Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −0.504664 | −0.291368 | −0.145684 | − | 0.989331i | \(-0.546538\pi\) | ||||
−0.145684 | + | 0.989331i | \(0.546538\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.903612 | −0.404107 | −0.202054 | − | 0.979374i | \(-0.564762\pi\) | ||||
−0.202054 | + | 0.979374i | \(0.564762\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.64438 | 0.621519 | 0.310759 | − | 0.950489i | \(-0.399417\pi\) | ||||
0.310759 | + | 0.950489i | \(0.399417\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.74531 | −0.915105 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.24007 | 0.675407 | 0.337703 | − | 0.941253i | \(-0.390350\pi\) | ||||
0.337703 | + | 0.941253i | \(0.390350\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.33083 | −1.75586 | −0.877929 | − | 0.478792i | \(-0.841075\pi\) | ||||
−0.877929 | + | 0.478792i | \(0.841075\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.456020 | 0.117744 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.81265 | −0.924702 | −0.462351 | − | 0.886697i | \(-0.652994\pi\) | ||||
−0.462351 | + | 0.886697i | \(0.652994\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50183 | −0.573959 | −0.286979 | − | 0.957937i | \(-0.592651\pi\) | ||||
−0.286979 | + | 0.957937i | \(0.592651\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.829861 | −0.181091 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.38058 | −0.913415 | −0.456707 | − | 0.889617i | \(-0.650971\pi\) | ||||
−0.456707 | + | 0.889617i | \(0.650971\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.18349 | −0.836697 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.89945 | 0.558000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.88754 | −0.350508 | −0.175254 | − | 0.984523i | \(-0.556075\pi\) | ||||
−0.175254 | + | 0.984523i | \(0.556075\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.57529 | 1.71977 | 0.859886 | − | 0.510486i | \(-0.170534\pi\) | ||||
0.859886 | + | 0.510486i | \(0.170534\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.13048 | −0.196792 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.48588 | −0.251160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.55568 | 1.40654 | 0.703272 | − | 0.710921i | \(-0.251721\pi\) | ||||
0.703272 | + | 0.710921i | \(0.251721\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.19494 | 0.511600 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.33053 | 0.363968 | 0.181984 | − | 0.983301i | \(-0.441748\pi\) | ||||
0.181984 | + | 0.983301i | \(0.441748\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.990005 | −0.150974 | −0.0754872 | − | 0.997147i | \(-0.524051\pi\) | ||||
−0.0754872 | + | 0.997147i | \(0.524051\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.48070 | 0.369801 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.32330 | −0.484753 | −0.242376 | − | 0.970182i | \(-0.577927\pi\) | ||||
−0.242376 | + | 0.970182i | \(0.577927\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.29600 | −0.613714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.92410 | 0.269428 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.47032 | −0.888767 | −0.444384 | − | 0.895837i | \(-0.646577\pi\) | ||||
−0.444384 | + | 0.895837i | \(0.646577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.02415 | −0.272937 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.26258 | 0.167233 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.39477 | 0.441961 | 0.220980 | − | 0.975278i | \(-0.429074\pi\) | ||||
0.220980 | + | 0.975278i | \(0.429074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.94685 | −1.27356 | −0.636782 | − | 0.771044i | \(-0.719735\pi\) | ||||
−0.636782 | + | 0.771044i | \(0.719735\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.51435 | −0.568755 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.72061 | 0.709555 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7402 | 1.43429 | 0.717146 | − | 0.696923i | \(-0.245448\pi\) | ||||
0.717146 | + | 0.696923i | \(0.245448\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.21072 | 0.266140 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.71165 | 1.15256 | 0.576280 | − | 0.817252i | \(-0.304504\pi\) | ||||
0.576280 | + | 0.817252i | \(0.304504\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.32458 | 0.389113 | 0.194556 | − | 0.980891i | \(-0.437673\pi\) | ||||
0.194556 | + | 0.980891i | \(0.437673\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.11125 | 0.243787 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.68354 | 0.419778 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.95388 | 0.669864 | 0.334932 | − | 0.942242i | \(-0.391287\pi\) | ||||
0.334932 | + | 0.942242i | \(0.391287\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.77270 | 0.752522 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.44942 | 1.03721 | 0.518604 | − | 0.855014i | \(-0.326452\pi\) | ||||
0.518604 | + | 0.855014i | \(0.326452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.44515 | 0.373679 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.952574 | 0.102127 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.70059 | −0.180262 | −0.0901310 | − | 0.995930i | \(-0.528729\pi\) | ||||
−0.0901310 | + | 0.995930i | \(0.528729\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.4103 | −1.09130 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.83230 | −0.501086 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.26068 | 0.231941 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7100 | 1.08744 | 0.543718 | − | 0.839268i | \(-0.317016\pi\) | ||||
0.543718 | + | 0.839268i | \(0.317016\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.14970 | −0.618068 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.40688 | 0.139990 | 0.0699950 | − | 0.997547i | \(-0.477702\pi\) | ||||
0.0699950 | + | 0.997547i | \(0.477702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.10665 | 0.404640 | 0.202320 | − | 0.979319i | \(-0.435152\pi\) | ||||
0.202320 | + | 0.979319i | \(0.435152\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.749872 | 0.0731800 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.3731 | 1.19615 | 0.598075 | − | 0.801440i | \(-0.295932\pi\) | ||||
0.598075 | + | 0.801440i | \(0.295932\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.3863 | 1.56952 | 0.784760 | − | 0.619800i | \(-0.212786\pi\) | ||||
