Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.287349.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 6x^{3} + 7x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.13797\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | −2.57090 | −1.48431 | −0.742156 | − | 0.670228i | \(-0.766196\pi\) | ||||
−0.742156 | + | 0.670228i | \(0.766196\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.350332 | −0.156673 | −0.0783366 | − | 0.996927i | \(-0.524961\pi\) | ||||
−0.0783366 | + | 0.996927i | \(0.524961\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.60954 | 1.20318 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.25100 | 0.377191 | 0.188596 | − | 0.982055i | \(-0.439606\pi\) | ||||
0.188596 | + | 0.982055i | \(0.439606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.92944 | −1.92188 | −0.960940 | − | 0.276756i | \(-0.910741\pi\) | ||||
−0.960940 | + | 0.276756i | \(0.910741\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.900670 | 0.232552 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.25921 | 0.547938 | 0.273969 | − | 0.961739i | \(-0.411663\pi\) | ||||
0.273969 | + | 0.961739i | \(0.411663\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.55720 | −1.27491 | −0.637454 | − | 0.770488i | \(-0.720013\pi\) | ||||
−0.637454 | + | 0.770488i | \(0.720013\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.22344 | −1.29768 | −0.648839 | − | 0.760926i | \(-0.724745\pi\) | ||||
−0.648839 | + | 0.760926i | \(0.724745\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.87727 | −0.975453 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.56706 | −0.301582 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.45254 | −1.01251 | −0.506255 | − | 0.862384i | \(-0.668971\pi\) | ||||
−0.506255 | + | 0.862384i | \(0.668971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2015 | −1.83225 | −0.916125 | − | 0.400893i | \(-0.868700\pi\) | ||||
−0.916125 | + | 0.400893i | \(0.868700\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.21620 | −0.559869 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.17277 | 0.357200 | 0.178600 | − | 0.983922i | \(-0.442843\pi\) | ||||
0.178600 | + | 0.983922i | \(0.442843\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17.8149 | 2.85267 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.54213 | 0.235173 | 0.117586 | − | 0.993063i | \(-0.462484\pi\) | ||||
0.117586 | + | 0.993063i | \(0.462484\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.26454 | −0.188506 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.11591 | −0.746232 | −0.373116 | − | 0.927785i | \(-0.621711\pi\) | ||||
−0.373116 | + | 0.927785i | \(0.621711\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.80820 | −0.813311 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0029 | 1.37400 | 0.687000 | − | 0.726657i | \(-0.258927\pi\) | ||||
0.687000 | + | 0.726657i | \(0.258927\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.438266 | −0.0590958 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.2870 | 1.89236 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.9497 | 1.55572 | 0.777858 | − | 0.628440i | \(-0.216306\pi\) | ||||
0.777858 | + | 0.628440i | \(0.216306\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.51926 | 0.194521 | 0.0972606 | − | 0.995259i | \(-0.468992\pi\) | ||||
0.0972606 | + | 0.995259i | \(0.468992\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.42760 | 0.301107 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6674 | −1.54757 | −0.773784 | − | 0.633449i | \(-0.781639\pi\) | ||||
−0.773784 | + | 0.633449i | \(0.781639\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.9999 | 1.92616 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.5641 | 1.96579 | 0.982896 | − | 0.184161i | \(-0.0589569\pi\) | ||||
0.982896 | + | 0.184161i | \(0.0589569\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.30087 | −0.620419 | −0.310210 | − | 0.950668i | \(-0.600399\pi\) | ||||
−0.310210 | + | 0.950668i | \(0.600399\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.5390 | 1.44788 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.4987 | −1.63123 | −0.815614 | − | 0.578596i | \(-0.803601\pi\) | ||||
−0.815614 | + | 0.578596i | \(0.803601\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.79985 | −0.755538 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.46607 | −0.599979 | −0.299990 | − | 0.953942i | \(-0.596983\pi\) | ||||
−0.299990 | + | 0.953942i | \(0.596983\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.791473 | −0.0858473 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.0179 | 1.50288 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.80671 | −0.721509 | −0.360755 | − | 0.932661i | \(-0.617481\pi\) | ||||
−0.360755 | + | 0.932661i | \(0.617481\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.2272 | 2.71963 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.94686 | 0.199744 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.91406 | 0.397412 | 0.198706 | − | 0.980059i | \(-0.436326\pi\) | ||||
0.198706 | + | 0.980059i | \(0.436326\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.51554 | 0.453829 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3873 | 1.03358 | 0.516788 | − | 0.856114i | \(-0.327128\pi\) | ||||
0.516788 | + | 0.856114i | \(0.327128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.7261 | −1.25394 | −0.626970 | − | 0.779044i | \(-0.715705\pi\) | ||||
−0.626970 | + | 0.779044i | \(0.715705\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9590 | −1.15612 | −0.578061 | − | 0.815993i | \(-0.696191\pi\) | ||||
−0.578061 | + | 0.815993i | \(0.696191\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3813 | −1.66483 | −0.832413 | − | 0.554155i | \(-0.813041\pi\) | ||||
