Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5776,2,Mod(1,5776)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5776, 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("5776.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5776 = 2^{4} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5776.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: | \(46.1215922075\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.34292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5776.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.146365 | 0.0845042 | 0.0422521 | − | 0.999107i | \(-0.486547\pi\) | ||||
0.0422521 | + | 0.999107i | \(0.486547\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.34292 | 1.04779 | 0.523894 | − | 0.851784i | \(-0.324479\pi\) | ||||
0.523894 | + | 0.851784i | \(0.324479\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.83221 | −1.44844 | −0.724220 | − | 0.689569i | \(-0.757800\pi\) | ||||
−0.724220 | + | 0.689569i | \(0.757800\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.97858 | −0.992859 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.34292 | −1.00793 | −0.503965 | − | 0.863724i | \(-0.668126\pi\) | ||||
−0.503965 | + | 0.863724i | \(0.668126\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.17513 | 1.71267 | 0.856337 | − | 0.516417i | \(-0.172735\pi\) | ||||
0.856337 | + | 0.516417i | \(0.172735\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.342923 | 0.0885424 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.19656 | 1.26035 | 0.630175 | − | 0.776453i | \(-0.282983\pi\) | ||||
0.630175 | + | 0.776453i | \(0.282983\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.560904 | −0.122399 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.34292 | −0.488533 | −0.244267 | − | 0.969708i | \(-0.578547\pi\) | ||||
−0.244267 | + | 0.969708i | \(0.578547\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.489289 | 0.0978577 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.875057 | −0.168405 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0501921 | 0.00932044 | 0.00466022 | − | 0.999989i | \(-0.498517\pi\) | ||||
0.00466022 | + | 0.999989i | \(0.498517\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.43910 | 0.617680 | 0.308840 | − | 0.951114i | \(-0.400059\pi\) | ||||
0.308840 | + | 0.951114i | \(0.400059\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.489289 | −0.0851742 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.97858 | −1.51766 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.43910 | −0.894182 | −0.447091 | − | 0.894488i | \(-0.647540\pi\) | ||||
−0.447091 | + | 0.894488i | \(0.647540\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.903827 | 0.144728 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.29273 | −1.13893 | −0.569467 | − | 0.822014i | \(-0.692850\pi\) | ||||
−0.569467 | + | 0.822014i | \(0.692850\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.86098 | 1.35129 | 0.675643 | − | 0.737229i | \(-0.263866\pi\) | ||||
0.675643 | + | 0.737229i | \(0.263866\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.97858 | −1.04030 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.7360 | −1.56601 | −0.783006 | − | 0.622014i | \(-0.786315\pi\) | ||||
−0.783006 | + | 0.622014i | \(0.786315\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.68585 | 1.09798 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.760597 | 0.106505 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.19656 | −0.439081 | −0.219540 | − | 0.975603i | \(-0.570456\pi\) | ||||
−0.219540 | + | 0.975603i | \(0.570456\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.83221 | −1.05610 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.85363 | −0.501700 | −0.250850 | − | 0.968026i | \(-0.580710\pi\) | ||||
−0.250850 | + | 0.968026i | \(0.580710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.92839 | 0.374941 | 0.187471 | − | 0.982270i | \(-0.439971\pi\) | ||||
0.187471 | + | 0.982270i | \(0.439971\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.4145 | 1.43810 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4679 | 1.79452 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.5181 | 1.40715 | 0.703577 | − | 0.710619i | \(-0.251585\pi\) | ||||
0.703577 | + | 0.710619i | \(0.251585\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.342923 | −0.0412831 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.48929 | −0.176746 | −0.0883730 | − | 0.996087i | \(-0.528167\pi\) | ||||
−0.0883730 | + | 0.996087i | \(0.528167\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.68585 | −0.899560 | −0.449780 | − | 0.893139i | \(-0.648498\pi\) | ||||
−0.449780 | + | 0.893139i | \(0.648498\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0716150 | 0.00826938 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.8108 | 1.45992 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.175135 | −0.0197042 | −0.00985210 | − | 0.999951i | \(-0.503136\pi\) | ||||
−0.00985210 | + | 0.999951i | \(0.503136\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.80765 | 0.978628 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.00735 | 0.769156 | 0.384578 | − | 0.923092i | \(-0.374347\pi\) | ||||
0.384578 | + | 0.923092i | \(0.374347\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.1751 | 1.32058 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.00734639 | 0.000787616 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.5468 | −1.43596 | −0.717980 | − | 0.696063i | \(-0.754933\pi\) | ||||