0.784760 | + | 0.619800i | \(0.212786\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.31774 | −0.409822 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9602 | −1.21920 | −0.609598 | − | 0.792711i | \(-0.708669\pi\) | ||||
−0.609598 | + | 0.792711i | \(0.708669\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.95835 | 0.369118 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.3801 | 1.60679 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.26945 | −0.574720 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.98208 | −0.543826 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.17614 | −0.106049 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.29830 | 0.742223 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.91021 | −0.169504 | −0.0847518 | − | 0.996402i | \(-0.527010\pi\) | ||||
−0.0847518 | + | 0.996402i | \(0.527010\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.499620 | 0.0439891 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9558 | 0.957209 | 0.478604 | − | 0.878031i | \(-0.341143\pi\) | ||||
0.478604 | + | 0.878031i | \(0.341143\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.11396 | −0.356726 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.61998 | −0.225492 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.43877 | 0.464666 | 0.232333 | − | 0.972636i | \(-0.425364\pi\) | ||||
0.232333 | + | 0.972636i | \(0.425364\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.81790 | 0.493468 | 0.246734 | − | 0.969083i | \(-0.420643\pi\) | ||||
0.246734 | + | 0.969083i | \(0.420643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.67715 | 0.141241 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.1815 | −1.18592 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.70561 | 0.141643 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.16804 | 0.178817 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.8512 | −1.95397 | −0.976984 | − | 0.213311i | \(-0.931575\pi\) | ||||
−0.976984 | + | 0.213311i | \(0.931575\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.8927 | −1.61885 | −0.809423 | − | 0.587226i | \(-0.800220\pi\) | ||||
−0.809423 | + | 0.587226i | \(0.800220\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.4669 | 0.846200 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.65234 | −0.694973 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.26936 | 0.580158 | 0.290079 | − | 0.957003i | \(-0.406318\pi\) | ||||
0.290079 | + | 0.957003i | \(0.406318\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.26534 | 0.258958 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.20336 | −0.567704 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.9948 | −1.01783 | −0.508916 | − | 0.860816i | \(-0.669954\pi\) | ||||
−0.508916 | + | 0.860816i | \(0.669954\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.02152 | 0.0795250 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.5064 | −0.890393 | −0.445197 | − | 0.895433i | \(-0.646866\pi\) | ||||
−0.445197 | + | 0.895433i | \(0.646866\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.0794 | 2.08303 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.86830 | 0.525232 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.45380 | 0.718759 | 0.359379 | − | 0.933192i | \(-0.382988\pi\) | ||||
0.359379 | + | 0.933192i | \(0.382988\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.87926 | −0.520023 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.71321 | −0.128773 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.6220 | −1.84033 | −0.920166 | − | 0.391529i | \(-0.871946\pi\) | ||||
−0.920166 | + | 0.391529i | \(0.871946\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.4415 | −1.74239 | −0.871195 | − | 0.490937i | \(-0.836654\pi\) | ||||
−0.871195 | + | 0.490937i | \(0.836654\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.01981 | 0.371075 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.73101 | −0.568395 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.54060 | −0.624550 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.76781 | 0.346807 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.50833 | 0.398569 | 0.199284 | − | 0.979942i | \(-0.436138\pi\) | ||||
0.199284 | + | 0.979942i | \(0.436138\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.739940 | 0.0532620 | 0.0266310 | − | 0.999645i | \(-0.491522\pi\) | ||||
0.0266310 | + | 0.999645i | \(0.491522\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.88699 | −0.206741 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.2205 | 1.65439 | 0.827197 | − | 0.561912i | \(-0.189934\pi\) | ||||
0.827197 | + | 0.561912i | \(0.189934\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.08418 | 0.0768556 | 0.0384278 | − | 0.999261i | \(-0.487765\pi\) | ||||
0.0384278 | + | 0.999261i | \(0.487765\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.92485 | −0.417907 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.10384 | −0.217847 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.10590 | −0.147082 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.0261 | 0.835870 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.60427 | −0.387656 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.5937 | −1.28004 | −0.640022 | − | 0.768356i | \(-0.721075\pi\) | ||||
−0.640022 | + | 0.768356i | \(0.721075\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.90112 | −0.335819 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.894580 | 0.0610099 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.7454 | 1.06887 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.67779 | −0.113375 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.1372 | 1.62365 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.75353 | 0.385285 | 0.192643 | − | 0.981269i | \(-0.438294\pi\) | ||||
0.192643 | + | 0.981269i | \(0.438294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.4850 | 0.765666 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.915535 | 0.0607662 | 0.0303831 | − | 0.999538i | \(-0.490327\pi\) | ||||
0.0303831 | + | 0.999538i | \(0.490327\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.4645 | 1.22017 | 0.610083 | − | 0.792338i | \(-0.291136\pi\) | ||||
0.610083 | + | 0.792338i | \(0.291136\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.85895 | −0.122310 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.57933 | 0.365514 | 0.182757 | − | 0.983158i | \(-0.441498\pi\) | ||||
