Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7168,2,Mod(1,7168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7168, 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("7168.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7168 = 2^{10} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7168.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: | \(57.2367681689\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.9433055232.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 6x^{6} + 32x^{5} + 9x^{4} - 76x^{3} - 4x^{2} + 48x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1792) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.21236\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7168.1 |
$q$-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 | ||||||||
\(3\) | 1.78579 | 1.03103 | 0.515513 | − | 0.856882i | \(-0.327601\pi\) | ||||
0.515513 | + | 0.856882i | \(0.327601\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.18248 | −1.87046 | −0.935231 | − | 0.354037i | \(-0.884809\pi\) | ||||
−0.935231 | + | 0.354037i | \(0.884809\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.189043 | 0.0630143 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.50362 | 1.35789 | 0.678946 | − | 0.734188i | \(-0.262437\pi\) | ||||
0.678946 | + | 0.734188i | \(0.262437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.84427 | −1.34356 | −0.671779 | − | 0.740752i | \(-0.734469\pi\) | ||||
−0.671779 | + | 0.740752i | \(0.734469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.46903 | −1.92850 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.13834 | 1.24623 | 0.623115 | − | 0.782130i | \(-0.285867\pi\) | ||||
0.623115 | + | 0.782130i | \(0.285867\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.12835 | −0.488278 | −0.244139 | − | 0.969740i | \(-0.578505\pi\) | ||||
−0.244139 | + | 0.969740i | \(0.578505\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.78579 | −0.389691 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.11888 | 1.48439 | 0.742195 | − | 0.670184i | \(-0.233785\pi\) | ||||
0.742195 | + | 0.670184i | \(0.233785\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.4932 | 2.49863 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.01978 | −0.966056 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.43932 | −1.01006 | −0.505029 | − | 0.863103i | \(-0.668518\pi\) | ||||
−0.505029 | + | 0.863103i | \(0.668518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.831138 | 0.149277 | 0.0746384 | − | 0.997211i | \(-0.476220\pi\) | ||||
0.0746384 | + | 0.997211i | \(0.476220\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.04251 | 1.40002 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.18248 | 0.706969 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.98492 | 1.31271 | 0.656357 | − | 0.754451i | \(-0.272097\pi\) | ||||
0.656357 | + | 0.754451i | \(0.272097\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.65084 | −1.38524 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.22639 | −0.347704 | −0.173852 | − | 0.984772i | \(-0.555621\pi\) | ||||
−0.173852 | + | 0.984772i | \(0.555621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.28804 | −0.348923 | −0.174462 | − | 0.984664i | \(-0.555818\pi\) | ||||
−0.174462 | + | 0.984664i | \(0.555818\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.790669 | −0.117866 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.83759 | −1.14323 | −0.571615 | − | 0.820522i | \(-0.693683\pi\) | ||||
−0.571615 | + | 0.820522i | \(0.693683\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.17599 | 1.28490 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.90235 | 1.08547 | 0.542736 | − | 0.839903i | \(-0.317388\pi\) | ||||
0.542736 | + | 0.839903i | \(0.317388\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.8363 | −2.53989 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.80079 | −0.503427 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.62811 | 0.342150 | 0.171075 | − | 0.985258i | \(-0.445276\pi\) | ||||
0.171075 | + | 0.985258i | \(0.445276\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.33370 | −0.298799 | −0.149400 | − | 0.988777i | \(-0.547734\pi\) | ||||
−0.149400 | + | 0.988777i | \(0.547734\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.189043 | −0.0238172 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.2611 | 2.51307 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.16822 | −0.997907 | −0.498954 | − | 0.866629i | \(-0.666282\pi\) | ||||
−0.498954 | + | 0.866629i | \(0.666282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.7128 | 1.53044 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.04851 | 0.717826 | 0.358913 | − | 0.933371i | \(-0.383147\pi\) | ||||
0.358913 | + | 0.933371i | \(0.383147\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.67177 | −0.897913 | −0.448957 | − | 0.893554i | \(-0.648204\pi\) | ||||
−0.448957 | + | 0.893554i | \(0.648204\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.3101 | 2.57615 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.50362 | −0.513235 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.90198 | 0.213989 | 0.106995 | − | 0.994260i | \(-0.465877\pi\) | ||||
0.106995 | + | 0.994260i | \(0.465877\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.53139 | −1.05904 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.2843 | −1.23861 | −0.619306 | − | 0.785149i | \(-0.712586\pi\) | ||||
−0.619306 | + | 0.785149i | \(0.712586\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.4910 | −2.33103 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.71349 | −1.04139 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.49938 | −0.264934 | −0.132467 | − | 0.991187i | \(-0.542290\pi\) | ||||
−0.132467 | + | 0.991187i | \(0.542290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.84427 | 0.507817 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.48424 | 0.153908 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.90180 | 0.913306 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.98784 | −0.201834 | −0.100917 | − | 0.994895i | \(-0.532178\pi\) | ||||
−0.100917 | + | 0.994895i | \(0.532178\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.851377 | 0.0855666 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.7459 | 1.56678 | 0.783390 | − | 0.621531i | \(-0.213489\pi\) | ||||
0.783390 | + | 0.621531i | \(0.213489\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.2106 | −1.49874 | −0.749371 | − | 0.662150i | \(-0.769644\pi\) | ||||
