Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2300,2,Mod(1,2300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2300, 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("2300.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2300.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: | \(18.3655924649\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.143376304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 12x^{4} + 22x^{2} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 460) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.26443\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2300.1 |
$q$-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 | ||||||||
\(3\) | 2.40050 | 1.38593 | 0.692965 | − | 0.720971i | \(-0.256304\pi\) | ||||
0.692965 | + | 0.720971i | \(0.256304\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.41307 | −1.66798 | −0.833992 | − | 0.551777i | \(-0.813950\pi\) | ||||
−0.833992 | + | 0.551777i | \(0.813950\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.76241 | 0.920804 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.29289 | 0.691332 | 0.345666 | − | 0.938358i | \(-0.387653\pi\) | ||||
0.345666 | + | 0.938358i | \(0.387653\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.92936 | −1.92186 | −0.960930 | − | 0.276792i | \(-0.910729\pi\) | ||||
−0.960930 | + | 0.276792i | \(0.910729\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.51387 | −0.367168 | −0.183584 | − | 0.983004i | \(-0.558770\pi\) | ||||
−0.183584 | + | 0.983004i | \(0.558770\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.89920 | 0.665121 | 0.332561 | − | 0.943082i | \(-0.392087\pi\) | ||||
0.332561 | + | 0.943082i | \(0.392087\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.5936 | −2.31171 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.570328 | −0.109760 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.68764 | −1.42756 | −0.713779 | − | 0.700371i | \(-0.753018\pi\) | ||||
−0.713779 | + | 0.700371i | \(0.753018\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.85746 | 0.692821 | 0.346410 | − | 0.938083i | \(-0.387401\pi\) | ||||
0.346410 | + | 0.938083i | \(0.387401\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.50408 | 0.958138 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.62830 | −1.41848 | −0.709242 | − | 0.704965i | \(-0.750963\pi\) | ||||
−0.709242 | + | 0.704965i | \(0.750963\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.6340 | −2.66356 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.44324 | −1.00626 | −0.503132 | − | 0.864209i | \(-0.667819\pi\) | ||||
−0.503132 | + | 0.864209i | \(0.667819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.48497 | 0.531453 | 0.265727 | − | 0.964048i | \(-0.414388\pi\) | ||||
0.265727 | + | 0.964048i | \(0.414388\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.19747 | 0.903994 | 0.451997 | − | 0.892019i | \(-0.350712\pi\) | ||||
0.451997 | + | 0.892019i | \(0.350712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.4752 | 1.78217 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.63405 | −0.508869 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.17710 | −0.299047 | −0.149524 | − | 0.988758i | \(-0.547774\pi\) | ||||
−0.149524 | + | 0.988758i | \(0.547774\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.95953 | 0.921812 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.7637 | −1.53150 | −0.765750 | − | 0.643138i | \(-0.777632\pi\) | ||||
−0.765750 | + | 0.643138i | \(0.777632\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.11443 | −0.654835 | −0.327418 | − | 0.944880i | \(-0.606178\pi\) | ||||
−0.327418 | + | 0.944880i | \(0.606178\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.1907 | −1.53589 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.94597 | −1.21509 | −0.607547 | − | 0.794284i | \(-0.707846\pi\) | ||||
−0.607547 | + | 0.794284i | \(0.707846\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.40050 | −0.288987 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.41407 | 0.405175 | 0.202588 | − | 0.979264i | \(-0.435065\pi\) | ||||
0.202588 | + | 0.979264i | \(0.435065\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.95307 | 1.04788 | 0.523939 | − | 0.851756i | \(-0.324462\pi\) | ||||
0.523939 | + | 0.851756i | \(0.324462\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.1187 | −1.15313 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.92694 | −0.216798 | −0.108399 | − | 0.994107i | \(-0.534572\pi\) | ||||
−0.108399 | + | 0.994107i | \(0.534572\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.65631 | −1.07292 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.04131 | −0.882648 | −0.441324 | − | 0.897348i | \(-0.645491\pi\) | ||||
−0.441324 | + | 0.897348i | \(0.645491\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.4542 | −1.97850 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.09273 | −0.115829 | −0.0579147 | − | 0.998322i | \(-0.518445\pi\) | ||||
−0.0579147 | + | 0.998322i | \(0.518445\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.5798 | 3.20563 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.25985 | 0.960201 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.9208 | 1.71805 | 0.859026 | − | 0.511933i | \(-0.171070\pi\) | ||||
0.859026 | + | 0.511933i | \(0.171070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.33390 | 0.636581 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.9497 | 1.28855 | 0.644274 | − | 0.764795i | \(-0.277160\pi\) | ||||
0.644274 | + | 0.764795i | \(0.277160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9754 | −1.08144 | −0.540721 | − | 0.841202i | \(-0.681848\pi\) | ||||
