Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 13 x^{10} + 60 x^{9} + 48 x^{8} - 289 x^{7} - 89 x^{6} + 602 x^{5} + 161 x^{4} + \cdots + 82 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.36915\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | −2.36915 | −1.36783 | −0.683916 | − | 0.729561i | \(-0.739724\pi\) | ||||
−0.683916 | + | 0.729561i | \(0.739724\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.61284 | 1.16850 | 0.584249 | − | 0.811575i | \(-0.301389\pi\) | ||||
0.584249 | + | 0.811575i | \(0.301389\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.25519 | −0.852382 | −0.426191 | − | 0.904633i | \(-0.640145\pi\) | ||||
−0.426191 | + | 0.904633i | \(0.640145\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.61289 | 0.870962 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.06042 | −1.82729 | −0.913643 | − | 0.406517i | \(-0.866743\pi\) | ||||
−0.913643 | + | 0.406517i | \(0.866743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.42929 | 1.50581 | 0.752907 | − | 0.658127i | \(-0.228651\pi\) | ||||
0.752907 | + | 0.658127i | \(0.228651\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.19022 | −1.59831 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.71401 | −1.08147 | −0.540734 | − | 0.841193i | \(-0.681854\pi\) | ||||
−0.540734 | + | 0.841193i | \(0.681854\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.34289 | 1.16591 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.23431 | 1.92549 | 0.962744 | − | 0.270415i | \(-0.0871609\pi\) | ||||
0.962744 | + | 0.270415i | \(0.0871609\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.82693 | 0.365385 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.917132 | 0.176502 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.85561 | 0.901664 | 0.450832 | − | 0.892609i | \(-0.351127\pi\) | ||||
0.450832 | + | 0.892609i | \(0.351127\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.261418 | −0.0469521 | −0.0234760 | − | 0.999724i | \(-0.507473\pi\) | ||||
−0.0234760 | + | 0.999724i | \(0.507473\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.3581 | 2.49942 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.89245 | −0.996006 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.91282 | 0.807663 | 0.403832 | − | 0.914833i | \(-0.367678\pi\) | ||||
0.403832 | + | 0.914833i | \(0.367678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.8628 | −2.05970 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.42987 | −0.848003 | −0.424001 | − | 0.905662i | \(-0.639375\pi\) | ||||
−0.424001 | + | 0.905662i | \(0.639375\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.25368 | −0.801179 | −0.400589 | − | 0.916258i | \(-0.631195\pi\) | ||||
−0.400589 | + | 0.916258i | \(0.631195\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.82705 | 1.01772 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.34302 | −0.195899 | −0.0979495 | − | 0.995191i | \(-0.531228\pi\) | ||||
−0.0979495 | + | 0.995191i | \(0.531228\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.91412 | −0.273445 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.36915 | 0.331748 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.39130 | 0.740553 | 0.370276 | − | 0.928922i | \(-0.379263\pi\) | ||||
0.370276 | + | 0.928922i | \(0.379263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.8349 | −2.13518 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.1682 | 1.47927 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.6581 | −1.62070 | −0.810350 | − | 0.585946i | \(-0.800723\pi\) | ||||
−0.810350 | + | 0.585946i | \(0.800723\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.89256 | −0.742392 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.1859 | 1.75954 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.44937 | −0.421407 | −0.210704 | − | 0.977550i | \(-0.567576\pi\) | ||||
−0.210704 | + | 0.977550i | \(0.567576\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −21.8775 | −2.63374 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.07941 | −0.246780 | −0.123390 | − | 0.992358i | \(-0.539377\pi\) | ||||
−0.123390 | + | 0.992358i | \(0.539377\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.551991 | −0.0646057 | −0.0323029 | − | 0.999478i | \(-0.510284\pi\) | ||||
−0.0323029 | + | 0.999478i | \(0.510284\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.32827 | −0.499786 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.6674 | 1.55755 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1411 | 1.70350 | 0.851752 | − | 0.523945i | \(-0.175540\pi\) | ||||
0.851752 | + | 0.523945i | \(0.175540\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.0115 | −1.11239 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.01331 | 0.769811 | 0.384906 | − | 0.922956i | \(-0.374234\pi\) | ||||
0.384906 | + | 0.922956i | \(0.374234\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.61284 | −0.283402 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.5037 | −1.23332 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.76169 | −0.928737 | −0.464369 | − | 0.885642i | \(-0.653719\pi\) | ||||
−0.464369 | + | 0.885642i | \(0.653719\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.2441 | −1.28353 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.619339 | 0.0642225 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.3170 | −1.26369 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.65497 | −0.168037 | −0.0840184 | − | 0.996464i | \(-0.526775\pi\) | ||||
−0.0840184 | + | 0.996464i | \(0.526775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.8352 | −1.59150 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3274 | −1.02761 | −0.513806 | − | 0.857906i | \(-0.671765\pi\) | ||||
−0.513806 | + | 0.857906i | \(0.671765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.42576 | 0.633149 | 0.316574 | − | 0.948568i | \(-0.397467\pi\) | ||||
0.316574 | + | 0.948568i | \(0.397467\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.9601 | 1.36237 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.5279 | −1.01777 | −0.508887 | − | 0.860833i | \(-0.669943\pi\) | ||||
−0.508887 | + | 0.860833i | \(0.669943\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.328812 | −0.0314945 | −0.0157473 | − | 0.999876i | \(-0.505013\pi\) | ||||
