 | + | 0.988283i | \(0.548775\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.48901 | −0.171516 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.9260 | −1.10360 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.0491 | 0.725711 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.3244 | 1.15359 | 0.576797 | − | 0.816888i | \(-0.304302\pi\) | ||||
0.576797 | + | 0.816888i | \(0.304302\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 37.5711 | 1.42721 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.60461 | −0.288459 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.9780 | −1.09762 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.1519 | 0.951334 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.4920 | 0.660664 | 0.330332 | − | 0.943865i | \(-0.392839\pi\) | ||||
0.330332 | + | 0.943865i | \(0.392839\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.309787 | −0.0116839 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −50.3236 | −1.89530 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.45488 | −0.0547165 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.5522 | 0.884520 | 0.442260 | − | 0.896887i | \(-0.354177\pi\) | ||||
0.442260 | + | 0.896887i | \(0.354177\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.8956 | −1.27119 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.5692 | 0.395821 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.41850 | −0.240038 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −67.4909 | −2.52049 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.9483 | −1.37794 | −0.688969 | − | 0.724791i | \(-0.741936\pi\) | ||||
−0.688969 | + | 0.724791i | \(0.741936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7856 | −0.401676 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.5238 | −0.465764 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.96693 | 0.110189 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.673508 | −0.0249790 | −0.0124895 | − | 0.999922i | \(-0.503976\pi\) | ||||
−0.0124895 | + | 0.999922i | \(0.503976\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.2304 | 0.415941 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.3021 | 0.824874 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.9339 | 0.810145 | 0.405073 | − | 0.914284i | \(-0.367246\pi\) | ||||
0.405073 | + | 0.914284i | \(0.367246\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.3757 | −0.677799 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −39.8677 | −1.46855 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.3303 | −0.527150 | −0.263575 | − | 0.964639i | \(-0.584902\pi\) | ||||
−0.263575 | + | 0.964639i | \(0.584902\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.63729 | −0.0601473 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5135 | 0.825941 | 0.412970 | − | 0.910745i | \(-0.364491\pi\) | ||||
0.412970 | + | 0.910745i | \(0.364491\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.8186 | 1.05583 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 37.1571 | 1.35951 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.75359 | 0.319849 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.43045 | 0.307631 | 0.153816 | − | 0.988100i | \(-0.450844\pi\) | ||||
0.153816 | + | 0.988100i | \(0.450844\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 85.1092 | 3.10155 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.47285 | −0.126390 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.9639 | −1.19809 | −0.599047 | − | 0.800714i | \(-0.704454\pi\) | ||||
−0.599047 | + | 0.800714i | \(0.704454\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −72.7070 | −2.63910 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.16427 | −0.295955 | −0.147977 | − | 0.988991i | \(-0.547276\pi\) | ||||
−0.147977 | + | 0.988991i | \(0.547276\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.5764 | −1.21555 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 33.7034 | 1.21855 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.2726 | −0.551462 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.77149 | −0.0999424 | −0.0499712 | − | 0.998751i | \(-0.515913\pi\) | ||||
−0.0499712 | + | 0.998751i | \(0.515913\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −86.2115 | −3.10483 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.7335 | 0.529927 | 0.264964 | − | 0.964258i | \(-0.414640\pi\) | ||||
0.264964 | + | 0.964258i | \(0.414640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.29869 | 0.154413 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.59313 | 0.164778 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.10656 | −0.111304 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.6373 | −0.631112 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.5238 | 0.447563 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.4468 | 0.372861 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.58665 | −0.199142 | −0.0995712 | − | 0.995030i | \(-0.531747\pi\) | ||||
−0.0995712 | + | 0.995030i | \(0.531747\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.9970 | −0.605109 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.41635 | −0.121471 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.83763 | 0.171789 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −60.1387 | −2.13290 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.3928 | −0.686928 | −0.343464 | − | 0.939166i | \(-0.611600\pi\) | ||||
