Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | 0.121745 | 0.0702893 | 0.0351447 | − | 0.999382i | \(-0.488811\pi\) | ||||
0.0351447 | + | 0.999382i | \(0.488811\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.25775 | 1.98724 | 0.993622 | − | 0.112763i | \(-0.0359702\pi\) | ||||
0.993622 | + | 0.112763i | \(0.0359702\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98518 | −0.995059 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.85102 | −0.859615 | −0.429807 | − | 0.902921i | \(-0.641419\pi\) | ||||
−0.429807 | + | 0.902921i | \(0.641419\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.22012 | −0.615751 | −0.307875 | − | 0.951427i | \(-0.599618\pi\) | ||||
−0.307875 | + | 0.951427i | \(0.599618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.121745 | 0.0314343 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.47382 | −1.81267 | −0.906333 | − | 0.422563i | \(-0.861130\pi\) | ||||
−0.906333 | + | 0.422563i | \(0.861130\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.221168 | −0.0507393 | −0.0253697 | − | 0.999678i | \(-0.508076\pi\) | ||||
−0.0253697 | + | 0.999678i | \(0.508076\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.640103 | 0.139682 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.75744 | 0.366452 | 0.183226 | − | 0.983071i | \(-0.441346\pi\) | ||||
0.183226 | + | 0.983071i | \(0.441346\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.728663 | −0.140231 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.610881 | 0.113438 | 0.0567189 | − | 0.998390i | \(-0.481936\pi\) | ||||
0.0567189 | + | 0.998390i | \(0.481936\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.10415 | −0.557522 | −0.278761 | − | 0.960361i | \(-0.589924\pi\) | ||||
−0.278761 | + | 0.960361i | \(0.589924\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.347096 | −0.0604217 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.25775 | 0.888722 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.19893 | 0.197102 | 0.0985512 | − | 0.995132i | \(-0.468579\pi\) | ||||
0.0985512 | + | 0.995132i | \(0.468579\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.270288 | −0.0432807 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.15702 | 0.649217 | 0.324608 | − | 0.945848i | \(-0.394767\pi\) | ||||
0.324608 | + | 0.945848i | \(0.394767\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.47381 | 1.13975 | 0.569873 | − | 0.821733i | \(-0.306992\pi\) | ||||
0.569873 | + | 0.821733i | \(0.306992\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.98518 | −0.445004 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.1133 | −1.47517 | −0.737587 | − | 0.675252i | \(-0.764035\pi\) | ||||
−0.737587 | + | 0.675252i | \(0.764035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.6440 | 2.94914 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.909897 | −0.127411 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.80692 | 0.935002 | 0.467501 | − | 0.883992i | \(-0.345154\pi\) | ||||
0.467501 | + | 0.883992i | \(0.345154\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.85102 | −0.384431 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0269260 | −0.00356643 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.527712 | 0.0687023 | 0.0343511 | − | 0.999410i | \(-0.489064\pi\) | ||||
0.0343511 | + | 0.999410i | \(0.489064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.958908 | −0.122776 | −0.0613878 | − | 0.998114i | \(-0.519553\pi\) | ||||
−0.0613878 | + | 0.998114i | \(0.519553\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.6953 | −1.97743 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.22012 | −0.275372 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.05123 | 0.494936 | 0.247468 | − | 0.968896i | \(-0.420401\pi\) | ||||
0.247468 | + | 0.968896i | \(0.420401\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.213959 | 0.0257577 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.66014 | −1.02777 | −0.513885 | − | 0.857859i | \(-0.671794\pi\) | ||||
−0.513885 | + | 0.857859i | \(0.671794\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3527 | −1.32874 | −0.664368 | − | 0.747406i | \(-0.731299\pi\) | ||||
−0.664368 | + | 0.747406i | \(0.731299\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.121745 | 0.0140579 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.9900 | −1.70826 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.00612 | −0.788250 | −0.394125 | − | 0.919057i | \(-0.628952\pi\) | ||||
−0.394125 | + | 0.919057i | \(0.628952\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.86682 | 0.985203 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.9997 | −1.86596 | −0.932979 | − | 0.359930i | \(-0.882801\pi\) | ||||
−0.932979 | + | 0.359930i | \(0.882801\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.47382 | −0.810649 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0743715 | 0.00797346 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.23370 | −0.978770 | −0.489385 | − | 0.872068i | \(-0.662779\pi\) | ||||
−0.489385 | + | 0.872068i | \(0.662779\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.6728 | −1.22365 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.377913 | −0.0391878 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.221168 | −0.0226913 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.669863 | 0.0680143 | 0.0340071 | − | 0.999422i | \(-0.489173\pi\) | ||||
0.0340071 | + | 0.999422i | \(0.489173\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.51080 | 0.855368 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.29915 | −0.626789 | −0.313394 | − | 0.949623i | \(-0.601466\pi\) | ||||
−0.313394 | + | 0.949623i | \(0.601466\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.756974 | 0.0745868 | 0.0372934 | − | 0.999304i | \(-0.488126\pi\) | ||||
0.0372934 | + | 0.999304i | \(0.488126\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.640103 | 0.0624677 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.1406 | −1.17367 | −0.586836 | − | 0.809705i | \(-0.699627\pi\) | ||||
−0.586836 | + | 0.809705i | \(0.699627\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.2467 | −1.46037 | −0.730183 | − | 0.683251i | \(-0.760565\pi\) | ||||
−0.730183 | + | 0.683251i | \(0.760565\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.145963 | 0.0138542 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.8551 | 1.02116 | 0.510581 | − | 0.859830i | \(-0.329430\pi\) | ||||
