Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, 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("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 9x^{5} + 5x^{4} + 25x^{3} - 4x^{2} - 17x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.960446\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.0395540 | −0.0228365 | −0.0114183 | − | 0.999935i | \(-0.503635\pi\) | ||||
−0.0114183 | + | 0.999935i | \(0.503635\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.949625 | 0.424685 | 0.212343 | − | 0.977195i | \(-0.431891\pi\) | ||||
0.212343 | + | 0.977195i | \(0.431891\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23977 | 0.468590 | 0.234295 | − | 0.972166i | \(-0.424722\pi\) | ||||
0.234295 | + | 0.972166i | \(0.424722\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99844 | −0.999478 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.02968 | −0.913483 | −0.456741 | − | 0.889600i | \(-0.650984\pi\) | ||||
−0.456741 | + | 0.889600i | \(0.650984\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.87052 | −0.796138 | −0.398069 | − | 0.917355i | \(-0.630320\pi\) | ||||
−0.398069 | + | 0.917355i | \(0.630320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0375615 | −0.00969833 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.912064 | 0.221208 | 0.110604 | − | 0.993865i | \(-0.464721\pi\) | ||||
0.110604 | + | 0.993865i | \(0.464721\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.10358 | −0.482595 | −0.241298 | − | 0.970451i | \(-0.577573\pi\) | ||||
−0.241298 | + | 0.970451i | \(0.577573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0490380 | −0.0107010 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.82122 | −0.796778 | −0.398389 | − | 0.917216i | \(-0.630431\pi\) | ||||
−0.398389 | + | 0.917216i | \(0.630431\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.09821 | −0.819642 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.237262 | 0.0456611 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0768876 | −0.0142777 | −0.00713883 | − | 0.999975i | \(-0.502272\pi\) | ||||
−0.00713883 | + | 0.999975i | \(0.502272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.57708 | −1.18128 | −0.590639 | − | 0.806936i | \(-0.701124\pi\) | ||||
−0.590639 | + | 0.806936i | \(0.701124\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.119836 | 0.0208608 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.17732 | 0.199003 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.49129 | −0.245166 | −0.122583 | − | 0.992458i | \(-0.539118\pi\) | ||||
−0.122583 | + | 0.992458i | \(0.539118\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.113540 | 0.0181810 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0656 | 1.57199 | 0.785995 | − | 0.618233i | \(-0.212151\pi\) | ||||
0.785995 | + | 0.618233i | \(0.212151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.744801 | 0.113581 | 0.0567905 | − | 0.998386i | \(-0.481913\pi\) | ||||
0.0567905 | + | 0.998386i | \(0.481913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.84739 | −0.424464 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.3191 | −1.50520 | −0.752598 | − | 0.658480i | \(-0.771200\pi\) | ||||
−0.752598 | + | 0.658480i | \(0.771200\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.46296 | −0.780423 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0360758 | −0.00505162 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.28582 | 0.313982 | 0.156991 | − | 0.987600i | \(-0.449821\pi\) | ||||
0.156991 | + | 0.987600i | \(0.449821\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.87706 | −0.387943 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0832051 | 0.0110208 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.377610 | −0.0491606 | −0.0245803 | − | 0.999698i | \(-0.507825\pi\) | ||||
−0.0245803 | + | 0.999698i | \(0.507825\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.54258 | 1.09377 | 0.546883 | − | 0.837209i | \(-0.315814\pi\) | ||||
0.546883 | + | 0.837209i | \(0.315814\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.71738 | −0.468346 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.72592 | −0.338108 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.45388 | 0.910636 | 0.455318 | − | 0.890329i | \(-0.349525\pi\) | ||||
0.455318 | + | 0.890329i | \(0.349525\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.151144 | 0.0181956 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.83565 | −1.16728 | −0.583638 | − | 0.812014i | \(-0.698371\pi\) | ||||
−0.583638 | + | 0.812014i | \(0.698371\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.8350 | 1.73631 | 0.868153 | − | 0.496297i | \(-0.165307\pi\) | ||||
0.868153 | + | 0.496297i | \(0.165307\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.162101 | 0.0187178 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.75611 | −0.428049 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.73971 | 1.09580 | 0.547901 | − | 0.836543i | \(-0.315427\pi\) | ||||
0.547901 | + | 0.836543i | \(0.315427\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.98592 | 0.998436 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.4173 | −1.47275 | −0.736373 | − | 0.676576i | \(-0.763463\pi\) | ||||
−0.736373 | + | 0.676576i | \(0.763463\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.866119 | 0.0939438 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.00304121 | 0.000326052 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.1009 | −1.60070 | −0.800348 | − | 0.599536i | \(-0.795352\pi\) | ||||
−0.800348 | + | 0.599536i | \(0.795352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.55879 | −0.373062 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.260150 | 0.0269763 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.99762 | −0.204951 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.86636 | −0.494104 | −0.247052 | − | 0.969002i | \(-0.579462\pi\) | ||||
−0.247052 | + | 0.969002i | \(0.579462\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.08430 | 0.913006 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.07427 | 0.305902 | 0.152951 | − | 0.988234i | \(-0.451122\pi\) | ||||
0.152951 | + | 0.988234i | \(0.451122\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.8957 | −1.66478 | −0.832391 | − | 0.554189i | \(-0.813028\pi\) | ||||
−0.832391 | + | 0.554189i | \(0.813028\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0465677 | −0.00454454 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.8737 | −1.82459 | −0.912297 | − | 0.409529i | \(-0.865693\pi\) | ||||