0.182757 | + | 0.983158i | \(0.441498\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00297 | 0.195892 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.00471 | −0.195177 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.4650 | 1.25908 | 0.629542 | − | 0.776966i | \(-0.283243\pi\) | ||||
0.629542 | + | 0.776966i | \(0.283243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.1410 | 1.36181 | 0.680905 | − | 0.732372i | \(-0.261587\pi\) | ||||
0.680905 | + | 0.732372i | \(0.261587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.1163 | −0.777260 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.88192 | 0.248007 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.8387 | 1.00779 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.76878 | −0.302209 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.2177 | 0.708056 | 0.354028 | − | 0.935235i | \(-0.384812\pi\) | ||||
0.354028 | + | 0.935235i | \(0.384812\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.81282 | −0.616926 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.73864 | −0.108878 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.41182 | 0.399958 | 0.199979 | − | 0.979800i | \(-0.435913\pi\) | ||||
0.199979 | + | 0.979800i | \(0.435913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.0688 | 0.874194 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.18190 | 0.320751 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.2453 | 1.18672 | 0.593358 | − | 0.804939i | \(-0.297802\pi\) | ||||
0.593358 | + | 0.804939i | \(0.297802\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.84666 | 0.359157 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.858225 | 0.0525225 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.43959 | 0.0877733 | 0.0438867 | − | 0.999037i | \(-0.486026\pi\) | ||||
0.0438867 | + | 0.999037i | \(0.486026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.34772 | −0.142614 | −0.0713068 | − | 0.997454i | \(-0.522717\pi\) | ||||
−0.0713068 | + | 0.997454i | \(0.522717\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.25371 | 0.317969 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.37131 | −0.565111 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9792 | 1.50086 | 0.750429 | − | 0.660952i | \(-0.229847\pi\) | ||||
0.750429 | + | 0.660952i | \(0.229847\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.2872 | −1.57377 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7529 | −0.999394 | −0.499697 | − | 0.866200i | \(-0.666555\pi\) | ||||
−0.499697 | + | 0.866200i | \(0.666555\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2363 | 1.44070 | 0.720349 | − | 0.693612i | \(-0.243982\pi\) | ||||
0.720349 | + | 0.693612i | \(0.243982\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.14088 | −0.0675801 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.83229 | 0.226213 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.46373 | −0.144925 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.40495 | −0.316844 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.2731 | 1.71015 | 0.855077 | − | 0.518500i | \(-0.173509\pi\) | ||||
0.855077 | + | 0.518500i | \(0.173509\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.06755 | −0.178600 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.49498 | 0.376877 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.7327 | 1.60383 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.62795 | −0.0938334 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.710002 | −0.0407886 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.98809 | 0.514656 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.9134 | −1.53603 | −0.768015 | − | 0.640432i | \(-0.778755\pi\) | ||||
−0.768015 | + | 0.640432i | \(0.778755\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.07248 | −0.117899 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.2381 | −1.94146 | −0.970731 | − | 0.240169i | \(-0.922797\pi\) | ||||
−0.970731 | + | 0.240169i | \(0.922797\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.3116 | −1.03503 | −0.517515 | − | 0.855674i | \(-0.673143\pi\) | ||||
−0.517515 | + | 0.855674i | \(0.673143\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.07922 | 0.229838 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.1256 | −0.737209 | −0.368605 | − | 0.929586i | \(-0.620164\pi\) | ||||
−0.368605 | + | 0.929586i | \(0.620164\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.22823 | −0.236735 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.24424 | −0.348520 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.53858 | 0.530741 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.4850 | 1.46912 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.26956 | −0.457307 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.46478 | −0.301283 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.68299 | −0.367330 | −0.183665 | − | 0.982989i | \(-0.558796\pi\) | ||||
−0.183665 | + | 0.982989i | \(0.558796\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −23.4880 | −1.28714 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.6086 | −0.579608 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.23845 | −0.230883 | −0.115442 | − | 0.993314i | \(-0.536828\pi\) | ||||
−0.115442 | + | 0.993314i | \(0.536828\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.54056 | 0.355234 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.4493 | 1.16155 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5750 | −1.00295 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.99763 | −0.107549 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.3621 | 1.89833 | 0.949167 | − | 0.314772i | \(-0.101928\pi\) | ||||
0.949167 | + | 0.314772i | \(0.101928\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.6227 | 1.15744 | 0.578718 | − | 0.815528i | \(-0.303553\pi\) | ||||
0.578718 | + | 0.815528i | \(0.303553\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.3559 | −0.979768 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.8602 | 1.26995 | 0.634976 | − | 0.772532i | \(-0.281010\pi\) | ||||
0.634976 | + | 0.772532i | \(0.281010\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.77556 | −0.465758 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.16397 | 0.167455 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.1745 | −0.695321 | −0.347661 | − | 0.937620i | \(-0.613024\pi\) | ||||