−0.540721 | + | 0.841202i | \(0.681848\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.8821 | −1.92208 | −0.961040 | − | 0.276411i | \(-0.910855\pi\) | ||||
−0.961040 | + | 0.276411i | \(0.910855\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.427249 | 0.0409231 | 0.0204615 | − | 0.999791i | \(-0.493486\pi\) | ||||
0.0204615 | + | 0.999791i | \(0.493486\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.7123 | −1.96592 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.38533 | 0.506609 | 0.253304 | − | 0.967387i | \(-0.418483\pi\) | ||||
0.253304 | + | 0.967387i | \(0.418483\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.1418 | −1.76966 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.68082 | 0.612430 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.74267 | −0.522061 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.4670 | −1.39461 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.16014 | −0.546624 | −0.273312 | − | 0.961925i | \(-0.588119\pi\) | ||||
−0.273312 | + | 0.961925i | \(0.588119\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.36569 | 0.736558 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6325 | 1.27845 | 0.639225 | − | 0.769020i | \(-0.279255\pi\) | ||||
0.639225 | + | 0.769020i | \(0.279255\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.7944 | −1.10941 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.972256 | −0.0830654 | −0.0415327 | − | 0.999137i | \(-0.513224\pi\) | ||||
−0.0415327 | + | 0.999137i | \(0.513224\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.74312 | 0.656763 | 0.328382 | − | 0.944545i | \(-0.393497\pi\) | ||||
0.328382 | + | 0.944545i | \(0.393497\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.8770 | 1.25287 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.8883 | −1.32864 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 29.9467 | 2.46996 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6823 | −1.44859 | −0.724293 | − | 0.689492i | \(-0.757834\pi\) | ||||
−0.724293 | + | 0.689492i | \(0.757834\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.01286 | −0.163804 | −0.0819022 | − | 0.996640i | \(-0.526100\pi\) | ||||
−0.0819022 | + | 0.996640i | \(0.526100\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.18194 | −0.338090 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.82703 | 0.465048 | 0.232524 | − | 0.972591i | \(-0.425302\pi\) | ||||
0.232524 | + | 0.972591i | \(0.425302\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.22612 | −0.414459 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.41307 | 0.347799 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.75147 | 0.528816 | 0.264408 | − | 0.964411i | \(-0.414823\pi\) | ||||
0.264408 | + | 0.964411i | \(0.414823\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.4541 | 1.81493 | 0.907466 | − | 0.420125i | \(-0.138014\pi\) | ||||
0.907466 | + | 0.420125i | \(0.138014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.0161 | 2.69355 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00878 | 0.612447 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.28850 | 0.630163 | 0.315081 | − | 0.949065i | \(-0.397968\pi\) | ||||
0.315081 | + | 0.949065i | \(0.397968\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −28.2387 | −2.12255 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.04002 | 0.0777345 | 0.0388673 | − | 0.999244i | \(-0.487625\pi\) | ||||
0.0388673 | + | 0.999244i | \(0.487625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.71850 | 0.202065 | 0.101032 | − | 0.994883i | \(-0.467785\pi\) | ||||
0.101032 | + | 0.994883i | \(0.467785\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.2772 | −0.907557 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.47114 | −0.253835 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.51690 | 0.183077 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.04858 | 0.582375 | 0.291187 | − | 0.956666i | \(-0.405950\pi\) | ||||
0.291187 | + | 0.956666i | \(0.405950\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.0276 | 1.15370 | 0.576848 | − | 0.816852i | \(-0.304283\pi\) | ||||
0.576848 | + | 0.816852i | \(0.304283\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.06316 | −0.289488 | −0.144744 | − | 0.989469i | \(-0.546236\pi\) | ||||
−0.144744 | + | 0.989469i | \(0.546236\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7042 | 1.32590 | 0.662952 | − | 0.748662i | \(-0.269303\pi\) | ||||
0.662952 | + | 0.748662i | \(0.269303\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.8753 | −1.68404 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 33.9261 | 2.38114 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.76241 | −0.192001 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.64753 | 0.459819 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.87839 | 0.542371 | 0.271185 | − | 0.962527i | \(-0.412584\pi\) | ||||
0.271185 | + | 0.962527i | \(0.412584\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.19548 | 0.561545 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.0232 | −1.15561 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.4919 | 1.45229 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.4902 | 0.705645 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.29263 | 0.153526 | 0.0767628 | − | 0.997049i | \(-0.475542\pi\) | ||||
0.0767628 | + | 0.997049i | \(0.475542\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.8325 | −0.851725 | −0.425862 | − | 0.904788i | \(-0.640029\pi\) | ||||
−0.425862 | + | 0.904788i | \(0.640029\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.2528 | −1.07401 | −0.537007 | − | 0.843578i | \(-0.680445\pi\) | ||||