−0.717980 | + | 0.696063i | \(0.754933\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23.6644 | −2.48071 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.503365 | 0.0521965 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.68585 | −0.374241 | −0.187120 | − | 0.982337i | \(-0.559915\pi\) | ||||
−0.187120 | + | 0.982337i | \(0.559915\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.95715 | 1.00073 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.61423 | −0.757644 | −0.378822 | − | 0.925469i | \(-0.623671\pi\) | ||||
−0.378822 | + | 0.925469i | \(0.623671\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.6430 | −1.63988 | −0.819942 | − | 0.572447i | \(-0.805994\pi\) | ||||
−0.819942 | + | 0.572447i | \(0.805994\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.31415 | −0.128248 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.29273 | 0.608341 | 0.304171 | − | 0.952618i | \(-0.401621\pi\) | ||||
0.304171 | + | 0.952618i | \(0.401621\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.1537 | 1.06833 | 0.534166 | − | 0.845380i | \(-0.320626\pi\) | ||||
0.534166 | + | 0.845380i | \(0.320626\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.796096 | −0.0755621 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.7606 | −1.67078 | −0.835388 | − | 0.549660i | \(-0.814757\pi\) | ||||
−0.835388 | + | 0.549660i | \(0.814757\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.48929 | −0.511879 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.3931 | −1.70044 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.9143 | −1.82554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.175135 | 0.0159213 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.06740 | −0.0962446 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5682 | −0.945253 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.4250 | −1.63496 | −0.817478 | − | 0.575960i | \(-0.804629\pi\) | ||||
−0.817478 | + | 0.575960i | \(0.804629\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.29694 | 0.114189 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.22533 | 0.281798 | 0.140899 | − | 0.990024i | \(-0.455001\pi\) | ||||
0.140899 | + | 0.990024i | \(0.455001\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.05019 | −0.176452 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.97858 | −0.510784 | −0.255392 | − | 0.966838i | \(-0.582205\pi\) | ||||
−0.255392 | + | 0.966838i | \(0.582205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.16779 | 0.777602 | 0.388801 | − | 0.921322i | \(-0.372889\pi\) | ||||
0.388801 | + | 0.921322i | \(0.372889\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.57139 | −0.132335 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.6430 | −1.72625 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.117596 | 0.00976584 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.12494 | 0.0927837 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.15058 | 0.503875 | 0.251937 | − | 0.967744i | \(-0.418932\pi\) | ||||
0.251937 | + | 0.967744i | \(0.418932\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.14637 | −0.418805 | −0.209403 | − | 0.977830i | \(-0.567152\pi\) | ||||
−0.209403 | + | 0.977830i | \(0.567152\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.4783 | −1.25135 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.05754 | 0.647197 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.41033 | 0.351982 | 0.175991 | − | 0.984392i | \(-0.443687\pi\) | ||||
0.175991 | + | 0.984392i | \(0.443687\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.467866 | −0.0371042 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.97858 | 0.707611 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3215 | −0.965094 | −0.482547 | − | 0.875870i | \(-0.660288\pi\) | ||||
−0.482547 | + | 0.875870i | \(0.660288\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.14637 | −0.0892444 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.78202 | −0.447426 | −0.223713 | − | 0.974655i | \(-0.571818\pi\) | ||||
−0.223713 | + | 0.974655i | \(0.571818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.1323 | 1.93325 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.82487 | −0.138742 | −0.0693710 | − | 0.997591i | \(-0.522099\pi\) | ||||
−0.0693710 | + | 0.997591i | \(0.522099\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.87506 | −0.141741 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.564039 | −0.0423958 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.26396 | −0.617678 | −0.308839 | − | 0.951114i | \(-0.599940\pi\) | ||||
−0.308839 | + | 0.951114i | \(0.599940\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.7146 | −1.61403 | −0.807017 | − | 0.590528i | \(-0.798920\pi\) | ||||
−0.807017 | + | 0.590528i | \(0.798920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.428615 | 0.0316841 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.7434 | −0.936912 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.3717 | −1.27034 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.35341 | 0.243924 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.58546 | 0.331792 | 0.165896 | − | 0.986143i | \(-0.446948\pi\) | ||||
0.165896 | + | 0.986143i | \(0.446948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.1751 | −0.876385 | −0.438193 | − | 0.898881i | \(-0.644381\pi\) | ||||
−0.438193 | + | 0.898881i | \(0.644381\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.11760 | 0.151644 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.26817 | −0.304095 | −0.152047 | − | 0.988373i | \(-0.548587\pi\) | ||||
