Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.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: | \(48.5490444289\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3040) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-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 | ||||||||
\(3\) | 2.21432 | 1.27844 | 0.639219 | − | 0.769025i | \(-0.279258\pi\) | ||||
0.639219 | + | 0.769025i | \(0.279258\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.52543 | 0.576557 | 0.288279 | − | 0.957547i | \(-0.406917\pi\) | ||||
0.288279 | + | 0.957547i | \(0.406917\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.90321 | 0.634404 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.90321 | −0.875351 | −0.437676 | − | 0.899133i | \(-0.644198\pi\) | ||||
−0.437676 | + | 0.899133i | \(0.644198\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.31111 | 0.363636 | 0.181818 | − | 0.983332i | \(-0.441802\pi\) | ||||
0.181818 | + | 0.983332i | \(0.441802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.21432 | −0.571735 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.80642 | −1.89334 | −0.946668 | − | 0.322211i | \(-0.895574\pi\) | ||||
−0.946668 | + | 0.322211i | \(0.895574\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.37778 | 0.737093 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.28100 | 0.892649 | 0.446325 | − | 0.894871i | \(-0.352733\pi\) | ||||
0.446325 | + | 0.894871i | \(0.352733\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.42864 | −0.467392 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.18421 | 1.70546 | 0.852732 | − | 0.522348i | \(-0.174944\pi\) | ||||
0.852732 | + | 0.522348i | \(0.174944\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.80642 | −1.40208 | −0.701038 | − | 0.713124i | \(-0.747279\pi\) | ||||
−0.701038 | + | 0.713124i | \(0.747279\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.42864 | −1.11908 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.52543 | −0.257844 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.16839 | −1.34287 | −0.671437 | − | 0.741061i | \(-0.734323\pi\) | ||||
−0.671437 | + | 0.741061i | \(0.734323\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.90321 | 0.464886 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.0509 | −1.72585 | −0.862927 | − | 0.505329i | \(-0.831371\pi\) | ||||
−0.862927 | + | 0.505329i | \(0.831371\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.09679 | −0.167259 | −0.0836293 | − | 0.996497i | \(-0.526651\pi\) | ||||
−0.0836293 | + | 0.996497i | \(0.526651\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.90321 | −0.283714 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.28100 | 0.624447 | 0.312224 | − | 0.950009i | \(-0.398926\pi\) | ||||
0.312224 | + | 0.950009i | \(0.398926\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.67307 | −0.667582 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17.2859 | −2.42051 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.54617 | −0.761825 | −0.380913 | − | 0.924611i | \(-0.624390\pi\) | ||||
−0.380913 | + | 0.924611i | \(0.624390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.90321 | 0.391469 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.21432 | −0.293294 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.86665 | 0.243017 | 0.121508 | − | 0.992590i | \(-0.461227\pi\) | ||||
0.121508 | + | 0.992590i | \(0.461227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.709636 | −0.0908596 | −0.0454298 | − | 0.998968i | \(-0.514466\pi\) | ||||
−0.0454298 | + | 0.998968i | \(0.514466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.90321 | 0.365770 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.31111 | −0.162623 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.45875 | −0.178215 | −0.0891074 | − | 0.996022i | \(-0.528401\pi\) | ||||
−0.0891074 | + | 0.996022i | \(0.528401\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.47949 | 1.14120 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.29529 | 0.272400 | 0.136200 | − | 0.990681i | \(-0.456511\pi\) | ||||
0.136200 | + | 0.990681i | \(0.456511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0415 | 1.64343 | 0.821716 | − | 0.569897i | \(-0.193017\pi\) | ||||
0.821716 | + | 0.569897i | \(0.193017\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.21432 | 0.255688 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.42864 | −0.504690 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.13335 | −0.690056 | −0.345028 | − | 0.938592i | \(-0.612131\pi\) | ||||
−0.345028 | + | 0.938592i | \(0.612131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0874 | −1.23194 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.7605 | 1.29088 | 0.645441 | − | 0.763810i | \(-0.276674\pi\) | ||||
0.645441 | + | 0.763810i | \(0.276674\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.80642 | 0.846726 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20.3368 | 2.18033 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.67307 | 0.389345 | 0.194672 | − | 0.980868i | \(-0.437636\pi\) | ||||
0.194672 | + | 0.980868i | \(0.437636\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17.2859 | −1.79247 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.2192 | −1.13914 | −0.569571 | − | 0.821942i | \(-0.692891\pi\) | ||||
−0.569571 | + | 0.821942i | \(0.692891\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.52543 | −0.555326 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.963435 | 0.0958654 | 0.0479327 | − | 0.998851i | \(-0.484737\pi\) | ||||
0.0479327 | + | 0.998851i | \(0.484737\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.8874 | −1.76250 | −0.881248 | − | 0.472653i | \(-0.843296\pi\) | ||||
−0.881248 | + | 0.472653i | \(0.843296\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.37778 | −0.329638 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5002 | −1.30512 | −0.652559 | − | 0.757738i | \(-0.726304\pi\) | ||||
−0.652559 | + | 0.757738i | \(0.726304\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5303 | −1.00862 | −0.504312 | − | 0.863521i | \(-0.668254\pi\) | ||||
−0.504312 | + | 0.863521i | \(0.668254\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.0874 | −1.71678 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.5970 | −1.74946 | −0.874731 | − | 0.484610i | \(-0.838962\pi\) | ||||