0.510581 | + | 0.859830i | \(0.329430\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.75744 | 0.163883 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.62746 | 0.612709 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −39.2955 | −3.60221 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.87169 | −0.261062 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.506094 | 0.0456330 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.2572 | 1.26512 | 0.632560 | − | 0.774512i | \(-0.282004\pi\) | ||||
0.632560 | + | 0.774512i | \(0.282004\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.909897 | 0.0801120 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.7172 | −1.02373 | −0.511867 | − | 0.859064i | \(-0.671046\pi\) | ||||
−0.511867 | + | 0.859064i | \(0.671046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.16284 | −0.100831 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.728663 | −0.0627134 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.69608 | 0.144906 | 0.0724530 | − | 0.997372i | \(-0.476917\pi\) | ||||
0.0724530 | + | 0.997372i | \(0.476917\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.2897 | −1.29686 | −0.648428 | − | 0.761276i | \(-0.724573\pi\) | ||||
−0.648428 | + | 0.761276i | \(0.724573\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.23124 | −0.103689 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.32961 | 0.529309 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.610881 | 0.0507309 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.51329 | 0.207293 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.12919 | −0.665969 | −0.332984 | − | 0.942932i | \(-0.608056\pi\) | ||||
−0.332984 | + | 0.942932i | \(0.608056\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.9517 | −1.29813 | −0.649067 | − | 0.760732i | \(-0.724840\pi\) | ||||
−0.649067 | + | 0.760732i | \(0.724840\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.3107 | 1.80371 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.10415 | −0.249331 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.5204 | 1.63770 | 0.818851 | − | 0.574006i | \(-0.194611\pi\) | ||||
0.818851 | + | 0.574006i | \(0.194611\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.828706 | 0.0657207 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.24021 | 0.728230 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.71269 | −0.447452 | −0.223726 | − | 0.974652i | \(-0.571822\pi\) | ||||
−0.223726 | + | 0.974652i | \(0.571822\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.347096 | −0.0270214 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.4923 | 0.966683 | 0.483341 | − | 0.875432i | \(-0.339423\pi\) | ||||
0.483341 | + | 0.875432i | \(0.339423\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.07106 | −0.620851 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.660225 | 0.0504887 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.53177 | −0.496601 | −0.248301 | − | 0.968683i | \(-0.579872\pi\) | ||||
−0.248301 | + | 0.968683i | \(0.579872\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.25775 | 0.397449 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0642461 | 0.00482904 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.8243 | −0.883791 | −0.441895 | − | 0.897067i | \(-0.645694\pi\) | ||||
−0.441895 | + | 0.897067i | \(0.645694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.73893 | 0.277912 | 0.138956 | − | 0.990299i | \(-0.455625\pi\) | ||||
0.138956 | + | 0.990299i | \(0.455625\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.116742 | −0.00862981 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.19893 | 0.0881469 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.3080 | 1.55820 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.83113 | −0.278674 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.5632 | 1.19847 | 0.599234 | − | 0.800574i | \(-0.295472\pi\) | ||||
0.599234 | + | 0.800574i | \(0.295472\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.6257 | −1.48467 | −0.742336 | − | 0.670028i | \(-0.766282\pi\) | ||||
−0.742336 | + | 0.670028i | \(0.766282\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.270288 | −0.0193557 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.39504 | 0.669369 | 0.334684 | − | 0.942330i | \(-0.391370\pi\) | ||||
0.334684 | + | 0.942330i | \(0.391370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.39683 | −0.240795 | −0.120397 | − | 0.992726i | \(-0.538417\pi\) | ||||
−0.120397 | + | 0.992726i | \(0.538417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.493215 | 0.0347887 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.21186 | 0.225428 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.15702 | 0.290339 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.24628 | −0.364642 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.630553 | 0.0436163 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.7190 | −1.63288 | −0.816441 | − | 0.577428i | \(-0.804056\pi\) | ||||
−0.816441 | + | 0.577428i | \(0.804056\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.05433 | −0.0722412 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.47381 | 0.509710 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.3208 | −1.10793 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.38213 | −0.0933959 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.5928 | 1.11615 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.4313 | 1.10032 | 0.550160 | − | 0.835059i | \(-0.314567\pi\) | ||||
0.550160 | + | 0.835059i | \(0.314567\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.98518 | −0.199012 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.9022 | −1.58645 | −0.793223 | − | 0.608932i | \(-0.791598\pi\) | ||||
−0.793223 | + | 0.608932i | \(0.791598\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.3058 | −0.879273 | −0.439636 | − | 0.898176i | \(-0.644893\pi\) | ||||
−0.439636 | + | 0.898176i | \(0.644893\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.82495 | −0.120073 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.15936 | −0.141465 | −0.0707323 | − | 0.997495i | \(-0.522534\pi\) | ||||