−0.912297 | + | 0.409529i | \(0.865693\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.31618 | −0.413415 | −0.206707 | − | 0.978403i | \(-0.566275\pi\) | ||||
−0.206707 | + | 0.978403i | \(0.566275\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0589863 | 0.00559873 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.74376 | −0.634400 | −0.317200 | − | 0.948359i | \(-0.602743\pi\) | ||||
−0.317200 | + | 0.948359i | \(0.602743\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.62872 | −0.338380 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.60706 | 0.795723 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.13075 | 0.103656 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.82104 | −0.165549 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.398136 | −0.0358987 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.63989 | −0.772776 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.331446 | −0.0294111 | −0.0147055 | − | 0.999892i | \(-0.504681\pi\) | ||||
−0.0147055 | + | 0.999892i | \(0.504681\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.0294599 | −0.00259380 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9506 | 1.30624 | 0.653120 | − | 0.757255i | \(-0.273460\pi\) | ||||
0.653120 | + | 0.757255i | \(0.273460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.60796 | −0.226139 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.225310 | 0.0193916 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.30018 | 0.538260 | 0.269130 | − | 0.963104i | \(-0.413264\pi\) | ||||
0.269130 | + | 0.963104i | \(0.413264\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.7160 | −1.67229 | −0.836145 | − | 0.548509i | \(-0.815196\pi\) | ||||
−0.836145 | + | 0.548509i | \(0.815196\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.408162 | 0.0343734 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.69675 | 0.727259 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0730144 | −0.00606352 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.216082 | 0.0178221 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.24667 | 0.593671 | 0.296835 | − | 0.954929i | \(-0.404069\pi\) | ||||
0.296835 | + | 0.954929i | \(0.404069\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0425 | 0.980007 | 0.490003 | − | 0.871721i | \(-0.336996\pi\) | ||||
0.490003 | + | 0.871721i | \(0.336996\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.73476 | −0.221093 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.24576 | −0.501671 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.55988 | −0.204301 | −0.102150 | − | 0.994769i | \(-0.532572\pi\) | ||||
−0.102150 | + | 0.994769i | \(0.532572\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0904135 | −0.00717026 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.73744 | −0.373362 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.6944 | 0.837653 | 0.418827 | − | 0.908066i | \(-0.362442\pi\) | ||||
0.418827 | + | 0.908066i | \(0.362442\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.113799 | 0.00885926 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.76013 | −0.366164 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.30746 | 0.482343 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.1831 | 1.76258 | 0.881289 | − | 0.472577i | \(-0.156676\pi\) | ||||
0.881289 | + | 0.472577i | \(0.156676\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.08085 | −0.384076 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0149360 | 0.00112266 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.85130 | −0.512090 | −0.256045 | − | 0.966665i | \(-0.582420\pi\) | ||||
−0.256045 | + | 0.966665i | \(0.582420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.93347 | 0.218043 | 0.109022 | − | 0.994039i | \(-0.465228\pi\) | ||||
0.109022 | + | 0.994039i | \(0.465228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.337893 | −0.0249778 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.41616 | −0.104118 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.76326 | −0.202070 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.294151 | 0.0213963 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.40287 | 0.680368 | 0.340184 | − | 0.940359i | \(-0.389511\pi\) | ||||
0.340184 | + | 0.940359i | \(0.389511\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.3656 | 1.53793 | 0.768963 | − | 0.639293i | \(-0.220773\pi\) | ||||
0.768963 | + | 0.639293i | \(0.220773\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.107821 | 0.00772121 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.49612 | 0.605324 | 0.302662 | − | 0.953098i | \(-0.402125\pi\) | ||||
0.302662 | + | 0.953098i | \(0.402125\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.14532 | 0.0811897 | 0.0405949 | − | 0.999176i | \(-0.487075\pi\) | ||||
0.0405949 | + | 0.999176i | \(0.487075\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.294831 | −0.0207958 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0953231 | −0.00669037 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.55859 | 0.667601 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.4577 | 0.796363 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.37318 | 0.440842 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.7779 | 1.56810 | 0.784048 | − | 0.620701i | \(-0.213152\pi\) | ||||
0.784048 | + | 0.620701i | \(0.213152\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.389039 | 0.0266565 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.707282 | 0.0482362 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.15408 | −0.553535 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.586783 | −0.0396511 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.61810 | −0.176112 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.652262 | −0.0436787 | −0.0218393 | − | 0.999761i | \(-0.506952\pi\) | ||||
−0.0218393 | + | 0.999761i | \(0.506952\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2882 | 0.819215 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.999405 | 0.0663329 | 0.0331664 | − | 0.999450i | \(-0.489441\pi\) | ||||
0.0331664 | + | 0.999450i | \(0.489441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.0664 | 1.06170 | 0.530850 | − | 0.847466i | \(-0.321873\pi\) | ||||