−0.749371 | + | 0.662150i | \(0.769644\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.46903 | 0.728903 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.26941 | 0.122718 | 0.0613592 | − | 0.998116i | \(-0.480456\pi\) | ||||
0.0613592 | + | 0.998116i | \(0.480456\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.02383 | −0.385413 | −0.192707 | − | 0.981256i | \(-0.561727\pi\) | ||||
−0.192707 | + | 0.981256i | \(0.561727\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.2594 | 1.35344 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.66487 | 0.156618 | 0.0783089 | − | 0.996929i | \(-0.475048\pi\) | ||||
0.0783089 | + | 0.996929i | \(0.475048\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −29.7746 | −2.77650 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.915774 | −0.0846634 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.13834 | −0.471031 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.28258 | 0.843871 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.97586 | −0.358492 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −31.3400 | −2.80313 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.86069 | −0.697523 | −0.348762 | − | 0.937211i | \(-0.613398\pi\) | ||||
−0.348762 | + | 0.937211i | \(0.613398\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.08596 | −0.359749 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.70009 | −0.672760 | −0.336380 | − | 0.941726i | \(-0.609203\pi\) | ||||
−0.336380 | + | 0.941726i | \(0.609203\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.12835 | 0.184552 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.9951 | 1.80697 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.6977 | −1.51201 | −0.756007 | − | 0.654564i | \(-0.772852\pi\) | ||||
−0.756007 | + | 0.654564i | \(0.772852\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.1930 | −1.37348 | −0.686738 | − | 0.726905i | \(-0.740958\pi\) | ||||
−0.686738 | + | 0.726905i | \(0.740958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.9963 | −1.17870 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.8167 | −1.82441 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.7499 | 1.88927 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.78579 | 0.147289 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.1806 | −0.997874 | −0.498937 | − | 0.866638i | \(-0.666276\pi\) | ||||
−0.498937 | + | 0.866638i | \(0.666276\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.7449 | 1.44406 | 0.722029 | − | 0.691863i | \(-0.243210\pi\) | ||||
0.722029 | + | 0.691863i | \(0.243210\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.971366 | 0.0785303 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.47622 | −0.279217 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.9789 | 1.11564 | 0.557818 | − | 0.829963i | \(-0.311639\pi\) | ||||
0.557818 | + | 0.829963i | \(0.311639\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.1119 | 1.11915 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.11888 | −0.561047 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5962 | −1.06494 | −0.532468 | − | 0.846450i | \(-0.678735\pi\) | ||||
−0.532468 | + | 0.846450i | \(0.678735\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −33.6377 | −2.61869 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.70735 | 0.519030 | 0.259515 | − | 0.965739i | \(-0.416437\pi\) | ||||
0.259515 | + | 0.965739i | \(0.416437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4669 | 0.805147 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.402350 | −0.0307685 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.8358 | −1.58411 | −0.792057 | − | 0.610448i | \(-0.790990\pi\) | ||||
−0.792057 | + | 0.610448i | \(0.790990\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.4932 | −0.944394 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.69325 | 0.352766 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.4086 | −1.67490 | −0.837448 | − | 0.546517i | \(-0.815953\pi\) | ||||
−0.837448 | + | 0.546517i | \(0.815953\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.42942 | −0.329236 | −0.164618 | − | 0.986357i | \(-0.552639\pi\) | ||||
−0.164618 | + | 0.986357i | \(0.552639\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.16749 | −0.308070 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −33.3968 | −2.45538 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.1411 | 1.69225 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.01978 | 0.365135 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.38976 | 0.534704 | 0.267352 | − | 0.963599i | \(-0.413851\pi\) | ||||
0.267352 | + | 0.963599i | \(0.413851\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.139138 | 0.0100154 | 0.00500769 | − | 0.999987i | \(-0.498406\pi\) | ||||
0.00500769 | + | 0.999987i | \(0.498406\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 36.1820 | 2.59104 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.4057 | −0.741377 | −0.370688 | − | 0.928757i | \(-0.620878\pi\) | ||||
−0.370688 | + | 0.928757i | \(0.620878\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.09550 | −0.361211 | −0.180605 | − | 0.983556i | \(-0.557806\pi\) | ||||
−0.180605 | + | 0.983556i | \(0.557806\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.5867 | −1.02887 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.43932 | 0.381766 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.31184 | 0.650367 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.34577 | 0.0935378 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.58529 | −0.663029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.5589 | 0.864592 | 0.432296 | − | 0.901732i | \(-0.357704\pi\) | ||||
0.432296 | + | 0.901732i | \(0.357704\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.8014 | 0.740097 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.56970 | 0.652648 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.831138 | −0.0564213 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.7002 | −0.925772 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.8915 | −1.67438 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.66949 | −0.647517 | −0.323758 | − | 0.946140i | \(-0.604946\pi\) | ||||
−0.323758 | + | 0.946140i | \(0.604946\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.36174 | 0.157450 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.99594 | −0.198847 | −0.0994237 | − | 0.995045i | \(-0.531700\pi\) | ||||
−0.0994237 | + | 0.995045i | \(0.531700\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.99569 | −0.594452 | −0.297226 | − | 0.954807i | \(-0.596061\pi\) | ||||