−0.152047 | + | 0.988373i | \(0.548587\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.86098 | 0.202810 | 0.101405 | − | 0.994845i | \(-0.467666\pi\) | ||||
0.101405 | + | 0.994845i | \(0.467666\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.68585 | 0.118910 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.192347 | −0.0135001 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.0863 | −1.19336 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.97858 | 0.485045 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2755 | −1.25814 | −0.629069 | − | 0.777349i | \(-0.716564\pi\) | ||||
−0.629069 | + | 0.777349i | \(0.716564\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.217980 | −0.0149358 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.7606 | 1.41586 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.1793 | −0.894672 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.12494 | −0.0760166 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.0894 | 2.15857 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0502 | 0.806941 | 0.403470 | − | 0.914993i | \(-0.367804\pi\) | ||||
0.403470 | + | 0.914993i | \(0.367804\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.45738 | −0.0971589 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.71462 | 0.578409 | 0.289205 | − | 0.957267i | \(-0.406609\pi\) | ||||
0.289205 | + | 0.957267i | \(0.406609\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5640 | 1.02850 | 0.514250 | − | 0.857640i | \(-0.328070\pi\) | ||||
0.514250 | + | 0.857640i | \(0.328070\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.87506 | 0.123370 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.4292 | −1.46939 | −0.734694 | − | 0.678399i | \(-0.762674\pi\) | ||||
−0.734694 | + | 0.678399i | \(0.762674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.1537 | −1.64085 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.0256337 | −0.00166509 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −30.7434 | −1.98862 | −0.994312 | − | 0.106505i | \(-0.966034\pi\) | ||||
−0.994312 | + | 0.106505i | \(0.966034\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.95715 | 0.319318 | 0.159659 | − | 0.987172i | \(-0.448960\pi\) | ||||
0.159659 | + | 0.987172i | \(0.448960\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.91431 | 0.251103 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.0073 | 1.15045 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.02563 | 0.0649969 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.5328 | −1.73785 | −0.868926 | − | 0.494942i | \(-0.835189\pi\) | ||||
−0.868926 | + | 0.494942i | \(0.835189\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.83221 | 0.492407 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.78202 | 0.111594 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.8866 | −0.741467 | −0.370733 | − | 0.928739i | \(-0.620894\pi\) | ||||
−0.370733 | + | 0.928739i | \(0.620894\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.8438 | 1.29517 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.149501 | −0.00925388 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.4219 | −1.19760 | −0.598802 | − | 0.800897i | \(-0.704357\pi\) | ||||
−0.598802 | + | 0.800897i | \(0.704357\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.48929 | −0.460063 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.98279 | −0.121345 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.4826 | 1.12690 | 0.563451 | − | 0.826150i | \(-0.309473\pi\) | ||||
0.563451 | + | 0.826150i | \(0.309473\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3429 | −0.992762 | −0.496381 | − | 0.868105i | \(-0.665338\pi\) | ||||
−0.496381 | + | 0.868105i | \(0.665338\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.46365 | −0.209630 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.63565 | −0.0986337 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7894 | 0.948691 | 0.474346 | − | 0.880339i | \(-0.342685\pi\) | ||||
0.474346 | + | 0.880339i | \(0.342685\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.2436 | −0.613269 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.42923 | 0.502846 | 0.251423 | − | 0.967877i | \(-0.419102\pi\) | ||||
0.251423 | + | 0.967877i | \(0.419102\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.81079 | −0.107640 | −0.0538201 | − | 0.998551i | \(-0.517140\pi\) | ||||
−0.0538201 | + | 0.998551i | \(0.517140\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.9473 | 1.64968 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.0042 | 0.588483 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.539481 | −0.0316249 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.2400 | 1.41612 | 0.708059 | − | 0.706154i | \(-0.249571\pi\) | ||||
0.708059 | + | 0.706154i | \(0.249571\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.02877 | −0.525675 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.92525 | 0.169740 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.4679 | −0.836698 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −33.9572 | −1.95726 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.11446 | −0.0640241 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.86098 | 0.392859 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.0031 | −1.25579 | −0.627893 | − | 0.778300i | \(-0.716082\pi\) | ||||