−0.0157473 | + | 0.999876i | \(0.505013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.6392 | −1.10475 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.58368 | −0.243052 | −0.121526 | − | 0.992588i | \(-0.538779\pi\) | ||||
−0.121526 | + | 0.992588i | \(0.538779\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.1278 | 2.24993 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.1861 | 1.31151 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.25519 | 0.206733 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.7287 | 2.33897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.8642 | 1.15992 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.29073 | −0.741545 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.01055 | 0.178407 | 0.0892037 | − | 0.996013i | \(-0.471568\pi\) | ||||
0.0892037 | + | 0.996013i | \(0.471568\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4468 | 1.09588 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4608 | 1.17607 | 0.588036 | − | 0.808835i | \(-0.299901\pi\) | ||||
0.588036 | + | 0.808835i | \(0.299901\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.6310 | 0.921824 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.39632 | 0.206242 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.1535 | −1.63639 | −0.818197 | − | 0.574939i | \(-0.805026\pi\) | ||||
−0.818197 | + | 0.574939i | \(0.805026\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2452 | 1.20826 | 0.604129 | − | 0.796886i | \(-0.293521\pi\) | ||||
0.604129 | + | 0.796886i | \(0.293521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.18181 | 0.267957 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −32.9038 | −2.75155 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.6869 | 1.05359 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.53483 | 0.374027 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.55596 | 0.537085 | 0.268543 | − | 0.963268i | \(-0.413458\pi\) | ||||
0.268543 | + | 0.963268i | \(0.413458\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.2739 | −1.81262 | −0.906311 | − | 0.422612i | \(-0.861113\pi\) | ||||
−0.906311 | + | 0.422612i | \(0.861113\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.61289 | −0.211239 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.683043 | −0.0548633 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.47766 | −0.756400 | −0.378200 | − | 0.925724i | \(-0.623457\pi\) | ||||
−0.378200 | + | 0.925724i | \(0.623457\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.7728 | −1.01295 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.8251 | −1.64125 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.15317 | 0.325301 | 0.162651 | − | 0.986684i | \(-0.447996\pi\) | ||||
0.162651 | + | 0.986684i | \(0.447996\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 37.5153 | 2.92056 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.32048 | −0.334329 | −0.167164 | − | 0.985929i | \(-0.553461\pi\) | ||||
−0.167164 | + | 0.985929i | \(0.553461\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.4772 | 1.26748 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.3172 | −0.941918 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.97592 | 0.530369 | 0.265185 | − | 0.964198i | \(-0.414567\pi\) | ||||
0.265185 | + | 0.964198i | \(0.414567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.12007 | −0.311448 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.36915 | −0.178076 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.5731 | −1.38822 | −0.694109 | − | 0.719870i | \(-0.744201\pi\) | ||||
−0.694109 | + | 0.719870i | \(0.744201\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.3636 | −1.73660 | −0.868300 | − | 0.496039i | \(-0.834787\pi\) | ||||
−0.868300 | + | 0.496039i | \(0.834787\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.9889 | 2.21685 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.8364 | 0.943752 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.06042 | 0.443182 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.06831 | −0.150447 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.19794 | 0.231395 | 0.115697 | − | 0.993285i | \(-0.463090\pi\) | ||||
0.115697 | + | 0.993285i | \(0.463090\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.6927 | −1.48950 | −0.744748 | − | 0.667346i | \(-0.767430\pi\) | ||||
−0.744748 | + | 0.667346i | \(0.767430\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −33.6085 | −2.40675 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.44238 | 0.102765 | 0.0513827 | − | 0.998679i | \(-0.483637\pi\) | ||||
0.0513827 | + | 0.998679i | \(0.483637\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.29939 | −0.446552 | −0.223276 | − | 0.974755i | \(-0.571675\pi\) | ||||
−0.223276 | + | 0.974755i | \(0.571675\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.17208 | 0.576414 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.9503 | −0.768562 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.1874 | −0.990889 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 24.1282 | 1.67703 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.5689 | 1.97615 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.51274 | 0.172984 | 0.0864920 | − | 0.996253i | \(-0.472434\pi\) | ||||
0.0864920 | + | 0.996253i | \(0.472434\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.92644 | 0.337554 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.7270 | −0.936175 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.589547 | 0.0400211 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.30775 | 0.0883697 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.42929 | −0.365214 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.19251 | −0.0798561 | −0.0399280 | − | 0.999203i | \(-0.512713\pi\) | ||||
−0.0399280 | + | 0.999203i | \(0.512713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.77355 | 0.318237 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −29.2551 | −1.94173 | −0.970865 | − | 0.239629i | \(-0.922974\pi\) | ||||
−0.970865 | + | 0.239629i | \(0.922974\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.7652 | −1.10787 | −0.553937 | − | 0.832559i | \(-0.686875\pi\) | ||||
−0.553937 | + | 0.832559i | \(0.686875\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −32.3802 | −2.13046 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.8680 | 0.777498 | 0.388749 | − | 0.921344i | \(-0.372907\pi\) | ||||
