Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-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 | ||||||||
\(3\) | −2.56466 | −1.48071 | −0.740355 | − | 0.672216i | \(-0.765342\pi\) | ||||
−0.740355 | + | 0.672216i | \(0.765342\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.26922 | −1.46204 | −0.731020 | − | 0.682356i | \(-0.760955\pi\) | ||||
−0.731020 | + | 0.682356i | \(0.760955\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64610 | 1.00013 | 0.500066 | − | 0.865987i | \(-0.333309\pi\) | ||||
0.500066 | + | 0.865987i | \(0.333309\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.57750 | 1.19250 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.86957 | 1.46823 | 0.734115 | − | 0.679025i | \(-0.237597\pi\) | ||||
0.734115 | + | 0.679025i | \(0.237597\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.70896 | 0.473981 | 0.236990 | − | 0.971512i | \(-0.423839\pi\) | ||||
0.236990 | + | 0.971512i | \(0.423839\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.38445 | 2.16486 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.816317 | −0.187276 | −0.0936380 | − | 0.995606i | \(-0.529850\pi\) | ||||
−0.0936380 | + | 0.995606i | \(0.529850\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.78637 | −1.48091 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.69055 | −1.60359 | −0.801795 | − | 0.597599i | \(-0.796122\pi\) | ||||
−0.801795 | + | 0.597599i | \(0.796122\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.68779 | 1.13756 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.48110 | −0.285038 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.446626 | −0.0829364 | −0.0414682 | − | 0.999140i | \(-0.513204\pi\) | ||||
−0.0414682 | + | 0.999140i | \(0.513204\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.86589 | −1.05354 | −0.526772 | − | 0.850006i | \(-0.676598\pi\) | ||||
−0.526772 | + | 0.850006i | \(0.676598\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.4888 | −2.17402 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.65069 | −1.46223 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.42139 | 1.38447 | 0.692234 | − | 0.721673i | \(-0.256627\pi\) | ||||
0.692234 | + | 0.721673i | \(0.256627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.38291 | −0.701828 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.93260 | 0.301822 | 0.150911 | − | 0.988547i | \(-0.451779\pi\) | ||||
0.150911 | + | 0.988547i | \(0.451779\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.18105 | −1.40010 | −0.700049 | − | 0.714095i | \(-0.746838\pi\) | ||||
−0.700049 | + | 0.714095i | \(0.746838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.6956 | −1.74348 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.424956 | 0.0619862 | 0.0309931 | − | 0.999520i | \(-0.490133\pi\) | ||||
0.0309931 | + | 0.999520i | \(0.490133\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.00185929 | 0.000265612 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.56466 | 0.359125 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.07461 | 0.422330 | 0.211165 | − | 0.977450i | \(-0.432274\pi\) | ||||
0.211165 | + | 0.977450i | \(0.432274\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.9197 | −2.14661 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.09358 | 0.277301 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.31581 | −1.06473 | −0.532365 | − | 0.846515i | \(-0.678697\pi\) | ||||
−0.532365 | + | 0.846515i | \(0.678697\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.46644 | 1.19266 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.58697 | −0.692978 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.42814 | 0.663153 | 0.331576 | − | 0.943428i | \(-0.392420\pi\) | ||||
0.331576 | + | 0.943428i | \(0.392420\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.7237 | 2.37445 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.9065 | 1.76908 | 0.884539 | − | 0.466466i | \(-0.154473\pi\) | ||||
0.884539 | + | 0.466466i | \(0.154473\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.04698 | −1.05887 | −0.529434 | − | 0.848351i | \(-0.677596\pi\) | ||||
−0.529434 | + | 0.848351i | \(0.677596\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.5873 | −1.68439 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.8854 | 1.46843 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.52263 | −0.958871 | −0.479436 | − | 0.877577i | \(-0.659159\pi\) | ||||
−0.479436 | + | 0.877577i | \(0.659159\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.93398 | −0.770442 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.03121 | 0.552247 | 0.276123 | − | 0.961122i | \(-0.410950\pi\) | ||||
0.276123 | + | 0.961122i | \(0.410950\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.26922 | 0.354597 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.14545 | 0.122805 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.630394 | −0.0668216 | −0.0334108 | − | 0.999442i | \(-0.510637\pi\) | ||||
−0.0334108 | + | 0.999442i | \(0.510637\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.52209 | 0.474043 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.0440 | 1.55999 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.66872 | 0.273805 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.4738 | 1.26652 | 0.633259 | − | 0.773940i | \(-0.281717\pi\) | ||||
0.633259 | + | 0.773940i | \(0.281717\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.4209 | 1.75087 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.53453 | −0.650210 | −0.325105 | − | 0.945678i | \(-0.605400\pi\) | ||||
−0.325105 | + | 0.945678i | \(0.605400\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.01515 | −0.592690 | −0.296345 | − | 0.955081i | \(-0.595768\pi\) | ||||
−0.296345 | + | 0.955081i | \(0.595768\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 22.1861 | 2.16514 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.70657 | 0.745022 | 0.372511 | − | 0.928028i | \(-0.378497\pi\) | ||||
0.372511 | + | 0.928028i | \(0.378497\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.37323 | 0.131531 | 0.0657656 | − | 0.997835i | \(-0.479051\pi\) | ||||
0.0657656 | + | 0.997835i | \(0.479051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.5980 | −2.04999 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.23707 | −0.586734 | −0.293367 | − | 0.956000i | \(-0.594776\pi\) | ||||