−0.627893 | + | 0.778300i | \(0.716082\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.43596 | −0.138577 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.4752 | 1.84150 | 0.920750 | − | 0.390153i | \(-0.127578\pi\) | ||||
0.920750 | + | 0.390153i | \(0.127578\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.24989 | −0.522834 | −0.261417 | − | 0.965226i | \(-0.584190\pi\) | ||||
−0.261417 | + | 0.965226i | \(0.584190\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.7434 | 1.50682 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.17513 | 0.346830 | 0.173415 | − | 0.984849i | \(-0.444520\pi\) | ||||
0.173415 | + | 0.984849i | \(0.444520\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.167788 | −0.00939434 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.921039 | 0.0514074 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.02142 | 0.167598 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.63252 | 0.0902785 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 41.1428 | 2.26827 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3643 | 0.569676 | 0.284838 | − | 0.958576i | \(-0.408060\pi\) | ||||
0.284838 | + | 0.958576i | \(0.408060\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.2008 | 0.887797 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.9859 | 1.47440 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6216 | 1.12333 | 0.561664 | − | 0.827365i | \(-0.310161\pi\) | ||||
0.561664 | + | 0.827365i | \(0.310161\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.59954 | −0.141188 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.4966 | −0.622578 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.62831 | −0.141915 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.803442 | −0.0432559 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.8108 | 1.49296 | 0.746481 | − | 0.665407i | \(-0.231742\pi\) | ||||
0.746481 | + | 0.665407i | \(0.231742\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.60688 | 0.300130 | 0.150065 | − | 0.988676i | \(-0.452052\pi\) | ||||
0.150065 | + | 0.988676i | \(0.452052\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.40360 | −0.288423 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.0105 | −1.59730 | −0.798648 | − | 0.601798i | \(-0.794451\pi\) | ||||
−0.798648 | + | 0.601798i | \(0.794451\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.48929 | −0.185192 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.91477 | −0.154266 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.97123 | 0.473483 | 0.236742 | − | 0.971573i | \(-0.423920\pi\) | ||||
0.236742 | + | 0.971573i | \(0.423920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0256337 | 0.00134542 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.0073 | −0.942548 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.4924 | 0.547700 | 0.273850 | − | 0.961772i | \(-0.411703\pi\) | ||||
0.273850 | + | 0.961772i | \(0.411703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.7220 | 1.13080 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2499 | 0.635982 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.3074 | −0.947922 | −0.473961 | − | 0.880546i | \(-0.657176\pi\) | ||||
−0.473961 | + | 0.880546i | \(0.657176\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.54683 | −0.0798778 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.309943 | 0.0159629 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.8438 | −1.27614 | −0.638069 | − | 0.769979i | \(-0.720267\pi\) | ||||
−0.638069 | + | 0.769979i | \(0.720267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.69679 | −0.138161 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.17200 | −0.162082 | −0.0810408 | − | 0.996711i | \(-0.525824\pi\) | ||||
−0.0810408 | + | 0.996711i | \(0.525824\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30.0147 | 1.52969 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −26.3931 | −1.34164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.3889 | −0.577440 | −0.288720 | − | 0.957414i | \(-0.593230\pi\) | ||||
−0.288720 | + | 0.957414i | \(0.593230\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.1751 | −0.615723 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.472077 | 0.0238131 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.410327 | −0.0206458 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.8855 | −0.947838 | −0.473919 | − | 0.880568i | \(-0.657161\pi\) | ||||
−0.473919 | + | 0.880568i | \(0.657161\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.0214 | −0.999822 | −0.499911 | − | 0.866077i | \(-0.666634\pi\) | ||||
−0.499911 | + | 0.866077i | \(0.666634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.2369 | 1.05788 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.6357 | 1.02539 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.1825 | 0.901272 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.9143 | 0.539678 | 0.269839 | − | 0.962905i | \(-0.413030\pi\) | ||||
0.269839 | + | 0.962905i | \(0.413030\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.875057 | −0.0431634 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.7679 | 0.726683 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.4177 | 0.805912 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.34185 | 0.0657106 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.4145 | 0.753049 | 0.376525 | − | 0.926407i | \(-0.377119\pi\) | ||||
0.376525 | + | 0.926407i | \(0.377119\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.96450 | −0.290692 | −0.145346 | − | 0.989381i | \(-0.546430\pi\) | ||||