−0.347661 | + | 0.937620i | \(0.613024\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.7409 | −0.670572 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.01894 | 0.158453 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.00413 | −0.157243 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.1119 | 0.841035 | 0.420517 | − | 0.907285i | \(-0.361849\pi\) | ||||
0.420517 | + | 0.907285i | \(0.361849\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.39805 | −0.333069 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.6397 | −0.552386 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.2917 | 1.72378 | 0.861889 | − | 0.507097i | \(-0.169281\pi\) | ||||
0.861889 | + | 0.507097i | \(0.169281\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.18785 | −0.216260 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.9497 | 0.615442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.4967 | 1.25831 | 0.629155 | − | 0.777280i | \(-0.283401\pi\) | ||||
0.629155 | + | 0.777280i | \(0.283401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.964013 | 0.0493879 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.4214 | −0.685800 | −0.342900 | − | 0.939372i | \(-0.611409\pi\) | ||||
−0.342900 | + | 0.939372i | \(0.611409\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.32849 | −0.169635 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.71788 | 0.138157 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.6525 | 1.40204 | 0.701019 | − | 0.713143i | \(-0.252729\pi\) | ||||
0.701019 | + | 0.713143i | \(0.252729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7016 | 0.844637 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.52897 | −0.278900 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.38000 | −0.270697 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.4470 | 1.52809 | 0.764047 | − | 0.645161i | \(-0.223210\pi\) | ||||
0.764047 | + | 0.645161i | \(0.223210\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.07617 | 0.103938 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.2726 | 0.662804 | 0.331402 | − | 0.943490i | \(-0.392478\pi\) | ||||
0.331402 | + | 0.943490i | \(0.392478\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −60.6195 | −3.01967 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.11989 | −0.304100 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.1653 | 0.949990 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.3887 | −1.40373 | −0.701865 | − | 0.712310i | \(-0.747649\pi\) | ||||
−0.701865 | + | 0.712310i | \(0.747649\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.74475 | −0.135389 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.58230 | 0.274687 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.53860 | −0.419144 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.93608 | −0.143781 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.5165 | 0.709177 | 0.354588 | − | 0.935022i | \(-0.384621\pi\) | ||||
0.354588 | + | 0.935022i | \(0.384621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.02209 | −0.0985507 | −0.0492753 | − | 0.998785i | \(-0.515691\pi\) | ||||
−0.0492753 | + | 0.998785i | \(0.515691\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.12349 | 0.443599 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.9502 | 0.773696 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.3564 | −0.791543 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.15690 | 0.345538 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.2765 | 1.07302 | 0.536511 | − | 0.843893i | \(-0.319742\pi\) | ||||
0.536511 | + | 0.843893i | \(0.319742\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.2817 | 0.494106 | 0.247053 | − | 0.969002i | \(-0.420538\pi\) | ||||
0.247053 | + | 0.969002i | \(0.420538\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.860757 | −0.0412701 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.9595 | 0.524262 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9755 | 0.523834 | 0.261917 | − | 0.965090i | \(-0.415645\pi\) | ||||
0.261917 | + | 0.965090i | \(0.415645\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.7939 | 0.561613 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.5555 | −1.78431 | −0.892157 | − | 0.451726i | \(-0.850808\pi\) | ||||
−0.892157 | + | 0.451726i | \(0.850808\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.53667 | 0.0728452 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0369 | 0.569323 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.14000 | 0.289765 | 0.144882 | − | 0.989449i | \(-0.453720\pi\) | ||||
0.144882 | + | 0.989449i | \(0.453720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.22056 | 0.245827 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.0391 | 0.471680 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.40689 | 0.441002 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.1136 | −1.26832 | −0.634161 | − | 0.773201i | \(-0.718654\pi\) | ||||
−0.634161 | + | 0.773201i | \(0.718654\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.0546 | −0.515984 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.4146 | −1.50970 | −0.754849 | − | 0.655899i | \(-0.772290\pi\) | ||||
−0.754849 | + | 0.655899i | \(0.772290\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.9999 | 1.71953 | 0.859766 | − | 0.510688i | \(-0.170609\pi\) | ||||
0.859766 | + | 0.510688i | \(0.170609\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.36652 | 0.202493 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1061 | 0.791577 | 0.395789 | − | 0.918342i | \(-0.370471\pi\) | ||||
0.395789 | + | 0.918342i | \(0.370471\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.3054 | 0.891440 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.66858 | −0.169039 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.21768 | −0.101969 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.4664 | 0.480230 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.7631 | 0.813315 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.9057 | −1.18366 | −0.591830 | − | 0.806063i | \(-0.701594\pi\) | ||||