−0.293367 | + | 0.956000i | \(0.594776\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.1421 | 2.34451 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.11381 | 0.565222 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.64610 | −0.242568 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.7127 | 1.15570 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.95648 | −0.446911 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.24855 | −0.201116 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.55441 | 0.226667 | 0.113334 | − | 0.993557i | \(-0.463847\pi\) | ||||
0.113334 | + | 0.993557i | \(0.463847\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.5463 | 2.07314 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3680 | 1.51745 | 0.758723 | − | 0.651414i | \(-0.225824\pi\) | ||||
0.758723 | + | 0.651414i | \(0.225824\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.16006 | −0.187301 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.84205 | 0.416737 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.6166 | −1.50509 | −0.752543 | − | 0.658544i | \(-0.771173\pi\) | ||||
−0.752543 | + | 0.658544i | \(0.771173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.85306 | −0.581269 | −0.290634 | − | 0.956834i | \(-0.593866\pi\) | ||||
−0.290634 | + | 0.956834i | \(0.593866\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.08987 | −0.0917836 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.32191 | 0.695913 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.46012 | 0.121256 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.00476845 | −0.000393295 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.6242 | 1.44383 | 0.721915 | − | 0.691982i | \(-0.243262\pi\) | ||||
0.721915 | + | 0.691982i | \(0.243262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.19339 | 0.422632 | 0.211316 | − | 0.977418i | \(-0.432225\pi\) | ||||
0.211316 | + | 0.977418i | \(0.432225\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.57750 | −0.289224 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.1769 | 1.54032 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.15908 | −0.491548 | −0.245774 | − | 0.969327i | \(-0.579042\pi\) | ||||
−0.245774 | + | 0.969327i | \(0.579042\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.88534 | −0.625348 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.3500 | −1.60380 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.7190 | −1.62284 | −0.811420 | − | 0.584464i | \(-0.801305\pi\) | ||||
−0.811420 | + | 0.584464i | \(0.801305\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 40.8287 | 3.17851 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.2322 | 1.95253 | 0.976263 | − | 0.216589i | \(-0.0694931\pi\) | ||||
0.976263 | + | 0.216589i | \(0.0694931\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0795 | −0.775342 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.92038 | −0.223327 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.9528 | 1.21287 | 0.606435 | − | 0.795133i | \(-0.292599\pi\) | ||||
0.606435 | + | 0.795133i | \(0.292599\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.0505 | 1.13771 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.56466 | −0.192772 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.47667 | 0.409346 | 0.204673 | − | 0.978830i | \(-0.434387\pi\) | ||||
0.204673 | + | 0.978830i | \(0.434387\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.68134 | −0.719608 | −0.359804 | − | 0.933028i | \(-0.617157\pi\) | ||||
−0.359804 | + | 0.933028i | \(0.617157\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.3273 | 1.57656 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −27.5314 | −2.02415 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.86957 | −0.356098 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.91915 | −0.285076 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.1195 | −0.876938 | −0.438469 | − | 0.898746i | \(-0.644479\pi\) | ||||
−0.438469 | + | 0.898746i | \(0.644479\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.25546 | 0.378296 | 0.189148 | − | 0.981949i | \(-0.439427\pi\) | ||||
0.189148 | + | 0.981949i | \(0.439427\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.3287 | 1.02610 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.8164 | 1.69685 | 0.848423 | − | 0.529320i | \(-0.177553\pi\) | ||||
0.848423 | + | 0.529320i | \(0.177553\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.01170 | −0.355270 | −0.177635 | − | 0.984096i | \(-0.556845\pi\) | ||||
−0.177635 | + | 0.984096i | \(0.556845\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.9214 | −0.981937 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.18182 | −0.0829474 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.31810 | −0.441276 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −27.5130 | −1.91228 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.97511 | −0.274964 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.88156 | 0.336060 | 0.168030 | − | 0.985782i | \(-0.446259\pi\) | ||||
0.168030 | + | 0.985782i | \(0.446259\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −38.2302 | −2.61949 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 30.0149 | 2.04700 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.5217 | −1.05368 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.2025 | 1.56788 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.70896 | −0.114957 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.4142 | 0.697388 | 0.348694 | − | 0.937237i | \(-0.386625\pi\) | ||||
0.348694 | + | 0.937237i | \(0.386625\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.3481 | 1.35654 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.49672 | 0.298458 | 0.149229 | − | 0.988803i | \(-0.452321\pi\) | ||||
0.149229 | + | 0.988803i | \(0.452321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.2079 | −1.26930 | −0.634648 | − | 0.772801i | \(-0.718855\pi\) | ||||
−0.634648 | + | 0.772801i | \(0.718855\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −33.0467 | −2.17431 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.65638 | 0.501586 | 0.250793 | − | 0.968041i | \(-0.419309\pi\) | ||||