−0.0707323 | + | 0.997495i | \(0.522534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1133 | −0.659718 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.852957 | −0.0554055 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.8319 | −1.47688 | −0.738438 | − | 0.674322i | \(-0.764436\pi\) | ||||
−0.738438 | + | 0.674322i | \(0.764436\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.4028 | 1.50751 | 0.753753 | − | 0.657158i | \(-0.228241\pi\) | ||||
0.753753 | + | 0.657158i | \(0.228241\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.26548 | 0.209481 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.6440 | 1.31889 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.491019 | 0.0312428 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.06962 | −0.131157 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.6817 | 1.74726 | 0.873628 | − | 0.486595i | \(-0.161761\pi\) | ||||
0.873628 | + | 0.486595i | \(0.161761\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.01051 | −0.315008 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.909897 | −0.0569800 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.3831 | −1.58335 | −0.791676 | − | 0.610941i | \(-0.790791\pi\) | ||||
−0.791676 | + | 0.610941i | \(0.790791\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.30366 | 0.391690 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.82359 | −0.112877 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.6763 | −0.658330 | −0.329165 | − | 0.944272i | \(-0.606767\pi\) | ||||
−0.329165 | + | 0.944272i | \(0.606767\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.80692 | 0.418146 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.12415 | −0.0687971 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.05826 | 0.186465 | 0.0932327 | − | 0.995644i | \(-0.470280\pi\) | ||||
0.0932327 | + | 0.995644i | \(0.470280\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.21259 | 0.498879 | 0.249440 | − | 0.968390i | \(-0.419754\pi\) | ||||
0.249440 | + | 0.968390i | \(0.419754\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.42111 | −0.0860093 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.85102 | −0.171923 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1239 | −0.788540 | −0.394270 | − | 0.918995i | \(-0.629002\pi\) | ||||
−0.394270 | + | 0.918995i | \(0.629002\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.26644 | 0.554767 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.9232 | −1.48680 | −0.743398 | − | 0.668850i | \(-0.766787\pi\) | ||||
−0.743398 | + | 0.668850i | \(0.766787\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.5782 | −1.04491 | −0.522457 | − | 0.852666i | \(-0.674984\pi\) | ||||
−0.522457 | + | 0.852666i | \(0.674984\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0269260 | −0.00159496 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.8566 | 1.29015 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.8579 | 2.28576 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0815522 | 0.00478068 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.62159 | 0.269996 | 0.134998 | − | 0.990846i | \(-0.456897\pi\) | ||||
0.134998 | + | 0.990846i | \(0.456897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.527712 | 0.0307246 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.07743 | 0.120545 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.90174 | −0.225643 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39.2955 | 2.26495 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.766888 | −0.0440566 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.958908 | −0.0549069 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.7975 | 1.70063 | 0.850316 | − | 0.526273i | \(-0.176411\pi\) | ||||
0.850316 | + | 0.526273i | \(0.176411\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0921575 | 0.00524266 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.3896 | 1.15619 | 0.578095 | − | 0.815969i | \(-0.303796\pi\) | ||||
0.578095 | + | 0.815969i | \(0.303796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.0868 | 0.683186 | 0.341593 | − | 0.939848i | \(-0.389034\pi\) | ||||
0.341593 | + | 0.939848i | \(0.389034\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.6953 | −0.884332 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.2249 | −0.630452 | −0.315226 | − | 0.949017i | \(-0.602080\pi\) | ||||
−0.315226 | + | 0.949017i | \(0.602080\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.74163 | −0.0975127 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.47805 | −0.0824967 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.65297 | 0.0919735 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.22012 | −0.123150 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.85620 | −0.102648 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −53.1731 | −2.93153 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5472 | 0.744621 | 0.372310 | − | 0.928108i | \(-0.378566\pi\) | ||||
0.372310 | + | 0.928108i | \(0.378566\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.57901 | −0.196129 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.05123 | 0.221342 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.0585 | −1.31055 | −0.655275 | − | 0.755390i | \(-0.727447\pi\) | ||||
−0.655275 | + | 0.755390i | \(0.727447\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.32155 | 0.0717768 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.84999 | 0.479254 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 71.7366 | 3.87341 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.213959 | 0.0115192 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.16350 | 0.384557 | 0.192278 | − | 0.981340i | \(-0.438412\pi\) | ||||
0.192278 | + | 0.981340i | \(0.438412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.33325 | 0.231953 | 0.115977 | − | 0.993252i | \(-0.463000\pi\) | ||||
0.115977 | + | 0.993252i | \(0.463000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.61772 | 0.0863476 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.09350 | 0.324324 | 0.162162 | − | 0.986764i | \(-0.448153\pi\) | ||||
0.162162 | + | 0.986764i | \(0.448153\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.66014 | −0.459633 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.78402 | −0.253197 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.81009 | 0.412201 | 0.206100 | − | 0.978531i | \(-0.433923\pi\) | ||||