−0.537007 | + | 0.843578i | \(0.680445\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.2899 | −1.59816 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.5410 | −1.41120 | −0.705598 | − | 0.708613i | \(-0.749321\pi\) | ||||
−0.705598 | + | 0.708613i | \(0.749321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.62563 | −0.300467 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0622 | −0.715555 | −0.357778 | − | 0.933807i | \(-0.616465\pi\) | ||||
−0.357778 | + | 0.933807i | \(0.616465\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.2164 | 1.17342 | 0.586710 | − | 0.809797i | \(-0.300423\pi\) | ||||
0.586710 | + | 0.809797i | \(0.300423\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.4690 | −1.37724 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.0896 | −1.27827 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.3032 | −1.22329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0182 | −0.632345 | −0.316172 | − | 0.948702i | \(-0.602398\pi\) | ||||
−0.316172 | + | 0.948702i | \(0.602398\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.29289 | −0.144153 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.3021 | 0.892141 | 0.446070 | − | 0.894998i | \(-0.352823\pi\) | ||||
0.446070 | + | 0.894998i | \(0.352823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.0773 | 2.36601 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.2364 | −1.31450 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.44361 | 0.582318 | 0.291159 | − | 0.956675i | \(-0.405959\pi\) | ||||
0.291159 | + | 0.956675i | \(0.405959\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.62311 | −0.160531 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.7630 | 1.44886 | 0.724428 | − | 0.689350i | \(-0.242104\pi\) | ||||
0.724428 | + | 0.689350i | \(0.242104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5939 | −1.06875 | −0.534375 | − | 0.845247i | \(-0.679453\pi\) | ||||
−0.534375 | + | 0.845247i | \(0.679453\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 73.4068 | 4.44278 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.6582 | 1.78199 | 0.890995 | − | 0.454014i | \(-0.150008\pi\) | ||||
0.890995 | + | 0.454014i | \(0.150008\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.6559 | 0.637952 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.25484 | −0.492442 | −0.246221 | − | 0.969214i | \(-0.579189\pi\) | ||||
−0.246221 | + | 0.969214i | \(0.579189\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.21317 | −0.547666 | −0.273833 | − | 0.961777i | \(-0.588292\pi\) | ||||
−0.273833 | + | 0.961777i | \(0.588292\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.4344 | 1.67843 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7082 | −0.865188 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 40.6185 | 2.38110 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.1138 | −0.649277 | −0.324639 | − | 0.945838i | \(-0.605243\pi\) | ||||
−0.324639 | + | 0.945838i | \(0.605243\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.30770 | −0.0758804 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.92936 | 0.400735 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.3794 | −0.886455 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.0859 | 1.78584 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.7800 | −1.07183 | −0.535916 | − | 0.844272i | \(-0.680033\pi\) | ||||
−0.535916 | + | 0.844272i | \(0.680033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.3465 | −1.49880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.51258 | 0.142475 | 0.0712377 | − | 0.997459i | \(-0.477305\pi\) | ||||
0.0712377 | + | 0.997459i | \(0.477305\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.9278 | −1.12638 | −0.563192 | − | 0.826326i | \(-0.690427\pi\) | ||||
−0.563192 | + | 0.826326i | \(0.690427\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.8849 | 1.56617 | 0.783087 | − | 0.621912i | \(-0.213644\pi\) | ||||
0.783087 | + | 0.621912i | \(0.213644\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.6269 | −0.986916 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −47.7271 | −2.66387 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.38901 | −0.244211 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.02561 | 0.0567165 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.3499 | −1.50785 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.5409 | −1.56875 | −0.784375 | − | 0.620287i | \(-0.787016\pi\) | ||||
−0.784375 | + | 0.620287i | \(0.787016\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −23.8349 | −1.30615 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.71371 | −0.202298 | −0.101149 | − | 0.994871i | \(-0.532252\pi\) | ||||
−0.101149 | + | 0.994871i | \(0.532252\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.9275 | 0.702125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.84472 | 0.478969 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −24.1624 | −1.30464 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.1459 | −0.759393 | −0.379696 | − | 0.925111i | \(-0.623972\pi\) | ||||
−0.379696 | + | 0.925111i | \(0.623972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.2802 | −1.13910 | −0.569550 | − | 0.821957i | \(-0.692883\pi\) | ||||
−0.569550 | + | 0.821957i | \(0.692883\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.95201 | 0.210943 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.4641 | −1.30209 | −0.651046 | − | 0.759038i | \(-0.725669\pi\) | ||||