−0.832413 | + | 0.554155i | \(0.813041\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.58597 | −0.530197 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.91509 | −0.650517 | −0.325258 | − | 0.945625i | \(-0.605451\pi\) | ||||
−0.325258 | + | 0.945625i | \(0.605451\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.18027 | 0.203311 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −25.0121 | −2.31237 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.43499 | −0.857727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.57090 | −0.231810 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.46032 | 0.309501 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.51170 | 0.844027 | 0.422013 | − | 0.906590i | \(-0.361323\pi\) | ||||
0.422013 | + | 0.906590i | \(0.361323\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.96467 | −0.349070 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1283 | 0.972281 | 0.486141 | − | 0.873881i | \(-0.338404\pi\) | ||||
0.486141 | + | 0.873881i | \(0.338404\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.548993 | 0.0472498 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.0604 | −1.71388 | −0.856938 | − | 0.515419i | \(-0.827636\pi\) | ||||
−0.856938 | + | 0.515419i | \(0.827636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.12561 | −0.519567 | −0.259784 | − | 0.965667i | \(-0.583651\pi\) | ||||
−0.259784 | + | 0.965667i | \(0.583651\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.1525 | 1.10764 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.66874 | −0.724916 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.91020 | 0.158633 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.24615 | 0.102088 | 0.0510442 | − | 0.998696i | \(-0.483745\pi\) | ||||
0.0510442 | + | 0.998696i | \(0.483745\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.13328 | −0.173604 | −0.0868020 | − | 0.996226i | \(-0.527665\pi\) | ||||
−0.0868020 | + | 0.996226i | \(0.527665\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.15469 | 0.659268 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.57393 | 0.287065 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.15769 | 0.651054 | 0.325527 | − | 0.945533i | \(-0.394458\pi\) | ||||
0.325527 | + | 0.945533i | \(0.394458\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −25.7164 | −2.03944 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.8075 | −1.00316 | −0.501581 | − | 0.865111i | \(-0.667248\pi\) | ||||
−0.501581 | + | 0.865111i | \(0.667248\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.12674 | 0.0877165 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7837 | 1.45352 | 0.726762 | − | 0.686890i | \(-0.241024\pi\) | ||||
0.726762 | + | 0.686890i | \(0.241024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.0171 | 2.69363 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.0589 | −1.53394 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.4467 | −0.870275 | −0.435137 | − | 0.900364i | \(-0.643300\pi\) | ||||
−0.435137 | + | 0.900364i | \(0.643300\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −30.7215 | −2.30917 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.7864 | 0.880957 | 0.440479 | − | 0.897763i | \(-0.354809\pi\) | ||||
0.440479 | + | 0.897763i | \(0.354809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.11415 | 0.0828138 | 0.0414069 | − | 0.999142i | \(-0.486816\pi\) | ||||
0.0414069 | + | 0.999142i | \(0.486816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.90587 | −0.288730 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.761189 | −0.0559638 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.82627 | 0.206677 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.5893 | −1.70686 | −0.853432 | − | 0.521204i | \(-0.825483\pi\) | ||||
−0.853432 | + | 0.521204i | \(0.825483\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.34661 | −0.240894 | −0.120447 | − | 0.992720i | \(-0.538433\pi\) | ||||
−0.120447 | + | 0.992720i | \(0.538433\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.24114 | −0.446937 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.00533 | 0.214121 | 0.107060 | − | 0.994253i | \(-0.465856\pi\) | ||||
0.107060 | + | 0.994253i | \(0.465856\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.95284 | −0.705538 | −0.352769 | − | 0.935710i | \(-0.614760\pi\) | ||||
−0.352769 | + | 0.935710i | \(0.614760\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.5666 | 2.29707 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.350332 | −0.0244683 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.4638 | −1.56134 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.95206 | −0.480884 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.2907 | 1.67224 | 0.836120 | − | 0.548546i | \(-0.184818\pi\) | ||||
0.836120 | + | 0.548546i | \(0.184818\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −42.5846 | −2.91785 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.540258 | −0.0368453 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.6280 | 0.920895 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.6550 | −1.05307 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.28073 | −0.420589 | −0.210295 | − | 0.977638i | \(-0.567442\pi\) | ||||
−0.210295 | + | 0.977638i | \(0.567442\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.6047 | −1.17365 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.3484 | −1.08508 | −0.542539 | − | 0.840031i | \(-0.682537\pi\) | ||||
−0.542539 | + | 0.840031i | \(0.682537\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.2276 | 1.79925 | 0.899626 | − | 0.436660i | \(-0.143839\pi\) | ||||
0.899626 | + | 0.436660i | \(0.143839\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.78533 | 0.444522 | 0.222261 | − | 0.974987i | \(-0.428656\pi\) | ||||