0.388749 | + | 0.921344i | \(0.372907\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.50908 | −0.228907 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −35.8715 | −2.33011 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.0664 | −1.23330 | −0.616652 | − | 0.787236i | \(-0.711511\pi\) | ||||
−0.616652 | + | 0.787236i | \(0.711511\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4893 | 0.675677 | 0.337838 | − | 0.941204i | \(-0.390304\pi\) | ||||
0.337838 | + | 0.941204i | \(0.390304\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.9673 | 1.34506 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.00128 | −0.319520 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.5937 | −1.62849 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.6156 | −1.05297 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.91962 | −0.121165 | −0.0605825 | − | 0.998163i | \(-0.519296\pi\) | ||||
−0.0605825 | + | 0.998163i | \(0.519296\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −55.9638 | −3.51842 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.19022 | 0.387646 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.0099 | −0.936293 | −0.468146 | − | 0.883651i | \(-0.655078\pi\) | ||||
−0.468146 | + | 0.883651i | \(0.655078\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.0794 | −0.688438 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.6872 | 0.785315 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.83895 | −0.483370 | −0.241685 | − | 0.970355i | \(-0.577700\pi\) | ||||
−0.241685 | + | 0.970355i | \(0.577700\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.0866 | 0.865334 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.7578 | 1.27036 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.83638 | −0.538764 | −0.269382 | − | 0.963033i | \(-0.586819\pi\) | ||||
−0.269382 | + | 0.963033i | \(0.586819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.0201 | −1.64136 | −0.820678 | − | 0.571391i | \(-0.806404\pi\) | ||||
−0.820678 | + | 0.571391i | \(0.806404\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 29.0081 | 1.75565 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.0720 | −0.667664 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.5367 | −1.47427 | −0.737133 | − | 0.675748i | \(-0.763821\pi\) | ||||
−0.737133 | + | 0.675748i | \(0.763821\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.683055 | −0.0408935 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.8388 | 0.765896 | 0.382948 | − | 0.923770i | \(-0.374909\pi\) | ||||
0.382948 | + | 0.923770i | \(0.374909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.3095 | 1.92060 | 0.960302 | − | 0.278964i | \(-0.0899911\pi\) | ||||
0.960302 | + | 0.278964i | \(0.0899911\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 29.1808 | 1.72852 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.2454 | 0.722822 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.92088 | 0.229846 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.83519 | 0.457737 | 0.228868 | − | 0.973457i | \(-0.426497\pi\) | ||||
0.228868 | + | 0.973457i | \(0.426497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.61284 | 0.152125 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.55821 | −0.322520 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 50.1358 | 2.89943 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.8481 | 0.682910 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.4671 | 1.40560 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.0735 | −1.89378 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.2355 | −1.32612 | −0.663059 | − | 0.748567i | \(-0.730742\pi\) | ||||
−0.663059 | + | 0.748567i | \(0.730742\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.2236 | −0.866041 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.8702 | 1.41026 | 0.705129 | − | 0.709079i | \(-0.250889\pi\) | ||||
0.705129 | + | 0.709079i | \(0.250889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.7144 | −1.11432 | −0.557162 | − | 0.830404i | \(-0.688110\pi\) | ||||
−0.557162 | + | 0.830404i | \(0.688110\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.3963 | −0.867483 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.20697 | 0.0677904 | 0.0338952 | − | 0.999425i | \(-0.489209\pi\) | ||||
0.0338952 | + | 0.999425i | \(0.489209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −29.4270 | −1.64760 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.9423 | 1.39214 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.71401 | 0.262295 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.91892 | 0.550203 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.779007 | 0.0430792 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.02876 | 0.166981 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.7735 | −1.25175 | −0.625873 | − | 0.779925i | \(-0.715257\pi\) | ||||
−0.625873 | + | 0.779925i | \(0.715257\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.8366 | 0.703444 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.01264 | −0.492413 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.6281 | −1.72289 | −0.861447 | − | 0.507848i | \(-0.830441\pi\) | ||||
−0.861447 | + | 0.507848i | \(0.830441\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.12112 | 0.332454 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.58430 | 0.0857948 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1030 | 1.08546 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −57.1624 | −3.07752 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.3370 | 0.662283 | 0.331141 | − | 0.943581i | \(-0.392566\pi\) | ||||
0.331141 | + | 0.943581i | \(0.392566\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.5046 | 0.936999 | 0.468499 | − | 0.883464i | \(-0.344795\pi\) | ||||
0.468499 | + | 0.883464i | \(0.344795\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.97938 | 0.265779 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.6537 | −0.673488 | −0.336744 | − | 0.941596i | \(-0.609326\pi\) | ||||
−0.336744 | + | 0.941596i | \(0.609326\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.43316 | −0.288362 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.34289 | −0.282776 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.6098 | 1.40441 | 0.702206 | − | 0.711974i | \(-0.252199\pi\) | ||||