−0.651046 | + | 0.759038i | \(0.725669\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.0373 | 0.848786 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.0252 | −1.21522 | −0.607612 | − | 0.794234i | \(-0.707872\pi\) | ||||
−0.607612 | + | 0.794234i | \(0.707872\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5947 | −0.557613 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.7853 | −0.723540 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.478057 | −0.0249544 | −0.0124772 | − | 0.999922i | \(-0.503972\pi\) | ||||
−0.0124772 | + | 0.999922i | \(0.503972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.7989 | −0.926573 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.60767 | 0.498806 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.3508 | −1.41617 | −0.708085 | − | 0.706127i | \(-0.750441\pi\) | ||||
−0.708085 | + | 0.706127i | \(0.750441\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 53.2704 | 2.74357 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.35358 | −0.377728 | −0.188864 | − | 0.982003i | \(-0.560481\pi\) | ||||
−0.188864 | + | 0.982003i | \(0.560481\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.7874 | −0.757583 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.34108 | 0.170721 | 0.0853606 | − | 0.996350i | \(-0.472796\pi\) | ||||
0.0853606 | + | 0.996350i | \(0.472796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.62693 | 0.489364 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.366568 | 0.0185858 | 0.00929288 | − | 0.999957i | \(-0.497042\pi\) | ||||
0.00929288 | + | 0.999957i | \(0.497042\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.51387 | 0.0765598 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 35.1254 | 1.77184 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.3222 | 0.568245 | 0.284122 | − | 0.958788i | \(-0.408298\pi\) | ||||
0.284122 | + | 0.958788i | \(0.408298\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.7129 | −1.53757 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.1673 | 1.85605 | 0.928024 | − | 0.372520i | \(-0.121506\pi\) | ||||
0.928024 | + | 0.372520i | \(0.121506\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.7298 | −1.33150 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.7837 | −0.980643 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.7745 | −0.681107 | −0.340553 | − | 0.940225i | \(-0.610614\pi\) | ||||
−0.340553 | + | 0.940225i | \(0.610614\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.33390 | −0.115123 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 51.9139 | 2.55452 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.5874 | 0.910228 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.50726 | 0.366753 | 0.183377 | − | 0.983043i | \(-0.441297\pi\) | ||||
0.183377 | + | 0.983043i | \(0.441297\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.65685 | −0.373172 | −0.186586 | − | 0.982439i | \(-0.559742\pi\) | ||||
−0.186586 | + | 0.982439i | \(0.559742\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.1200 | 0.832402 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.5703 | 1.09225 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −38.1398 | −1.84141 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.22764 | 0.299975 | 0.149987 | − | 0.988688i | \(-0.452077\pi\) | ||||
0.149987 | + | 0.988688i | \(0.452077\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.704087 | −0.0338362 | −0.0169181 | − | 0.999857i | \(-0.505385\pi\) | ||||
−0.0169181 | + | 0.999857i | \(0.505385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.89920 | −0.138687 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.8570 | −1.66363 | −0.831816 | − | 0.555052i | \(-0.812699\pi\) | ||||
−0.831816 | + | 0.555052i | \(0.812699\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 34.4616 | 1.64103 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.8165 | 1.17907 | 0.589533 | − | 0.807745i | \(-0.299312\pi\) | ||||
0.589533 | + | 0.807745i | \(0.299312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −42.4463 | −2.00764 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.77738 | 0.319844 | 0.159922 | − | 0.987130i | \(-0.448876\pi\) | ||||
0.159922 | + | 0.987130i | \(0.448876\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.7736 | −0.695662 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.83188 | −0.227021 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.47169 | −0.0688429 | −0.0344214 | − | 0.999407i | \(-0.510959\pi\) | ||||
−0.0344214 | + | 0.999407i | \(0.510959\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.863404 | 0.0403003 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.8037 | 1.20180 | 0.600899 | − | 0.799325i | \(-0.294809\pi\) | ||||
0.600899 | + | 0.799325i | \(0.294809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.3469 | 0.713231 | 0.356616 | − | 0.934251i | \(-0.383931\pi\) | ||||
0.356616 | + | 0.934251i | \(0.383931\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.2933 | −0.476315 | −0.238157 | − | 0.971227i | \(-0.576543\pi\) | ||||
−0.238157 | + | 0.971227i | \(0.576543\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 43.8922 | 2.02676 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.9878 | 0.644524 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.99065 | 0.367410 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.01404 | −0.275364 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.50453 | 0.205817 | 0.102909 | − | 0.994691i | \(-0.467185\pi\) | ||||
0.102909 | + | 0.994691i | \(0.467185\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 59.7886 | 2.72613 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.5936 | 0.482025 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.2669 | 1.23558 | 0.617790 | − | 0.786343i | \(-0.288028\pi\) | ||||