−0.297226 | + | 0.954807i | \(0.596061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.04251 | −0.529158 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.53066 | 0.493350 | 0.246675 | − | 0.969098i | \(-0.420662\pi\) | ||||
0.246675 | + | 0.969098i | \(0.420662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.7806 | 2.13837 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.39653 | 0.220629 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.87072 | 0.121007 | 0.0605034 | − | 0.998168i | \(-0.480729\pi\) | ||||
0.0605034 | + | 0.998168i | \(0.480729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4911 | 0.933454 | 0.466727 | − | 0.884401i | \(-0.345433\pi\) | ||||
0.466727 | + | 0.884401i | \(0.345433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.96173 | −0.125845 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.18248 | −0.267209 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.3103 | 0.656029 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.1514 | −1.27704 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.33974 | 0.400161 | 0.200080 | − | 0.979779i | \(-0.435880\pi\) | ||||
0.200080 | + | 0.979779i | \(0.435880\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.0607 | 2.01564 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −38.3784 | −2.40335 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.1594 | 0.758483 | 0.379241 | − | 0.925298i | \(-0.376185\pi\) | ||||
0.379241 | + | 0.925298i | \(0.376185\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.98492 | −0.496159 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.02827 | −0.0636480 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.0299529 | −0.00184698 | −0.000923488 | − | 1.00000i | \(-0.500294\pi\) | ||||
−0.000923488 | 1.00000i | \(0.500294\pi\) | ||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −33.0514 | −2.03033 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.46336 | −0.273153 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0622 | 1.10127 | 0.550637 | − | 0.834745i | \(-0.314385\pi\) | ||||
0.550637 | + | 0.834745i | \(0.314385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0906 | −0.612958 | −0.306479 | − | 0.951877i | \(-0.599151\pi\) | ||||
−0.306479 | + | 0.951877i | \(0.599151\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.65084 | 0.523573 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 56.2644 | 3.39287 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.86651 | −0.532737 | −0.266368 | − | 0.963871i | \(-0.585824\pi\) | ||||
−0.266368 | + | 0.963871i | \(0.585824\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.157121 | 0.00940657 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6731 | −0.696356 | −0.348178 | − | 0.937428i | \(-0.613200\pi\) | ||||
−0.348178 | + | 0.937428i | \(0.613200\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.5547 | −0.746297 | −0.373149 | − | 0.927772i | \(-0.621722\pi\) | ||||
−0.373149 | + | 0.927772i | \(0.621722\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.8967 | 0.941642 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.22639 | 0.131420 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.40252 | 0.553090 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.54986 | −0.208096 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.3152 | −1.42051 | −0.710256 | − | 0.703944i | \(-0.751421\pi\) | ||||
−0.710256 | + | 0.703944i | \(0.751421\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.9920 | −0.639980 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.6072 | −1.31180 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −34.4858 | −1.99436 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.28804 | 0.131881 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28.1189 | 1.61539 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.76065 | 0.558893 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.2536 | 1.55544 | 0.777722 | − | 0.628608i | \(-0.216375\pi\) | ||||
0.777722 | + | 0.628608i | \(0.216375\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.1629 | −1.54524 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.78650 | 0.328122 | 0.164061 | − | 0.986450i | \(-0.447541\pi\) | ||||
0.164061 | + | 0.986450i | \(0.447541\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.03673 | 0.171646 | 0.0858231 | − | 0.996310i | \(-0.472648\pi\) | ||||
0.0858231 | + | 0.996310i | \(0.472648\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.790669 | 0.0445491 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.69828 | −0.263882 | −0.131941 | − | 0.991258i | \(-0.542121\pi\) | ||||
−0.131941 | + | 0.991258i | \(0.542121\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.4966 | −1.37155 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.26690 | 0.126526 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.9362 | −0.608507 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −60.5202 | −3.35706 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.18572 | −0.397371 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.83759 | 0.432101 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −36.0648 | −1.98230 | −0.991151 | − | 0.132738i | \(-0.957623\pi\) | ||||
−0.991151 | + | 0.132738i | \(0.957623\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.50949 | 0.0827197 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 34.1634 | 1.86655 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.3282 | −1.70656 | −0.853279 | − | 0.521454i | \(-0.825390\pi\) | ||||
−0.853279 | + | 0.521454i | \(0.825390\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.97311 | 0.161477 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.74313 | 0.202702 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −53.1712 | −2.86264 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.1006 | 1.83062 | 0.915308 | − | 0.402755i | \(-0.131947\pi\) | ||||
0.915308 | + | 0.402755i | \(0.131947\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.6604 | −1.58769 | −0.793843 | − | 0.608123i | \(-0.791923\pi\) | ||||
−0.793843 | + | 0.608123i | \(0.791923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.3171 | 1.29795 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.605671 | −0.0322366 | −0.0161183 | − | 0.999870i | \(-0.505131\pi\) | ||||
−0.0161183 | + | 0.999870i | \(0.505131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.2978 | −1.34267 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.17599 | −0.485645 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.6214 | −0.613354 | −0.306677 | − | 0.951814i | \(-0.599217\pi\) | ||||