0.530850 | + | 0.847466i | \(0.321873\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.148569 | 0.00977514 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.9924 | −1.57179 | −0.785896 | − | 0.618359i | \(-0.787798\pi\) | ||||
−0.785896 | + | 0.618359i | \(0.787798\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.79928 | −0.639235 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.385244 | −0.0250243 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.81344 | −0.117302 | −0.0586509 | − | 0.998279i | \(-0.518680\pi\) | ||||
−0.0586509 | + | 0.998279i | \(0.518680\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.60250 | −0.425304 | −0.212652 | − | 0.977128i | \(-0.568210\pi\) | ||||
−0.212652 | + | 0.977128i | \(0.568210\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.06722 | −0.0684619 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.18777 | −0.331434 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.03837 | 0.384212 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.530710 | 0.0336324 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.2755 | −1.46913 | −0.734567 | − | 0.678536i | \(-0.762615\pi\) | ||||
−0.734567 | + | 0.678536i | \(0.762615\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.5771 | 0.727843 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0342585 | −0.00214535 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.40517 | 0.150030 | 0.0750151 | − | 0.997182i | \(-0.476100\pi\) | ||||
0.0750151 | + | 0.997182i | \(0.476100\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.84886 | −0.114882 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.230543 | 0.0142702 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.8866 | −0.917945 | −0.458973 | − | 0.888450i | \(-0.651782\pi\) | ||||
−0.458973 | + | 0.888450i | \(0.651782\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.17068 | 0.133344 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.597302 | 0.0365543 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.3302 | 1.11761 | 0.558805 | − | 0.829299i | \(-0.311260\pi\) | ||||
0.558805 | + | 0.829299i | \(0.311260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4803 | 1.00111 | 0.500553 | − | 0.865706i | \(-0.333130\pi\) | ||||
0.500553 | + | 0.865706i | \(0.333130\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.140764 | 0.00851944 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.4163 | 0.748729 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.7791 | 1.18841 | 0.594205 | − | 0.804313i | \(-0.297467\pi\) | ||||
0.594205 | + | 0.804313i | \(0.297467\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.7209 | 1.18066 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.3136 | 1.09250 | 0.546250 | − | 0.837622i | \(-0.316055\pi\) | ||||
0.546250 | + | 0.837622i | \(0.316055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.52286 | −0.506631 | −0.253316 | − | 0.967384i | \(-0.581521\pi\) | ||||
−0.253316 | + | 0.967384i | \(0.581521\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0790137 | 0.00468037 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.4791 | 0.736619 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1681 | −0.951067 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.192484 | 0.0112836 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.5538 | −1.66813 | −0.834066 | − | 0.551665i | \(-0.813993\pi\) | ||||
−0.834066 | + | 0.551665i | \(0.813993\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.358588 | −0.0208778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.718828 | −0.0417106 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.9689 | 0.634346 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.923384 | 0.0532230 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.121600 | −0.00698573 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.11225 | 0.464506 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.0965 | 0.747455 | 0.373728 | − | 0.927538i | \(-0.378079\pi\) | ||||
0.373728 | + | 0.927538i | \(0.378079\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.668292 | 0.0380178 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.66348 | −0.434556 | −0.217278 | − | 0.976110i | \(-0.569718\pi\) | ||||
−0.217278 | + | 0.976110i | \(0.569718\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.47042 | 0.535300 | 0.267650 | − | 0.963516i | \(-0.413753\pi\) | ||||
0.267650 | + | 0.963516i | \(0.413753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.53012 | −0.198900 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.08696 | −0.510374 | −0.255187 | − | 0.966892i | \(-0.582137\pi\) | ||||
−0.255187 | + | 0.966892i | \(0.582137\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.232945 | 0.0130424 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.746532 | 0.0416674 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.91860 | −0.106754 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.7640 | 0.652549 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.170722 | 0.00944095 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.7933 | −0.705320 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0330 | −0.826287 | −0.413143 | − | 0.910666i | \(-0.635569\pi\) | ||||
−0.413143 | + | 0.910666i | \(0.635569\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.47153 | 0.245038 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.07839 | 0.386734 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.26580 | 0.286847 | 0.143423 | − | 0.989661i | \(-0.454189\pi\) | ||||
0.143423 | + | 0.989661i | \(0.454189\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.266743 | 0.0144875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.9264 | 1.07908 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.4512 | −0.834289 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.143530 | 0.00772742 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.9180 | 1.33767 | 0.668835 | − | 0.743411i | \(-0.266793\pi\) | ||||
0.668835 | + | 0.743411i | \(0.266793\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.6911 | 0.893452 | 0.446726 | − | 0.894671i | \(-0.352590\pi\) | ||||
0.446726 | + | 0.894671i | \(0.352590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.681065 | −0.0363526 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.5946 | −1.09614 | −0.548069 | − | 0.836433i | \(-0.684637\pi\) | ||||
−0.548069 | + | 0.836433i | \(0.684637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.34018 | −0.495725 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0447258 | −0.00236714 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.96132 | −0.525738 | −0.262869 | − | 0.964831i | \(-0.584669\pi\) | ||||