−0.874731 | + | 0.484610i | \(0.838962\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.28100 | −0.399205 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.49532 | 0.230692 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.9081 | −1.09162 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.57136 | −0.233760 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24.4701 | −2.20640 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.2050 | 1.34922 | 0.674611 | − | 0.738174i | \(-0.264312\pi\) | ||||
0.674611 | + | 0.738174i | \(0.264312\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.42864 | −0.213830 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0923 | 0.969142 | 0.484571 | − | 0.874752i | \(-0.338976\pi\) | ||||
0.484571 | + | 0.874752i | \(0.338976\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.52543 | −0.132271 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.42864 | 0.209024 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.1017 | 1.03392 | 0.516959 | − | 0.856010i | \(-0.327064\pi\) | ||||
0.516959 | + | 0.856010i | \(0.327064\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3412 | −0.877131 | −0.438565 | − | 0.898699i | \(-0.644513\pi\) | ||||
−0.438565 | + | 0.898699i | \(0.644513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.47949 | 0.798317 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.80642 | −0.318309 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.18421 | −0.762707 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.3477 | −0.853462 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.65878 | 0.463585 | 0.231793 | − | 0.972765i | \(-0.425541\pi\) | ||||
0.231793 | + | 0.972765i | \(0.425541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4795 | −0.934188 | −0.467094 | − | 0.884208i | \(-0.654699\pi\) | ||||
−0.467094 | + | 0.884208i | \(0.654699\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.8573 | −1.20114 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.80642 | 0.627027 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.488863 | 0.0390155 | 0.0195077 | − | 0.999810i | \(-0.493790\pi\) | ||||
0.0195077 | + | 0.999810i | \(0.493790\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.2810 | −0.973946 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.53035 | 0.514664 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.1798 | 1.65893 | 0.829464 | − | 0.558561i | \(-0.188646\pi\) | ||||
0.829464 | + | 0.558561i | \(0.188646\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.42864 | 0.500469 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.4494 | −1.27289 | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2810 | −0.867769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.90321 | −0.145542 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.8415 | 1.50852 | 0.754259 | − | 0.656577i | \(-0.227996\pi\) | ||||
0.754259 | + | 0.656577i | \(0.227996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.52543 | 0.115311 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.13335 | 0.310682 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.7052 | 1.54758 | 0.773789 | − | 0.633443i | \(-0.218359\pi\) | ||||
0.773789 | + | 0.633443i | \(0.218359\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5111 | 0.855616 | 0.427808 | − | 0.903870i | \(-0.359286\pi\) | ||||
0.427808 | + | 0.903870i | \(0.359286\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.57136 | −0.116158 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.16839 | 0.600552 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.6637 | 1.65733 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.70471 | −0.269478 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.0731 | 0.728866 | 0.364433 | − | 0.931230i | \(-0.381263\pi\) | ||||
0.364433 | + | 0.931230i | \(0.381263\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7304 | −0.916353 | −0.458176 | − | 0.888861i | \(-0.651497\pi\) | ||||
−0.458176 | + | 0.888861i | \(0.651497\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.90321 | −0.207903 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.2351 | −0.871712 | −0.435856 | − | 0.900016i | \(-0.643554\pi\) | ||||
−0.435856 | + | 0.900016i | \(0.643554\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.24443 | −0.371768 | −0.185884 | − | 0.982572i | \(-0.559515\pi\) | ||||
−0.185884 | + | 0.982572i | \(0.559515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.23014 | −0.227837 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.0098 | 0.983298 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0509 | 0.771825 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.14764 | 0.566300 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.90321 | 0.200819 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.7239 | −1.15132 | −0.575661 | − | 0.817688i | \(-0.695255\pi\) | ||||
−0.575661 | + | 0.817688i | \(0.695255\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.08250 | 0.348247 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.09679 | 0.0748003 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.9081 | −0.808377 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 31.0923 | 2.10103 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.2351 | −0.688485 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.5002 | −1.84155 | −0.920776 | − | 0.390092i | \(-0.872443\pi\) | ||||
−0.920776 | + | 0.390092i | \(0.872443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.90321 | 0.126881 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.3067 | −1.28143 | −0.640714 | − | 0.767780i | \(-0.721362\pi\) | ||||
−0.640714 | + | 0.767780i | \(0.721362\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.2400 | 1.27141 | 0.635707 | − | 0.771930i | \(-0.280709\pi\) | ||||
0.635707 | + | 0.771930i | \(0.280709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.80642 | −0.645215 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.9906 | −0.982069 | −0.491034 | − | 0.871140i | \(-0.663381\pi\) | ||||
−0.491034 | + | 0.871140i | \(0.663381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.28100 | −0.279261 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.5812 | −0.882194 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.7748 | −0.761647 | −0.380824 | − | 0.924648i | \(-0.624359\pi\) | ||||