−0.591830 | + | 0.806063i | \(0.701594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −54.1646 | −2.46969 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.63527 | 0.165411 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.67768 | −0.439441 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.2178 | 1.23336 | 0.616679 | − | 0.787215i | \(-0.288478\pi\) | ||||
0.616679 | + | 0.787215i | \(0.288478\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.55801 | 0.296563 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.8341 | −0.534067 | −0.267033 | − | 0.963687i | \(-0.586043\pi\) | ||||
−0.267033 | + | 0.963687i | \(0.586043\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.19653 | 0.324115 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.55694 | 0.249766 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.9697 | 0.716338 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.3820 | 1.36009 | 0.680043 | − | 0.733173i | \(-0.261961\pi\) | ||||
0.680043 | + | 0.733173i | \(0.261961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.80687 | 0.259432 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.4753 | −0.467070 | −0.233535 | − | 0.972348i | \(-0.575029\pi\) | ||||
−0.233535 | + | 0.972348i | \(0.575029\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.27127 | −0.0565710 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.6660 | −0.606929 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.2343 | −0.630922 | −0.315461 | − | 0.948938i | \(-0.602159\pi\) | ||||
−0.315461 | + | 0.948938i | \(0.602159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.46689 | 0.241841 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.25393 | −0.320269 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.71082 | −0.163518 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.44442 | −0.327405 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.77099 | −0.209423 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.7488 | 1.34713 | 0.673564 | − | 0.739129i | \(-0.264763\pi\) | ||||
0.673564 | + | 0.739129i | \(0.264763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.425051 | −0.0185862 | −0.00929308 | − | 0.999957i | \(-0.502958\pi\) | ||||
−0.00929308 | + | 0.999957i | \(0.502958\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.47171 | 0.151518 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.5072 | −1.59028 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.81049 | −0.165674 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.31970 | −0.404440 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.7542 | −0.639076 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.1805 | −0.483373 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.4258 | 0.536213 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.62335 | −0.414507 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.367014 | −0.0157792 | −0.00788959 | − | 0.999969i | \(-0.502511\pi\) | ||||
−0.00788959 | + | 0.999969i | \(0.502511\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.8301 | 0.507676 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.8068 | −0.634255 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.30136 | 0.397697 | 0.198849 | − | 0.980030i | \(-0.436280\pi\) | ||||
0.198849 | + | 0.980030i | \(0.436280\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.3072 | 1.16544 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.72231 | 0.201177 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.79047 | 0.416333 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.90156 | 0.165612 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.6404 | −0.493221 | −0.246611 | − | 0.969115i | \(-0.579317\pi\) | ||||
−0.246611 | + | 0.969115i | \(0.579317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.26756 | 0.265089 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.31013 | 0.181974 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.3326 | 1.57338 | 0.786691 | − | 0.617347i | \(-0.211792\pi\) | ||||
0.786691 | + | 0.617347i | \(0.211792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.7110 | 0.492686 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.1369 | 0.467706 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.3662 | −1.73416 | −0.867080 | − | 0.498169i | \(-0.834006\pi\) | ||||
−0.867080 | + | 0.498169i | \(0.834006\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5571 | 0.567347 | 0.283674 | − | 0.958921i | \(-0.408447\pi\) | ||||
0.283674 | + | 0.958921i | \(0.408447\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.77985 | −0.116130 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.3261 | 0.764252 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.30733 | −0.220947 | −0.110473 | − | 0.993879i | \(-0.535237\pi\) | ||||
−0.110473 | + | 0.993879i | \(0.535237\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.373421 | −0.0155188 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.5385 | 0.644644 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.4940 | −0.600280 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.7049 | −0.649317 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.4287 | −0.554262 | −0.277131 | − | 0.960832i | \(-0.589384\pi\) | ||||
−0.277131 | + | 0.960832i | \(0.589384\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.9557 | −0.987078 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.7186 | −0.482037 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.3057 | 0.792792 | 0.396396 | − | 0.918080i | \(-0.370261\pi\) | ||||
0.396396 | + | 0.918080i | \(0.370261\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.66515 | 0.232249 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.547147 | −0.0223932 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.6643 | −1.29377 | −0.646885 | − | 0.762588i | \(-0.723929\pi\) | ||||
−0.646885 | + | 0.762588i | \(0.723929\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.1201 | 1.47337 | 0.736684 | − | 0.676237i | \(-0.236391\pi\) | ||||
0.736684 | + | 0.676237i | \(0.236391\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −32.2305 | −1.31253 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.40548 | 0.219764 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.9429 | 1.33711 | 0.668556 | − | 0.743662i | \(-0.266913\pi\) | ||||
0.668556 | + | 0.743662i | \(0.266913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.56640 | 0.0634736 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.0392 | 0.851156 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.0719 | −1.33576 | −0.667881 | − | 0.744268i | \(-0.732798\pi\) | ||||