0.206100 | + | 0.978531i | \(0.433923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9511 | −0.997426 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.349612 | −0.0183499 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.3527 | −0.594229 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.1452 | 1.78237 | 0.891183 | − | 0.453645i | \(-0.149877\pi\) | ||||
0.891183 | + | 0.453645i | \(0.149877\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.4094 | −0.646009 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.7891 | 1.85808 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.9968 | −0.672951 | −0.336476 | − | 0.941692i | \(-0.609235\pi\) | ||||
−0.336476 | + | 0.941692i | \(0.609235\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.121745 | 0.00628687 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.35623 | −0.0698494 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.1953 | −0.677799 | −0.338900 | − | 0.940822i | \(-0.610055\pi\) | ||||
−0.338900 | + | 0.940822i | \(0.610055\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.73573 | 0.0889243 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.26583 | −0.473462 | −0.236731 | − | 0.971575i | \(-0.576076\pi\) | ||||
−0.236731 | + | 0.971575i | \(0.576076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.9900 | −0.763959 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.3107 | −1.13411 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.3487 | −0.981019 | −0.490509 | − | 0.871436i | \(-0.663189\pi\) | ||||
−0.490509 | + | 0.871436i | \(0.663189\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.1348 | −0.664256 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.42650 | −0.0719576 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.00612 | −0.352516 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3736 | 0.671200 | 0.335600 | − | 0.942005i | \(-0.391061\pi\) | ||||
0.335600 | + | 0.942005i | \(0.391061\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.141570 | −0.00708737 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.89159 | 0.343294 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.86682 | 0.440596 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.41816 | −0.169432 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.92283 | −0.292865 | −0.146433 | − | 0.989221i | \(-0.546779\pi\) | ||||
−0.146433 | + | 0.989221i | \(0.546779\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.206489 | 0.0101853 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.77458 | 0.136528 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.9997 | −0.834482 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.86144 | −0.0911551 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.49806 | 0.122038 | 0.0610191 | − | 0.998137i | \(-0.480565\pi\) | ||||
0.0610191 | + | 0.998137i | \(0.480565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.7368 | 1.64423 | 0.822115 | − | 0.569321i | \(-0.192794\pi\) | ||||
0.822115 | + | 0.569321i | \(0.192794\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.1899 | 1.46789 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.47382 | −0.362533 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.04170 | −0.243985 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.770596 | 0.0372047 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.4626 | −1.41917 | −0.709583 | − | 0.704622i | \(-0.751117\pi\) | ||||
−0.709583 | + | 0.704622i | \(0.751117\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.0820591 | −0.00394351 | −0.00197176 | − | 0.999998i | \(-0.500628\pi\) | ||||
−0.00197176 | + | 0.999998i | \(0.500628\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0743715 | 0.00356584 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.388690 | −0.0185936 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.4428 | 0.880228 | 0.440114 | − | 0.897942i | \(-0.354938\pi\) | ||||
0.440114 | + | 0.897942i | \(0.354938\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −61.6259 | −2.93457 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.9358 | −0.804645 | −0.402322 | − | 0.915498i | \(-0.631797\pi\) | ||||
−0.402322 | + | 0.915498i | \(0.631797\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.23370 | −0.437719 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.989685 | −0.0468105 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.4738 | 0.777445 | 0.388722 | − | 0.921355i | \(-0.372917\pi\) | ||||
0.388722 | + | 0.921355i | \(0.372917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.8517 | −0.558076 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.94204 | −0.0912449 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.6728 | −0.547232 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.35231 | −0.0632584 | −0.0316292 | − | 0.999500i | \(-0.510070\pi\) | ||||
−0.0316292 | + | 0.999500i | \(0.510070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.44590 | 0.254193 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.9966 | 1.02449 | 0.512243 | − | 0.858841i | \(-0.328815\pi\) | ||||
0.512243 | + | 0.858841i | \(0.328815\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.6477 | −0.913104 | −0.456552 | − | 0.889697i | \(-0.650916\pi\) | ||||
−0.456552 | + | 0.889697i | \(0.650916\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.377913 | −0.0175253 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.16680 | −0.146542 | −0.0732711 | − | 0.997312i | \(-0.523344\pi\) | ||||
−0.0732711 | + | 0.997312i | \(0.523344\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.3004 | 0.983559 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.49824 | 0.115113 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.3080 | −0.979742 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.221168 | −0.0101479 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.3199 | −0.930383 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.9142 | −1.00128 | −0.500642 | − | 0.865654i | \(-0.666903\pi\) | ||||
−0.500642 | + | 0.865654i | \(0.666903\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.66176 | −0.121366 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.12495 | 0.0511868 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.669863 | 0.0304169 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.5948 | 1.93015 | 0.965077 | − | 0.261966i | \(-0.0843709\pi\) | ||||