0.250793 | + | 0.968041i | \(0.419309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.38927 | −0.0906263 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.8577 | 1.41981 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.18581 | −0.206073 | −0.103036 | − | 0.994678i | \(-0.532856\pi\) | ||||
−0.103036 | + | 0.994678i | \(0.532856\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.4039 | −1.57200 | −0.785998 | − | 0.618229i | \(-0.787850\pi\) | ||||
−0.785998 | + | 0.618229i | \(0.787850\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2266 | 1.42584 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.00607842 | −0.000388336 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.39505 | −0.0887652 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.9034 | −0.817717 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.03155 | −0.380708 | −0.190354 | − | 0.981715i | \(-0.560964\pi\) | ||||
−0.190354 | + | 0.981715i | \(0.560964\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −37.4497 | −2.35444 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.38445 | −0.525055 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.6479 | −1.72463 | −0.862315 | − | 0.506373i | \(-0.830986\pi\) | ||||
−0.862315 | + | 0.506373i | \(0.830986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.2839 | 1.38465 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.59781 | −0.0989017 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.6355 | 0.655810 | 0.327905 | − | 0.944711i | \(-0.393657\pi\) | ||||
0.327905 | + | 0.944711i | \(0.393657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.0516 | −0.617463 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.61675 | 0.0989434 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.6905 | 0.651814 | 0.325907 | − | 0.945402i | \(-0.394330\pi\) | ||||
0.325907 | + | 0.945402i | \(0.394330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.14955 | −0.434304 | −0.217152 | − | 0.976138i | \(-0.569677\pi\) | ||||
−0.217152 | + | 0.976138i | \(0.569677\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.5976 | −0.701921 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 27.6971 | 1.67020 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.88059 | 0.233162 | 0.116581 | − | 0.993181i | \(-0.462807\pi\) | ||||
0.116581 | + | 0.993181i | \(0.462807\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.9852 | −1.25635 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.6086 | −0.990787 | −0.495393 | − | 0.868669i | \(-0.664976\pi\) | ||||
−0.495393 | + | 0.868669i | \(0.664976\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.16530 | −0.247601 | −0.123801 | − | 0.992307i | \(-0.539508\pi\) | ||||
−0.123801 | + | 0.992307i | \(0.539508\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.84437 | −0.405426 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.11387 | 0.301862 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −31.9910 | −1.87534 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.6479 | −0.738900 | −0.369450 | − | 0.929251i | \(-0.620454\pi\) | ||||
−0.369450 | + | 0.929251i | \(0.620454\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.26922 | −0.190341 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.21233 | −0.418502 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.1429 | −0.760071 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.2940 | −1.40028 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.7589 | 0.962772 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.1862 | 1.55668 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.1944 | 1.09548 | 0.547740 | − | 0.836648i | \(-0.315488\pi\) | ||||
0.547740 | + | 0.836648i | \(0.315488\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.4268 | 0.877602 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.7635 | 0.837159 | 0.418579 | − | 0.908180i | \(-0.362528\pi\) | ||||
0.418579 | + | 0.908180i | \(0.362528\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.0953 | −1.70108 | −0.850542 | − | 0.525907i | \(-0.823726\pi\) | ||||
−0.850542 | + | 0.525907i | \(0.823726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −30.9479 | −1.74371 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.74801 | −0.491337 | −0.245669 | − | 0.969354i | \(-0.579008\pi\) | ||||
−0.245669 | + | 0.969354i | \(0.579008\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.17488 | −0.121770 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.7648 | −1.10316 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.816317 | 0.0454211 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.72022 | 0.539181 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.52187 | −0.194760 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.12448 | 0.0619944 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0942 | 0.774689 | 0.387345 | − | 0.921935i | \(-0.373392\pi\) | ||||
0.387345 | + | 0.921935i | \(0.373392\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 30.1275 | 1.65098 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.7458 | −0.969555 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.944659 | −0.0514589 | −0.0257294 | − | 0.999669i | \(-0.508191\pi\) | ||||
−0.0257294 | + | 0.999669i | \(0.508191\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.9960 | 0.868783 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.5644 | −1.54685 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5178 | −0.999867 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −64.4810 | −3.47154 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.5103 | −1.36947 | −0.684733 | − | 0.728794i | \(-0.740081\pi\) | ||||
−0.684733 | + | 0.728794i | \(0.740081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.5143 | −1.57986 | −0.789932 | − | 0.613195i | \(-0.789884\pi\) | ||||
−0.789932 | + | 0.613195i | \(0.789884\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.53115 | −0.135103 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.4536 | −1.08863 | −0.544317 | − | 0.838880i | \(-0.683211\pi\) | ||||
−0.544317 | + | 0.838880i | \(0.683211\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −48.7327 | −2.58646 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.78637 | 0.359173 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.6994 | 0.670247 | 0.335124 | − | 0.942174i | \(-0.391222\pi\) | ||||