−0.380824 | + | 0.924648i | \(0.624359\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.4889 | −0.675647 | −0.337824 | − | 0.941209i | \(-0.609691\pi\) | ||||
−0.337824 | + | 0.941209i | \(0.609691\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −17.2652 | −1.10756 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.67307 | 0.298552 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.31111 | −0.0834238 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 26.0415 | 1.65031 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0509 | 0.697524 | 0.348762 | − | 0.937211i | \(-0.386602\pi\) | ||||
0.348762 | + | 0.937211i | \(0.386602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.4286 | −0.781382 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.2859 | 1.08249 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6795 | 1.10282 | 0.551409 | − | 0.834235i | \(-0.314090\pi\) | ||||
0.551409 | + | 0.834235i | \(0.314090\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.4603 | −0.774244 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.4795 | 1.08195 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.1383 | −1.30344 | −0.651721 | − | 0.758459i | \(-0.725953\pi\) | ||||
−0.651721 | + | 0.758459i | \(0.725953\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.54617 | 0.340699 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.13335 | 0.497753 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.5812 | 1.07194 | 0.535972 | − | 0.844235i | \(-0.319945\pi\) | ||||
0.535972 | + | 0.844235i | \(0.319945\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.0049 | 1.27596 | 0.637979 | − | 0.770054i | \(-0.279771\pi\) | ||||
0.637979 | + | 0.770054i | \(0.279771\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.42864 | 0.268033 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.90321 | −0.175070 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.85728 | 0.412014 | 0.206007 | − | 0.978551i | \(-0.433953\pi\) | ||||
0.206007 | + | 0.978551i | \(0.433953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.8573 | −0.889482 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0321 | 1.01605 | 0.508026 | − | 0.861342i | \(-0.330376\pi\) | ||||
0.508026 | + | 0.861342i | \(0.330376\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.7605 | −1.65019 | −0.825095 | − | 0.564994i | \(-0.808878\pi\) | ||||
−0.825095 | + | 0.564994i | \(0.808878\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.21432 | 0.131165 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.8573 | −0.995054 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 43.9403 | 2.58472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.8430 | −1.45632 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.3432 | 1.88951 | 0.944756 | − | 0.327775i | \(-0.106299\pi\) | ||||
0.944756 | + | 0.327775i | \(0.106299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.86665 | −0.108680 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.05086 | 0.409132 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.61285 | 0.324599 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.67307 | −0.0964342 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.13335 | 0.122558 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.709636 | 0.0406336 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.1541 | −1.49269 | −0.746347 | − | 0.665558i | \(-0.768194\pi\) | ||||
−0.746347 | + | 0.665558i | \(0.768194\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −39.6084 | −2.25324 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.1289 | 0.801177 | 0.400588 | − | 0.916258i | \(-0.368806\pi\) | ||||
0.400588 | + | 0.916258i | \(0.368806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.99063 | −0.395134 | −0.197567 | − | 0.980289i | \(-0.563304\pi\) | ||||
−0.197567 | + | 0.980289i | \(0.563304\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.90321 | −0.163577 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.62867 | 0.484634 | 0.242317 | − | 0.970197i | \(-0.422093\pi\) | ||||
0.242317 | + | 0.970197i | \(0.422093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.6637 | −1.49288 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.8938 | −1.66851 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.80642 | 0.434361 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.31111 | 0.0727272 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.3176 | −1.28946 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.53035 | 0.360030 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4286 | 0.683140 | 0.341570 | − | 0.939856i | \(-0.389041\pi\) | ||||
0.341570 | + | 0.939856i | \(0.389041\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.5462 | −0.851925 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.45875 | 0.0797001 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.05731 | −0.275489 | −0.137745 | − | 0.990468i | \(-0.543985\pi\) | ||||
−0.137745 | + | 0.990468i | \(0.543985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −41.1798 | −2.23658 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.6637 | 1.22731 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8064 | −0.961457 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.47949 | −0.510359 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.59856 | 0.193181 | 0.0965903 | − | 0.995324i | \(-0.469206\pi\) | ||||
0.0965903 | + | 0.995324i | \(0.469206\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.917502 | −0.0491128 | −0.0245564 | − | 0.999698i | \(-0.507817\pi\) | ||||
−0.0245564 | + | 0.999698i | \(0.507817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.18421 | −0.169960 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.9304 | 1.11401 | 0.557007 | − | 0.830508i | \(-0.311950\pi\) | ||||
0.557007 | + | 0.830508i | \(0.311950\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.29529 | −0.121821 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −26.3684 | −1.39556 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.41435 | −0.232980 | −0.116490 | − | 0.993192i | \(-0.537164\pi\) | ||||
−0.116490 | + | 0.993192i | \(0.537164\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.69381 | −0.298848 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.0415 | −0.734965 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.8336 | −0.930907 | −0.465454 | − | 0.885072i | \(-0.654109\pi\) | ||||