−0.145346 | + | 0.989381i | \(0.546430\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 31.9781 | 1.55483 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.54262 | 0.123335 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.2222 | −0.543080 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.02142 | −0.145876 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.0189 | 1.39779 | 0.698896 | − | 0.715224i | \(-0.253675\pi\) | ||||
0.698896 | + | 0.715224i | \(0.253675\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.3822 | −0.883391 | −0.441695 | − | 0.897165i | \(-0.645623\pi\) | ||||
−0.441695 | + | 0.897165i | \(0.645623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0172120 | 0.000825254 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.61423 | −0.363407 | −0.181704 | − | 0.983353i | \(-0.558161\pi\) | ||||
−0.181704 | + | 0.983353i | \(0.558161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.8929 | −1.09014 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.50337 | −0.356496 | −0.178248 | − | 0.983986i | \(-0.557043\pi\) | ||||
−0.178248 | + | 0.983986i | \(0.557043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.7392 | −1.50458 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.900232 | 0.0425795 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.31836 | 0.439761 | 0.219880 | − | 0.975527i | \(-0.429433\pi\) | ||||
0.219880 | + | 0.975527i | \(0.429433\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.3790 | 1.14796 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.753250 | −0.0353908 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −55.4439 | −2.59925 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.4893 | 1.05200 | 0.526002 | − | 0.850483i | \(-0.323690\pi\) | ||||
0.526002 | + | 0.850483i | \(0.323690\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.54729 | −0.212249 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.34606 | 0.155841 | 0.0779207 | − | 0.996960i | \(-0.475172\pi\) | ||||
0.0779207 | + | 0.996960i | \(0.475172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0147 | 1.20901 | 0.604503 | − | 0.796603i | \(-0.293372\pi\) | ||||
0.604503 | + | 0.796603i | \(0.293372\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.17935 | 0.0546908 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.3429 | 0.524888 | 0.262444 | − | 0.964947i | \(-0.415472\pi\) | ||||
0.262444 | + | 0.964947i | \(0.415472\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −44.1396 | −2.03818 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.645520 | 0.0297440 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −29.6216 | −1.36200 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.52119 | 0.435945 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.5040 | 0.525630 | 0.262815 | − | 0.964846i | \(-0.415349\pi\) | ||||
0.262815 | + | 0.964846i | \(0.415349\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.5872 | −1.53144 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.31415 | 0.0597961 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.63565 | −0.392125 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.3832 | −1.01428 | −0.507141 | − | 0.861863i | \(-0.669298\pi\) | ||||
−0.507141 | + | 0.861863i | \(0.669298\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.80344 | −0.0815545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0319 | 0.994286 | 0.497143 | − | 0.867669i | \(-0.334382\pi\) | ||||
0.497143 | + | 0.867669i | \(0.334382\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.260826 | 0.0117470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.3288 | 1.04855 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.70727 | 0.256006 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.21063 | 0.0541954 | 0.0270977 | − | 0.999633i | \(-0.491373\pi\) | ||||
0.0270977 | + | 0.999633i | \(0.491373\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.846288 | −0.0378094 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.4924 | 1.35959 | 0.679795 | − | 0.733402i | \(-0.262069\pi\) | ||||
0.679795 | + | 0.733402i | \(0.262069\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.8396 | −0.793850 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.67850 | 0.163368 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.846288 | −0.0375111 | −0.0187555 | − | 0.999824i | \(-0.505970\pi\) | ||||
−0.0187555 | + | 0.999824i | \(0.505970\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.4538 | 1.30296 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38.9933 | −1.71825 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.8898 | 1.57843 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.267097 | −0.0117243 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.6044 | −1.86653 | −0.933266 | − | 0.359187i | \(-0.883054\pi\) | ||||
−0.933266 | + | 0.359187i | \(0.883054\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7245 | 0.512676 | 0.256338 | − | 0.966587i | \(-0.417484\pi\) | ||||
0.256338 | + | 0.966587i | \(0.417484\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.274444 | −0.0119777 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.8715 | 0.778493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5107 | −0.761335 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.4783 | 0.498118 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −45.0336 | −1.95062 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.7434 | 0.637412 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.20956 | −0.0521963 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.6932 | −1.10668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.1323 | −0.779568 | −0.389784 | − | 0.920906i | \(-0.627450\pi\) | ||||