0.222261 | + | 0.974987i | \(0.428656\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.79227 | 0.116915 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.2747 | 2.42125 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.4094 | −1.19081 | −0.595403 | − | 0.803427i | \(-0.703007\pi\) | ||||
−0.595403 | + | 0.803427i | \(0.703007\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3612 | 1.05392 | 0.526958 | − | 0.849891i | \(-0.323332\pi\) | ||||
0.526958 | + | 0.849891i | \(0.323332\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.1829 | 1.42304 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.5083 | 2.45022 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.0527 | 0.890556 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.18246 | 0.453353 | 0.226677 | − | 0.973970i | \(-0.427214\pi\) | ||||
0.226677 | + | 0.973970i | \(0.427214\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.78554 | −0.489473 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.03480 | 0.127424 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 30.1418 | 1.88020 | 0.940098 | − | 0.340904i | \(-0.110733\pi\) | ||||
0.940098 | + | 0.340904i | \(0.110733\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.6811 | −1.21823 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.7667 | 0.725567 | 0.362784 | − | 0.931873i | \(-0.381826\pi\) | ||||
0.362784 | + | 0.931873i | \(0.381826\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.50433 | −0.215269 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.4994 | 1.07094 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.7876 | 1.32842 | 0.664208 | − | 0.747548i | \(-0.268769\pi\) | ||||
0.664208 | + | 0.747548i | \(0.268769\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.9648 | −1.57725 | −0.788623 | − | 0.614877i | \(-0.789206\pi\) | ||||
−0.788623 | + | 0.614877i | \(0.789206\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.10147 | −0.367932 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.4372 | 1.34812 | 0.674059 | − | 0.738677i | \(-0.264549\pi\) | ||||
0.674059 | + | 0.738677i | \(0.264549\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −36.8228 | −2.20453 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.42259 | 0.442795 | 0.221397 | − | 0.975184i | \(-0.428938\pi\) | ||||
0.221397 | + | 0.975184i | \(0.428938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.14755 | 0.305990 | 0.152995 | − | 0.988227i | \(-0.451108\pi\) | ||||
0.152995 | + | 0.988227i | \(0.451108\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.00520 | −0.296482 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8960 | −0.699764 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0627 | −0.589883 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0377 | 0.703248 | 0.351624 | − | 0.936141i | \(-0.385630\pi\) | ||||
0.351624 | + | 0.936141i | \(0.385630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.18636 | −0.243739 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.96040 | −0.113754 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 43.1250 | 2.49398 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.7048 | −1.53415 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.532245 | −0.0304763 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.2014 | −1.60954 | −0.804770 | − | 0.593587i | \(-0.797711\pi\) | ||||
−0.804770 | + | 0.593587i | \(0.797711\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 32.7175 | 1.86124 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.5467 | −0.938280 | −0.469140 | − | 0.883124i | \(-0.655436\pi\) | ||||
−0.469140 | + | 0.883124i | \(0.655436\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.91307 | −0.503796 | −0.251898 | − | 0.967754i | \(-0.581055\pi\) | ||||
−0.251898 | + | 0.967754i | \(0.581055\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.1314 | 0.906027 | 0.453014 | − | 0.891504i | \(-0.350349\pi\) | ||||
0.453014 | + | 0.891504i | \(0.350349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.82113 | −0.381910 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.7455 | 1.71605 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.5549 | −0.698571 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.7967 | 1.87471 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 44.6856 | 2.47112 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.805642 | 0.0442821 | 0.0221410 | − | 0.999755i | \(-0.492952\pi\) | ||||
0.0221410 | + | 0.999755i | \(0.492952\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.84268 | 0.429776 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.43779 | 0.242463 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.3992 | −0.784374 | −0.392187 | − | 0.919885i | \(-0.628281\pi\) | ||||
−0.392187 | + | 0.919885i | \(0.628281\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.7780 | 0.965569 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.7621 | −0.691108 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.60527 | −0.301777 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.2254 | −0.548930 | −0.274465 | − | 0.961597i | \(-0.588501\pi\) | ||||
−0.274465 | + | 0.961597i | \(0.588501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.18647 | −0.331154 | −0.165577 | − | 0.986197i | \(-0.552949\pi\) | ||||
−0.165577 | + | 0.986197i | \(0.552949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.8589 | 0.579604 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.1981 | 1.12826 | 0.564129 | − | 0.825687i | \(-0.309212\pi\) | ||||
0.564129 | + | 0.825687i | \(0.309212\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.80292 | −0.307987 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.54401 | 0.450936 | 0.225468 | − | 0.974251i | \(-0.427609\pi\) | ||||