0.335124 | + | 0.942174i | \(0.391222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3336 | −0.964928 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −32.6038 | −1.71126 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.5765 | 1.54811 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.72214 | −0.0898952 | −0.0449476 | − | 0.998989i | \(-0.514312\pi\) | ||||
−0.0449476 | + | 0.998989i | \(0.514312\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.91390 | 0.359923 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.13573 | 0.422386 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.3648 | 1.31334 | 0.656670 | − | 0.754178i | \(-0.271964\pi\) | ||||
0.656670 | + | 0.754178i | \(0.271964\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.76678 | 0.297795 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.763266 | −0.0393102 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.8219 | −0.607251 | −0.303625 | − | 0.952791i | \(-0.598197\pi\) | ||||
−0.303625 | + | 0.952791i | \(0.598197\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.55120 | −0.335628 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.8150 | −0.552623 | −0.276311 | − | 0.961068i | \(-0.589112\pi\) | ||||
−0.276311 | + | 0.961068i | \(0.589112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −42.1251 | −2.14690 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.8452 | −1.66962 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.9524 | −1.41724 | −0.708621 | − | 0.705589i | \(-0.750682\pi\) | ||||
−0.708621 | + | 0.705589i | \(0.750682\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.69055 | 0.388928 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −44.5430 | −2.24690 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.8624 | 1.40191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.4024 | −0.823215 | −0.411608 | − | 0.911361i | \(-0.635033\pi\) | ||||
−0.411608 | + | 0.911361i | \(0.635033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.53983 | 0.277338 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.29379 | 0.0646087 | 0.0323044 | − | 0.999478i | \(-0.489715\pi\) | ||||
0.0323044 | + | 0.999478i | \(0.489715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0246 | −0.499360 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.6687 | 1.12642 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 41.0085 | 2.03272 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.1342 | −1.73727 | −0.868637 | − | 0.495449i | \(-0.835003\pi\) | ||||
−0.868637 | + | 0.495449i | \(0.835003\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 45.1806 | 2.22859 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.64610 | 0.130206 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.4481 | −0.807407 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.5758 | 0.860690 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6658 | −0.618765 | −0.309382 | − | 0.950938i | \(-0.600122\pi\) | ||||
−0.309382 | + | 0.950938i | \(0.600122\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.87488 | 0.481272 | 0.240636 | − | 0.970615i | \(-0.422644\pi\) | ||||
0.240636 | + | 0.970615i | \(0.422644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.52028 | 0.0739186 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.68779 | −0.275899 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.0045 | −1.06487 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.3429 | −1.03044 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.0785 | −0.967149 | −0.483575 | − | 0.875303i | \(-0.660662\pi\) | ||||
−0.483575 | + | 0.875303i | \(0.660662\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.0793 | 1.87803 | 0.939015 | − | 0.343876i | \(-0.111740\pi\) | ||||
0.939015 | + | 0.343876i | \(0.111740\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.74471 | −0.179545 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.27793 | 0.300314 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.7106 | −1.56119 | −0.780595 | − | 0.625038i | \(-0.785084\pi\) | ||||
−0.780595 | + | 0.625038i | \(0.785084\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.00665161 | 0.000316743 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.0887 | −1.47707 | −0.738534 | − | 0.674216i | \(-0.764482\pi\) | ||||
−0.738534 | + | 0.674216i | \(0.764482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.06089 | 0.0976958 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −45.2001 | −2.13789 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.1453 | 0.667558 | 0.333779 | − | 0.942651i | \(-0.391676\pi\) | ||||
0.333779 | + | 0.942651i | \(0.391676\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.41095 | 0.443144 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.3193 | −0.625796 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.7837 | −0.693070 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.09246 | 0.331771 | 0.165886 | − | 0.986145i | \(-0.446952\pi\) | ||||
0.165886 | + | 0.986145i | \(0.446952\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.48110 | 0.0691319 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.5736 | −1.42395 | −0.711977 | − | 0.702203i | \(-0.752200\pi\) | ||||
−0.711977 | + | 0.702203i | \(0.752200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3222 | 0.526189 | 0.263094 | − | 0.964770i | \(-0.415257\pi\) | ||||
0.263094 | + | 0.964770i | \(0.415257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −49.1823 | −2.28077 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.87967 | −0.0869809 | −0.0434904 | − | 0.999054i | \(-0.513848\pi\) | ||||
−0.0434904 | + | 0.999054i | \(0.513848\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.3634 | 0.663241 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.7960 | 0.727840 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −44.7078 | −2.05567 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.64304 | −0.213037 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.9994 | 0.503629 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.8189 | 0.585708 | 0.292854 | − | 0.956157i | \(-0.405395\pi\) | ||||
0.292854 | + | 0.956157i | \(0.405395\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.3918 | 0.656211 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 52.1909 | 2.37477 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −40.7794 | −1.85170 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.6486 | 0.482534 | 0.241267 | − | 0.970459i | \(-0.422437\pi\) | ||||