−0.262869 | + | 0.964831i | \(0.584669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5749 | −0.767102 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0720295 | 0.00378057 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0877 | 0.737383 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.377347 | −0.0196973 | −0.00984867 | − | 0.999952i | \(-0.503135\pi\) | ||||
−0.00984867 | + | 0.999952i | \(0.503135\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −30.1812 | −1.57117 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.83390 | 0.147129 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.7304 | 0.607376 | 0.303688 | − | 0.952772i | \(-0.401782\pi\) | ||||
0.303688 | + | 0.952772i | \(0.401782\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.341742 | 0.0176475 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.220707 | 0.0113670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.2301 | 1.29598 | 0.647992 | − | 0.761647i | \(-0.275609\pi\) | ||||
0.647992 | + | 0.761647i | \(0.275609\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0131100 | 0.000671647 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.43389 | 0.124366 | 0.0621829 | − | 0.998065i | \(-0.480194\pi\) | ||||
0.0621829 | + | 0.998065i | \(0.480194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.56690 | −0.181786 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.23324 | −0.113522 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.53105 | 0.229734 | 0.114867 | − | 0.993381i | \(-0.463356\pi\) | ||||
0.114867 | + | 0.993381i | \(0.463356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.48519 | −0.176254 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.591356 | −0.0298300 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.24907 | 0.465371 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.6635 | 1.63933 | 0.819667 | − | 0.572840i | \(-0.194158\pi\) | ||||
0.819667 | + | 0.572840i | \(0.194158\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.103155 | 0.00516423 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.3745 | −0.767765 | −0.383883 | − | 0.923382i | \(-0.625413\pi\) | ||||
−0.383883 | + | 0.923382i | \(0.625413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.8796 | 0.940460 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.53326 | 0.424021 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.51812 | 0.223955 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.5233 | −1.85541 | −0.927704 | − | 0.373316i | \(-0.878221\pi\) | ||||
−0.927704 | + | 0.373316i | \(0.878221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.249197 | −0.0122920 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.468150 | −0.0230362 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.7415 | −0.625453 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.779847 | 0.0381893 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.28954 | −0.160705 | −0.0803523 | − | 0.996767i | \(-0.525605\pi\) | ||||
−0.0803523 | + | 0.996767i | \(0.525605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.1287 | 1.85828 | 0.929140 | − | 0.369727i | \(-0.120549\pi\) | ||||
0.929140 | + | 0.369727i | \(0.120549\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.9412 | 1.50441 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.73783 | −0.181311 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.5909 | 0.512528 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.343991 | −0.0166080 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.7620 | −1.00007 | −0.500034 | − | 0.866006i | \(-0.666679\pi\) | ||||
−0.500034 | + | 0.866006i | \(0.666679\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2343 | −0.684057 | −0.342029 | − | 0.939690i | \(-0.611114\pi\) | ||||
−0.342029 | + | 0.939690i | \(0.611114\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.00288801 | 0.000138470 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.03824 | 0.384521 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.58593 | 0.457511 | 0.228756 | − | 0.973484i | \(-0.426534\pi\) | ||||
0.228756 | + | 0.973484i | \(0.426534\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.3803 | 0.780016 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.25114 | −0.154466 | −0.0772331 | − | 0.997013i | \(-0.524609\pi\) | ||||
−0.0772331 | + | 0.997013i | \(0.524609\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.3402 | −0.679792 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.286635 | −0.0135574 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.7412 | −1.21480 | −0.607401 | − | 0.794395i | \(-0.707788\pi\) | ||||
−0.607401 | + | 0.794395i | \(0.707788\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.4957 | −1.43599 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.476330 | −0.0223799 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.37952 | −0.158434 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.60084 | −0.308774 | −0.154387 | − | 0.988010i | \(-0.549340\pi\) | ||||
−0.154387 | + | 0.988010i | \(0.549340\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.216398 | 0.0101006 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.5339 | −1.28238 | −0.641190 | − | 0.767382i | \(-0.721559\pi\) | ||||
−0.641190 | + | 0.767382i | \(0.721559\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.2087 | −0.939179 | −0.469589 | − | 0.882885i | \(-0.655598\pi\) | ||||
−0.469589 | + | 0.882885i | \(0.655598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.247045 | 0.0114564 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.3548 | 0.756808 | 0.378404 | − | 0.925640i | \(-0.376473\pi\) | ||||
0.378404 | + | 0.925640i | \(0.376473\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.24112 | 0.426715 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.101254 | 0.00466552 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.25651 | −0.103754 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.62093 | 0.395555 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.85390 | −0.313818 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.4284 | 1.20755 | 0.603773 | − | 0.797156i | \(-0.293663\pi\) | ||||