−0.465454 | + | 0.885072i | \(0.654109\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.0321 | −1.09489 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.46028 | −0.439236 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.73975 | −0.193637 | −0.0968184 | − | 0.995302i | \(-0.530867\pi\) | ||||
−0.0968184 | + | 0.995302i | \(0.530867\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.21432 | −0.114347 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0415 | 0.620168 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.3274 | −1.50645 | −0.753224 | − | 0.657764i | \(-0.771502\pi\) | ||||
−0.753224 | + | 0.657764i | \(0.771502\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 33.6686 | 1.72490 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.7447 | 1.36659 | 0.683294 | − | 0.730143i | \(-0.260547\pi\) | ||||
0.683294 | + | 0.730143i | \(0.260547\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.42864 | 0.225704 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.08742 | −0.106110 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.3876 | 0.881588 | 0.440794 | − | 0.897608i | \(-0.354697\pi\) | ||||
0.440794 | + | 0.897608i | \(0.354697\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.4193 | −1.69009 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.5620 | 1.23899 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.13335 | 0.308602 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.152089 | −0.00763313 | −0.00381656 | − | 0.999993i | \(-0.501215\pi\) | ||||
−0.00381656 | + | 0.999993i | \(0.501215\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.37778 | −0.169101 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.3783 | −1.71677 | −0.858384 | − | 0.513007i | \(-0.828531\pi\) | ||||
−0.858384 | + | 0.513007i | \(0.828531\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.2351 | −0.509845 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.0874 | 0.550938 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.7146 | 1.17549 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.3368 | 0.807801 | 0.403901 | − | 0.914803i | \(-0.367654\pi\) | ||||
0.403901 | + | 0.914803i | \(0.367654\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.7971 | 1.32180 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.84743 | 0.140113 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.7605 | −0.577300 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.8988 | −1.12136 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.161933 | −0.00791096 | −0.00395548 | − | 0.999992i | \(-0.501259\pi\) | ||||
−0.00395548 | + | 0.999992i | \(0.501259\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.9590 | 0.729057 | 0.364528 | − | 0.931192i | \(-0.381230\pi\) | ||||
0.364528 | + | 0.931192i | \(0.381230\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.14764 | 0.396152 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.80642 | −0.378667 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.08250 | −0.0523857 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.42864 | −0.406939 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3269 | 0.497431 | 0.248715 | − | 0.968577i | \(-0.419992\pi\) | ||||
0.248715 | + | 0.968577i | \(0.419992\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.7491 | 0.612683 | 0.306342 | − | 0.951922i | \(-0.400895\pi\) | ||||
0.306342 | + | 0.951922i | \(0.400895\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.3368 | −0.975074 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.28100 | −0.204788 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.5714 | −0.647726 | −0.323863 | − | 0.946104i | \(-0.604982\pi\) | ||||
−0.323863 | + | 0.946104i | \(0.604982\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.89384 | −0.423516 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.280996 | −0.0133505 | −0.00667527 | − | 0.999978i | \(-0.502125\pi\) | ||||
−0.00667527 | + | 0.999978i | \(0.502125\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.67307 | −0.174120 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.5303 | 0.592665 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.4286 | −0.586544 | −0.293272 | − | 0.956029i | \(-0.594744\pi\) | ||||
−0.293272 | + | 0.956029i | \(0.594744\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.0830 | 1.51073 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.4193 | −1.19430 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.24443 | 0.338880 | 0.169440 | − | 0.985540i | \(-0.445804\pi\) | ||||
0.169440 | + | 0.985540i | \(0.445804\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.9590 | 0.884930 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.32741 | −0.341271 | −0.170636 | − | 0.985334i | \(-0.554582\pi\) | ||||
−0.170636 | + | 0.985334i | \(0.554582\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.8528 | 1.06206 | 0.531031 | − | 0.847353i | \(-0.321805\pi\) | ||||
0.531031 | + | 0.847353i | \(0.321805\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.2859 | 0.801615 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.6494 | −0.492796 | −0.246398 | − | 0.969169i | \(-0.579247\pi\) | ||||
−0.246398 | + | 0.969169i | \(0.579247\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.22522 | −0.102751 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.08250 | 0.0498789 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.18421 | 0.146410 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.5555 | −0.483305 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.9032 | −0.680945 | −0.340473 | − | 0.940254i | \(-0.610587\pi\) | ||||
−0.340473 | + | 0.940254i | \(0.610587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.7096 | −0.488317 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.4603 | 0.657966 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.2192 | 0.509440 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.7576 | 1.57502 | 0.787508 | − | 0.616304i | \(-0.211371\pi\) | ||||
0.787508 | + | 0.616304i | \(0.211371\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 46.8988 | 2.12084 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.1338 | −1.40505 | −0.702525 | − | 0.711659i | \(-0.747944\pi\) | ||||