0.241267 | + | 0.970459i | \(0.422437\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 53.1374 | 2.40295 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.4725 | 1.91676 | 0.958378 | − | 0.285502i | \(-0.0921602\pi\) | ||||
0.958378 | + | 0.285502i | \(0.0921602\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.446626 | 0.0201150 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −56.9527 | −2.55984 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 39.4442 | 1.76931 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.9722 | 1.25221 | 0.626103 | − | 0.779740i | \(-0.284649\pi\) | ||||
0.626103 | + | 0.779740i | \(0.284649\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −64.7121 | −2.89112 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.1497 | −0.809255 | −0.404628 | − | 0.914482i | \(-0.632599\pi\) | ||||
−0.404628 | + | 0.914482i | \(0.632599\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.3628 | 0.950632 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.8504 | 1.14806 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.43748 | −0.285336 | −0.142668 | − | 0.989771i | \(-0.545568\pi\) | ||||
−0.142668 | + | 0.989771i | \(0.545568\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.9392 | −1.05901 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.20905 | 0.0533808 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.6648 | 0.866537 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.06935 | 0.0910101 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −40.9136 | −1.79591 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.9810 | −1.66398 | −0.831989 | − | 0.554792i | \(-0.812798\pi\) | ||||
−0.831989 | + | 0.554792i | \(0.812798\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.39808 | 0.0611339 | 0.0305669 | − | 0.999533i | \(-0.490269\pi\) | ||||
0.0305669 | + | 0.999533i | \(0.490269\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −38.5994 | −1.68462 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.86589 | 0.255522 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.1446 | 1.57150 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.57750 | 0.155250 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.30274 | 0.143058 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.1945 | −1.08925 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.0458 | −0.606122 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.00905393 | 0.000389980 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.3633 | 1.30542 | 0.652710 | − | 0.757608i | \(-0.273632\pi\) | ||||
0.652710 | + | 0.757608i | \(0.273632\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.8294 | 1.06553 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.48938 | −0.192304 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.23866 | 0.181232 | 0.0906159 | − | 0.995886i | \(-0.471116\pi\) | ||||
0.0906159 | + | 0.995886i | \(0.471116\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −29.7498 | −1.26969 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.364588 | 0.0155320 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.5518 | −0.958999 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 70.6087 | 2.99717 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.1581 | −0.599898 | −0.299949 | − | 0.953955i | \(-0.596970\pi\) | ||||
−0.299949 | + | 0.953955i | \(0.596970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.6901 | −0.663619 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.4888 | 0.527278 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.7101 | −0.619955 | −0.309978 | − | 0.950744i | \(-0.600322\pi\) | ||||
−0.309978 | + | 0.950744i | \(0.600322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.3904 | 0.857829 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.3480 | −0.770545 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.6477 | 0.781751 | 0.390875 | − | 0.920444i | \(-0.372172\pi\) | ||||
0.390875 | + | 0.920444i | \(0.372172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.25266 | −0.136120 | −0.0680598 | − | 0.997681i | \(-0.521681\pi\) | ||||
−0.0680598 | + | 0.997681i | \(0.521681\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.0825 | 1.29849 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −43.7423 | −1.82418 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.9268 | 0.454889 | 0.227444 | − | 0.973791i | \(-0.426963\pi\) | ||||
0.227444 | + | 0.973791i | \(0.426963\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.4785 | −0.560147 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.3131 | 0.552320 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.9720 | 0.620078 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.9874 | −0.826377 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.06489 | −0.167776 | −0.0838880 | − | 0.996475i | \(-0.526734\pi\) | ||||
−0.0838880 | + | 0.996475i | \(0.526734\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.78843 | 0.197304 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −61.0810 | −2.51253 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.5320 | −0.473562 | −0.236781 | − | 0.971563i | \(-0.576092\pi\) | ||||
−0.236781 | + | 0.971563i | \(0.576092\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.65069 | 0.354644 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.8533 | 0.526052 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.70831 | 0.110658 | 0.0553292 | − | 0.998468i | \(-0.482379\pi\) | ||||
0.0553292 | + | 0.998468i | \(0.482379\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.29209 | −0.379032 | −0.189516 | − | 0.981878i | \(-0.560692\pi\) | ||||
−0.189516 | + | 0.981878i | \(0.560692\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.4192 | 0.790810 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −41.5606 | −1.68968 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.4328 | 0.788754 | 0.394377 | − | 0.918949i | \(-0.370960\pi\) | ||||
0.394377 | + | 0.918949i | \(0.370960\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.03097 | 0.122821 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.726233 | 0.0293803 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.6537 | 0.470687 | 0.235343 | − | 0.971912i | \(-0.424379\pi\) | ||||