−0.667881 | + | 0.744268i | \(0.732798\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.06277 | 0.0428550 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.05961 | −0.123175 | −0.0615876 | − | 0.998102i | \(-0.519616\pi\) | ||||
−0.0615876 | + | 0.998102i | \(0.519616\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.2067 | 1.29450 | 0.647248 | − | 0.762280i | \(-0.275920\pi\) | ||||
0.647248 | + | 0.762280i | \(0.275920\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.7013 | −0.509685 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.79642 | −0.112036 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.4190 | 0.536759 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.82827 | 0.112950 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.6198 | −1.30064 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.93992 | 0.236464 | 0.118232 | − | 0.992986i | \(-0.462277\pi\) | ||||
0.118232 | + | 0.992986i | \(0.462277\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.38358 | 0.372964 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.72609 | 0.0684976 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.1973 | 1.07759 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.6615 | −1.05471 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.50720 | 0.0990286 | 0.0495143 | − | 0.998773i | \(-0.484233\pi\) | ||||
0.0495143 | + | 0.998773i | \(0.484233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.1241 | 1.30629 | 0.653144 | − | 0.757234i | \(-0.273450\pi\) | ||||
0.653144 | + | 0.757234i | \(0.273450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.451462 | −0.0177763 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.2107 | 0.991133 | 0.495567 | − | 0.868570i | \(-0.334960\pi\) | ||||
0.495567 | + | 0.868570i | \(0.334960\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.60451 | 0.298503 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.94616 | −0.311434 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.7885 | −1.63531 | −0.817656 | − | 0.575708i | \(-0.804727\pi\) | ||||
−0.817656 | + | 0.575708i | \(0.804727\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.89975 | −0.386815 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.12702 | −0.356079 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.0338 | 0.858315 | 0.429158 | − | 0.903230i | \(-0.358810\pi\) | ||||
0.429158 | + | 0.903230i | \(0.358810\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.5753 | −1.07255 | −0.536277 | − | 0.844042i | \(-0.680170\pi\) | ||||
−0.536277 | + | 0.844042i | \(0.680170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.1812 | −0.473078 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.71743 | 0.144156 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.26854 | 0.320159 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.90360 | −0.112260 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.2816 | −0.860173 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.6341 | −0.679746 | −0.339873 | − | 0.940471i | \(-0.610384\pi\) | ||||
−0.339873 | + | 0.940471i | \(0.610384\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.1298 | −0.466877 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.3902 | −1.28329 | −0.641646 | − | 0.767001i | \(-0.721748\pi\) | ||||
−0.641646 | + | 0.767001i | \(0.721748\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.6113 | 0.675862 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.462037 | −0.0177053 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.00658 | 0.0385155 | 0.0192578 | − | 0.999815i | \(-0.493870\pi\) | ||||
0.0192578 | + | 0.999815i | \(0.493870\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.91454 | −0.187775 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.31834 | −0.355517 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.9625 | 1.56055 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.46921 | 0.0939332 | 0.0469666 | − | 0.998896i | \(-0.485045\pi\) | ||||
0.0469666 | + | 0.998896i | \(0.485045\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.1125 | −0.384141 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.25712 | −0.199414 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.88550 | −0.336562 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.81569 | −0.106499 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.94490 | −0.300075 | −0.150037 | − | 0.988680i | \(-0.547939\pi\) | ||||
−0.150037 | + | 0.988680i | \(0.547939\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.4048 | −0.807298 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.51549 | −0.0570766 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.31345 | 0.0870064 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.0345 | 1.91664 | 0.958320 | − | 0.285698i | \(-0.0922253\pi\) | ||||
0.958320 | + | 0.285698i | \(0.0922253\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.3453 | −0.612996 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41.9453 | −1.57087 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.8146 | 0.479238 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.82326 | −0.366856 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.9358 | −1.86229 | −0.931145 | − | 0.364649i | \(-0.881189\pi\) | ||||
−0.931145 | + | 0.364649i | \(0.881189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.75291 | 0.251492 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.6691 | −0.396787 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.89651 | 0.293269 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.6832 | 1.43468 | 0.717340 | − | 0.696724i | \(-0.245360\pi\) | ||||
0.717340 | + | 0.696724i | \(0.245360\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.2034 | −0.526053 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.77454 | 0.139606 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.8816 | −1.17757 | −0.588787 | − | 0.808288i | \(-0.700394\pi\) | ||||
−0.588787 | + | 0.808288i | \(0.700394\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.95906 | −0.0722611 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.2989 | 0.968731 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.0431 | −1.76729 | −0.883647 | − | 0.468154i | \(-0.844919\pi\) | ||||