−0.306677 | + | 0.951814i | \(0.599217\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4701 | −0.761585 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.5767 | 0.870052 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.0871 | 1.67951 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1299 | −0.685376 | −0.342688 | − | 0.939449i | \(-0.611337\pi\) | ||||
−0.342688 | + | 0.939449i | \(0.611337\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.420883 | −0.0219103 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.90235 | −0.410270 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.4801 | −0.956863 | −0.478431 | − | 0.878125i | \(-0.658794\pi\) | ||||
−0.478431 | + | 0.878125i | \(0.658794\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −55.9666 | −2.89010 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.3495 | 1.35707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.13943 | 0.212628 | 0.106314 | − | 0.994333i | \(-0.466095\pi\) | ||||
0.106314 | + | 0.994333i | \(0.466095\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.0375 | −0.719164 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.3667 | −1.75606 | −0.878029 | − | 0.478608i | \(-0.841142\pi\) | ||||
−0.878029 | + | 0.478608i | \(0.841142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.8363 | 0.959987 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.432538 | −0.0219872 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.5339 | 0.534089 | 0.267044 | − | 0.963684i | \(-0.413953\pi\) | ||||
0.267044 | + | 0.963684i | \(0.413953\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.5792 | 1.84989 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.7507 | −0.693633 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.95499 | −0.400259 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.2088 | 0.562554 | 0.281277 | − | 0.959627i | \(-0.409242\pi\) | ||||
0.281277 | + | 0.959627i | \(0.409242\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.80079 | 0.190278 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.4031 | −0.769192 | −0.384596 | − | 0.923085i | \(-0.625659\pi\) | ||||
−0.384596 | + | 0.923085i | \(0.625659\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.02625 | −0.200562 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 39.8649 | 1.98090 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.9610 | 1.78252 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.6029 | 1.11764 | 0.558820 | − | 0.829289i | \(-0.311254\pi\) | ||||
0.558820 | + | 0.829289i | \(0.311254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.6043 | −1.55892 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.62811 | −0.129321 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 47.1964 | 2.31678 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.9174 | −1.41609 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.7468 | 0.622720 | 0.311360 | − | 0.950292i | \(-0.399215\pi\) | ||||
0.311360 | + | 0.950292i | \(0.399215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.9413 | −1.50799 | −0.753994 | − | 0.656882i | \(-0.771875\pi\) | ||||
−0.753994 | + | 0.656882i | \(0.771875\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.48164 | −0.0720399 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 64.1941 | 3.11387 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.33370 | 0.112936 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −38.9601 | −1.88101 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.1089 | 0.631434 | 0.315717 | − | 0.948853i | \(-0.397755\pi\) | ||||
0.315717 | + | 0.948853i | \(0.397755\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.1859 | 1.69093 | 0.845463 | − | 0.534033i | \(-0.179324\pi\) | ||||
0.845463 | + | 0.534033i | \(0.179324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 40.6265 | 1.94789 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.1515 | −0.724795 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.82251 | −0.230166 | −0.115083 | − | 0.993356i | \(-0.536713\pi\) | ||||
−0.115083 | + | 0.993356i | \(0.536713\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.189043 | 0.00900204 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.7618 | −0.843888 | −0.421944 | − | 0.906622i | \(-0.638652\pi\) | ||||
−0.421944 | + | 0.906622i | \(0.638652\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.4536 | 0.495548 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.7520 | −1.02883 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.9204 | −1.41203 | −0.706015 | − | 0.708197i | \(-0.749509\pi\) | ||||
−0.706015 | + | 0.708197i | \(0.749509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0268 | −0.472144 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 31.6886 | 1.48886 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.2611 | −0.949853 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.1293 | 1.36261 | 0.681305 | − | 0.732000i | \(-0.261413\pi\) | ||||
0.681305 | + | 0.732000i | \(0.261413\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.7933 | −1.20393 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.1181 | −0.471247 | −0.235624 | − | 0.971844i | \(-0.575713\pi\) | ||||
−0.235624 | + | 0.971844i | \(0.575713\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.1547 | 1.86615 | 0.933074 | − | 0.359686i | \(-0.117116\pi\) | ||||
0.933074 | + | 0.359686i | \(0.117116\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.20779 | −0.287880 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.3127 | −1.86545 | −0.932726 | − | 0.360587i | \(-0.882577\pi\) | ||||
−0.932726 | + | 0.360587i | \(0.882577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.16822 | 0.377174 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.9633 | 1.15025 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.3045 | −0.473800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.5899 | −1.22003 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.49388 | 0.0684002 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.6994 | −0.580249 | −0.290124 | − | 0.956989i | \(-0.593697\pi\) | ||||
−0.290124 | + | 0.956989i | \(0.593697\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.6811 | −1.76371 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.7128 | −0.578454 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.31409 | 0.377523 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.2373 | 1.55144 | 0.775721 | − | 0.631076i | \(-0.217386\pi\) | ||||
0.775721 | + | 0.631076i | \(0.217386\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.2799 | −1.09798 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.2843 | −1.36671 | −0.683356 | − | 0.730085i | \(-0.739480\pi\) | ||||