0.702206 | + | 0.711974i | \(0.252199\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.22193 | 0.169575 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −60.9553 | −3.19932 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.44226 | −0.0754916 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.8798 | 0.881119 | 0.440560 | − | 0.897723i | \(-0.354780\pi\) | ||||
0.440560 | + | 0.897723i | \(0.354780\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.1876 | −0.738578 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.1584 | −0.631234 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.4599 | −1.47360 | −0.736800 | − | 0.676111i | \(-0.763664\pi\) | ||||
−0.736800 | + | 0.676111i | \(0.763664\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.6420 | 1.01431 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.3625 | 1.35774 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.1179 | 1.49569 | 0.747843 | − | 0.663876i | \(-0.231090\pi\) | ||||
0.747843 | + | 0.663876i | \(0.231090\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.76330 | −0.244031 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.0664 | −1.63852 | −0.819258 | − | 0.573425i | \(-0.805614\pi\) | ||||
−0.819258 | + | 0.573425i | \(0.805614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 35.7107 | 1.81999 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.7273 | −0.697796 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.3753 | −0.982369 | −0.491184 | − | 0.871056i | \(-0.663436\pi\) | ||||
−0.491184 | + | 0.871056i | \(0.663436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.23431 | −0.466999 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31.8906 | −1.60867 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 39.5612 | 1.99054 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.83768 | 0.343173 | 0.171587 | − | 0.985169i | \(-0.445111\pi\) | ||||
0.171587 | + | 0.985169i | \(0.445111\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.1865 | −1.26090 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4316 | −0.520930 | −0.260465 | − | 0.965483i | \(-0.583876\pi\) | ||||
−0.260465 | + | 0.965483i | \(0.583876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.41931 | −0.0707011 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −26.1584 | −1.29982 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.7738 | −1.47583 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.7407 | −0.679436 | −0.339718 | − | 0.940527i | \(-0.610332\pi\) | ||||
−0.339718 | + | 0.940527i | \(0.610332\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 45.3776 | 2.23831 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.25519 | −0.110971 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.3247 | 0.899522 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.7490 | −1.65269 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.01763 | −0.440540 | −0.220270 | − | 0.975439i | \(-0.570694\pi\) | ||||
−0.220270 | + | 0.975439i | \(0.570694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 40.4142 | 1.96967 | 0.984833 | − | 0.173507i | \(-0.0555100\pi\) | ||||
0.984833 | + | 0.173507i | \(0.0555100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.50915 | −0.170621 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.82693 | −0.0886190 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.5464 | 1.38146 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 77.9541 | 3.76366 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.1119 | −0.487074 | −0.243537 | − | 0.969892i | \(-0.578308\pi\) | ||||
−0.243537 | + | 0.969892i | \(0.578308\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.9409 | 0.718014 | 0.359007 | − | 0.933335i | \(-0.383115\pi\) | ||||
0.359007 | + | 0.933335i | \(0.383115\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −30.0573 | −1.44114 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −43.5307 | −2.08236 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.7125 | −1.08401 | −0.542004 | − | 0.840376i | \(-0.682334\pi\) | ||||
−0.542004 | + | 0.840376i | \(0.682334\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00137 | −0.238160 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.53378 | −0.0728720 | −0.0364360 | − | 0.999336i | \(-0.511601\pi\) | ||||
−0.0364360 | + | 0.999336i | \(0.511601\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.8929 | −1.08523 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.5321 | −0.734642 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.8416 | −0.653228 | −0.326614 | − | 0.945158i | \(-0.605908\pi\) | ||||
−0.326614 | + | 0.945158i | \(0.605908\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.9073 | 1.54954 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 52.7702 | 2.47936 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31.9918 | −1.49980 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.4282 | −1.42337 | −0.711685 | − | 0.702499i | \(-0.752068\pi\) | ||||
−0.711685 | + | 0.702499i | \(0.752068\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.917132 | −0.0428081 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.5661 | 0.771561 | 0.385780 | − | 0.922591i | \(-0.373932\pi\) | ||||
0.385780 | + | 0.922591i | \(0.373932\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.7244 | 0.684300 | 0.342150 | − | 0.939645i | \(-0.388845\pi\) | ||||
0.342150 | + | 0.939645i | \(0.388845\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.61823 | 0.0750438 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.384116 | −0.0177747 | −0.00888737 | − | 0.999961i | \(-0.502829\pi\) | ||||
−0.00888737 | + | 0.999961i | \(0.502829\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.77898 | 0.359200 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.4540 | 1.03463 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.8395 | 1.46398 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.61216 | −0.395153 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.0869 | 0.644993 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.5628 | 1.35076 | 0.675380 | − | 0.737469i | \(-0.263979\pi\) | ||||
0.675380 | + | 0.737469i | \(0.263979\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.6731 | 1.21619 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 49.3379 | 2.24495 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.32417 | −0.196351 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.39436 | 0.380385 | 0.190192 | − | 0.981747i | \(-0.439089\pi\) | ||||