0.965077 | + | 0.261966i | \(0.0843709\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.695489 | −0.0314511 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.35002 | −0.286572 | −0.143286 | − | 0.989681i | \(-0.545767\pi\) | ||||
−0.143286 | + | 0.989681i | \(0.545767\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.56561 | −0.205625 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.51080 | 0.382532 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −45.5329 | −2.04243 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.6397 | −0.744896 | −0.372448 | − | 0.928053i | \(-0.621482\pi\) | ||||
−0.372448 | + | 0.928053i | \(0.621482\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.52087 | 0.0679475 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.4627 | 0.466507 | 0.233253 | − | 0.972416i | \(-0.425063\pi\) | ||||
0.233253 | + | 0.972416i | \(0.425063\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.29915 | −0.280309 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.982609 | −0.0436392 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.5559 | 1.53167 | 0.765833 | − | 0.643040i | \(-0.222327\pi\) | ||||
0.765833 | + | 0.643040i | \(0.222327\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −59.6898 | −2.64052 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.161157 | 0.00711525 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.756974 | 0.0333562 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.8332 | 1.26808 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.795208 | −0.0349058 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.9805 | 0.656307 | 0.328153 | − | 0.944624i | \(-0.393574\pi\) | ||||
0.328153 | + | 0.944624i | \(0.393574\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.4264 | −1.19927 | −0.599636 | − | 0.800273i | \(-0.704688\pi\) | ||||
−0.599636 | + | 0.800273i | \(0.704688\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.640103 | 0.0279364 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.1998 | 1.01060 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.9114 | −0.865713 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.57531 | −0.0683628 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.22908 | −0.399756 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.1406 | −0.524882 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.43955 | −0.0621211 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −58.8563 | −2.53512 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.42242 | 0.319115 | 0.159557 | − | 0.987189i | \(-0.448993\pi\) | ||||
0.159557 | + | 0.987189i | \(0.448993\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.455194 | 0.0195343 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.2467 | −0.653096 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8172 | 0.676297 | 0.338148 | − | 0.941093i | \(-0.390199\pi\) | ||||
0.338148 | + | 0.941093i | \(0.390199\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.86251 | 0.122169 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.135107 | −0.00575575 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.8364 | −1.56644 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.145963 | 0.00619578 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.7864 | 1.00786 | 0.503930 | − | 0.863744i | \(-0.331887\pi\) | ||||
0.503930 | + | 0.863744i | \(0.331887\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.5928 | −0.701800 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.59414 | 0.109524 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.2900 | 0.475817 | 0.237908 | − | 0.971288i | \(-0.423538\pi\) | ||||
0.237908 | + | 0.971288i | \(0.423538\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.8551 | 0.456678 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 46.6196 | 1.95784 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.1065 | −0.465609 | −0.232805 | − | 0.972524i | \(-0.574790\pi\) | ||||
−0.232805 | + | 0.972524i | \(0.574790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5404 | 0.734041 | 0.367021 | − | 0.930213i | \(-0.380378\pi\) | ||||
0.367021 | + | 0.930213i | \(0.380378\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.01648 | 0.0842395 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.75744 | 0.0732905 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.06969 | −0.169423 | −0.0847117 | − | 0.996406i | \(-0.526997\pi\) | ||||
−0.0847117 | + | 0.996406i | \(0.526997\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.51107 | −0.104357 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −89.3802 | −3.70811 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.4067 | −0.803742 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.62746 | 0.274012 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.0592 | 0.910482 | 0.455241 | − | 0.890368i | \(-0.349553\pi\) | ||||
0.455241 | + | 0.890368i | \(0.349553\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.686537 | 0.0282883 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.14380 | 0.0470495 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.8222 | −0.690807 | −0.345403 | − | 0.938454i | \(-0.612258\pi\) | ||||
−0.345403 | + | 0.938454i | \(0.612258\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.2955 | −1.61096 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.413545 | −0.0169253 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.55428 | −0.308659 | −0.154330 | − | 0.988019i | \(-0.549322\pi\) | ||||
−0.154330 | + | 0.988019i | \(0.549322\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.5529 | −1.00153 | −0.500766 | − | 0.865583i | \(-0.666948\pi\) | ||||
−0.500766 | + | 0.865583i | \(0.666948\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.0936 | −0.492491 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.87169 | −0.116751 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.7767 | −1.28978 | −0.644889 | − | 0.764277i | \(-0.723096\pi\) | ||||
−0.644889 | + | 0.764277i | \(0.723096\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.391027 | 0.0158452 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.4527 | 0.908339 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.8595 | 1.69069 | 0.845345 | − | 0.534221i | \(-0.179395\pi\) | ||||