−0.883647 | + | 0.468154i | \(0.844919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.99319 | −0.293637 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.0402 | −1.17544 | −0.587720 | − | 0.809065i | \(-0.699974\pi\) | ||||
−0.587720 | + | 0.809065i | \(0.699974\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.5522 | 0.789613 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25.9416 | −0.949154 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.3461 | 0.743430 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.66117 | −0.206305 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.9753 | 0.654188 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.0515857 | 0.00187491 | 0.000937457 | − | 1.00000i | \(-0.499702\pi\) | ||||
0.000937457 | 1.00000i | \(0.499702\pi\) | ||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.95217 | 0.179752 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.1301 | −1.05597 | −0.527983 | − | 0.849255i | \(-0.677052\pi\) | ||||
−0.527983 | + | 0.849255i | \(0.677052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.9453 | 0.975486 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.45802 | −0.341956 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.4917 | −0.776020 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.8609 | 0.644081 | 0.322040 | − | 0.946726i | \(-0.395631\pi\) | ||||
0.322040 | + | 0.946726i | \(0.395631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.23581 | −0.116535 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.4310 | 1.77791 | 0.888955 | − | 0.457994i | \(-0.151432\pi\) | ||||
0.888955 | + | 0.457994i | \(0.151432\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.0581 | −1.43893 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.10002 | −0.254712 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.83059 | −0.208903 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.7548 | 0.778447 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.47284 | −0.195583 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.56868 | −0.234446 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.6160 | −1.80427 | −0.902134 | − | 0.431457i | \(-0.858000\pi\) | ||||
−0.902134 | + | 0.431457i | \(0.858000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.71240 | −0.345771 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.3116 | −0.757753 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 62.9718 | 2.23619 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.95060 | −0.104647 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.383072 | 0.0135691 | 0.00678455 | − | 0.999977i | \(-0.497840\pi\) | ||||
0.00678455 | + | 0.999977i | \(0.497840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.6706 | 0.448252 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.66865 | 0.164959 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.44729 | 0.262809 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.50904 | 0.229414 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.726508 | −0.0255743 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.4113 | −0.998889 | −0.499444 | − | 0.866346i | \(-0.666463\pi\) | ||||
−0.499444 | + | 0.866346i | \(0.666463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.5040 | 1.38717 | 0.693587 | − | 0.720373i | \(-0.256029\pi\) | ||||
0.693587 | + | 0.720373i | \(0.256029\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.18481 | 0.0415530 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.7423 | 0.411313 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.47682 | 0.0866530 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.5796 | 0.998652 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.34741 | 0.0470250 | 0.0235125 | − | 0.999724i | \(-0.492515\pi\) | ||||
0.0235125 | + | 0.999724i | \(0.492515\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.3804 | 1.51214 | 0.756072 | − | 0.654488i | \(-0.227116\pi\) | ||||
0.756072 | + | 0.654488i | \(0.227116\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.72936 | 0.164655 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.3486 | 0.533722 | 0.266861 | − | 0.963735i | \(-0.414014\pi\) | ||||
0.266861 | + | 0.963735i | \(0.414014\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.51968 | 0.191706 | 0.0958532 | − | 0.995395i | \(-0.469442\pi\) | ||||
0.0958532 | + | 0.995395i | \(0.469442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.6061 | −0.437301 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.3791 | 0.567503 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.3973 | 0.359815 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.7631 | 0.959632 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.3809 | −0.910771 | −0.455385 | − | 0.890294i | \(-0.650498\pi\) | ||||
−0.455385 | + | 0.890294i | \(0.650498\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.4372 | −0.877144 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.45458 | 0.291191 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.4693 | −0.841769 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.83684 | −0.337998 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.2312 | −0.419773 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.4789 | −1.28476 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.1217 | −1.03135 | −0.515673 | − | 0.856785i | \(-0.672458\pi\) | ||||
−0.515673 | + | 0.856785i | \(0.672458\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.20628 | −0.212250 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.4983 | −1.00764 | −0.503821 | − | 0.863808i | \(-0.668073\pi\) | ||||
−0.503821 | + | 0.863808i | \(0.668073\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.2468 | 1.30497 | 0.652483 | − | 0.757804i | \(-0.273728\pi\) | ||||
0.652483 | + | 0.757804i | \(0.273728\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.93402 | −0.0659112 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.2451 | −1.64228 | −0.821141 | − | 0.570725i | \(-0.806662\pi\) | ||||
−0.821141 | + | 0.570725i | \(0.806662\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.54256 | −0.290456 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.24336 | 0.0422266 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3371 | 0.452431 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −74.3252 | −2.51841 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.4023 | −0.995118 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.6456 | 0.461305 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.5579 | 1.47085 | 0.735423 | − | 0.677608i | \(-0.236983\pi\) | ||||