0.190192 | + | 0.981747i | \(0.439089\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.83949 | −0.444957 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.2433 | −1.90642 | −0.953208 | − | 0.302316i | \(-0.902240\pi\) | ||||
−0.953208 | + | 0.302316i | \(0.902240\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.85561 | −0.218686 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −41.3748 | −1.85966 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.68946 | 0.210351 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.8615 | −0.486227 | −0.243114 | − | 0.969998i | \(-0.578169\pi\) | ||||
−0.243114 | + | 0.969998i | \(0.578169\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.2359 | 0.457305 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.9612 | −1.64802 | −0.824008 | − | 0.566578i | \(-0.808267\pi\) | ||||
−0.824008 | + | 0.566578i | \(0.808267\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.9838 | −1.20076 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.0370 | −1.73369 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.67091 | 0.428655 | 0.214328 | − | 0.976762i | \(-0.431244\pi\) | ||||
0.214328 | + | 0.976762i | \(0.431244\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.24485 | 0.0550687 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.32337 | −0.190882 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.7895 | 0.739833 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.13924 | 0.357963 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.5270 | −0.725456 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.39688 | 0.280253 | 0.140126 | − | 0.990134i | \(-0.455249\pi\) | ||||
0.140126 | + | 0.990134i | \(0.455249\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.1391 | −1.01180 | −0.505902 | − | 0.862591i | \(-0.668840\pi\) | ||||
−0.505902 | + | 0.862591i | \(0.668840\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.76107 | 0.426008 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.261418 | 0.0113875 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 62.2726 | 2.70750 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.61289 | 0.113390 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.4803 | −1.27693 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.5078 | −1.18927 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 44.0025 | 1.89885 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.6004 | 0.499663 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.6644 | −1.14639 | −0.573196 | − | 0.819418i | \(-0.694297\pi\) | ||||
−0.573196 | + | 0.819418i | \(0.694297\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 55.3519 | 2.37538 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.859134 | −0.0368012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.5239 | 0.920294 | 0.460147 | − | 0.887843i | \(-0.347797\pi\) | ||||
0.460147 | + | 0.887843i | \(0.347797\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.0741 | −1.41157 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.8894 | −0.975121 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.1460 | −1.45204 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −30.4114 | −1.29089 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.3005 | 1.19913 | 0.599565 | − | 0.800326i | \(-0.295340\pi\) | ||||
0.599565 | + | 0.800326i | \(0.295340\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.5238 | −1.20643 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.3581 | −0.606198 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.369301 | −0.0155642 | −0.00778209 | − | 0.999970i | \(-0.502477\pi\) | ||||
−0.00778209 | + | 0.999970i | \(0.502477\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.75073 | −0.284005 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.5778 | 0.948179 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.2674 | 0.598120 | 0.299060 | − | 0.954234i | \(-0.403327\pi\) | ||||
0.299060 | + | 0.954234i | \(0.403327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.6239 | 1.23972 | 0.619860 | − | 0.784713i | \(-0.287189\pi\) | ||||
0.619860 | + | 0.784713i | \(0.287189\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.57640 | −0.316509 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.8704 | 0.703545 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.7653 | −0.448167 | −0.224084 | − | 0.974570i | \(-0.571939\pi\) | ||||
−0.224084 | + | 0.974570i | \(0.571939\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 49.0243 | 2.03738 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.8164 | −0.656173 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.6736 | −1.35320 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 37.0660 | 1.53249 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.82168 | −0.405384 | −0.202692 | − | 0.979243i | \(-0.564969\pi\) | ||||
−0.202692 | + | 0.979243i | \(0.564969\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.23233 | 0.0507772 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.41722 | −0.140566 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.6900 | 1.38348 | 0.691741 | − | 0.722146i | \(-0.256844\pi\) | ||||
0.691741 | + | 0.722146i | \(0.256844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.89245 | 0.241567 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.9242 | 0.610808 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.78884 | −0.399961 | −0.199981 | − | 0.979800i | \(-0.564088\pi\) | ||||
−0.199981 | + | 0.979800i | \(0.564088\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.64087 | 0.107723 | 0.0538616 | − | 0.998548i | \(-0.482847\pi\) | ||||
0.0538616 | + | 0.998548i | \(0.482847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.01281 | −0.367030 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 67.2250 | 2.73308 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.4789 | 0.628268 | 0.314134 | − | 0.949379i | \(-0.398286\pi\) | ||||
0.314134 | + | 0.949379i | \(0.398286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.9430 | 1.05126 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.29162 | −0.294987 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0780 | 0.649382 | 0.324691 | − | 0.945820i | \(-0.394740\pi\) | ||||