0.603773 | + | 0.797156i | \(0.293663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.28076 | 0.195186 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.187385 | 0.00852629 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.62122 | −0.209839 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.5253 | 0.975407 | 0.487703 | − | 0.873009i | \(-0.337835\pi\) | ||||
0.487703 | + | 0.873009i | \(0.337835\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.423008 | −0.0191291 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.06918 | −0.273898 | −0.136949 | − | 0.990578i | \(-0.543730\pi\) | ||||
−0.136949 | + | 0.990578i | \(0.543730\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0701264 | −0.00315833 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.62668 | 0.387740 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.1940 | −0.546974 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.64230 | 0.297350 | 0.148675 | − | 0.988886i | \(-0.452499\pi\) | ||||
0.148675 | + | 0.988886i | \(0.452499\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.0395540 | 0.00176714 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.8481 | 0.795806 | 0.397903 | − | 0.917427i | \(-0.369738\pi\) | ||||
0.397903 | + | 0.917427i | \(0.369738\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.91941 | 0.129912 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.188282 | 0.00836190 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −42.7605 | −1.89533 | −0.947663 | − | 0.319271i | \(-0.896562\pi\) | ||||
−0.947663 | + | 0.319271i | \(0.896562\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.3920 | 0.813615 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.499100 | −0.0220358 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.0446 | −0.707008 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.2636 | 1.37497 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.916984 | −0.0402511 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.5909 | −0.945913 | −0.472957 | − | 0.881086i | \(-0.656813\pi\) | ||||
−0.472957 | + | 0.881086i | \(0.656813\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.67558 | 0.423084 | 0.211542 | − | 0.977369i | \(-0.432152\pi\) | ||||
0.211542 | + | 0.977369i | \(0.432152\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.200968 | 0.00877096 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.99871 | −0.261308 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.39831 | −0.365144 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.13224 | 0.0491350 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.8936 | −1.25152 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.9230 | −0.774879 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.270996 | 0.0116943 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5510 | 0.712903 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.5143 | −0.967965 | −0.483982 | − | 0.875078i | \(-0.660810\pi\) | ||||
−0.483982 | + | 0.875078i | \(0.660810\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.116030 | −0.00497934 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.09875 | −0.175571 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.84060 | 0.206969 | 0.103485 | − | 0.994631i | \(-0.467001\pi\) | ||||
0.103485 | + | 0.994631i | \(0.467001\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.6144 | −1.09319 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.161739 | 0.00689033 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0750 | 0.513482 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0560149 | 0.00237770 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.5882 | −1.33843 | −0.669217 | − | 0.743067i | \(-0.733370\pi\) | ||||
−0.669217 | + | 0.743067i | \(0.733370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.13796 | −0.0904263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.109298 | 0.00461457 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.3929 | 1.70236 | 0.851178 | − | 0.524877i | \(-0.175889\pi\) | ||||
0.851178 | + | 0.524877i | \(0.175889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.40405 | −0.269420 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.1405 | 0.467857 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.53972 | −0.148393 | −0.0741964 | − | 0.997244i | \(-0.523639\pi\) | ||||
−0.0741964 | + | 0.997244i | \(0.523639\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.3498 | −0.893460 | −0.446730 | − | 0.894669i | \(-0.647412\pi\) | ||||
−0.446730 | + | 0.894669i | \(0.647412\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.371921 | −0.0155372 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.6601 | 0.653073 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.47187 | 0.311058 | 0.155529 | − | 0.987831i | \(-0.450292\pi\) | ||||
0.155529 | + | 0.987831i | \(0.450292\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.845093 | −0.0351209 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.6345 | −0.690114 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.92532 | −0.286817 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.17348 | 0.337932 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.32749 | −0.261163 | −0.130582 | − | 0.991438i | \(-0.541685\pi\) | ||||
−0.130582 | + | 0.991438i | \(0.541685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.8354 | 0.570079 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.336056 | −0.0138235 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.4067 | −1.00227 | −0.501133 | − | 0.865371i | \(-0.667083\pi\) | ||||
−0.501133 | + | 0.865371i | \(0.667083\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.07379 | 0.0440211 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.0453021 | −0.00185409 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0464 | −0.982510 | −0.491255 | − | 0.871016i | \(-0.663462\pi\) | ||||
−0.491255 | + | 0.871016i | \(0.663462\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.6360 | −0.964131 | −0.482065 | − | 0.876135i | \(-0.660113\pi\) | ||||
−0.482065 | + | 0.876135i | \(0.660113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.3500 | −0.910162 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.72931 | −0.0703064 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.4194 | −0.869387 | −0.434693 | − | 0.900579i | \(-0.643143\pi\) | ||||
−0.434693 | + | 0.900579i | \(0.643143\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.00377041 | 0.000152785 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.6212 | 1.19834 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.6553 | −0.632312 | −0.316156 | − | 0.948707i | \(-0.602392\pi\) | ||||