0.225468 | + | 0.974251i | \(0.427609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.8824 | 0.625392 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.2565 | 1.27313 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.85706 | 0.0972031 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.9729 | −0.938177 | −0.469088 | − | 0.883151i | \(-0.655417\pi\) | ||||
−0.469088 | + | 0.883151i | \(0.655417\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.60954 | 0.187905 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.5814 | −1.84233 | −0.921166 | − | 0.389169i | \(-0.872762\pi\) | ||||
−0.921166 | + | 0.389169i | \(0.872762\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.89615 | −0.459395 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.7830 | 1.94592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0487 | 0.978466 | 0.489233 | − | 0.872153i | \(-0.337277\pi\) | ||||
0.489233 | + | 0.872153i | \(0.337277\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.4537 | −1.25280 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.2921 | −1.49676 | −0.748378 | − | 0.663273i | \(-0.769167\pi\) | ||||
−0.748378 | + | 0.663273i | \(0.769167\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.56639 | 0.282955 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.6600 | 0.591188 | 0.295594 | − | 0.955314i | \(-0.404482\pi\) | ||||
0.295594 | + | 0.955314i | \(0.404482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0600 | −0.711047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.6097 | −1.44317 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.07935 | 0.255570 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.82656 | 0.141861 | 0.0709304 | − | 0.997481i | \(-0.477403\pi\) | ||||
0.0709304 | + | 0.997481i | \(0.477403\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.46635 | −0.472727 | −0.236364 | − | 0.971665i | \(-0.575956\pi\) | ||||
−0.236364 | + | 0.971665i | \(0.575956\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 70.6909 | 3.52137 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.38220 | 0.118373 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.71813 | 0.134733 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.323971 | −0.0160194 | −0.00800968 | − | 0.999968i | \(-0.502550\pi\) | ||||
−0.00800968 | + | 0.999968i | \(0.502550\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 51.5734 | 2.54393 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.91494 | 0.0940007 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.7483 | 0.771199 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.52610 | −0.221114 | −0.110557 | − | 0.993870i | \(-0.535264\pi\) | ||||
−0.110557 | + | 0.993870i | \(0.535264\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.43415 | −0.167370 | −0.0836851 | − | 0.996492i | \(-0.526669\pi\) | ||||
−0.0836851 | + | 0.996492i | \(0.526669\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.4661 | −0.897851 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.0188 | −0.534488 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.2865 | 1.07600 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.9366 | 1.53833 | 0.769166 | − | 0.639048i | \(-0.220672\pi\) | ||||
0.769166 | + | 0.639048i | \(0.220672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.8577 | −0.617904 | −0.308952 | − | 0.951078i | \(-0.599978\pi\) | ||||
−0.308952 | + | 0.951078i | \(0.599978\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.91093 | −0.235461 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.5849 | 1.65442 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.62979 | −0.316422 | −0.158211 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158211 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.36364 | −0.397369 | −0.198684 | − | 0.980064i | \(-0.563667\pi\) | ||||
−0.198684 | + | 0.980064i | \(0.563667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.38461 | 0.113041 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.20373 | −0.151531 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.4022 | 0.774067 | 0.387034 | − | 0.922066i | \(-0.373500\pi\) | ||||
0.387034 | + | 0.922066i | \(0.373500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.25100 | 0.0589074 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.48446 | 0.257682 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.0384 | 1.07769 | 0.538844 | − | 0.842405i | \(-0.318861\pi\) | ||||
0.538844 | + | 0.842405i | \(0.318861\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.54032 | −0.165248 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.1948 | −0.800843 | −0.400422 | − | 0.916331i | \(-0.631136\pi\) | ||||
−0.400422 | + | 0.916331i | \(0.631136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.625032 | 0.0290477 | 0.0145239 | − | 0.999895i | \(-0.495377\pi\) | ||||
0.0145239 | + | 0.999895i | \(0.495377\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.18821 | −0.426093 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.5985 | 1.27711 | 0.638554 | − | 0.769577i | \(-0.279533\pi\) | ||||
0.638554 | + | 0.769577i | \(0.279533\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.9726 | −0.966367 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.92921 | 0.0887052 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.1039 | 1.24361 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 36.1058 | 1.65317 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.39232 | 0.0636167 | 0.0318084 | − | 0.999494i | \(-0.489873\pi\) | ||||
0.0318084 | + | 0.999494i | \(0.489873\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.0560 | −0.686497 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.37122 | −0.0622639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0344 | −0.726587 | −0.363293 | − | 0.931675i | \(-0.618348\pi\) | ||||