−0.702525 | + | 0.711659i | \(0.747944\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −71.6958 | −3.22902 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.52543 | 0.248350 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.50129 | 0.157054 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.8015 | −0.931203 | −0.465602 | − | 0.884994i | \(-0.654162\pi\) | ||||
−0.465602 | + | 0.884994i | \(0.654162\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −36.4242 | −1.62731 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.5986 | −0.517154 | −0.258577 | − | 0.965991i | \(-0.583254\pi\) | ||||
−0.258577 | + | 0.965991i | \(0.583254\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.963435 | −0.0428723 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.9797 | −1.10939 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.5018 | 0.554131 | 0.277066 | − | 0.960851i | \(-0.410638\pi\) | ||||
0.277066 | + | 0.960851i | \(0.410638\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.4193 | 0.947533 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.42864 | 0.107227 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.8874 | 0.788213 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.4286 | −0.546611 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 43.9353 | 1.92855 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.8064 | −0.692492 | −0.346246 | − | 0.938144i | \(-0.612544\pi\) | ||||
−0.346246 | + | 0.938144i | \(0.612544\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.90967 | 0.127231 | 0.0636154 | − | 0.997974i | \(-0.479737\pi\) | ||||
0.0636154 | + | 0.997974i | \(0.479737\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.37778 | 0.147419 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 60.9403 | 2.65460 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.67307 | −0.203177 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.55262 | 0.154171 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.4889 | −0.627582 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.5002 | 0.583666 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 45.8479 | 1.97848 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.5669 | 0.584368 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.18913 | −0.180105 | −0.0900524 | − | 0.995937i | \(-0.528703\pi\) | ||||
−0.0900524 | + | 0.995937i | \(0.528703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.4893 | 1.09385 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.5303 | 0.451071 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2143 | 0.778788 | 0.389394 | − | 0.921071i | \(-0.372684\pi\) | ||||
0.389394 | + | 0.921071i | \(0.372684\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.35059 | −0.0576417 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.18421 | −0.391260 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.35599 | −0.397857 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.0874 | 0.767768 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.6548 | 1.72260 | 0.861300 | − | 0.508097i | \(-0.169651\pi\) | ||||
0.861300 | + | 0.508097i | \(0.169651\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.43801 | −0.0608212 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 50.1847 | 2.11880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.4400 | −0.903589 | −0.451794 | − | 0.892122i | \(-0.649216\pi\) | ||||
−0.451794 | + | 0.892122i | \(0.649216\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.5970 | 0.782383 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.9131 | −0.710282 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.1941 | 1.05619 | 0.528095 | − | 0.849185i | \(-0.322907\pi\) | ||||
0.528095 | + | 0.849185i | \(0.322907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.27163 | −0.220611 | −0.110305 | − | 0.993898i | \(-0.535183\pi\) | ||||
−0.110305 | + | 0.993898i | \(0.535183\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.3051 | 0.931810 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.28100 | 0.178530 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.3145 | 0.970595 | 0.485298 | − | 0.874349i | \(-0.338711\pi\) | ||||
0.485298 | + | 0.874349i | \(0.338711\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.1891 | −1.17150 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.9398 | 0.744267 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.1017 | 0.666865 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.49532 | −0.103169 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.9131 | 1.19337 | 0.596685 | − | 0.802476i | \(-0.296484\pi\) | ||||
0.596685 | + | 0.802476i | \(0.296484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.80642 | 0.321658 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.0923 | −1.11443 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.6128 | −0.723273 | −0.361636 | − | 0.932319i | \(-0.617782\pi\) | ||||
−0.361636 | + | 0.932319i | \(0.617782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.9081 | 0.488186 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.6128 | −0.475282 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.4286 | −1.24328 | −0.621640 | − | 0.783303i | \(-0.713533\pi\) | ||||
−0.621640 | + | 0.783303i | \(0.713533\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.4479 | −0.711713 | −0.355856 | − | 0.934541i | \(-0.615811\pi\) | ||||
−0.355856 | + | 0.934541i | \(0.615811\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.77631 | −0.113060 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.57136 | 0.104541 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.4592 | −0.992769 | −0.496385 | − | 0.868103i | \(-0.665339\pi\) | ||||
−0.496385 | + | 0.868103i | \(0.665339\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.0223 | 1.25709 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.61285 | 0.227072 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.1432 | 0.490459 | 0.245230 | − | 0.969465i | \(-0.421137\pi\) | ||||
0.245230 | + | 0.969465i | \(0.421137\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.4701 | 0.986731 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.3876 | 1.02207 | 0.511034 | − | 0.859561i | \(-0.329263\pi\) | ||||