0.324691 | + | 0.945820i | \(0.394740\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 33.6120 | 1.35537 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.1336 | −1.69623 | −0.848116 | − | 0.529810i | \(-0.822263\pi\) | ||||
−0.848116 | + | 0.529810i | \(0.822263\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6412 | −0.709061 | −0.354530 | − | 0.935045i | \(-0.615359\pi\) | ||||
−0.354530 | + | 0.935045i | \(0.615359\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.46909 | 0.339853 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.7593 | 0.791639 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7970 | −1.23188 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −67.6841 | −2.70304 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.91282 | −0.195887 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.2793 | 1.60350 | 0.801748 | − | 0.597663i | \(-0.203904\pi\) | ||||
0.801748 | + | 0.597663i | \(0.203904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.95306 | −0.236613 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.25324 | 0.208468 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.3923 | −0.411758 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.43326 | −0.214936 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.22392 | −0.245830 | −0.122915 | − | 0.992417i | \(-0.539224\pi\) | ||||
−0.122915 | + | 0.992417i | \(0.539224\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.6123 | 1.60159 | 0.800796 | − | 0.598937i | \(-0.204410\pi\) | ||||
0.800796 | + | 0.598937i | \(0.204410\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.5214 | 1.28053 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.4761 | −1.66991 | −0.834953 | − | 0.550321i | \(-0.814505\pi\) | ||||
−0.834953 | + | 0.550321i | \(0.814505\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.06042 | −0.237892 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.39673 | −0.0547421 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.45550 | −0.0569582 | −0.0284791 | − | 0.999594i | \(-0.509066\pi\) | ||||
−0.0284791 | + | 0.999594i | \(0.509066\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35.1708 | 1.37424 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.44229 | −0.0562691 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.1468 | −0.473172 | −0.236586 | − | 0.971611i | \(-0.576028\pi\) | ||||
−0.236586 | + | 0.971611i | \(0.576028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.1812 | −0.940541 | −0.470271 | − | 0.882522i | \(-0.655844\pi\) | ||||
−0.470271 | + | 0.882522i | \(0.655844\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.8628 | 0.499550 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 27.7771 | 1.07715 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.8382 | 1.73614 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.82523 | 0.109230 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 76.7133 | 2.96148 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.6407 | 1.10402 | 0.552009 | − | 0.833838i | \(-0.313861\pi\) | ||||
0.552009 | + | 0.833838i | \(0.313861\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.67553 | 0.0644913 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.3915 | 1.16804 | 0.584020 | − | 0.811739i | \(-0.301479\pi\) | ||||
0.584020 | + | 0.811739i | \(0.301479\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.73228 | 0.143232 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 69.3098 | 2.65596 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.1625 | −1.61330 | −0.806651 | − | 0.591028i | \(-0.798722\pi\) | ||||
−0.806651 | + | 0.591028i | \(0.798722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −50.0450 | −1.91212 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.7192 | 1.51538 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.2710 | 1.11513 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.37017 | −0.242333 | −0.121166 | − | 0.992632i | \(-0.538663\pi\) | ||||
−0.121166 | + | 0.992632i | \(0.538663\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 35.7114 | 1.35656 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37.2203 | 1.41185 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.42987 | 0.205671 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.1171 | −1.06349 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.0562 | −1.02190 | −0.510948 | − | 0.859611i | \(-0.670706\pi\) | ||||
−0.510948 | + | 0.859611i | \(0.670706\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.1591 | −0.873463 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.31355 | 0.313107 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.2902 | 0.875918 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.8377 | 1.00791 | 0.503955 | − | 0.863730i | \(-0.331878\pi\) | ||||
0.503955 | + | 0.863730i | \(0.331878\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 39.5619 | 1.48369 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.41402 | −0.0904056 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −85.9723 | −3.21518 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 45.1712 | 1.68695 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.3047 | −0.533476 | −0.266738 | − | 0.963769i | \(-0.585946\pi\) | ||||
−0.266738 | + | 0.963769i | \(0.585946\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4913 | −0.539685 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.8508 | −0.924211 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.87084 | 0.329455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.1343 | −0.858005 | −0.429003 | − | 0.903303i | \(-0.641135\pi\) | ||||
−0.429003 | + | 0.903303i | \(0.641135\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.6404 | −0.727422 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.25368 | 0.194314 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.4479 | 1.67866 | 0.839329 | − | 0.543624i | \(-0.182948\pi\) | ||||
0.839329 | + | 0.543624i | \(0.182948\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.8488 | 0.437049 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.9046 | 0.770032 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.6465 | −1.45842 | −0.729210 | − | 0.684290i | \(-0.760112\pi\) | ||||
−0.729210 | + | 0.684290i | \(0.760112\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 60.6355 | 2.22750 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.5081 | −1.55947 | −0.779736 | − | 0.626108i | \(-0.784647\pi\) | ||||