−0.363293 | + | 0.931675i | \(0.618348\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.9269 | 1.48901 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.1447 | −1.36041 | −0.680206 | − | 0.733021i | \(-0.738110\pi\) | ||||
−0.680206 | + | 0.733021i | \(0.738110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.3184 | −0.554793 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.58194 | −0.0711028 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.06347 | 0.316204 | 0.158102 | − | 0.987423i | \(-0.449462\pi\) | ||||
0.158102 | + | 0.987423i | \(0.449462\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −48.2910 | −2.15748 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.6493 | −1.76788 | −0.883938 | − | 0.467604i | \(-0.845117\pi\) | ||||
−0.883938 | + | 0.467604i | \(0.845117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.63901 | −0.161934 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −90.0256 | −3.99818 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.7420 | 0.786401 | 0.393200 | − | 0.919453i | \(-0.371368\pi\) | ||||
0.393200 | + | 0.919453i | \(0.371368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.70849 | 0.384489 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.45836 | 0.196459 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.40001 | −0.281472 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.4283 | 1.29176 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.2800 | 0.537996 | 0.268998 | − | 0.963141i | \(-0.413308\pi\) | ||||
0.268998 | + | 0.963141i | \(0.413308\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.1346 | 0.661790 | 0.330895 | − | 0.943668i | \(-0.392649\pi\) | ||||
0.330895 | + | 0.943668i | \(0.392649\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.0474 | −1.00396 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.7313 | 0.683968 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 43.1329 | 1.87181 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.92944 | −0.300147 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.18963 | 0.181133 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.3017 | −1.30761 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.3632 | 1.52038 | 0.760192 | − | 0.649699i | \(-0.225105\pi\) | ||||
0.760192 | + | 0.649699i | \(0.225105\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.86436 | −0.122922 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.08923 | 0.260834 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.3881 | 0.444164 | 0.222082 | − | 0.975028i | \(-0.428715\pi\) | ||||
0.222082 | + | 0.975028i | \(0.428715\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.48383 | 0.234044 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.3008 | 1.29086 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.95694 | 0.0830676 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.6247 | 1.12813 | 0.564063 | − | 0.825732i | \(-0.309237\pi\) | ||||
0.564063 | + | 0.825732i | \(0.309237\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.6861 | −0.451974 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.26607 | −0.306774 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.5864 | −1.62622 | −0.813111 | − | 0.582109i | \(-0.802228\pi\) | ||||
−0.813111 | + | 0.582109i | \(0.802228\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.42258 | 0.101919 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.7060 | 0.868043 | 0.434021 | − | 0.900903i | \(-0.357094\pi\) | ||||
0.434021 | + | 0.900903i | \(0.357094\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.83108 | −0.118477 | −0.0592386 | − | 0.998244i | \(-0.518867\pi\) | ||||
−0.0592386 | + | 0.998244i | \(0.518867\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 60.6459 | 2.53352 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.3534 | 1.26582 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.6015 | 1.06580 | 0.532902 | − | 0.846177i | \(-0.321102\pi\) | ||||
0.532902 | + | 0.846177i | \(0.321102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.60381 | 0.357562 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.5136 | 0.518261 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.76253 | 0.362286 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.22208 | −0.380636 | −0.190318 | − | 0.981722i | \(-0.560952\pi\) | ||||
−0.190318 | + | 0.981722i | \(0.560952\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56.6920 | 2.33595 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.72641 | −0.317822 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.03402 | 0.206722 | 0.103361 | − | 0.994644i | \(-0.467040\pi\) | ||||
0.103361 | + | 0.994644i | \(0.467040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.5878 | 1.04724 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.7279 | 1.74582 | 0.872908 | − | 0.487885i | \(-0.162231\pi\) | ||||
0.872908 | + | 0.487885i | \(0.162231\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.8634 | 0.565501 | 0.282750 | − | 0.959194i | \(-0.408753\pi\) | ||||
0.282750 | + | 0.959194i | \(0.408753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −45.7235 | −1.86200 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.30538 | 0.134383 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.3140 | −1.35217 | −0.676086 | − | 0.736823i | \(-0.736325\pi\) | ||||
−0.676086 | + | 0.736823i | \(0.736325\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.4504 | 1.43417 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.5324 | 0.829296 | 0.414648 | − | 0.909982i | \(-0.363905\pi\) | ||||