0.511034 | + | 0.859561i | \(0.329263\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.4429 | −0.821671 | −0.410835 | − | 0.911710i | \(-0.634763\pi\) | ||||
−0.410835 | + | 0.911710i | \(0.634763\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.3970 | −0.417217 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.60300 | 0.224480 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.42864 | 0.256735 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 63.7659 | 2.54251 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.65878 | 0.225273 | 0.112636 | − | 0.993636i | \(-0.464071\pi\) | ||||
0.112636 | + | 0.993636i | \(0.464071\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −37.0321 | −1.47189 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.2050 | −0.603390 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.12690 | −0.242757 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.36842 | 0.172812 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.20342 | 0.324016 | 0.162008 | − | 0.986789i | \(-0.448203\pi\) | ||||
0.162008 | + | 0.986789i | \(0.448203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0874 | −0.397809 | −0.198905 | − | 0.980019i | \(-0.563738\pi\) | ||||
−0.198905 | + | 0.980019i | \(0.563738\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.42864 | 0.0956276 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.3733 | −1.23341 | −0.616707 | − | 0.787193i | \(-0.711534\pi\) | ||||
−0.616707 | + | 0.787193i | \(0.711534\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.41927 | −0.212725 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.3684 | −1.03346 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.4099 | −1.11177 | −0.555883 | − | 0.831261i | \(-0.687620\pi\) | ||||
−0.555883 | + | 0.831261i | \(0.687620\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.0923 | −0.433414 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.7239 | 1.04260 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.74620 | 0.379658 | 0.189829 | − | 0.981817i | \(-0.439207\pi\) | ||||
0.189829 | + | 0.981817i | \(0.439207\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6128 | −0.607269 | −0.303635 | − | 0.952789i | \(-0.598200\pi\) | ||||
−0.303635 | + | 0.952789i | \(0.598200\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.6637 | −0.880185 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.52543 | 0.0591535 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.3176 | 1.52238 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −60.8943 | −2.35431 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.06022 | 0.0795340 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0350 | 0.849388 | 0.424694 | − | 0.905337i | \(-0.360382\pi\) | ||||
0.424694 | + | 0.905337i | \(0.360382\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.42864 | −0.0934784 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.4953 | −1.17203 | −0.586015 | − | 0.810300i | \(-0.699304\pi\) | ||||
−0.586015 | + | 0.810300i | \(0.699304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.1141 | −0.656780 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.7511 | −1.63823 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.2968 | 0.432261 | 0.216130 | − | 0.976365i | \(-0.430656\pi\) | ||||
0.216130 | + | 0.976365i | \(0.430656\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.1017 | −0.462383 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42.6035 | 1.62542 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.27163 | −0.277027 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.5161 | −0.704384 | −0.352192 | − | 0.935928i | \(-0.614564\pi\) | ||||
−0.352192 | + | 0.935928i | \(0.614564\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.42864 | −0.320178 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.3412 | 0.392265 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 86.2677 | 3.26762 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −33.1941 | −1.25551 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.0781 | 1.02272 | 0.511362 | − | 0.859365i | \(-0.329141\pi\) | ||||
0.511362 | + | 0.859365i | \(0.329141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.16839 | 0.308077 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.47949 | −0.357018 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.46965 | 0.0552719 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.01921 | 0.263612 | 0.131806 | − | 0.991276i | \(-0.457922\pi\) | ||||
0.131806 | + | 0.991276i | \(0.457922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.6731 | −0.437774 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33.4193 | −1.25156 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.80642 | 0.142352 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.0731 | −0.973719 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.0272 | 1.34359 | 0.671794 | − | 0.740738i | \(-0.265524\pi\) | ||||
0.671794 | + | 0.740738i | \(0.265524\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.2859 | −1.01618 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.2257 | −0.863773 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.18421 | 0.341093 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.9442 | 0.591338 | 0.295669 | − | 0.955290i | \(-0.404457\pi\) | ||||
0.295669 | + | 0.955290i | \(0.404457\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.96836 | −0.184013 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.56199 | 0.316677 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.9621 | 0.404893 | 0.202446 | − | 0.979293i | \(-0.435111\pi\) | ||||
0.202446 | + | 0.979293i | \(0.435111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.3477 | 0.381680 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.23506 | 0.156001 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.7146 | 0.504498 | 0.252249 | − | 0.967662i | \(-0.418830\pi\) | ||||
0.252249 | + | 0.967662i | \(0.418830\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.90321 | −0.106652 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.6523 | −1.23458 | −0.617292 | − | 0.786734i | \(-0.711770\pi\) | ||||
−0.617292 | + | 0.786734i | \(0.711770\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.65878 | −0.207322 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.3827 | 0.818940 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.5936 | −0.752475 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.7150 | 1.33975 | 0.669875 | − | 0.742474i | \(-0.266348\pi\) | ||||