−0.316156 | + | 0.948707i | \(0.602392\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.378080 | −0.0152457 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.3465 | 0.456793 | 0.228397 | − | 0.973568i | \(-0.426652\pi\) | ||||
0.228397 | + | 0.973568i | \(0.426652\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.48960 | −0.140259 | −0.0701294 | − | 0.997538i | \(-0.522341\pi\) | ||||
−0.0701294 | + | 0.997538i | \(0.522341\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.906629 | −0.0363818 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.7217 | −0.750070 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.2864 | 0.491456 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.252085 | −0.0100673 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.36015 | −0.0542327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.47130 | 0.0585717 | 0.0292858 | − | 0.999571i | \(-0.490677\pi\) | ||||
0.0292858 | + | 0.999571i | \(0.490677\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.900957 | −0.0358098 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.314750 | −0.0124905 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.6815 | 0.621325 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.4916 | 1.16667 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.6705 | 1.21141 | 0.605706 | − | 0.795688i | \(-0.292891\pi\) | ||||
0.605706 | + | 0.795688i | \(0.292891\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.60725 | −0.378873 | −0.189436 | − | 0.981893i | \(-0.560666\pi\) | ||||
−0.189436 | + | 0.981893i | \(0.560666\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0279758 | −0.00110155 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.7775 | −0.463023 | −0.231512 | − | 0.972832i | \(-0.574367\pi\) | ||||
−0.231512 | + | 0.972832i | \(0.574367\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.14404 | 0.0449074 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.322526 | 0.0126408 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0014 | 0.743582 | 0.371791 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371791 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.1975 | 0.554741 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −44.4818 | −1.73540 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2717 | −0.711766 | −0.355883 | − | 0.934531i | \(-0.615820\pi\) | ||||
−0.355883 | + | 0.934531i | \(0.615820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.75810 | −0.262860 | −0.131430 | − | 0.991325i | \(-0.541957\pi\) | ||||
−0.131430 | + | 0.991325i | \(0.541957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.103556 | 0.00402179 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.47659 | −0.0960380 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.293804 | 0.0113761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.0257996 | 0.000997468 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.8813 | −0.999136 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.78348 | 0.0687482 | 0.0343741 | − | 0.999409i | \(-0.489056\pi\) | ||||
0.0343741 | + | 0.999409i | \(0.489056\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.972350 | −0.0374258 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.7045 | −1.02634 | −0.513169 | − | 0.858287i | \(-0.671529\pi\) | ||||
−0.513169 | + | 0.858287i | \(0.671529\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.03318 | −0.231532 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0395305 | −0.00151481 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.9664 | −1.49101 | −0.745505 | − | 0.666500i | \(-0.767792\pi\) | ||||
−0.745505 | + | 0.666500i | \(0.767792\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.98281 | 0.228591 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.635491 | −0.0242455 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.56150 | −0.249973 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.79132 | 0.258354 | 0.129177 | − | 0.991622i | \(-0.458766\pi\) | ||||
0.129177 | + | 0.991622i | \(0.458766\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.2625 | 0.427826 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.7228 | −0.710197 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.18051 | 0.347737 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.948994 | 0.0358942 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.87709 | −0.373052 | −0.186526 | − | 0.982450i | \(-0.559723\pi\) | ||||
−0.186526 | + | 0.982450i | \(0.559723\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.13704 | 0.118316 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.387601 | 0.0145979 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.81140 | 0.143342 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.4489 | −0.467530 | −0.233765 | − | 0.972293i | \(-0.575105\pi\) | ||||
−0.233765 | + | 0.972293i | \(0.575105\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.2039 | −1.09523 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.1324 | 0.941217 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.25865 | 0.308856 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.0717289 | 0.00267877 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.66173 | 0.248441 | 0.124220 | − | 0.992255i | \(-0.460357\pi\) | ||||
0.124220 | + | 0.992255i | \(0.460357\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.9468 | −0.780100 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.261155 | 0.00971247 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.315102 | 0.0117026 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.7916 | −0.956556 | −0.478278 | − | 0.878209i | \(-0.658739\pi\) | ||||
−0.478278 | + | 0.878209i | \(0.658739\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9156 | −0.996872 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.679306 | 0.0251250 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.2454 | 1.56037 | 0.780184 | − | 0.625550i | \(-0.215125\pi\) | ||||
0.780184 | + | 0.625550i | \(0.215125\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.205197 | 0.00756880 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.5829 | −0.831851 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.7987 | −0.728308 | −0.364154 | − | 0.931339i | \(-0.618642\pi\) | ||||
−0.364154 | + | 0.931339i | \(0.618642\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.238842 | −0.00877407 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.45381 | 0.273454 | 0.136727 | − | 0.990609i | \(-0.456342\pi\) | ||||