0.414648 | + | 0.909982i | \(0.363905\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.900670 | 0.0363185 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4990 | 1.34862 | 0.674310 | − | 0.738448i | \(-0.264441\pi\) | ||||
0.674310 | + | 0.738448i | \(0.264441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0499 | 0.403938 | 0.201969 | − | 0.979392i | \(-0.435266\pi\) | ||||
0.201969 | + | 0.979392i | \(0.435266\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.75254 | 0.391356 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1741 | 0.926963 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.8731 | 0.713782 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.90873 | 0.195724 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.66012 | −0.185517 | −0.0927583 | − | 0.995689i | \(-0.529568\pi\) | ||||
−0.0927583 | + | 0.995689i | \(0.529568\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −62.4490 | −2.48213 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.33225 | −0.132236 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 59.7886 | 2.36520 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.4812 | 1.28293 | 0.641466 | − | 0.767152i | \(-0.278327\pi\) | ||||
0.641466 | + | 0.767152i | \(0.278327\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.0063 | 0.749534 | 0.374767 | − | 0.927119i | \(-0.377723\pi\) | ||||
0.374767 | + | 0.927119i | \(0.377723\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.38895 | 0.0546899 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.9845 | −0.549787 | −0.274893 | − | 0.961475i | \(-0.588643\pi\) | ||||
−0.274893 | + | 0.961475i | \(0.588643\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.9491 | 0.586803 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.28550 | −0.363370 | −0.181685 | − | 0.983357i | \(-0.558155\pi\) | ||||
−0.181685 | + | 0.983357i | \(0.558155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.89859 | −0.152331 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.1337 | −0.746476 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.3849 | 1.72899 | 0.864495 | − | 0.502641i | \(-0.167638\pi\) | ||||
0.864495 | + | 0.502641i | \(0.167638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.5880 | 0.411826 | 0.205913 | − | 0.978570i | \(-0.433984\pi\) | ||||
0.205913 | + | 0.978570i | \(0.433984\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 40.2476 | 1.56309 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.9336 | 1.31391 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.1472 | 0.624285 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.90060 | 0.0733717 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.47114 | 0.172350 | 0.0861749 | − | 0.996280i | \(-0.472536\pi\) | ||||
0.0861749 | + | 0.996280i | \(0.472536\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.64299 | 0.294179 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.5640 | −0.444439 | −0.222219 | − | 0.974997i | \(-0.571330\pi\) | ||||
−0.222219 | + | 0.974997i | \(0.571330\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.0300 | 1.61059 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.45605 | −0.208770 | −0.104385 | − | 0.994537i | \(-0.533287\pi\) | ||||
−0.104385 | + | 0.994537i | \(0.533287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.02781 | 0.268519 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −69.9996 | −2.67065 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −69.3143 | −2.64067 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.81414 | 0.183139 | 0.0915694 | − | 0.995799i | \(-0.470812\pi\) | ||||
0.0915694 | + | 0.995799i | \(0.470812\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.14600 | 0.0814023 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.25921 | 0.0855736 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.4444 | −0.659808 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.4352 | 0.545209 | 0.272604 | − | 0.962126i | \(-0.412115\pi\) | ||||
0.272604 | + | 0.962126i | \(0.412115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0745 | −0.455398 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.60774 | −0.173538 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.1880 | −1.17129 | −0.585646 | − | 0.810567i | \(-0.699159\pi\) | ||||
−0.585646 | + | 0.810567i | \(0.699159\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −52.3335 | −1.96266 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 63.4887 | 2.37767 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.03694 | 0.113575 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47.3288 | 1.76753 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.6718 | 1.77786 | 0.888930 | − | 0.458043i | \(-0.151449\pi\) | ||||
0.888930 | + | 0.458043i | \(0.151449\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −42.0630 | −1.56434 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.5935 | 0.987657 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.960319 | −0.0356163 | −0.0178081 | − | 0.999841i | \(-0.505669\pi\) | ||||
−0.0178081 | + | 0.999841i | \(0.505669\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −36.6306 | −1.35669 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.48400 | 0.128860 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4179 | 1.08657 | 0.543287 | − | 0.839547i | \(-0.317180\pi\) | ||||
0.543287 | + | 0.839547i | \(0.317180\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.8469 | −0.583729 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.3624 | −0.528330 | −0.264165 | − | 0.964478i | \(-0.585096\pi\) | ||||
−0.264165 | + | 0.964478i | \(0.585096\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −99.0010 | −3.63689 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.1675 | −0.923304 | −0.461652 | − | 0.887061i | \(-0.652743\pi\) | ||||