0.617790 | + | 0.786343i | \(0.288028\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.2069 | 0.732902 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.4866 | 1.10507 | 0.552533 | − | 0.833491i | \(-0.313661\pi\) | ||||
0.552533 | + | 0.833491i | \(0.313661\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.6381 | 0.524154 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.0665 | −0.675826 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.1892 | −1.08286 | −0.541429 | − | 0.840746i | \(-0.682117\pi\) | ||||
−0.541429 | + | 0.840746i | \(0.682117\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 56.3016 | 2.51537 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.6230 | −1.36541 | −0.682706 | − | 0.730693i | \(-0.739197\pi\) | ||||
−0.682706 | + | 0.730693i | \(0.739197\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 84.0562 | 3.73307 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.56826 | −0.113836 | −0.0569181 | − | 0.998379i | \(-0.518127\pi\) | ||||
−0.0569181 | + | 0.998379i | \(0.518127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.5105 | −1.74784 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.65349 | −0.0730035 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.2101 | 0.624960 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.8966 | 0.873362 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −44.1355 | −1.93361 | −0.966807 | − | 0.255509i | \(-0.917757\pi\) | ||||
−0.966807 | + | 0.255509i | \(0.917757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −42.2884 | −1.84914 | −0.924572 | − | 0.381008i | \(-0.875577\pi\) | ||||
−0.924572 | + | 0.381008i | \(0.875577\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.83970 | −0.254381 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.4961 | −1.41021 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.6475 | 1.93390 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.49656 | 0.107735 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.6042 | 1.23207 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.2776 | 0.441871 | 0.220935 | − | 0.975288i | \(-0.429089\pi\) | ||||
0.220935 | + | 0.975288i | \(0.429089\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.52577 | 0.280048 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.87305 | 0.165600 | 0.0827998 | − | 0.996566i | \(-0.473614\pi\) | ||||
0.0827998 | + | 0.996566i | \(0.473614\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.1282 | −0.602975 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.2880 | −0.949500 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.50373 | 0.361615 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.62364 | 0.407767 | 0.203883 | − | 0.978995i | \(-0.434644\pi\) | ||||
0.203883 | + | 0.978995i | \(0.434644\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.1486 | −1.02138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.33248 | −0.351797 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.35865 | −0.141550 | −0.0707751 | − | 0.997492i | \(-0.522547\pi\) | ||||
−0.0707751 | + | 0.997492i | \(0.522547\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.6140 | 1.78962 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.26939 | −0.178982 | −0.0894910 | − | 0.995988i | \(-0.528524\pi\) | ||||
−0.0894910 | + | 0.995988i | \(0.528524\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4567 | 0.688689 | 0.344345 | − | 0.938843i | \(-0.388101\pi\) | ||||
0.344345 | + | 0.938843i | \(0.388101\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.3206 | 0.807131 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.98780 | −0.0827530 | −0.0413765 | − | 0.999144i | \(-0.513174\pi\) | ||||
−0.0413765 | + | 0.999144i | \(0.513174\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 38.4744 | 1.59894 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.4869 | 1.47224 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.99184 | −0.206741 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.9720 | 1.19580 | 0.597900 | − | 0.801570i | \(-0.296002\pi\) | ||||
0.597900 | + | 0.801570i | \(0.296002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.1835 | 0.460810 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.75363 | −0.401211 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.4799 | 0.799944 | 0.399972 | − | 0.916527i | \(-0.369020\pi\) | ||||
0.399972 | + | 0.916527i | \(0.369020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.8994 | 1.83761 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.8442 | 1.54627 | 0.773136 | − | 0.634240i | \(-0.218687\pi\) | ||||
0.773136 | + | 0.634240i | \(0.218687\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2347 | −0.825389 | −0.412695 | − | 0.910869i | \(-0.635412\pi\) | ||||
−0.412695 | + | 0.910869i | \(0.635412\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.4749 | −1.11886 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.4075 | −0.990670 | −0.495335 | − | 0.868702i | \(-0.664955\pi\) | ||||
−0.495335 | + | 0.868702i | \(0.664955\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 81.4396 | 3.30010 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −42.9445 | −1.73735 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6964 | −0.432025 | −0.216012 | − | 0.976391i | \(-0.569305\pi\) | ||||
−0.216012 | + | 0.976391i | \(0.569305\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.4738 | 1.10605 | 0.553026 | − | 0.833164i | \(-0.313473\pi\) | ||||