−0.389784 | + | 0.920906i | \(0.627450\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.17827 | −0.136393 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.1323 | 1.11938 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.4036 | −1.85580 | −0.927902 | − | 0.372824i | \(-0.878389\pi\) | ||||
−0.927902 | + | 0.372824i | \(0.878389\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.72242 | −0.372264 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.671153 | 0.0285403 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.86519 | −0.0791730 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.19656 | 0.389671 | 0.194835 | − | 0.980836i | \(-0.437583\pi\) | ||||
0.194835 | + | 0.980836i | \(0.437583\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 54.7178 | 2.31431 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.54262 | −0.107349 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.3576 | −1.74302 | −0.871508 | − | 0.490382i | \(-0.836857\pi\) | ||||
−0.871508 | + | 0.490382i | \(0.836857\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.6117 | −1.75062 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −33.7528 | −1.41748 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.22219 | 0.0512369 | 0.0256185 | − | 0.999672i | \(-0.491844\pi\) | ||||
0.0256185 | + | 0.999672i | \(0.491844\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.32150 | 0.180849 | 0.0904246 | − | 0.995903i | \(-0.471178\pi\) | ||||
0.0904246 | + | 0.995903i | \(0.471178\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.671153 | 0.0280378 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.14637 | −0.0478067 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.03863 | 0.0848695 | 0.0424347 | − | 0.999099i | \(-0.486489\pi\) | ||||
0.0424347 | + | 0.999099i | \(0.486489\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.78202 | −0.0740582 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.8536 | −1.11408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.6858 | 0.442563 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −43.0937 | −1.78170 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.66021 | 0.357445 | 0.178723 | − | 0.983900i | \(-0.442804\pi\) | ||||
0.178723 | + | 0.983900i | \(0.442804\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.624713 | −0.0256973 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.9718 | 0.450560 | 0.225280 | − | 0.974294i | \(-0.427670\pi\) | ||||
0.225280 | + | 0.974294i | \(0.427670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −46.6577 | −1.91278 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.418749 | 0.0171383 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −45.4219 | −1.85589 | −0.927944 | − | 0.372720i | \(-0.878425\pi\) | ||||
−0.927944 | + | 0.372720i | \(0.878425\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.8757 | 1.21865 | 0.609327 | − | 0.792919i | \(-0.291440\pi\) | ||||
0.609327 | + | 0.792919i | \(0.291440\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −34.3074 | −1.39711 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.410327 | 0.0166822 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.7764 | 1.41153 | 0.705765 | − | 0.708446i | \(-0.250604\pi\) | ||||
0.705765 | + | 0.708446i | \(0.250604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0281529 | −0.00114081 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −66.2965 | −2.68207 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.7606 | 0.596175 | 0.298087 | − | 0.954539i | \(-0.403651\pi\) | ||||
0.298087 | + | 0.954539i | \(0.403651\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.50085 | −0.100844 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.0361 | −1.04817 | −0.524087 | − | 0.851665i | \(-0.675593\pi\) | ||||
−0.524087 | + | 0.851665i | \(0.675593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.7497 | 1.63787 | 0.818933 | − | 0.573888i | \(-0.194566\pi\) | ||||
0.818933 | + | 0.573888i | \(0.194566\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.05019 | 0.0822714 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 51.9143 | 2.07990 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.2070 | −1.08828 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.2646 | −1.12698 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.8213 | −1.26678 | −0.633392 | − | 0.773831i | \(-0.718338\pi\) | ||||
−0.633392 | + | 0.773831i | \(0.718338\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.67491 | −0.106318 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −43.1684 | −1.71309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 47.4611 | 1.88048 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.43596 | 0.175484 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.16465 | −0.322484 | −0.161242 | − | 0.986915i | \(-0.551550\pi\) | ||||
−0.161242 | + | 0.986915i | \(0.551550\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.59702 | −0.260161 | −0.130081 | − | 0.991503i | \(-0.541524\pi\) | ||||
−0.130081 | + | 0.991503i | \(0.541524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.03863 | 0.119646 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.60015 | −0.102223 | −0.0511113 | − | 0.998693i | \(-0.516276\pi\) | ||||