0.669875 | + | 0.742474i | \(0.266348\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.4701 | 0.891741 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.4795 | 0.417782 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.6222 | −1.47644 | −0.738220 | − | 0.674560i | \(-0.764333\pi\) | ||||
−0.738220 | + | 0.674560i | \(0.764333\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.5210 | −0.998948 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.1481 | −1.27412 | −0.637059 | − | 0.770815i | \(-0.719849\pi\) | ||||
−0.637059 | + | 0.770815i | \(0.719849\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0633 | −0.581530 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.8573 | 0.537166 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.44738 | 0.0883696 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.1383 | 1.48348 | 0.741742 | − | 0.670685i | \(-0.234000\pi\) | ||||
0.741742 | + | 0.670685i | \(0.234000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.1481 | 1.40989 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.0484 | −1.62028 | −0.810139 | − | 0.586237i | \(-0.800609\pi\) | ||||
−0.810139 | + | 0.586237i | \(0.800609\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.80642 | −0.280415 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −27.5910 | −0.989823 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.0509 | 0.395938 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.66370 | −0.238446 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.3051 | −0.797120 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.488863 | −0.0174483 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4400 | 0.906839 | 0.453419 | − | 0.891297i | \(-0.350204\pi\) | ||||
0.453419 | + | 0.891297i | \(0.350204\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −46.8069 | −1.66637 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.3684 | −1.00866 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.930409 | −0.0330398 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.2810 | 0.435562 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.5684 | −0.728572 | −0.364286 | − | 0.931287i | \(-0.618687\pi\) | ||||
−0.364286 | + | 0.931287i | \(0.618687\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.4193 | −1.18229 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.99063 | 0.247002 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.7654 | −1.43858 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.53035 | −0.230165 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38.9304 | 1.37042 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.2039 | 1.87055 | 0.935275 | − | 0.353923i | \(-0.115152\pi\) | ||||
0.935275 | + | 0.353923i | \(0.115152\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.7467 | 0.868973 | 0.434487 | − | 0.900678i | \(-0.356930\pi\) | ||||
0.434487 | + | 0.900678i | \(0.356930\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 46.5116 | 1.63123 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.1798 | −0.741895 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.09679 | 0.0383718 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.80642 | 0.133007 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.61237 | 0.230773 | 0.115387 | − | 0.993321i | \(-0.463189\pi\) | ||||
0.115387 | + | 0.993321i | \(0.463189\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.7418 | −1.31559 | −0.657797 | − | 0.753195i | \(-0.728512\pi\) | ||||
−0.657797 | + | 0.753195i | \(0.728512\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.42864 | −0.223816 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.1318 | 0.873919 | 0.436960 | − | 0.899481i | \(-0.356055\pi\) | ||||
0.436960 | + | 0.899481i | \(0.356055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.5116 | 0.434546 | 0.217273 | − | 0.976111i | \(-0.430284\pi\) | ||||
0.217273 | + | 0.976111i | \(0.430284\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.1842 | 0.526734 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.4800 | 1.26396 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.4494 | 0.569254 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.9590 | 0.655319 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.3269 | −0.563668 | −0.281834 | − | 0.959463i | \(-0.590943\pi\) | ||||
−0.281834 | + | 0.959463i | \(0.590943\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.3497 | 1.90861 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37.7146 | 1.29896 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.2810 | 0.388078 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.92242 | −0.134776 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −61.4706 | −2.10967 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.9688 | −1.19872 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.8287 | −0.507725 | −0.253862 | − | 0.967240i | \(-0.581701\pi\) | ||||
−0.253862 | + | 0.967240i | \(0.581701\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.90321 | 0.0650885 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.0796 | −0.344312 | −0.172156 | − | 0.985070i | \(-0.555073\pi\) | ||||
−0.172156 | + | 0.985070i | \(0.555073\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.7783 | −1.25486 | −0.627430 | − | 0.778673i | \(-0.715893\pi\) | ||||
−0.627430 | + | 0.778673i | \(0.715893\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −37.3274 | −1.27211 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.7857 | 0.605432 | 0.302716 | − | 0.953081i | \(-0.402107\pi\) | ||||
0.302716 | + | 0.953081i | \(0.402107\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.8415 | −0.674630 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 97.2978 | 3.30441 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.8064 | 0.604042 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.91258 | −0.0648053 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.3526 | −0.722676 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.52543 | −0.0515689 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.8321 | 0.906055 | 0.453028 | − | 0.891496i | \(-0.350344\pi\) | ||||