0.553026 | + | 0.833164i | \(0.313473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.389330 | −0.0156485 | −0.00782425 | − | 0.999969i | \(-0.502491\pi\) | ||||
−0.00782425 | + | 0.999969i | \(0.502491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.570328 | 0.0228865 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.82230 | 0.193201 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.9574 | 0.637278 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.0621 | 0.520822 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.9330 | −0.475047 | −0.237523 | − | 0.971382i | \(-0.576336\pi\) | ||||
−0.237523 | + | 0.971382i | \(0.576336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.9121 | 0.751689 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −86.4451 | −3.42508 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.43106 | 0.373087 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.8525 | 0.902621 | 0.451311 | − | 0.892367i | \(-0.350957\pi\) | ||||
0.451311 | + | 0.892367i | \(0.350957\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.9279 | −1.37742 | −0.688711 | − | 0.725036i | \(-0.741823\pi\) | ||||
−0.688711 | + | 0.725036i | \(0.741823\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.3738 | −1.03686 | −0.518430 | − | 0.855120i | \(-0.673483\pi\) | ||||
−0.518430 | + | 0.855120i | \(0.673483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.9728 | −1.05877 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40.8643 | −1.60160 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.17022 | 0.0849274 | 0.0424637 | − | 0.999098i | \(-0.486479\pi\) | ||||
0.0424637 | + | 0.999098i | \(0.486479\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.7321 | 0.964891 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7820 | 0.770596 | 0.385298 | − | 0.922792i | \(-0.374099\pi\) | ||||
0.385298 | + | 0.922792i | \(0.374099\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.7505 | 1.77949 | 0.889743 | − | 0.456461i | \(-0.150883\pi\) | ||||
0.889743 | + | 0.456461i | \(0.150883\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.1817 | 0.977976 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.68764 | 0.297666 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.50346 | 0.212776 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.7268 | −0.452708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.99940 | −0.269807 | −0.134904 | − | 0.990859i | \(-0.543072\pi\) | ||||
−0.134904 | + | 0.990859i | \(0.543072\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.7178 | −1.02685 | −0.513425 | − | 0.858134i | \(-0.671624\pi\) | ||||
−0.513425 | + | 0.858134i | \(0.671624\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −74.6728 | −2.86568 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.8045 | −1.18043 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.8947 | 0.761248 | 0.380624 | − | 0.924730i | \(-0.375709\pi\) | ||||
0.380624 | + | 0.924730i | \(0.375709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −39.0148 | −1.48851 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0859 | 0.574727 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.24438 | 0.0473385 | 0.0236693 | − | 0.999720i | \(-0.492465\pi\) | ||||
0.0236693 | + | 0.999720i | \(0.492465\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −27.9520 | −1.06181 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.75424 | 0.369468 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −51.7091 | −1.95582 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.8454 | −1.12724 | −0.563622 | − | 0.826033i | \(-0.690592\pi\) | ||||
−0.563622 | + | 0.826033i | \(0.690592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.0151 | −0.943464 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −57.1481 | −2.14928 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.2255 | 0.947362 | 0.473681 | − | 0.880697i | \(-0.342925\pi\) | ||||
0.473681 | + | 0.880697i | \(0.342925\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.32301 | −0.199628 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.85746 | −0.144463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.5549 | −0.991710 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.7787 | −0.886797 | −0.443398 | − | 0.896325i | \(-0.646227\pi\) | ||||
−0.443398 | + | 0.896325i | \(0.646227\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.4353 | 1.80383 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.7285 | 1.62628 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.5849 | −1.35686 | −0.678429 | − | 0.734666i | \(-0.737339\pi\) | ||||
−0.678429 | + | 0.734666i | \(0.737339\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.5675 | −0.835833 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.27580 | −0.195133 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.7593 | 0.803698 | 0.401849 | − | 0.915706i | \(-0.368368\pi\) | ||||
0.401849 | + | 0.915706i | \(0.368368\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.8050 | −0.840032 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.72303 | 0.100168 | 0.0500842 | − | 0.998745i | \(-0.484051\pi\) | ||||
0.0500842 | + | 0.998745i | \(0.484051\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −48.2251 | −1.77159 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.0161 | 1.17456 | 0.587278 | − | 0.809385i | \(-0.300200\pi\) | ||||
0.587278 | + | 0.809385i | \(0.300200\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −22.2134 | −0.812746 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 87.7413 | 3.20600 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0949 | −1.31712 | −0.658561 | − | 0.752527i | \(-0.728835\pi\) | ||||