−0.461652 | + | 0.887061i | \(0.652743\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.436566 | −0.0159945 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.7300 | −0.721883 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0272 | −0.511861 | −0.255931 | − | 0.966695i | \(-0.582382\pi\) | ||||
−0.255931 | + | 0.966695i | \(0.582382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.4654 | −0.672917 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.747357 | 0.0271991 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.2649 | 1.02731 | 0.513653 | − | 0.857998i | \(-0.328292\pi\) | ||||
0.513653 | + | 0.857998i | \(0.328292\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.0159 | 0.726530 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.807994 | 0.0292897 | 0.0146449 | − | 0.999893i | \(-0.495338\pi\) | ||||
0.0146449 | + | 0.999893i | \(0.495338\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.85685 | −0.103290 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −82.8046 | −2.98990 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.4595 | 0.485362 | 0.242681 | − | 0.970106i | \(-0.421973\pi\) | ||||
0.242681 | + | 0.970106i | \(0.421973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −77.4917 | −2.79080 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.16587 | 0.113868 | 0.0569342 | − | 0.998378i | \(-0.481867\pi\) | ||||
0.0569342 | + | 0.998378i | \(0.481867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 49.7556 | 1.78727 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.55720 | −0.199107 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.7217 | 0.741479 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.54448 | 0.305355 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.85790 | −0.102003 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.32819 | −0.225576 | −0.112788 | − | 0.993619i | \(-0.535978\pi\) | ||||
−0.112788 | + | 0.993619i | \(0.535978\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.2511 | −1.07697 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.5276 | −0.373847 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.00928 | 0.319526 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.7544 | −1.26648 | −0.633242 | − | 0.773954i | \(-0.718276\pi\) | ||||
−0.633242 | + | 0.773954i | \(0.718276\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.5579 | −0.408889 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.5691 | −0.868105 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.63139 | −0.234017 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −56.0139 | −1.97178 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.1618 | −0.357269 | −0.178634 | − | 0.983916i | \(-0.557168\pi\) | ||||
−0.178634 | + | 0.983916i | \(0.557168\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.3227 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 66.7528 | 2.34112 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.48689 | 0.157169 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.56994 | −0.299824 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.0837 | −1.57343 | −0.786716 | − | 0.617315i | \(-0.788220\pi\) | ||||
−0.786716 | + | 0.617315i | \(0.788220\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.31875 | −0.220258 | −0.110129 | − | 0.993917i | \(-0.535126\pi\) | ||||
−0.110129 | + | 0.993917i | \(0.535126\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.6863 | 0.546126 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.7160 | 1.24197 | 0.620983 | − | 0.783824i | \(-0.286734\pi\) | ||||
0.620983 | + | 0.783824i | \(0.286734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.5906 | −0.819334 | −0.409667 | − | 0.912235i | \(-0.634355\pi\) | ||||
−0.409667 | + | 0.912235i | \(0.634355\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.6838 | −2.00103 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.58052 | −0.227728 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.9865 | 0.552573 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.93987 | 0.170543 | 0.0852716 | − | 0.996358i | \(-0.472824\pi\) | ||||
0.0852716 | + | 0.996358i | \(0.472824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.730160 | 0.0251779 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.0828 | −0.657245 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.2676 | −0.422019 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.2339 | −0.454185 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.5221 | −0.463531 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.5482 | 0.498123 | 0.249061 | − | 0.968488i | \(-0.419878\pi\) | ||||
0.249061 | + | 0.968488i | \(0.419878\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.02728 | 0.240328 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.5690 | 0.361030 | 0.180515 | − | 0.983572i | \(-0.442224\pi\) | ||||
0.180515 | + | 0.983572i | \(0.442224\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.75541 | 0.128133 | 0.0640664 | − | 0.997946i | \(-0.479593\pi\) | ||||
0.0640664 | + | 0.997946i | \(0.479593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47.7794 | −1.62643 | −0.813215 | − | 0.581964i | \(-0.802285\pi\) | ||||
−0.813215 | + | 0.581964i | \(0.802285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.01014 | 0.136349 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.5834 | 1.03867 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.1379 | −0.615285 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 87.7779 | 2.97424 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.1279 | 0.478158 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.57739 | −0.255870 | −0.127935 | − | 0.991783i | \(-0.540835\pi\) | ||||