−0.343464 | + | 0.939166i | \(0.611600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.9290 | 1.34183 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −106.780 | −3.77287 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −43.9898 | −1.55237 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.7674 | −0.626218 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.2119 | 0.887500 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.3947 | −1.34989 | −0.674943 | − | 0.737870i | \(-0.735832\pi\) | ||||
−0.674943 | + | 0.737870i | \(0.735832\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.0758 | 1.79351 | 0.896757 | − | 0.442524i | \(-0.145917\pi\) | ||||
0.896757 | + | 0.442524i | \(0.145917\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 64.3757 | 2.25775 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.3757 | 0.643674 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.39088 | 0.0836463 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.9688 | 0.592937 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.4578 | −1.51669 | −0.758345 | − | 0.651854i | \(-0.773991\pi\) | ||||
−0.758345 | + | 0.651854i | \(0.773991\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2272 | −0.391357 | −0.195678 | − | 0.980668i | \(-0.562691\pi\) | ||||
−0.195678 | + | 0.980668i | \(0.562691\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −29.5711 | −1.02954 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.3424 | −0.498733 | −0.249366 | − | 0.968409i | \(-0.580222\pi\) | ||||
−0.249366 | + | 0.968409i | \(0.580222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.8536 | 1.24525 | 0.622624 | − | 0.782521i | \(-0.286067\pi\) | ||||
0.622624 | + | 0.782521i | \(0.286067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −56.4091 | −1.95681 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.8498 | 0.479868 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.8430 | −1.06737 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.1453 | 0.627193 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.2045 | 0.421346 | 0.210673 | − | 0.977557i | \(-0.432434\pi\) | ||||
0.210673 | + | 0.977557i | \(0.432434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.64823 | −0.0567680 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.6373 | 0.537939 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.76467 | 0.0606348 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.7335 | 0.711572 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.21313 | −0.212983 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.9179 | 0.442299 | 0.221150 | − | 0.975240i | \(-0.429019\pi\) | ||||
0.221150 | + | 0.975240i | \(0.429019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.61315 | 0.123567 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.3456 | −1.07075 | −0.535373 | − | 0.844616i | \(-0.679829\pi\) | ||||
−0.535373 | + | 0.844616i | \(0.679829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.9765 | −1.53458 | −0.767290 | − | 0.641300i | \(-0.778395\pi\) | ||||
−0.767290 | + | 0.641300i | \(0.778395\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 46.0601 | 1.56973 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.7985 | 0.503746 | 0.251873 | − | 0.967760i | \(-0.418954\pi\) | ||||
0.251873 | + | 0.967760i | \(0.418954\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.8016 | 0.537269 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.3290 | 0.588525 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.3597 | 0.521043 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.0060 | −0.610110 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 99.2404 | 3.35878 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.4044 | −0.655988 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.1954 | −0.378043 | −0.189022 | − | 0.981973i | \(-0.560532\pi\) | ||||
−0.189022 | + | 0.981973i | \(0.560532\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 103.505 | 3.49115 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.3567 | 0.618453 | 0.309227 | − | 0.950988i | \(-0.399930\pi\) | ||||
0.309227 | + | 0.950988i | \(0.399930\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.6594 | −1.60387 | −0.801934 | − | 0.597413i | \(-0.796195\pi\) | ||||
−0.801934 | + | 0.597413i | \(0.796195\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 48.2163 | 1.62077 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.4622 | −1.15713 | −0.578563 | − | 0.815638i | \(-0.696386\pi\) | ||||
−0.578563 | + | 0.815638i | \(0.696386\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.0502 | 0.370610 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −58.8387 | −1.97117 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.06615 | 0.136068 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.0402 | −0.335608 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.8376 | −1.09642 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.44887 | 0.0483225 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.3266 | 1.51005 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35.4489 | −1.17967 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.1152 | −0.768376 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.8233 | 0.757835 | 0.378918 | − | 0.925430i | \(-0.376296\pi\) | ||||