−0.658561 | + | 0.752527i | \(0.728835\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.0488 | −0.876386 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.8188 | 1.70166 | 0.850830 | − | 0.525442i | \(-0.176100\pi\) | ||||
0.850830 | + | 0.525442i | \(0.176100\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.50408 | −0.199786 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.8182 | −1.04466 | −0.522330 | − | 0.852744i | \(-0.674937\pi\) | ||||
−0.522330 | + | 0.852744i | \(0.674937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.88548 | −0.0682590 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 81.5148 | 2.94333 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.6243 | 1.86162 | 0.930811 | − | 0.365501i | \(-0.119102\pi\) | ||||
0.930811 | + | 0.365501i | \(0.119102\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.3322 | 1.23645 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.9610 | −0.933753 | −0.466877 | − | 0.884322i | \(-0.654621\pi\) | ||||
−0.466877 | + | 0.884322i | \(0.654621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 91.4046 | 3.27912 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.6802 | −0.669288 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.82807 | 0.280110 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.38448 | 0.156688 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −53.2258 | −1.89730 | −0.948648 | − | 0.316333i | \(-0.897548\pi\) | ||||
−0.948648 | + | 0.316333i | \(0.897548\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.6694 | 0.807053 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.7658 | −0.845015 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.4397 | 1.25850 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.1874 | −1.10471 | −0.552357 | − | 0.833608i | \(-0.686271\pi\) | ||||
−0.552357 | + | 0.833608i | \(0.686271\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.38218 | −0.331918 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.01858 | −0.106656 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.5284 | 0.724431 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 57.0432 | 2.00802 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.60251 | −0.0563414 | −0.0281707 | − | 0.999603i | \(-0.508968\pi\) | ||||
−0.0281707 | + | 0.999603i | \(0.508968\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.9545 | −1.29765 | −0.648824 | − | 0.760938i | \(-0.724739\pi\) | ||||
−0.648824 | + | 0.760938i | \(0.724739\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −42.2341 | −1.48121 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.1036 | 0.353481 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 84.4739 | 2.95176 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.5583 | −0.577890 | −0.288945 | − | 0.957346i | \(-0.593304\pi\) | ||||
−0.288945 | + | 0.957346i | \(0.593304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.63201 | 0.266035 | 0.133018 | − | 0.991114i | \(-0.457533\pi\) | ||||
0.133018 | + | 0.991114i | \(0.457533\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.1969 | 0.667543 | 0.333772 | − | 0.942654i | \(-0.391679\pi\) | ||||
0.333772 | + | 0.942654i | \(0.391679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.32413 | −0.219646 | −0.109823 | − | 0.993951i | \(-0.535028\pi\) | ||||
−0.109823 | + | 0.993951i | \(0.535028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 71.1946 | 2.46971 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.8858 | −0.654355 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.20002 | −0.0760438 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.1158 | 0.798046 | 0.399023 | − | 0.916941i | \(-0.369349\pi\) | ||||
0.399023 | + | 0.916941i | \(0.369349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.0997 | 1.03792 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.8158 | −0.682491 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.3428 | 0.870789 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.1163 | −0.759028 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.62830 | 0.295774 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.7049 | 1.29099 | 0.645496 | − | 0.763764i | \(-0.276651\pi\) | ||||
0.645496 | + | 0.763764i | \(0.276651\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.7133 | −0.673395 | −0.336697 | − | 0.941613i | \(-0.609310\pi\) | ||||
−0.336697 | + | 0.941613i | \(0.609310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00609 | 0.0684471 | 0.0342235 | − | 0.999414i | \(-0.489104\pi\) | ||||
0.0342235 | + | 0.999414i | \(0.489104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 68.2570 | 2.32619 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.8127 | −0.572312 | −0.286156 | − | 0.958183i | \(-0.592377\pi\) | ||||
−0.286156 | + | 0.958183i | \(0.592377\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −35.3071 | −1.19909 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.41826 | −0.149879 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 68.9192 | 2.33524 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.7424 | 1.58199 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.8922 | −0.502874 | −0.251437 | − | 0.967874i | \(-0.580903\pi\) | ||||
−0.251437 | + | 0.967874i | \(0.580903\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.6788 | −0.899853 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.5218 | −0.556632 | −0.278316 | − | 0.960490i | \(-0.589776\pi\) | ||||
−0.278316 | + | 0.960490i | \(0.589776\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.7254 | −1.30321 | −0.651607 | − | 0.758557i | \(-0.725905\pi\) | ||||