−0.0511113 | + | 0.998693i | \(0.516276\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.8824 | 0.505679 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.92900 | −0.0756035 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.39312 | −0.0936498 | −0.0468249 | − | 0.998903i | \(-0.514910\pi\) | ||||
−0.0468249 | + | 0.998903i | \(0.514910\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.55669 | 0.295264 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.8929 | 0.893137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.6833 | −0.883617 | −0.441808 | − | 0.897109i | \(-0.645663\pi\) | ||||
−0.441808 | + | 0.897109i | \(0.645663\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.5500 | 1.57721 | 0.788605 | − | 0.614900i | \(-0.210803\pi\) | ||||
0.788605 | + | 0.614900i | \(0.210803\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.69679 | 0.182408 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.117596 | −0.00455334 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.76373 | 0.0681898 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.78937 | −0.377914 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1004 | −0.774813 | −0.387406 | − | 0.921909i | \(-0.626629\pi\) | ||||
−0.387406 | + | 0.921909i | \(0.626629\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.428156 | −0.0164797 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.3717 | −0.744515 | −0.372257 | − | 0.928130i | \(-0.621416\pi\) | ||||
−0.372257 | + | 0.928130i | \(0.621416\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.1249 | 0.542066 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.27552 | 0.0488780 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.1151 | 0.616626 | 0.308313 | − | 0.951285i | \(-0.400236\pi\) | ||||
0.308313 | + | 0.951285i | \(0.400236\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0073 | −0.535193 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.27804 | 0.0869126 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.7392 | −0.752003 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.4145 | −0.586397 | −0.293198 | − | 0.956052i | \(-0.594720\pi\) | ||||
−0.293198 | + | 0.956052i | \(0.594720\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −38.1579 | −1.44950 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.4794 | 0.814761 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.8971 | −1.43545 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.28287 | −0.124169 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.8297 | 1.35327 | 0.676634 | − | 0.736319i | \(-0.263438\pi\) | ||||
0.676634 | + | 0.736319i | \(0.263438\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.68164 | −0.138658 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.1793 | 1.09740 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.82800 | 0.331543 | 0.165771 | − | 0.986164i | \(-0.446989\pi\) | ||||
0.165771 | + | 0.986164i | \(0.446989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.521652 | 0.0195635 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.05754 | −0.301757 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −48.3650 | −1.80875 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.49977 | −0.168047 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.2671 | 0.606660 | 0.303330 | − | 0.952886i | \(-0.401901\pi\) | ||||
0.303330 | + | 0.952886i | \(0.401901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 63.7795 | 2.37527 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.725556 | 0.0269837 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.0245584 | 0.000912077 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.7606 | −1.51173 | −0.755863 | − | 0.654729i | \(-0.772783\pi\) | ||||
−0.755863 | + | 0.654729i | \(0.772783\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.8500 | −0.957409 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.0466 | 1.70309 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.6827 | 0.726998 | 0.363499 | − | 0.931595i | \(-0.381582\pi\) | ||||
0.363499 | + | 0.931595i | \(0.381582\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.63565 | 0.0972176 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.5040 | −1.41831 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.7549 | 1.57277 | 0.786383 | − | 0.617739i | \(-0.211951\pi\) | ||||
0.786383 | + | 0.617739i | \(0.211951\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.6848 | 0.612105 | 0.306052 | − | 0.952015i | \(-0.400992\pi\) | ||||
0.306052 | + | 0.952015i | \(0.400992\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.4103 | 0.527954 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.8719 | −0.763664 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.1151 | −0.881146 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.8610 | 1.12613 | 0.563067 | − | 0.826412i | \(-0.309621\pi\) | ||||
0.563067 | + | 0.826412i | \(0.309621\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.02984 | −0.146856 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0575 | −0.438819 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9828 | −0.580904 | −0.290452 | − | 0.956890i | \(-0.593806\pi\) | ||||
−0.290452 | + | 0.956890i | \(0.593806\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.14637 | 0.0416104 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.9975 | 0.833658 | 0.416829 | − | 0.908985i | \(-0.363141\pi\) | ||||
0.416829 | + | 0.908985i | \(0.363141\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.7434 | −1.54741 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −36.2646 | −1.31115 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.7967 | −0.859249 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.9462 | 1.07989 | 0.539944 | − | 0.841701i | \(-0.318445\pi\) | ||||