0.136727 | + | 0.990609i | \(0.456342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.88162 | 0.252123 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 40.2311 | 1.47198 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.3992 | −0.854987 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 54.5391 | 1.99016 | 0.995080 | − | 0.0990702i | \(-0.0315868\pi\) | ||||
0.995080 | + | 0.0990702i | \(0.0315868\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.920637 | 0.0335499 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.4359 | 0.416194 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.9960 | 1.52637 | 0.763185 | − | 0.646180i | \(-0.223635\pi\) | ||||
0.763185 | + | 0.646180i | \(0.223635\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.457919 | −0.0166214 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.0099 | −0.834108 | −0.417054 | − | 0.908882i | \(-0.636937\pi\) | ||||
−0.417054 | + | 0.908882i | \(0.636937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.35108 | −0.193722 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.59700 | −0.0938948 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.08394 | 0.0391387 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.0412 | −1.01119 | −0.505596 | − | 0.862770i | \(-0.668727\pi\) | ||||
−0.505596 | + | 0.862770i | \(0.668727\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.0951339 | −0.00342616 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.49512 | 0.161678 | 0.0808390 | − | 0.996727i | \(-0.474240\pi\) | ||||
0.0808390 | + | 0.996727i | \(0.474240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.9542 | 0.968225 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0731296 | 0.00262351 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.1739 | −0.758634 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.7989 | 1.06629 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.0182425 | −0.000651934 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.43093 | −0.0867636 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.4824 | 0.801411 | 0.400706 | − | 0.916207i | \(-0.368765\pi\) | ||||
0.400706 | + | 0.916207i | \(0.368765\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.588823 | 0.0209627 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.36074 | −0.297274 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.5216 | −0.870789 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0858589 | −0.00304510 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.5407 | −0.373369 | −0.186685 | − | 0.982420i | \(-0.559774\pi\) | ||||
−0.186685 | + | 0.982420i | \(0.559774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.41168 | −0.332961 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 45.2792 | 1.59986 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −44.9453 | −1.58608 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.49879 | −0.158562 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.725031 | −0.0255223 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.3965 | 1.17416 | 0.587079 | − | 0.809530i | \(-0.300278\pi\) | ||||
0.587079 | + | 0.809530i | \(0.300278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.2379 | 0.640419 | 0.320209 | − | 0.947347i | \(-0.396247\pi\) | ||||
0.320209 | + | 0.947347i | \(0.396247\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.651861 | −0.0228618 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.1557 | 0.355739 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.56675 | −0.0548137 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.6708 | 0.372868 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.4067 | −1.72431 | −0.862154 | − | 0.506647i | \(-0.830885\pi\) | ||||
−0.862154 | + | 0.506647i | \(0.830885\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.48844 | −0.295888 | −0.147944 | − | 0.988996i | \(-0.547266\pi\) | ||||
−0.147944 | + | 0.988996i | \(0.547266\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.491113 | −0.0170984 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.7054 | −0.789545 | −0.394772 | − | 0.918779i | \(-0.629177\pi\) | ||||
−0.394772 | + | 0.918779i | \(0.629177\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.1609 | 1.22119 | 0.610594 | − | 0.791944i | \(-0.290931\pi\) | ||||
0.610594 | + | 0.791944i | \(0.290931\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.782342 | −0.0271392 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.98257 | −0.172636 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.949625 | −0.0328631 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.56049 | −0.0539384 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.6085 | −1.47101 | −0.735504 | − | 0.677520i | \(-0.763055\pi\) | ||||
−0.735504 | + | 0.677520i | \(0.763055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9941 | −0.999796 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.724378 | −0.0249489 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.52034 | −0.155504 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.25768 | −0.0775748 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.337113 | 0.0115697 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.69852 | 0.195343 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.5614 | −1.11488 | −0.557441 | − | 0.830217i | \(-0.688217\pi\) | ||||
−0.557441 | + | 0.830217i | \(0.688217\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.98972 | 0.204844 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.4053 | 0.355439 | 0.177720 | − | 0.984081i | \(-0.443128\pi\) | ||||
0.177720 | + | 0.984081i | \(0.443128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.6257 | −1.18141 | −0.590706 | − | 0.806887i | \(-0.701151\pi\) | ||||
−0.590706 | + | 0.806887i | \(0.701151\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.493599 | −0.0168218 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.611644 | −0.0208206 | −0.0104103 | − | 0.999946i | \(-0.503314\pi\) | ||||
−0.0104103 | + | 0.999946i | \(0.503314\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.0153 | 0.748541 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.639514 | 0.0217190 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.5082 | −1.00100 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.3965 | −0.724993 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.5915 | 0.493846 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.7115 | −0.362115 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.3415 | −0.821953 | −0.410976 | − | 0.911646i | \(-0.634812\pi\) | ||||