−0.651607 | + | 0.758557i | \(0.725905\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.16364 | −0.0390711 | −0.0195355 | − | 0.999809i | \(-0.506219\pi\) | ||||
−0.0195355 | + | 0.999809i | \(0.506219\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.1851 | 0.911760 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.1408 | −0.741746 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.9677 | 0.601266 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.6340 | 0.555392 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.6548 | −0.989042 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.29584 | 0.109800 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.9183 | −1.22857 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.2796 | −1.00542 | −0.502709 | − | 0.864456i | \(-0.667663\pi\) | ||||
−0.502709 | + | 0.864456i | \(0.667663\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 35.7725 | 1.18650 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.2296 | −0.935290 | −0.467645 | − | 0.883916i | \(-0.654897\pi\) | ||||
−0.467645 | + | 0.883916i | \(0.654897\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.4378 | −0.610203 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −64.5744 | −2.13243 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.28150 | 0.108247 | 0.0541233 | − | 0.998534i | \(-0.482764\pi\) | ||||
0.0541233 | + | 0.998534i | \(0.482764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −45.0814 | −1.48548 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.6573 | −0.778690 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.3187 | −0.995796 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.64745 | 0.250905 | 0.125452 | − | 0.992100i | \(-0.459962\pi\) | ||||
0.125452 | + | 0.992100i | \(0.459962\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.1680 | 1.18536 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.03146 | 0.197461 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.95226 | 0.161783 | 0.0808917 | − | 0.996723i | \(-0.474223\pi\) | ||||
0.0808917 | + | 0.996723i | \(0.474223\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −47.8366 | −1.56109 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.62677 | −0.281225 | −0.140612 | − | 0.990065i | \(-0.544907\pi\) | ||||
−0.140612 | + | 0.990065i | \(0.544907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.44324 | 0.209821 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.6807 | 1.51692 | 0.758460 | − | 0.651720i | \(-0.225952\pi\) | ||||
0.758460 | + | 0.651720i | \(0.225952\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −62.0391 | −2.01387 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 66.9378 | 2.17061 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.2343 | 0.396307 | 0.198154 | − | 0.980171i | \(-0.436505\pi\) | ||||
0.198154 | + | 0.980171i | \(0.436505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −42.3134 | −1.36780 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.29063 | 0.138552 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.1200 | −0.520000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −54.9227 | −1.76986 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.8318 | 1.76327 | 0.881635 | − | 0.471932i | \(-0.156443\pi\) | ||||
0.881635 | + | 0.471932i | \(0.156443\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.5358 | −0.338460 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.3804 | 1.29587 | 0.647935 | − | 0.761696i | \(-0.275633\pi\) | ||||
0.647935 | + | 0.761696i | \(0.275633\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.1709 | −1.09547 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6700 | 0.341363 | 0.170681 | − | 0.985326i | \(-0.445403\pi\) | ||||
0.170681 | + | 0.985326i | \(0.445403\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.50551 | −0.0800765 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.18024 | 0.0376821 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.27812 | −0.200241 | −0.100120 | − | 0.994975i | \(-0.531923\pi\) | ||||
−0.100120 | + | 0.994975i | \(0.531923\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −65.6535 | −2.08977 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.48497 | −0.110816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.2864 | 1.94683 | 0.973413 | − | 0.229057i | \(-0.0735643\pi\) | ||||
0.973413 | + | 0.229057i | \(0.0735643\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −68.5125 | −2.17418 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.9799 | −1.26618 | −0.633088 | − | 0.774080i | \(-0.718213\pi\) | ||||
−0.633088 | + | 0.774080i | \(0.718213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.92096 | 0.155692 |
(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 | 2300.2.a.n.1.6 | 6 | ||
4.3 | odd | 2 | 9200.2.a.cy.1.1 | 6 | |||
5.2 | odd | 4 | 460.2.c.a.369.3 | ✓ | 12 | ||
5.3 | odd | 4 | 460.2.c.a.369.10 | yes | 12 | ||
5.4 | even | 2 | 2300.2.a.o.1.1 | 6 | |||
15.2 | even | 4 | 4140.2.f.b.829.8 | 12 | |||
15.8 | even | 4 | 4140.2.f.b.829.7 | 12 | |||
20.3 | even | 4 | 1840.2.e.f.369.3 | 12 | |||
20.7 | even | 4 | 1840.2.e.f.369.10 | 12 | |||
20.19 | odd | 2 | 9200.2.a.cx.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.c.a.369.3 | ✓ | 12 | 5.2 | odd | 4 | ||
460.2.c.a.369.10 | yes | 12 | 5.3 | odd | 4 | ||
1840.2.e.f.369.3 | 12 | 20.3 | even | 4 | |||
1840.2.e.f.369.10 | 12 | 20.7 | even | 4 | |||
2300.2.a.n.1.6 | 6 | 1.1 | even | 1 | trivial | ||
2300.2.a.o.1.1 | 6 | 5.4 | even | 2 | |||
4140.2.f.b.829.7 | 12 | 15.8 | even | 4 | |||
4140.2.f.b.829.8 | 12 | 15.2 | even | 4 | |||
9200.2.a.cx.1.6 | 6 | 20.19 | odd | 2 | |||
9200.2.a.cy.1.1 | 6 | 4.3 | odd | 2 |