0.235343 | + | 0.971912i | \(0.424379\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.2038 | 0.653401 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.16618 | −0.0469484 | −0.0234742 | − | 0.999724i | \(-0.507473\pi\) | ||||
−0.0234742 | + | 0.999724i | \(0.507473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.7148 | −0.993373 | −0.496686 | − | 0.867930i | \(-0.665450\pi\) | ||||
−0.496686 | + | 0.867930i | \(0.665450\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.3905 | 0.457085 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.66809 | −0.0668305 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.0880 | −0.843519 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.1948 | 0.407142 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.42139 | −0.335783 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.3103 | 1.72416 | 0.862079 | − | 0.506774i | \(-0.169162\pi\) | ||||
0.862079 | + | 0.506774i | \(0.169162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.5196 | −0.497608 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.35092 | −0.331396 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.00317745 | 0.000125895 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 53.3281 | 2.10963 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.1745 | −0.836341 | −0.418170 | − | 0.908369i | \(-0.637328\pi\) | ||||
−0.418170 | + | 0.908369i | \(0.637328\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.3045 | −0.603549 | −0.301774 | − | 0.953379i | \(-0.597579\pi\) | ||||
−0.301774 | + | 0.953379i | \(0.597579\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −76.9781 | −3.03101 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.2202 | −0.834252 | −0.417126 | − | 0.908849i | \(-0.636963\pi\) | ||||
−0.417126 | + | 0.908849i | \(0.636963\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.86957 | 0.191147 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 39.8081 | 1.56020 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.8483 | 0.894124 | 0.447062 | − | 0.894503i | \(-0.352470\pi\) | ||||
0.447062 | + | 0.894503i | \(0.352470\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −56.7797 | −2.21856 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32.3656 | −1.26270 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.273160 | 0.0106408 | 0.00532041 | − | 0.999986i | \(-0.498306\pi\) | ||||
0.00532041 | + | 0.999986i | \(0.498306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.3951 | −0.521011 | −0.260505 | − | 0.965472i | \(-0.583889\pi\) | ||||
−0.260505 | + | 0.965472i | \(0.583889\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.38291 | 0.170218 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.06171 | 0.273841 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.43480 | 0.132996 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.7090 | −1.03263 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.4944 | −1.56327 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.76182 | 0.260649 | 0.130324 | − | 0.991471i | \(-0.458398\pi\) | ||||
0.130324 | + | 0.991471i | \(0.458398\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.42420 | −0.324248 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.4982 | 1.59490 | 0.797452 | − | 0.603382i | \(-0.206181\pi\) | ||||
0.797452 | + | 0.603382i | \(0.206181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.0068 | 1.26669 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.5326 | −0.441929 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.36872 | −0.128901 | −0.0644503 | − | 0.997921i | \(-0.520529\pi\) | ||||
−0.0644503 | + | 0.997921i | \(0.520529\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 57.5924 | 2.20049 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.2619 | 1.87946 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.25439 | 0.200176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.4479 | 0.625708 | 0.312854 | − | 0.949801i | \(-0.398715\pi\) | ||||
0.312854 | + | 0.949801i | \(0.398715\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 46.0975 | 1.75110 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.4041 | 0.849838 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.93260 | −0.0732026 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.6360 | −0.742703 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.9004 | 0.978244 | 0.489122 | − | 0.872215i | \(-0.337317\pi\) | ||||
0.489122 | + | 0.872215i | \(0.337317\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.87452 | −0.259278 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.56302 | 0.134191 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.2910 | −0.650296 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.5244 | −0.395253 | −0.197627 | − | 0.980277i | \(-0.563323\pi\) | ||||
−0.197627 | + | 0.980277i | \(0.563323\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.4898 | −1.14345 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.1119 | 1.68945 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.2061 | −1.01745 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.17052 | 0.305134 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.54966 | −0.132380 | −0.0661899 | − | 0.997807i | \(-0.521084\pi\) | ||||
−0.0661899 | + | 0.997807i | \(0.521084\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.9167 | −0.592769 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 62.5879 | 2.32767 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.54032 | −0.0943450 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0818 | 0.596441 | 0.298221 | − | 0.954497i | \(-0.403607\pi\) | ||||
0.298221 | + | 0.954497i | \(0.403607\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −36.2019 | −1.34081 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.18105 | 0.339574 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.5819 | 1.12957 | 0.564785 | − | 0.825238i | \(-0.308959\pi\) | ||||
0.564785 | + | 0.825238i | \(0.308959\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0155891 | 0.000575013 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.4327 | 0.973661 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.0584 | 0.553934 | 0.276967 | − | 0.960879i | \(-0.410671\pi\) | ||||
0.276967 | + | 0.960879i | \(0.410671\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.57785 | 0.131435 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.8727 | 1.05924 | 0.529618 | − | 0.848236i | \(-0.322335\pi\) | ||||