−0.410976 | + | 0.911646i | \(0.634812\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.12942 | 0.0380943 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.9917 | −1.71795 | −0.858977 | − | 0.512014i | \(-0.828900\pi\) | ||||
−0.858977 | + | 0.512014i | \(0.828900\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.7274 | −1.77442 | −0.887210 | − | 0.461366i | \(-0.847360\pi\) | ||||
−0.887210 | + | 0.461366i | \(0.847360\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0141836 | 0.000476776 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.3444 | 0.548791 | 0.274395 | − | 0.961617i | \(-0.411522\pi\) | ||||
0.274395 | + | 0.961617i | \(0.411522\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.410918 | −0.0137817 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.2245 | −0.912054 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.7071 | 0.726400 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.50617 | −0.217477 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.433862 | −0.0144862 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.505696 | 0.0168659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.08482 | 0.0694554 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.0365235 | −0.00121543 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.78570 | 0.0925997 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.2683 | 1.37029 | 0.685146 | − | 0.728406i | \(-0.259738\pi\) | ||||
0.685146 | + | 0.728406i | \(0.259738\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.21801 | −0.305742 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.1161 | 0.467687 | 0.233843 | − | 0.972274i | \(-0.424870\pi\) | ||||
0.233843 | + | 0.972274i | \(0.424870\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.6503 | 1.34533 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.320872 | −0.0106077 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.5353 | 0.612091 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.5244 | −0.677036 | −0.338518 | − | 0.940960i | \(-0.609926\pi\) | ||||
−0.338518 | + | 0.940960i | \(0.609926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.518018 | −0.0170693 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.2334 | 0.929314 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.11161 | 0.200948 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 50.6606 | 1.66391 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.5819 | −0.708079 | −0.354040 | − | 0.935230i | \(-0.615192\pi\) | ||||
−0.354040 | + | 0.935230i | \(0.615192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4918 | 0.376628 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.303121 | 0.00992374 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.62406 | −0.0858160 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.8393 | −0.811465 | −0.405732 | − | 0.913992i | \(-0.632984\pi\) | ||||
−0.405732 | + | 0.913992i | \(0.632984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.374593 | −0.0122244 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.3993 | 0.730197 | 0.365099 | − | 0.930969i | \(-0.381035\pi\) | ||||
0.365099 | + | 0.930969i | \(0.381035\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −38.4630 | −1.25253 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.279333 | 0.00908671 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.8252 | 1.58661 | 0.793304 | − | 0.608826i | \(-0.208359\pi\) | ||||
0.793304 | + | 0.608826i | \(0.208359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.5841 | −1.38234 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.359425 | 0.0116552 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.2303 | −1.07644 | −0.538218 | − | 0.842806i | \(-0.680902\pi\) | ||||
−0.538218 | + | 0.842806i | \(0.680902\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.92920 | 0.288942 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.00921390 | −0.000297843 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.81078 | 0.252223 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2579 | 0.395417 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 56.5917 | 1.82364 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.2893 | 0.653135 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.5138 | −1.20636 | −0.603181 | − | 0.797604i | \(-0.706100\pi\) | ||||
−0.603181 | + | 0.797604i | \(0.706100\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0758884 | 0.00243789 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.5961 | −1.20652 | −0.603259 | − | 0.797546i | \(-0.706131\pi\) | ||||
−0.603259 | + | 0.797546i | \(0.706131\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.4434 | −0.783618 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.465313 | −0.0149019 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.9736 | 1.63079 | 0.815395 | − | 0.578904i | \(-0.196520\pi\) | ||||
0.815395 | + | 0.578904i | \(0.196520\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.7510 | 1.46221 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.9418 | 0.413199 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.1745 | 1.28137 | 0.640684 | − | 0.767804i | \(-0.278651\pi\) | ||||
0.640684 | + | 0.767804i | \(0.278651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.06813 | 0.257072 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.506028 | 0.0161070 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.84604 | −0.0904990 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.2318 | −1.02388 | −0.511938 | − | 0.859022i | \(-0.671072\pi\) | ||||
−0.511938 | + | 0.859022i | \(0.671072\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.594614 | 0.0188695 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.08763 | 0.0344801 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.6267 | 1.00163 | 0.500813 | − | 0.865555i | \(-0.333034\pi\) | ||||
0.500813 | + | 0.865555i | \(0.333034\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.353826 | −0.0111945 |
(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 | 1336.2.a.b.1.5 | ✓ | 7 | |
4.3 | odd | 2 | 2672.2.a.l.1.3 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.b.1.5 | ✓ | 7 | 1.1 | even | 1 | trivial | |
2672.2.a.l.1.3 | 7 | 4.3 | odd | 2 |