0.845345 | + | 0.534221i | \(0.179395\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.506094 | 0.0204077 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.8914 | −1.08261 | −0.541303 | − | 0.840828i | \(-0.682069\pi\) | ||||
−0.541303 | + | 0.840828i | \(0.682069\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.9722 | 0.641976 | 0.320988 | − | 0.947083i | \(-0.395985\pi\) | ||||
0.320988 | + | 0.947083i | \(0.395985\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.28059 | −0.0513881 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −48.5485 | −1.94506 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0767665 | 0.00306576 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.96056 | −0.357281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.5843 | 1.21754 | 0.608772 | − | 0.793346i | \(-0.291663\pi\) | ||||
0.608772 | + | 0.793346i | \(0.291663\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.88766 | −0.114774 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.2572 | 0.565778 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −45.8321 | −1.81593 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.8521 | 1.02269 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.8408 | 1.09964 | 0.549822 | − | 0.835282i | \(-0.314696\pi\) | ||||
0.549822 | + | 0.835282i | \(0.314696\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.03072 | −0.198392 | −0.0991961 | − | 0.995068i | \(-0.531627\pi\) | ||||
−0.0991961 | + | 0.995068i | \(0.531627\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.909897 | 0.0358272 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.4014 | −1.11658 | −0.558288 | − | 0.829647i | \(-0.688542\pi\) | ||||
−0.558288 | + | 0.829647i | \(0.688542\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.50452 | −0.0590575 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.98698 | −0.0778757 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.3180 | −0.716837 | −0.358419 | − | 0.933561i | \(-0.616684\pi\) | ||||
−0.358419 | + | 0.933561i | \(0.616684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.7172 | −0.457828 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 33.8899 | 1.32217 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.3127 | 1.68722 | 0.843611 | − | 0.536954i | \(-0.180425\pi\) | ||||
0.843611 | + | 0.536954i | \(0.180425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.7535 | 1.50734 | 0.753669 | − | 0.657254i | \(-0.228282\pi\) | ||||
0.753669 | + | 0.657254i | \(0.228282\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.02008 | 0.0784535 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.16284 | −0.0450932 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.07359 | 0.0415695 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.00042 | 0.0773407 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.73386 | 0.105540 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.4072 | −1.05647 | −0.528235 | − | 0.849098i | \(-0.677146\pi\) | ||||
−0.528235 | + | 0.849098i | \(0.677146\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.728663 | −0.0280463 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.5573 | −1.59718 | −0.798588 | − | 0.601878i | \(-0.794419\pi\) | ||||
−0.798588 | + | 0.601878i | \(0.794419\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.52197 | 0.135161 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.90997 | −0.111510 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.94348 | −0.303949 | −0.151974 | − | 0.988384i | \(-0.548563\pi\) | ||||
−0.151974 | + | 0.988384i | \(0.548563\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.69608 | 0.0648039 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.61991 | −0.0618035 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.1122 | −0.575729 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.6262 | 1.58354 | 0.791768 | − | 0.610823i | \(-0.209161\pi\) | ||||
0.791768 | + | 0.610823i | \(0.209161\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44.7477 | 1.69982 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.2897 | −0.579972 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.0688 | −1.17681 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.262891 | −0.00994345 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.4480 | 0.923389 | 0.461694 | − | 0.887039i | \(-0.347242\pi\) | ||||
0.461694 | + | 0.887039i | \(0.347242\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.265164 | −0.0100008 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.23124 | −0.0463711 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.1194 | −1.24558 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.1347 | −0.906397 | −0.453198 | − | 0.891410i | \(-0.649717\pi\) | ||||
−0.453198 | + | 0.891410i | \(0.649717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.9145 | 0.784355 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.45537 | −0.204305 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.32961 | 0.236714 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.77967 | −0.103809 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.49446 | −0.204909 | −0.102454 | − | 0.994738i | \(-0.532670\pi\) | ||||
−0.102454 | + | 0.994738i | \(0.532670\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.97998 | 0.148222 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.84916 | 0.105962 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.610881 | 0.0226875 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8304 | 1.47723 | 0.738613 | − | 0.674130i | \(-0.235481\pi\) | ||||
0.738613 | + | 0.674130i | \(0.235481\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.2029 | −0.970478 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −55.8579 | −2.06598 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.1024 | 1.11186 | 0.555929 | − | 0.831230i | \(-0.312363\pi\) | ||||
0.555929 | + | 0.831230i | \(0.312363\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.51329 | 0.0927042 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.5501 | −0.425455 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.9335 | 0.438981 | 0.219490 | − | 0.975615i | \(-0.429561\pi\) | ||||
0.219490 | + | 0.975615i | \(0.429561\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0597789 | 0.00219603 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.94786 | −0.218206 | −0.109103 | − | 0.994030i | \(-0.534798\pi\) | ||||