−0.127935 | + | 0.991783i | \(0.540835\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.9477 | −1.04384 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.4566 | 1.80100 | 0.900499 | − | 0.434857i | \(-0.143201\pi\) | ||||
0.900499 | + | 0.434857i | \(0.143201\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.4484 | 1.63042 | 0.815209 | − | 0.579167i | \(-0.196622\pi\) | ||||
0.815209 | + | 0.579167i | \(0.196622\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.7627 | 0.361785 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.3614 | 0.717246 | 0.358623 | − | 0.933483i | \(-0.383246\pi\) | ||||
0.358623 | + | 0.933483i | \(0.383246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.50662 | −0.284982 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.4301 | 0.951378 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.12916 | −0.138022 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −110.870 | −3.70185 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55.6242 | 1.85517 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.5986 | 0.752867 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.390321 | −0.0129747 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.6280 | −0.718146 | −0.359073 | − | 0.933310i | \(-0.616907\pi\) | ||||
−0.359073 | + | 0.933310i | \(0.616907\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 37.4934 | 1.24358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.3774 | −1.60282 | −0.801408 | − | 0.598118i | \(-0.795915\pi\) | ||||
−0.801408 | + | 0.598118i | \(0.795915\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.83807 | −0.226307 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.36835 | 0.0452363 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.2774 | 1.65850 | 0.829248 | − | 0.558880i | \(-0.188769\pi\) | ||||
0.829248 | + | 0.558880i | \(0.188769\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 72.5031 | 2.38906 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −114.780 | −3.77802 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.5972 | −0.348432 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45.9353 | −1.50871 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.32962 | −0.207668 | −0.103834 | − | 0.994595i | \(-0.533111\pi\) | ||||
−0.103834 | + | 0.994595i | \(0.533111\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 42.5401 | 1.39270 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.990133 | −0.0323808 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.72442 | 0.121672 | 0.0608358 | − | 0.998148i | \(-0.480623\pi\) | ||||
0.0608358 | + | 0.998148i | \(0.480623\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.9146 | 0.747790 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.8875 | −1.69149 | −0.845743 | − | 0.533591i | \(-0.820842\pi\) | ||||
−0.845743 | + | 0.533591i | \(0.820842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.22344 | −0.202663 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.6641 | −0.671492 | −0.335746 | − | 0.941953i | \(-0.608988\pi\) | ||||
−0.335746 | + | 0.941953i | \(0.608988\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.7320 | 1.19237 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −41.4721 | −1.34483 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.96240 | −0.0635682 | −0.0317841 | − | 0.999495i | \(-0.510119\pi\) | ||||
−0.0317841 | + | 0.999495i | \(0.510119\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.26410 | 0.267420 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.5365 | 0.566873 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.0713 | 2.35714 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −43.1666 | −1.39102 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.17243 | 0.0377417 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.4844 | −0.980312 | −0.490156 | − | 0.871635i | \(-0.663060\pi\) | ||||
−0.490156 | + | 0.871635i | \(0.663060\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 32.2773 | 1.03690 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.2833 | −0.586739 | −0.293369 | − | 0.955999i | \(-0.594777\pi\) | ||||
−0.293369 | + | 0.955999i | \(0.594777\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −86.8881 | −2.78265 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.2505 | −0.903814 | −0.451907 | − | 0.892065i | \(-0.649256\pi\) | ||||
−0.451907 | + | 0.892065i | \(0.649256\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.51520 | −0.272147 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −62.7385 | −2.00309 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.1779 | −1.18579 | −0.592895 | − | 0.805280i | \(-0.702015\pi\) | ||||
−0.592895 | + | 0.805280i | \(0.702015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.05286 | −0.0335470 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.59738 | −0.305179 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.7085 | −0.340167 | −0.170083 | − | 0.985430i | \(-0.554404\pi\) | ||||
−0.170083 | + | 0.985430i | \(0.554404\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.07123 | −0.0657284 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.48680 | 0.110539 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.6742 | −0.433065 | −0.216533 | − | 0.976275i | \(-0.569475\pi\) | ||||
−0.216533 | + | 0.976275i | \(0.569475\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.40486 | −0.107725 |
(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 | 8036.2.a.k.1.1 | 5 | ||
7.6 | odd | 2 | 1148.2.a.d.1.5 | ✓ | 5 | ||
28.27 | even | 2 | 4592.2.a.bc.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.a.d.1.5 | ✓ | 5 | 7.6 | odd | 2 | ||
4592.2.a.bc.1.1 | 5 | 28.27 | even | 2 | |||
8036.2.a.k.1.1 | 5 | 1.1 | even | 1 | trivial |