−0.779736 | + | 0.626108i | \(0.784647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.1297 | 0.627582 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.3250 | 0.670476 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.7425 | 0.867533 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.6674 | 0.571712 | 0.285856 | − | 0.958273i | \(-0.407722\pi\) | ||||
0.285856 | + | 0.958273i | \(0.407722\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.54786 | 0.165733 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −58.1980 | −2.11804 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.5551 | 1.54669 | 0.773345 | − | 0.633985i | \(-0.218582\pi\) | ||||
0.773345 | + | 0.633985i | \(0.218582\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 132.587 | 4.81260 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.1326 | 1.30981 | 0.654903 | − | 0.755713i | \(-0.272709\pi\) | ||||
0.654903 | + | 0.755713i | \(0.272709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.741535 | 0.0268454 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.82705 | −0.246833 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.42929 | 0.196040 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.5262 | 0.848378 | 0.424189 | − | 0.905574i | \(-0.360559\pi\) | ||||
0.424189 | + | 0.905574i | \(0.360559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.5608 | 1.28069 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.44290 | −0.303670 | −0.151835 | − | 0.988406i | \(-0.548518\pi\) | ||||
−0.151835 | + | 0.988406i | \(0.548518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.477592 | −0.0171556 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.2487 | 0.941666 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.5965 | 0.917089 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.6021 | 0.450938 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.45323 | 0.159146 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.7636 | −0.883851 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.5998 | 1.87498 | 0.937491 | − | 0.348009i | \(-0.113142\pi\) | ||||
0.937491 | + | 0.348009i | \(0.113142\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.5717 | 0.661169 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.82668 | 0.207173 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.7244 | −2.44047 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −33.3733 | −1.18363 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.46355 | −0.193529 | −0.0967645 | − | 0.995307i | \(-0.530849\pi\) | ||||
−0.0967645 | + | 0.995307i | \(0.530849\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.34302 | 0.0475125 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.8933 | −0.808895 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.34530 | 0.118053 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −54.4127 | −1.91780 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.9347 | 0.736938 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.54210 | 0.265166 | 0.132583 | − | 0.991172i | \(-0.457673\pi\) | ||||
0.132583 | + | 0.991172i | \(0.457673\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.2599 | −1.30837 | −0.654187 | − | 0.756333i | \(-0.726989\pi\) | ||||
−0.654187 | + | 0.756333i | \(0.726989\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 64.0148 | 2.24510 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.8516 | 0.380114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.7659 | 0.866450 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −31.9924 | −1.11790 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.2056 | 1.47299 | 0.736494 | − | 0.676445i | \(-0.236480\pi\) | ||||
0.736494 | + | 0.676445i | \(0.236480\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.40358 | −0.292930 | −0.146465 | − | 0.989216i | \(-0.546790\pi\) | ||||
−0.146465 | + | 0.989216i | \(0.546790\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.2311 | 0.913251 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.2908 | 1.40105 | 0.700525 | − | 0.713628i | \(-0.252949\pi\) | ||||
0.700525 | + | 0.713628i | \(0.252949\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.4352 | 1.12652 | 0.563261 | − | 0.826279i | \(-0.309547\pi\) | ||||
0.563261 | + | 0.826279i | \(0.309547\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 58.1311 | 2.01655 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.91412 | 0.0663202 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.2887 | −0.390662 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.239755 | −0.00828714 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.7784 | −1.33878 | −0.669390 | − | 0.742911i | \(-0.733445\pi\) | ||||
−0.669390 | + | 0.742911i | \(0.733445\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.42307 | −0.187002 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.4170 | −1.04762 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 43.0522 | 1.48104 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −58.0232 | −1.99370 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −76.5463 | −2.62706 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.3666 | 1.55515 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.0484 | 0.857640 | 0.428820 | − | 0.903390i | \(-0.358929\pi\) | ||||
0.428820 | + | 0.903390i | \(0.358929\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.1828 | −1.10063 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.6693 | 1.25260 | 0.626300 | − | 0.779582i | \(-0.284569\pi\) | ||||
0.626300 | + | 0.779582i | \(0.284569\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.8294 | −0.437734 | −0.218867 | − | 0.975755i | \(-0.570236\pi\) | ||||
−0.218867 | + | 0.975755i | \(0.570236\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.0112 | −0.988699 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.0474 | −1.19303 | −0.596513 | − | 0.802603i | \(-0.703448\pi\) | ||||
−0.596513 | + | 0.802603i | \(0.703448\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.2270 | 0.619735 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.36915 | −0.0804607 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −91.7613 | −3.11279 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.7276 | −0.634561 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.32425 | −0.146354 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.6972 | 0.632080 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.6076 | 0.527032 | 0.263516 | − | 0.964655i | \(-0.415118\pi\) | ||||