0.735423 | + | 0.677608i | \(0.236983\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.7731 | −0.498284 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.3211 | −0.785707 | −0.392854 | − | 0.919601i | \(-0.628512\pi\) | ||||
−0.392854 | + | 0.919601i | \(0.628512\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.2831 | −0.413358 | −0.206679 | − | 0.978409i | \(-0.566266\pi\) | ||||
−0.206679 | + | 0.978409i | \(0.566266\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.54808 | 0.0520382 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.4765 | −0.956147 | −0.478074 | − | 0.878320i | \(-0.658665\pi\) | ||||
−0.478074 | + | 0.878320i | \(0.658665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.14112 | −0.105350 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.1713 | 0.508258 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.31431 | 0.278228 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.2487 | 0.743692 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.9957 | −0.467303 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.0738 | −0.602794 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.6691 | 0.821845 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.821567 | 0.0273400 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.1820 | 0.704113 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.7628 | −1.32030 | −0.660152 | − | 0.751132i | \(-0.729508\pi\) | ||||
−0.660152 | + | 0.751132i | \(0.729508\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.86233 | −0.128105 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.5528 | −0.515288 | −0.257644 | − | 0.966240i | \(-0.582946\pi\) | ||||
−0.257644 | + | 0.966240i | \(0.582946\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.1674 | 0.700538 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.53596 | −0.149954 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.0155 | 0.594923 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.9114 | 1.44850 | 0.724251 | − | 0.689536i | \(-0.242185\pi\) | ||||
0.724251 | + | 0.689536i | \(0.242185\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.5822 | 0.447549 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −61.4828 | −2.02373 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.7926 | −1.17685 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.2740 | −0.370288 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.3530 | −0.667760 | −0.333880 | − | 0.942616i | \(-0.608358\pi\) | ||||
−0.333880 | + | 0.942616i | \(0.608358\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.7479 | 0.352247 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.2787 | 0.565679 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.71738 | 0.252385 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.18883 | −0.104175 | −0.0520873 | − | 0.998643i | \(-0.516587\pi\) | ||||
−0.0520873 | + | 0.998643i | \(0.516587\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.24118 | 0.301574 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.4542 | 1.87295 | 0.936476 | − | 0.350730i | \(-0.114067\pi\) | ||||
0.936476 | + | 0.350730i | \(0.114067\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.2091 | −0.332454 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.30825 | −0.140147 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.3526 | −0.628873 | −0.314437 | − | 0.949278i | \(-0.601816\pi\) | ||||
−0.314437 | + | 0.949278i | \(0.601816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.0474 | −0.683226 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.62403 | 0.214799 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.2274 | −0.946768 | −0.473384 | − | 0.880856i | \(-0.656968\pi\) | ||||
−0.473384 | + | 0.880856i | \(0.656968\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.97739 | −0.161065 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.13383 | 0.0689770 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.94343 | 0.288799 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.6861 | 1.95762 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −33.9680 | −1.09460 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.668618 | −0.0215236 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.64094 | −0.245716 | −0.122858 | − | 0.992424i | \(-0.539206\pi\) | ||||
−0.122858 | + | 0.992424i | \(0.539206\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.81378 | −0.154641 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.57369 | −0.0825936 | −0.0412968 | − | 0.999147i | \(-0.513149\pi\) | ||||
−0.0412968 | + | 0.999147i | \(0.513149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.56686 | 0.306700 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.3660 | −0.428054 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.3351 | −1.35442 | −0.677210 | − | 0.735790i | \(-0.736811\pi\) | ||||
−0.677210 | + | 0.735790i | \(0.736811\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.80944 | −0.121750 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.9855 | −1.43628 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.6878 | 1.58479 | 0.792397 | − | 0.610006i | \(-0.208833\pi\) | ||||
0.792397 | + | 0.610006i | \(0.208833\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.9823 | −0.668553 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.75787 | 0.0877841 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.33680 | 0.137902 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.75140 | −0.0874010 | −0.0437005 | − | 0.999045i | \(-0.513915\pi\) | ||||
−0.0437005 | + | 0.999045i | \(0.513915\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.37266 | 0.107028 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.979679 | −0.0310579 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.7084 | 1.60595 | 0.802975 | − | 0.596012i | \(-0.203249\pi\) | ||||
0.802975 | + | 0.596012i | \(0.203249\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.8068 | 0.784852 |
(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 | 6008.2.a.e.1.21 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.21 | ✓ | 50 | 1.1 | even | 1 | trivial |