−0.683356 | + | 0.730085i | \(0.739480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.9491 | −1.25876 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.56087 | −0.160049 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.04851 | −0.271313 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.2171 | −0.994574 | −0.497287 | − | 0.867586i | \(-0.665670\pi\) | ||||
−0.497287 | + | 0.867586i | \(0.665670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.9779 | 0.535134 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.6238 | 1.27627 | 0.638137 | − | 0.769923i | \(-0.279706\pi\) | ||||
0.638137 | + | 0.769923i | \(0.279706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −65.8571 | −2.93060 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.6917 | 0.830128 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.2622 | −0.942431 | −0.471215 | − | 0.882018i | \(-0.656185\pi\) | ||||
−0.471215 | + | 0.882018i | \(0.656185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.67177 | 0.339379 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.6839 | 0.471704 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 63.6180 | 2.80334 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −35.2975 | −1.55238 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −37.2083 | −1.63326 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.7033 | −1.03846 | −0.519230 | − | 0.854635i | \(-0.673781\pi\) | ||||
−0.519230 | + | 0.854635i | \(0.673781\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.6640 | 0.859847 | 0.429923 | − | 0.902865i | \(-0.358541\pi\) | ||||
0.429923 | + | 0.902865i | \(0.358541\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.3101 | −0.973694 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.27067 | 0.186033 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.6785 | 1.20341 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.496825 | 0.0215604 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.7852 | 0.467160 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.30928 | −0.229540 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −40.0170 | −1.72686 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.50362 | 0.193985 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.2602 | 0.527106 | 0.263553 | − | 0.964645i | \(-0.415106\pi\) | ||||
0.263553 | + | 0.964645i | \(0.415106\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.91002 | −0.339451 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.8296 | 0.720901 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.75986 | −0.246274 | −0.123137 | − | 0.992390i | \(-0.539295\pi\) | ||||
−0.123137 | + | 0.992390i | \(0.539295\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.441169 | −0.0188286 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5768 | 0.493188 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.90198 | −0.0808804 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −59.6396 | −2.53156 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.57936 | −0.109291 | −0.0546455 | − | 0.998506i | \(-0.517403\pi\) | ||||
−0.0546455 | + | 0.998506i | \(0.517403\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0839 | 0.468798 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 41.3252 | 1.74475 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.1195 | −0.637212 | −0.318606 | − | 0.947887i | \(-0.603215\pi\) | ||||
−0.318606 | + | 0.947887i | \(0.603215\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.96329 | −0.292948 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.53139 | 0.400281 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.0034 | 0.461288 | 0.230644 | − | 0.973038i | \(-0.425917\pi\) | ||||
0.230644 | + | 0.973038i | \(0.425917\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.9982 | 1.71572 | 0.857861 | − | 0.513881i | \(-0.171793\pi\) | ||||
0.857861 | + | 0.513881i | \(0.171793\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.1966 | 0.551294 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 88.9373 | 3.70894 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.85596 | 0.118895 | 0.0594476 | − | 0.998231i | \(-0.481066\pi\) | ||||
0.0594476 | + | 0.998231i | \(0.481066\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.248472 | 0.0103261 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.2843 | 0.468152 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.5892 | 1.47395 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.83021 | 0.158360 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.8280 | 1.02476 | 0.512381 | − | 0.858758i | \(-0.328763\pi\) | ||||
0.512381 | + | 0.858758i | \(0.328763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.76895 | −0.0728885 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.5824 | −0.764379 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.72713 | −0.317315 | −0.158658 | − | 0.987334i | \(-0.550717\pi\) | ||||
−0.158658 | + | 0.987334i | \(0.550717\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.4910 | 0.881045 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.09950 | −0.372418 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.28771 | −0.297768 | −0.148884 | − | 0.988855i | \(-0.547568\pi\) | ||||
−0.148884 | + | 0.988855i | \(0.547568\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0313 | 0.817095 | 0.408547 | − | 0.912737i | \(-0.366035\pi\) | ||||
0.408547 | + | 0.912737i | \(0.366035\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.54414 | −0.0628824 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −38.8242 | −1.57843 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.2219 | 0.699014 | 0.349507 | − | 0.936934i | \(-0.386349\pi\) | ||||
0.349507 | + | 0.936934i | \(0.386349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.71349 | 0.393610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.9674 | 1.53600 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.3993 | 1.51054 | 0.755271 | − | 0.655412i | \(-0.227505\pi\) | ||||
0.755271 | + | 0.655412i | \(0.227505\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.6290 | 0.670545 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.1036 | −0.889856 | −0.444928 | − | 0.895566i | \(-0.646771\pi\) | ||||
−0.444928 | + | 0.895566i | \(0.646771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.4908 | 1.22553 | 0.612764 | − | 0.790266i | \(-0.290058\pi\) | ||||