0.263516 | + | 0.964655i | \(0.415118\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.5628 | −0.626106 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.6422 | 0.695453 | 0.347726 | − | 0.937596i | \(-0.386954\pi\) | ||||
0.347726 | + | 0.937596i | \(0.386954\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8510 | 0.668040 | 0.334020 | − | 0.942566i | \(-0.391595\pi\) | ||||
0.334020 | + | 0.942566i | \(0.391595\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.19022 | −0.208082 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.0138328 | −0.000464460 0 | −0.000232230 | − | 1.00000i | \(-0.500074\pi\) | ||||
−0.000232230 | 1.00000i | \(0.500074\pi\) | ||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.53417 | −0.152071 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 60.6738 | 2.03265 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.33099 | 0.211859 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −48.5285 | −1.62213 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −118.779 | −3.96593 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.26934 | −0.0423350 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.39130 | −0.179610 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −28.0698 | −0.934106 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −61.0452 | −2.02921 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.63211 | 0.187011 | 0.0935056 | − | 0.995619i | \(-0.470193\pi\) | ||||
0.0935056 | + | 0.995619i | \(0.470193\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.9842 | −0.895011 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.6162 | 0.451124 | 0.225562 | − | 0.974229i | \(-0.427578\pi\) | ||||
0.225562 | + | 0.974229i | \(0.427578\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.5036 | −1.40667 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 78.3562 | 2.59038 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.3566 | −1.00246 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.6397 | 0.482918 | 0.241459 | − | 0.970411i | \(-0.422374\pi\) | ||||
0.241459 | + | 0.970411i | \(0.422374\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 55.0483 | 1.81390 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.2897 | −0.371605 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.97537 | 0.295108 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.7898 | 0.551449 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.5903 | −1.79105 | −0.895525 | − | 0.445012i | \(-0.853200\pi\) | ||||
−0.895525 | + | 0.445012i | \(0.853200\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.02317 | 0.295722 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −58.9213 | −1.92900 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.8349 | 0.517857 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.6633 | 0.773047 | 0.386524 | − | 0.922280i | \(-0.373676\pi\) | ||||
0.386524 | + | 0.922280i | \(0.373676\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 46.7064 | 1.52421 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.03358 | 0.261887 | 0.130944 | − | 0.991390i | \(-0.458199\pi\) | ||||
0.130944 | + | 0.991390i | \(0.458199\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50.1411 | −1.63282 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.40416 | −0.175797 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.9876 | 1.88435 | 0.942173 | − | 0.335128i | \(-0.108780\pi\) | ||||
0.942173 | + | 0.335128i | \(0.108780\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.99692 | −0.0972842 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.85950 | −0.0927258 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.7105 | 0.994809 | 0.497405 | − | 0.867519i | \(-0.334286\pi\) | ||||
0.497405 | + | 0.867519i | \(0.334286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.35569 | 0.270384 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 69.7171 | 2.25364 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.1948 | 1.39483 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9317 | −0.997796 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.5083 | −0.886443 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −54.0668 | −1.74047 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.3529 | −0.879610 | −0.439805 | − | 0.898093i | \(-0.644953\pi\) | ||||
−0.439805 | + | 0.898093i | \(0.644953\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.1682 | −0.358775 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.1142 | 0.420855 | 0.210428 | − | 0.977609i | \(-0.432514\pi\) | ||||
0.210428 | + | 0.977609i | \(0.432514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.1256 | −1.02990 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23.4994 | −0.752584 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.5068 | −0.624078 | −0.312039 | − | 0.950069i | \(-0.601012\pi\) | ||||
−0.312039 | + | 0.950069i | \(0.601012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53.0996 | 1.69707 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.859149 | −0.0274305 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.2597 | 0.550500 | 0.275250 | − | 0.961373i | \(-0.411239\pi\) | ||||
0.275250 | + | 0.961373i | \(0.411239\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.76871 | 0.120081 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.17559 | −0.228401 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.5141 | −1.54266 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.2804 | −1.31132 | −0.655658 | − | 0.755058i | \(-0.727609\pi\) | ||||
−0.655658 | + | 0.755058i | \(0.727609\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 53.9540 | 1.71218 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.4593 | −0.521795 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.9074 | 0.947178 | 0.473589 | − | 0.880746i | \(-0.342958\pi\) | ||||
0.473589 | + | 0.880746i | \(0.342958\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.50571 | 0.142554 |
(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 | 4012.2.a.g.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.g.1.3 | ✓ | 12 | 1.1 | even | 1 | trivial |