0.453028 | + | 0.891496i | \(0.350344\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 71.6182 | 2.41562 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.8524 | −0.938370 | −0.469185 | − | 0.883100i | \(-0.655452\pi\) | ||||
−0.469185 | + | 0.883100i | \(0.655452\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.8751 | 0.466935 | 0.233467 | − | 0.972365i | \(-0.424993\pi\) | ||||
0.233467 | + | 0.972365i | \(0.424993\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.13335 | −0.138941 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.1827 | 0.879128 | 0.439564 | − | 0.898211i | \(-0.355133\pi\) | ||||
0.439564 | + | 0.898211i | \(0.355133\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.1941 | 0.777904 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32.1891 | 1.07838 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.28100 | −0.143258 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.7052 | −0.692098 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.4286 | 0.414980 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −71.6958 | −2.39119 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.2958 | 1.44239 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.70471 | −0.123285 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.5111 | −0.382643 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.84590 | 0.0612922 | 0.0306461 | − | 0.999530i | \(-0.490244\pi\) | ||||
0.0306461 | + | 0.999530i | \(0.490244\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.83362 | 0.0608174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.1467 | −1.56204 | −0.781021 | − | 0.624505i | \(-0.785301\pi\) | ||||
−0.781021 | + | 0.624505i | \(0.785301\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.1432 | −1.12997 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.57136 | 0.0519476 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.9206 | 0.558766 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.4509 | −0.509679 | −0.254839 | − | 0.966983i | \(-0.582023\pi\) | ||||
−0.254839 | + | 0.966983i | \(0.582023\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −57.9135 | −1.90832 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.00937 | 0.0990546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.16839 | −0.268575 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −34.0435 | −1.11814 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.8163 | 0.584533 | 0.292266 | − | 0.956337i | \(-0.405591\pi\) | ||||
0.292266 | + | 0.956337i | \(0.405591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.67307 | 0.153154 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.2859 | 1.02425 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.6637 | −0.741182 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.6953 | 1.00277 | 0.501387 | − | 0.865223i | \(-0.332823\pi\) | ||||
0.501387 | + | 0.865223i | \(0.332823\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.4795 | −0.505154 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.0696 | 0.360858 | 0.180429 | − | 0.983588i | \(-0.442251\pi\) | ||||
0.180429 | + | 0.983588i | \(0.442251\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.3087 | −1.54058 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.70471 | 0.120514 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.3033 | 0.367307 | 0.183653 | − | 0.982991i | \(-0.441208\pi\) | ||||
0.183653 | + | 0.982991i | \(0.441208\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.4099 | 0.597611 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.1066 | 0.619575 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.8637 | −0.675843 | −0.337921 | − | 0.941174i | \(-0.609724\pi\) | ||||
−0.337921 | + | 0.941174i | \(0.609724\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0731 | −0.325959 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −59.0420 | −1.90856 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.4603 | 0.596114 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.9403 | 0.965815 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.6938 | −0.827972 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.7304 | 0.409805 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.7007 | 1.82337 | 0.911687 | − | 0.410886i | \(-0.134781\pi\) | ||||
0.911687 | + | 0.410886i | \(0.134781\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.2859 | 0.555304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.8760 | 0.798309 | 0.399155 | − | 0.916884i | \(-0.369304\pi\) | ||||
0.399155 | + | 0.916884i | \(0.369304\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.7748 | −0.505716 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.90321 | 0.0929772 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.9847 | −0.703351 | −0.351676 | − | 0.936122i | \(-0.614388\pi\) | ||||
−0.351676 | + | 0.936122i | \(0.614388\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6637 | −0.340813 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.0415 | −0.639875 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.7540 | −0.949006 | −0.474503 | − | 0.880254i | \(-0.657372\pi\) | ||||
−0.474503 | + | 0.880254i | \(0.657372\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.2351 | 0.389842 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.4603 | 0.460276 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.69535 | −0.149303 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.9719 | 1.23798 | 0.618992 | − | 0.785398i | \(-0.287542\pi\) | ||||
0.618992 | + | 0.785398i | \(0.287542\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.5210 | 0.873352 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.24443 | 0.166260 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.8287 | 0.596311 | 0.298155 | − | 0.954517i | \(-0.403629\pi\) | ||||
0.298155 | + | 0.954517i | \(0.403629\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.8381 | 0.627649 |
(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 | 6080.2.a.bt.1.3 | 3 | ||
4.3 | odd | 2 | 6080.2.a.bu.1.1 | 3 | |||
8.3 | odd | 2 | 3040.2.a.m.1.3 | yes | 3 | ||
8.5 | even | 2 | 3040.2.a.l.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3040.2.a.l.1.1 | ✓ | 3 | 8.5 | even | 2 | ||
3040.2.a.m.1.3 | yes | 3 | 8.3 | odd | 2 | ||
6080.2.a.bt.1.3 | 3 | 1.1 | even | 1 | trivial | ||
6080.2.a.bu.1.1 | 3 | 4.3 | odd | 2 |