0.612764 | + | 0.790266i | \(0.290058\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −35.7352 | −1.43400 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.49938 | 0.100135 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 68.6132 | 2.74453 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.1173 | −0.683600 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 41.0292 | 1.63594 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.3151 | −1.60492 | −0.802458 | − | 0.596708i | \(-0.796475\pi\) | ||||
−0.802458 | + | 0.596708i | \(0.796475\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.4276 | 0.891417 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.8772 | 1.30469 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.84427 | −0.191937 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.14343 | 0.0452333 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.875535 | −0.0345815 | −0.0172908 | − | 0.999851i | \(-0.505504\pi\) | ||||
−0.0172908 | + | 0.999851i | \(0.505504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.4431 | 1.59492 | 0.797459 | − | 0.603373i | \(-0.206177\pi\) | ||||
0.797459 | + | 0.603373i | \(0.206177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.0895 | 0.672897 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.32973 | −0.130905 | −0.0654526 | − | 0.997856i | \(-0.520849\pi\) | ||||
−0.0654526 | + | 0.997856i | \(0.520849\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.8360 | 0.464603 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.48424 | −0.0581718 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.3589 | −1.14890 | −0.574452 | − | 0.818539i | \(-0.694785\pi\) | ||||
−0.574452 | + | 0.818539i | \(0.694785\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.2055 | 1.25837 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.45029 | −0.0565814 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.2836 | 1.14073 | 0.570364 | − | 0.821392i | \(-0.306802\pi\) | ||||
0.570364 | + | 0.821392i | \(0.306802\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.7308 | −0.534066 | −0.267033 | − | 0.963687i | \(-0.586043\pi\) | ||||
−0.267033 | + | 0.963687i | \(0.586043\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −44.4509 | −1.72633 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.90180 | −0.345197 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.7219 | −1.49932 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.2677 | −0.667606 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.5101 | −0.405737 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.3202 | 1.90115 | 0.950577 | − | 0.310490i | \(-0.100493\pi\) | ||||
0.950577 | + | 0.310490i | \(0.100493\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −62.7129 | −2.41382 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3000 | 0.664892 | 0.332446 | − | 0.943122i | \(-0.392126\pi\) | ||||
0.332446 | + | 0.943122i | \(0.392126\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.98784 | 0.0762861 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.35011 | −0.205017 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.37135 | −0.205529 | −0.102764 | − | 0.994706i | \(-0.532769\pi\) | ||||
−0.102764 | + | 0.994706i | \(0.532769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 74.0202 | 2.82816 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.0644 | −0.612895 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.2811 | −1.45839 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.8853 | 1.70752 | 0.853759 | − | 0.520668i | \(-0.174317\pi\) | ||||
0.853759 | + | 0.520668i | \(0.174317\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.851377 | −0.0323411 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 67.7271 | 2.56904 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.4399 | −0.433319 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.4482 | 0.508657 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.61013 | 0.325200 | 0.162600 | − | 0.986692i | \(-0.448012\pi\) | ||||
0.162600 | + | 0.986692i | \(0.448012\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.9947 | −0.640969 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 58.5392 | 2.20472 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.7459 | −0.592187 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.07942 | −0.115650 | −0.0578250 | − | 0.998327i | \(-0.518417\pi\) | ||||
−0.0578250 | + | 0.998327i | \(0.518417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.359556 | 0.0134844 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.91677 | 0.221585 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 91.2481 | 3.41248 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.34071 | 0.124761 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.5677 | −1.58751 | −0.793754 | − | 0.608239i | \(-0.791876\pi\) | ||||
−0.793754 | + | 0.608239i | \(0.791876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.2106 | 0.566471 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.8781 | 0.962416 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −67.9543 | −2.52376 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.44163 | 0.127643 | 0.0638214 | − | 0.997961i | \(-0.479671\pi\) | ||||
0.0638214 | + | 0.997961i | \(0.479671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.0909 | 0.929294 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.7567 | −0.434839 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.1501 | −0.448775 | −0.224388 | − | 0.974500i | \(-0.572038\pi\) | ||||
−0.224388 | + | 0.974500i | \(0.572038\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.46903 | −0.275499 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36.7866 | −1.35505 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.9556 | 1.02836 | 0.514181 | − | 0.857682i | \(-0.328096\pi\) | ||||
0.514181 | + | 0.857682i | \(0.328096\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.4120 | 0.676383 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.0786 | 0.516495 | 0.258248 | − | 0.966079i | \(-0.416855\pi\) | ||||
0.258248 | + | 0.966079i | \(0.416855\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 50.9452 | 1.86649 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.13322 | −0.0780503 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.26941 | −0.0463832 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.6318 | −1.00830 | −0.504148 | − | 0.863617i | \(-0.668194\pi\) | ||||
−0.504148 | + | 0.863617i | \(0.668194\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.3214 | 0.412576 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −74.2176 | −2.70106 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.76084 | 0.100344 | 0.0501722 | − | 0.998741i | \(-0.484023\pi\) | ||||