0.529618 | + | 0.848236i | \(0.322335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −57.6173 | −2.11094 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.9992 | 0.658555 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.3924 | 0.745121 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.3230 | −1.25247 | −0.626233 | − | 0.779636i | \(-0.715404\pi\) | ||||
−0.626233 | + | 0.779636i | \(0.715404\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.4689 | 0.563719 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.9783 | −0.617905 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.975245 | −0.0354459 | −0.0177229 | − | 0.999843i | \(-0.505642\pi\) | ||||
−0.0177229 | + | 0.999843i | \(0.505642\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 96.0458 | 3.48624 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.0776 | −0.872811 | −0.436406 | − | 0.899750i | \(-0.643749\pi\) | ||||
−0.436406 | + | 0.899750i | \(0.643749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.63370 | 0.131549 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.6956 | 0.422857 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.70896 | 0.0617070 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.7698 | −0.748977 | −0.374488 | − | 0.927232i | \(-0.622182\pi\) | ||||
−0.374488 | + | 0.927232i | \(0.622182\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 70.9076 | 2.55368 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.4978 | −1.42064 | −0.710319 | − | 0.703880i | \(-0.751449\pi\) | ||||
−0.710319 | + | 0.703880i | \(0.751449\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.3640 | −1.19847 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −57.1506 | −2.05027 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.57762 | −0.0565240 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 72.5883 | 2.59741 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.661499 | 0.0236400 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.1354 | 0.718662 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.4965 | −0.516744 | −0.258372 | − | 0.966046i | \(-0.583186\pi\) | ||||
−0.258372 | + | 0.966046i | \(0.583186\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.2764 | −0.971065 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.5039 | −0.586812 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.2114 | −0.504661 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.7789 | 0.914284 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.6341 | −0.376679 | −0.188340 | − | 0.982104i | \(-0.560311\pi\) | ||||
−0.188340 | + | 0.982104i | \(0.560311\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.424956 | −0.0150339 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.25523 | −0.0796848 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −44.0549 | −1.55466 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 66.5286 | 2.34482 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.4177 | −0.965147 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.4744 | −0.368259 | −0.184130 | − | 0.982902i | \(-0.558947\pi\) | ||||
−0.184130 | + | 0.982902i | \(0.558947\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.8786 | −1.71636 | −0.858179 | − | 0.513350i | \(-0.828404\pi\) | ||||
−0.858179 | + | 0.513350i | \(0.828404\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.3362 | 0.643078 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 67.7351 | 2.37266 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.49465 | 0.262205 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.1778 | 0.565297 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.6347 | −0.685256 | −0.342628 | − | 0.939471i | \(-0.611317\pi\) | ||||
−0.342628 | + | 0.939471i | \(0.611317\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.6968 | −0.547157 | −0.273579 | − | 0.961850i | \(-0.588207\pi\) | ||||
−0.273579 | + | 0.961850i | \(0.588207\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −71.0338 | −2.47308 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.5659 | 1.20197 | 0.600987 | − | 0.799259i | \(-0.294774\pi\) | ||||
0.600987 | + | 0.799259i | \(0.294774\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.7573 | 0.582005 | 0.291002 | − | 0.956722i | \(-0.406011\pi\) | ||||
0.291002 | + | 0.956722i | \(0.406011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.95241 | −0.345245 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.00185929 | −6.44205e−5 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −82.4896 | −2.85467 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.68798 | 0.300300 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.58638 | −0.227387 | −0.113694 | − | 0.993516i | \(-0.536268\pi\) | ||||
−0.113694 | + | 0.993516i | \(0.536268\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8005 | −0.993122 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.5955 | 1.46707 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.9519 | 1.13358 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.6391 | 1.15585 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.6826 | 0.366625 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −64.7651 | −2.22012 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.5678 | −1.52597 | −0.762987 | − | 0.646414i | \(-0.776268\pi\) | ||||
−0.762987 | + | 0.646414i | \(0.776268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.54735 | 0.326513 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.7487 | 0.572123 | 0.286062 | − | 0.958211i | \(-0.407654\pi\) | ||||
0.286062 | + | 0.958211i | \(0.407654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.9026 | −1.29322 | −0.646610 | − | 0.762820i | \(-0.723814\pi\) | ||||
−0.646610 | + | 0.762820i | \(0.723814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.1154 | −0.446970 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.7099 | −0.568811 | −0.284405 | − | 0.958704i | \(-0.591796\pi\) | ||||
−0.284405 | + | 0.958704i | \(0.591796\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52.1532 | −1.77326 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.56466 | −0.0871006 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41.5016 | −1.40784 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.27648 | 0.314322 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 44.6249 | 1.51032 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.94989 | −0.201143 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.9147 | −1.61796 | −0.808981 | − | 0.587834i | \(-0.799981\pi\) | ||||