−0.109103 | + | 0.994030i | \(0.534798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.12919 | −0.297830 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 50.7471 | 1.85674 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −63.8321 | −2.33237 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.54531 | −0.348313 | −0.174157 | − | 0.984718i | \(-0.555720\pi\) | ||||
−0.174157 | + | 0.984718i | \(0.555720\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.37010 | 0.122813 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.9517 | −0.580543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.1181 | −1.27639 | −0.638195 | − | 0.769875i | \(-0.720319\pi\) | ||||
−0.638195 | + | 0.769875i | \(0.720319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.610003 | −0.0221417 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.1653 | −1.02099 | −0.510495 | − | 0.859881i | \(-0.670538\pi\) | ||||
−0.510495 | + | 0.859881i | \(0.670538\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −80.1632 | −2.90210 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.3107 | 0.806644 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.17159 | −0.0423035 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.6462 | −1.03301 | −0.516505 | − | 0.856284i | \(-0.672767\pi\) | ||||
−0.516505 | + | 0.856284i | \(0.672767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.09025 | −0.111293 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.87121 | 0.139238 | 0.0696189 | − | 0.997574i | \(-0.477822\pi\) | ||||
0.0696189 | + | 0.997574i | \(0.477822\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.10415 | −0.111504 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.767437 | 0.0275317 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.919398 | −0.0329408 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.6902 | 0.883486 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.445126 | −0.0159075 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.5204 | 0.732403 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.7115 | 1.48685 | 0.743426 | − | 0.668818i | \(-0.233199\pi\) | ||||
0.743426 | + | 0.668818i | \(0.233199\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.29978 | −0.0462736 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.0735 | 2.02930 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.12889 | 0.0755992 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.828706 | 0.0293912 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.0464 | 1.34767 | 0.673836 | − | 0.738881i | \(-0.264645\pi\) | ||||
0.673836 | + | 0.738881i | \(0.264645\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 75.5848 | 2.67400 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.5642 | 0.973935 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.3668 | 1.14220 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.24021 | 0.325675 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.372327 | 0.0131065 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.45585 | 0.156659 | 0.0783297 | − | 0.996928i | \(-0.475041\pi\) | ||||
0.0783297 | + | 0.996928i | \(0.475041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.3150 | −0.572896 | −0.286448 | − | 0.958096i | \(-0.592475\pi\) | ||||
−0.286448 | + | 0.958096i | \(0.592475\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.999838 | 0.0350659 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.71269 | −0.200107 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.65297 | −0.0578300 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34.8455 | 1.21760 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.5436 | 0.996179 | 0.498090 | − | 0.867126i | \(-0.334035\pi\) | ||||
0.498090 | + | 0.867126i | \(0.334035\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.1112 | 1.57248 | 0.786239 | − | 0.617922i | \(-0.212025\pi\) | ||||
0.786239 | + | 0.617922i | \(0.212025\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.347096 | −0.0120843 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.0250 | −0.939750 | −0.469875 | − | 0.882733i | \(-0.655701\pi\) | ||||
−0.469875 | + | 0.882733i | \(0.655701\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.59653 | 0.159644 | 0.0798221 | − | 0.996809i | \(-0.474565\pi\) | ||||
0.0798221 | + | 0.996809i | \(0.474565\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.59777 | −0.0554259 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −154.289 | −5.34580 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.4923 | 0.432314 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.26188 | 0.0781820 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.87295 | 0.271804 | 0.135902 | − | 0.990722i | \(-0.456607\pi\) | ||||
0.135902 | + | 0.990722i | \(0.456607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6268 | −0.987132 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.03427 | −0.104506 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.07106 | −0.277653 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.0986 | −0.518795 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.14005 | −0.0734462 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.10705 | 0.0722287 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.6219 | −1.04847 | −0.524236 | − | 0.851573i | \(-0.675649\pi\) | ||||
−0.524236 | + | 0.851573i | \(0.675649\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.660225 | 0.0225792 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.99842 | −0.341540 | −0.170770 | − | 0.985311i | \(-0.554625\pi\) | ||||
−0.170770 | + | 0.985311i | \(0.554625\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.2232 | −0.655887 | −0.327944 | − | 0.944697i | \(-0.606356\pi\) | ||||
−0.327944 | + | 0.944697i | \(0.606356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.66092 | 0.0906839 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.0999 | −1.80754 | −0.903771 | − | 0.428015i | \(-0.859213\pi\) | ||||
−0.903771 | + | 0.428015i | \(0.859213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.53177 | −0.222087 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.73075 | 0.160665 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.9746 | 0.677591 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.99422 | −0.304758 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.99966 | −0.0676782 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.25775 | 0.177744 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.2618 | −1.05563 | −0.527817 | − | 0.849358i | \(-0.676989\pi\) | ||||