0.0501722 | + | 0.998741i | \(0.484023\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 57.2537 | 2.07818 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.5598 | 1.25279 | 0.626396 | − | 0.779505i | \(-0.284529\pi\) | ||||
0.626396 | + | 0.779505i | \(0.284529\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.02383 | 0.145673 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.06272 | −0.146888 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.7313 | −0.459699 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.7370 | 1.79356 | 0.896781 | − | 0.442474i | \(-0.145899\pi\) | ||||
0.896781 | + | 0.442474i | \(0.145899\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.7141 | 0.782015 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.1791 | −0.509986 | −0.254993 | − | 0.966943i | \(-0.582073\pi\) | ||||
−0.254993 | + | 0.966943i | \(0.582073\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3835 | 0.372988 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.2594 | −0.511553 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.73855 | 0.169776 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.2402 | 0.974730 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.3042 | 0.975772 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −58.4664 | −2.08675 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.1039 | −0.467104 | −0.233552 | − | 0.972344i | \(-0.575035\pi\) | ||||
−0.233552 | + | 0.972344i | \(0.575035\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.0534896 | −0.00190428 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.66487 | −0.0591960 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.3050 | 0.401454 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −59.0229 | −2.09333 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.2441 | −1.07130 | −0.535651 | − | 0.844440i | \(-0.679934\pi\) | ||||
−0.535651 | + | 0.844440i | \(0.679934\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.2722 | −1.42473 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.472490 | −0.0166946 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.5507 | −1.21927 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29.7746 | 1.04942 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.2553 | 1.13544 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.36939 | −0.0481450 | −0.0240725 | − | 0.999710i | \(-0.507663\pi\) | ||||
−0.0240725 | + | 0.999710i | \(0.507663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.7374 | −1.04422 | −0.522110 | − | 0.852878i | \(-0.674855\pi\) | ||||
−0.522110 | + | 0.852878i | \(0.674855\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.0196 | −0.631976 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 56.8659 | 1.99192 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.86976 | 0.170371 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.915774 | 0.0319997 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.1869 | 0.634727 | 0.317363 | − | 0.948304i | \(-0.397203\pi\) | ||||
0.317363 | + | 0.948304i | \(0.397203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.5715 | −1.44909 | −0.724546 | − | 0.689226i | \(-0.757951\pi\) | ||||
−0.724546 | + | 0.689226i | \(0.757951\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 100.476 | 3.49814 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.0708 | 1.60204 | 0.801019 | − | 0.598639i | \(-0.204292\pi\) | ||||
0.801019 | + | 0.598639i | \(0.204292\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.574936 | 0.0199683 | 0.00998417 | − | 0.999950i | \(-0.496822\pi\) | ||||
0.00998417 | + | 0.999950i | \(0.496822\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.8337 | −0.549265 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.13834 | 0.178033 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.0534 | −0.970827 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.17213 | −0.144210 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.6700 | −0.989799 | −0.494899 | − | 0.868950i | \(-0.664795\pi\) | ||||
−0.494899 | + | 0.868950i | \(0.664795\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.586242 | 0.0202152 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.8456 | −0.717961 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −43.7777 | −1.50600 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.28258 | −0.318953 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.4200 | −0.769452 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56.8437 | 1.94858 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.8044 | 0.404175 | 0.202087 | − | 0.979367i | \(-0.435227\pi\) | ||||
0.202087 | + | 0.979367i | \(0.435227\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.68282 | 0.0575513 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.6998 | 1.66355 | 0.831777 | − | 0.555110i | \(-0.187324\pi\) | ||||
0.831777 | + | 0.555110i | \(0.187324\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.0381681 | 0.00130228 | 0.000651140 | − | 1.00000i | \(-0.499793\pi\) | ||||
0.000651140 | 1.00000i | \(0.499793\pi\) | ||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.97586 | 0.135497 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.64855 | 0.0561173 | 0.0280587 | − | 0.999606i | \(-0.491067\pi\) | ||||
0.0280587 | + | 0.999606i | \(0.491067\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 87.1452 | 2.96303 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.7909 | 0.570250 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.56579 | 0.290574 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.5690 | 1.34075 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.375786 | −0.0127184 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.3400 | 1.05949 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.2259 | −1.49340 | −0.746701 | − | 0.665160i | \(-0.768363\pi\) | ||||
−0.746701 | + | 0.665160i | \(0.768363\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −43.4219 | −1.46458 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.02249 | 0.0344486 | 0.0172243 | − | 0.999852i | \(-0.494517\pi\) | ||||
0.0172243 | + | 0.999852i | \(0.494517\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.6948 | −0.359908 | −0.179954 | − | 0.983675i | \(-0.557595\pi\) | ||||
−0.179954 | + | 0.983675i | \(0.557595\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.6294 | −0.659836 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.15374 | 0.139469 | 0.0697344 | − | 0.997566i | \(-0.477785\pi\) | ||||