−0.808981 | + | 0.587834i | \(0.799981\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.4377 | 1.09410 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.34644 | −0.0453626 | −0.0226813 | − | 0.999743i | \(-0.507220\pi\) | ||||
−0.0226813 | + | 0.999743i | \(0.507220\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.5391 | −1.06137 | −0.530687 | − | 0.847568i | \(-0.678066\pi\) | ||||
−0.530687 | + | 0.847568i | \(0.678066\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.38445 | 0.281840 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.95728 | −0.233603 | −0.116801 | − | 0.993155i | \(-0.537264\pi\) | ||||
−0.116801 | + | 0.993155i | \(0.537264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.75923 | 0.226697 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.7655 | −1.13119 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.346899 | −0.0116085 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.9044 | −0.598480 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.7070 | 1.12544 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.61986 | 0.0873772 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.07461 | −0.102430 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 62.3060 | 2.07341 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31.6504 | 1.05210 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 58.9293 | 1.95672 | 0.978358 | − | 0.206922i | \(-0.0663445\pi\) | ||||
0.978358 | + | 0.206922i | \(0.0663445\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23.3773 | −0.775376 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.9891 | 1.82187 | 0.910935 | − | 0.412549i | \(-0.135361\pi\) | ||||
0.910935 | + | 0.412549i | \(0.135361\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.4998 | 0.810826 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −69.7235 | −2.30499 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.9574 | 1.51765 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.0470 | −1.38700 | −0.693502 | − | 0.720455i | \(-0.743933\pi\) | ||||
−0.693502 | + | 0.720455i | \(0.743933\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −49.2271 | −1.62209 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.4747 | 0.838509 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.8991 | 1.57491 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.5192 | −0.706784 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.0139 | −1.21439 | −0.607193 | − | 0.794554i | \(-0.707705\pi\) | ||||
−0.607193 | + | 0.794554i | \(0.707705\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.00151777 | −4.97428e−5 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −37.8633 | −1.23959 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.9197 | 0.520630 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.31474 | −0.0429508 | −0.0214754 | − | 0.999769i | \(-0.506836\pi\) | ||||
−0.0214754 | + | 0.999769i | \(0.506836\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 77.1842 | 2.51881 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.3093 | 1.86823 | 0.934116 | − | 0.356970i | \(-0.116190\pi\) | ||||
0.934116 | + | 0.356970i | \(0.116190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.8628 | −0.483999 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.8126 | 0.416792 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.6406 | 0.345772 | 0.172886 | − | 0.984942i | \(-0.444691\pi\) | ||||
0.172886 | + | 0.984942i | \(0.444691\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.4609 | −0.501883 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.4357 | 0.727528 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.9657 | −1.22983 | −0.614915 | − | 0.788593i | \(-0.710810\pi\) | ||||
−0.614915 | + | 0.788593i | \(0.710810\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.6214 | 1.28212 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.57783 | 0.180306 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.6153 | −1.50528 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.40865 | 0.109956 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.5703 | 0.888439 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.1813 | −0.553084 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.6933 | −0.761924 | −0.380962 | − | 0.924591i | \(-0.624407\pi\) | ||||
−0.380962 | + | 0.924591i | \(0.624407\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.09358 | −0.0672555 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.9751 | −1.63587 | −0.817934 | − | 0.575312i | \(-0.804881\pi\) | ||||
−0.817934 | + | 0.575312i | \(0.804881\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.1339 | −0.581346 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −24.9291 | −0.798370 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.2571 | −0.424132 | −0.212066 | − | 0.977255i | \(-0.568019\pi\) | ||||
−0.212066 | + | 0.977255i | \(0.568019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.06975 | −0.0981095 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.91272 | 0.156851 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.2246 | 1.37865 | 0.689325 | − | 0.724452i | \(-0.257907\pi\) | ||||
0.689325 | + | 0.724452i | \(0.257907\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −77.8609 | −2.48085 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.88391 | −0.0917958 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 70.6074 | 2.24518 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.6680 | 1.64129 | 0.820644 | − | 0.571440i | \(-0.193615\pi\) | ||||
0.820644 | + | 0.571440i | \(0.193615\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.1470 | −1.14709 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.3844 | 0.519419 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.8260 | 0.406203 | 0.203102 | − | 0.979158i | \(-0.434898\pi\) | ||||
0.203102 | + | 0.979158i | \(0.434898\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.4729 | −0.394626 |
(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 | 8024.2.a.x.1.2 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.x.1.2 | ✓ | 22 | 1.1 | even | 1 | trivial |