0.378918 | + | 0.925430i | \(0.376296\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.93385 | 0.196814 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.8580 | −1.91692 | −0.958461 | − | 0.285225i | \(-0.907932\pi\) | ||||
−0.958461 | + | 0.285225i | \(0.907932\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.8376 | −0.557244 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.2726 | −0.504897 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.5430 | −0.843503 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.4477 | 1.79606 | 0.898031 | − | 0.439931i | \(-0.144997\pi\) | ||||
0.898031 | + | 0.439931i | \(0.144997\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.1152 | −0.629868 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.96577 | −0.262196 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.52698 | −0.0830867 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 43.9898 | 1.44481 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.6814 | 1.33471 | 0.667357 | − | 0.744738i | \(-0.267425\pi\) | ||||
0.667357 | + | 0.744738i | \(0.267425\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.48476 | 0.0486610 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.7414 | 0.711782 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.2726 | −0.499468 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.6213 | 0.608331 | 0.304166 | − | 0.952619i | \(-0.401622\pi\) | ||||
0.304166 | + | 0.952619i | \(0.401622\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.14594 | 0.233199 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.3437 | −0.402394 | −0.201197 | − | 0.979551i | \(-0.564483\pi\) | ||||
−0.201197 | + | 0.979551i | \(0.564483\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −62.3056 | −2.02895 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −30.5031 | −0.992266 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.2461 | −1.14534 | −0.572672 | − | 0.819784i | \(-0.694093\pi\) | ||||
−0.572672 | + | 0.819784i | \(0.694093\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.8677 | −0.644933 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 61.2239 | 1.98532 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.4559 | −1.05135 | −0.525675 | − | 0.850685i | \(-0.676187\pi\) | ||||
−0.525675 | + | 0.850685i | \(0.676187\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.5618 | 0.633006 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.96693 | −0.322185 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.37782 | −0.173659 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9008 | −0.932283 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −35.7022 | −1.15049 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.7213 | 0.441705 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.9097 | 0.672412 | 0.336206 | − | 0.941788i | \(-0.390856\pi\) | ||||
0.336206 | + | 0.941788i | \(0.390856\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.89588 | −0.125154 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.88533 | 0.317235 | 0.158618 | − | 0.987340i | \(-0.449296\pi\) | ||||
0.158618 | + | 0.987340i | \(0.449296\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.11031 | −0.292063 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.3556 | −0.427722 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.2795 | 0.488834 | 0.244417 | − | 0.969670i | \(-0.421403\pi\) | ||||
0.244417 | + | 0.969670i | \(0.421403\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.3869 | 1.54645 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 136.944 | 4.37228 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.9157 | 1.24122 | 0.620610 | − | 0.784120i | \(-0.286885\pi\) | ||||
0.620610 | + | 0.784120i | \(0.286885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.6874 | 0.531706 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −60.2876 | −1.91898 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.9517 | 1.52478 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.7973 | −1.58186 | −0.790932 | − | 0.611905i | \(-0.790404\pi\) | ||||
−0.790932 | + | 0.611905i | \(0.790404\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 88.0651 | 2.79466 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.1096 | 0.891135 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.8235 | 0.659488 | 0.329744 | − | 0.944070i | \(-0.393037\pi\) | ||||
0.329744 | + | 0.944070i | \(0.393037\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.6667 | −0.337480 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1856.2.a.bc.1.1 | 6 | ||
4.3 | odd | 2 | inner | 1856.2.a.bc.1.6 | 6 | ||
8.3 | odd | 2 | 928.2.a.i.1.1 | ✓ | 6 | ||
8.5 | even | 2 | 928.2.a.i.1.6 | yes | 6 | ||
24.5 | odd | 2 | 8352.2.a.bi.1.3 | 6 | |||
24.11 | even | 2 | 8352.2.a.bi.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.2.a.i.1.1 | ✓ | 6 | 8.3 | odd | 2 | ||
928.2.a.i.1.6 | yes | 6 | 8.5 | even | 2 | ||
1856.2.a.bc.1.1 | 6 | 1.1 | even | 1 | trivial | ||
1856.2.a.bc.1.6 | 6 | 4.3 | odd | 2 | inner | ||
8352.2.a.bi.1.3 | 6 | 24.5 | odd | 2 | |||
8352.2.a.bi.1.4 | 6 | 24.11 | even | 2 |