0.0697344 | + | 0.997566i | \(0.477785\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.86069 | 0.263639 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −42.9257 | −1.43807 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.6812 | 0.558214 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 93.7235 | 3.13283 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −61.5843 | −2.05624 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.52083 | −0.150778 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.6050 | 1.35275 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.08596 | 0.135972 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.5260 | 0.615825 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.85902 | 0.161341 | 0.0806706 | − | 0.996741i | \(-0.474294\pi\) | ||||
0.0806706 | + | 0.996741i | \(0.474294\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.97666 | 0.0987295 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.2511 | −0.704082 | −0.352041 | − | 0.935985i | \(-0.614512\pi\) | ||||
−0.352041 | + | 0.935985i | \(0.614512\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.8202 | −1.68190 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.4305 | 0.576233 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.70009 | 0.254279 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2571 | 0.470297 | 0.235149 | − | 0.971959i | \(-0.424442\pi\) | ||||
0.235149 | + | 0.971959i | \(0.424442\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.6692 | 1.60370 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.3006 | −0.964441 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 99.7569 | 3.27999 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.87545 | −0.0944422 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.9394 | 1.04790 | 0.523948 | − | 0.851750i | \(-0.324458\pi\) | ||||
0.523948 | + | 0.851750i | \(0.324458\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.12835 | −0.0697540 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.3335 | 0.338303 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −96.7873 | −3.16528 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.91109 | 0.160438 | 0.0802191 | − | 0.996777i | \(-0.474438\pi\) | ||||
0.0802191 | + | 0.996777i | \(0.474438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.42296 | 0.176972 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.0908 | 1.79591 | 0.897954 | − | 0.440090i | \(-0.145053\pi\) | ||||
0.897954 | + | 0.440090i | \(0.145053\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.8494 | −0.516128 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20.9951 | −0.682972 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.0597 | −1.59423 | −0.797113 | − | 0.603830i | \(-0.793641\pi\) | ||||
−0.797113 | + | 0.603830i | \(0.793641\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.1641 | 1.20640 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.39014 | −0.272069 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.6312 | −1.83446 | −0.917232 | − | 0.398354i | \(-0.869582\pi\) | ||||
−0.917232 | + | 0.398354i | \(0.869582\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.9075 | −1.00014 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −43.7458 | −1.41410 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.6977 | 0.571487 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3092 | −0.977716 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.239973 | 0.00773302 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.581943 | −0.0187334 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.2953 | −1.52092 | −0.760458 | − | 0.649388i | \(-0.775025\pi\) | ||||
−0.760458 | + | 0.649388i | \(0.775025\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.5298 | −0.627386 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.80126 | −0.0898966 | −0.0449483 | − | 0.998989i | \(-0.514312\pi\) | ||||
−0.0449483 | + | 0.998989i | \(0.514312\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.1930 | 0.519125 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −108.076 | −3.46121 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.0570 | −0.705665 | −0.352832 | − | 0.935687i | \(-0.614781\pi\) | ||||
−0.352832 | + | 0.935687i | \(0.614781\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.2562 | −0.359751 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.760677 | −0.0242865 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55.5608 | −1.77212 | −0.886058 | − | 0.463575i | \(-0.846566\pi\) | ||||
−0.886058 | + | 0.463575i | \(0.846566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.5217 | 1.38672 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.9963 | 0.445507 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.2883 | −0.517938 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9880 | 0.444345 | 0.222173 | − | 0.975007i | \(-0.428685\pi\) | ||||
0.222173 | + | 0.975007i | \(0.428685\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −64.4042 | −2.04380 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.3119 | 0.675631 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.9439 | 0.441608 | 0.220804 | − | 0.975318i | \(-0.429132\pi\) | ||||
0.220804 | + | 0.975318i | \(0.429132\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.0825 | −1.26816 |
(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 | 7168.2.a.ba.1.6 | 8 | ||
4.3 | odd | 2 | 7168.2.a.bb.1.3 | 8 | |||
8.3 | odd | 2 | 7168.2.a.bf.1.6 | 8 | |||
8.5 | even | 2 | 7168.2.a.be.1.3 | 8 | |||
32.3 | odd | 8 | 1792.2.m.h.1345.2 | yes | 16 | ||
32.5 | even | 8 | 1792.2.m.g.449.2 | yes | 16 | ||
32.11 | odd | 8 | 1792.2.m.h.449.2 | yes | 16 | ||
32.13 | even | 8 | 1792.2.m.g.1345.2 | yes | 16 | ||
32.19 | odd | 8 | 1792.2.m.e.1345.7 | yes | 16 | ||
32.21 | even | 8 | 1792.2.m.f.449.7 | yes | 16 | ||
32.27 | odd | 8 | 1792.2.m.e.449.7 | ✓ | 16 | ||
32.29 | even | 8 | 1792.2.m.f.1345.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.e.449.7 | ✓ | 16 | 32.27 | odd | 8 | ||
1792.2.m.e.1345.7 | yes | 16 | 32.19 | odd | 8 | ||
1792.2.m.f.449.7 | yes | 16 | 32.21 | even | 8 | ||
1792.2.m.f.1345.7 | yes | 16 | 32.29 | even | 8 | ||
1792.2.m.g.449.2 | yes | 16 | 32.5 | even | 8 | ||
1792.2.m.g.1345.2 | yes | 16 | 32.13 | even | 8 | ||
1792.2.m.h.449.2 | yes | 16 | 32.11 | odd | 8 | ||
1792.2.m.h.1345.2 | yes | 16 | 32.3 | odd | 8 | ||
7168.2.a.ba.1.6 | 8 | 1.1 | even | 1 | trivial | ||
7168.2.a.bb.1.3 | 8 | 4.3 | odd | 2 | |||
7168.2.a.be.1.3 | 8 | 8.5 | even | 2 | |||
7168.2.a.bf.1.6 | 8 | 8.3 | odd | 2 |