−0.527817 | + | 0.849358i | \(0.676989\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.562654 | 0.0189779 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.3521 | 1.32580 | 0.662902 | − | 0.748706i | \(-0.269324\pi\) | ||||
0.662902 | + | 0.748706i | \(0.269324\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.3262 | −1.42439 | −0.712195 | − | 0.701981i | \(-0.752299\pi\) | ||||
−0.712195 | + | 0.701981i | \(0.752299\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0642461 | 0.00215961 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.3401 | 1.38807 | 0.694033 | − | 0.719944i | \(-0.255832\pi\) | ||||
0.694033 | + | 0.719944i | \(0.255832\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 74.9607 | 2.51410 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.2795 | −0.846895 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.23673 | 0.0748493 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.8243 | −0.395243 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.475016 | −0.0158603 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.89626 | −0.0632440 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.8737 | −1.69485 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.78401 | 0.159202 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.73893 | 0.124286 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.3739 | 1.67264 | 0.836319 | − | 0.548243i | \(-0.184703\pi\) | ||||
0.836319 | + | 0.548243i | \(0.184703\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.8041 | 0.623692 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.59547 | −0.218518 | −0.109259 | − | 0.994013i | \(-0.534848\pi\) | ||||
−0.109259 | + | 0.994013i | \(0.534848\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.4665 | 1.60401 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.116742 | −0.00385937 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −61.6060 | −2.03441 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.2272 | −0.898144 | −0.449072 | − | 0.893496i | \(-0.648245\pi\) | ||||
−0.449072 | + | 0.893496i | \(0.648245\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.62768 | 0.119536 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.2266 | 0.632850 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.19893 | 0.0394205 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.25970 | −0.0742183 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.3297 | −1.32318 | −0.661588 | − | 0.749868i | \(-0.730117\pi\) | ||||
−0.661588 | + | 0.749868i | \(0.730117\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.56578 | −0.149637 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.48233 | 0.0812678 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.3080 | 0.696846 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.165480 | 0.00540600 | 0.00270300 | − | 0.999996i | \(-0.499140\pi\) | ||||
0.00270300 | + | 0.999996i | \(0.499140\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.47150 | 0.0480206 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.4796 | 1.54779 | 0.773895 | − | 0.633314i | \(-0.218306\pi\) | ||||
0.773895 | + | 0.633314i | \(0.218306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.30572 | 0.237907 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.83113 | −0.124627 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.0973 | 0.978029 | 0.489015 | − | 0.872276i | \(-0.337356\pi\) | ||||
0.489015 | + | 0.872276i | \(0.337356\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.2044 | 0.818170 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.36657 | −0.0443140 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.9511 | 1.26175 | 0.630875 | − | 0.775884i | \(-0.282696\pi\) | ||||
0.630875 | + | 0.775884i | \(0.282696\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.5632 | 0.535971 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.212035 | −0.00685410 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.91757 | 0.287963 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.3643 | −0.689170 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.2418 | 1.16787 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.6257 | −0.663966 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.4556 | 1.14017 | 0.570087 | − | 0.821584i | \(-0.306909\pi\) | ||||
0.570087 | + | 0.821584i | \(0.306909\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.201240 | 0.00646476 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.8874 | −0.606125 | −0.303063 | − | 0.952971i | \(-0.598009\pi\) | ||||
−0.303063 | + | 0.952971i | \(0.598009\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −80.3895 | −2.57717 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.270288 | −0.00865614 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54.5149 | 1.74409 | 0.872044 | − | 0.489428i | \(-0.162794\pi\) | ||||
0.872044 | + | 0.489428i | \(0.162794\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.3255 | 0.841366 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.5140 | 1.45315 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.32748 | 0.0423402 | 0.0211701 | − | 0.999776i | \(-0.493261\pi\) | ||||
0.0211701 | + | 0.999776i | \(0.493261\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.39504 | 0.299351 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.47354 | −0.206055 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.1348 | 0.417663 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.7720 | −0.373950 | −0.186975 | − | 0.982365i | \(-0.559868\pi\) | ||||
−0.186975 | + | 0.982365i | \(0.559868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.64930 | 0.0523389 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.39683 | −0.107687 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.3756 | −0.391940 | −0.195970 | − | 0.980610i | \(-0.562786\pi\) | ||||
−0.195970 | + | 0.980610i | \(0.562786\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.873614 | −0.0276399 |
(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 | 8020.2.a.d.1.17 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.d.1.17 | ✓ | 29 | 1.1 | even | 1 | trivial |