0.539944 | + | 0.841701i | \(0.318445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.73979 | −0.0626570 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.50758 | 0.198094 | 0.0990469 | − | 0.995083i | \(-0.468421\pi\) | ||||
0.0990469 | + | 0.995083i | \(0.468421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.68271 | 0.0604447 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.05081 | 0.109447 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.97858 | 0.178147 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.0439210 | −0.00156961 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.3331 | 0.368803 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.40719 | 0.299684 | 0.149842 | − | 0.988710i | \(-0.452123\pi\) | ||||
0.149842 | + | 0.988710i | \(0.452123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.84269 | −0.101203 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 68.0624 | 2.42002 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0832 | 0.642152 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.09617 | −0.0388773 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.2186 | 1.17666 | 0.588332 | − | 0.808620i | \(-0.299785\pi\) | ||||
0.588332 | + | 0.808620i | \(0.299785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.7904 | −1.97372 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.3503 | 1.42571 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.6932 | 0.906693 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.0361 | 0.741426 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.70521 | 0.0952279 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.8971 | 0.453438 | 0.226719 | − | 0.973960i | \(-0.427200\pi\) | ||||
0.226719 | + | 0.973960i | \(0.427200\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.66863 | 0.0937084 | 0.0468542 | − | 0.998902i | \(-0.485080\pi\) | ||||
0.0468542 | + | 0.998902i | \(0.485080\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.39204 | −0.0838925 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.8683 | −1.01121 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 70.4863 | 2.46299 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.6535 | −1.17451 | −0.587257 | − | 0.809400i | \(-0.699792\pi\) | ||||
−0.587257 | + | 0.809400i | \(0.699792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.8396 | −0.621848 | −0.310924 | − | 0.950435i | \(-0.600638\pi\) | ||||
−0.310924 | + | 0.950435i | \(0.600638\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.239403 | −0.00833495 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.75325 | −0.130513 | −0.0652567 | − | 0.997869i | \(-0.520787\pi\) | ||||
−0.0652567 | + | 0.997869i | \(0.520787\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.77781 | 0.0964773 | 0.0482386 | − | 0.998836i | \(-0.484639\pi\) | ||||
0.0482386 | + | 0.998836i | \(0.484639\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.31102 | 0.0801683 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 39.9399 | 1.38384 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.5468 | −0.468807 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.00941 | −0.104020 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 56.2228 | 1.94103 | 0.970513 | − | 0.241047i | \(-0.0774908\pi\) | ||||
0.970513 | + | 0.241047i | \(0.0774908\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9975 | −0.999913 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.23375 | 0.0424926 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 58.8830 | 2.02564 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.671153 | −0.0230611 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.265037 | −0.00909605 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.7434 | 0.436838 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3246 | −0.353509 | −0.176754 | − | 0.984255i | \(-0.556560\pi\) | ||||
−0.176754 | + | 0.984255i | \(0.556560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.1789 | 1.81656 | 0.908278 | − | 0.418367i | \(-0.137397\pi\) | ||||
0.908278 | + | 0.418367i | \(0.137397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.2530 | 0.349829 | 0.174914 | − | 0.984584i | \(-0.444035\pi\) | ||||
0.174914 | + | 0.984584i | \(0.444035\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.09052 | 0.139404 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.7679 | 0.366545 | 0.183273 | − | 0.983062i | \(-0.441331\pi\) | ||||
0.183273 | + | 0.983062i | \(0.441331\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.27552 | −0.145372 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.46427 | 0.0497293 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.585462 | 0.0198604 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 71.1256 | 2.41000 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.9786 | 0.371569 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40.4998 | 1.36914 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.7276 | 0.767457 | 0.383729 | − | 0.923446i | \(-0.374640\pi\) | ||||
0.383729 | + | 0.923446i | \(0.374640\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.54790 | 0.119668 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.44644 | −0.284568 | −0.142284 | − | 0.989826i | \(-0.545445\pi\) | ||||
−0.142284 | + | 0.989826i | \(0.545445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.0393 | −1.51569 | −0.757846 | − | 0.652434i | \(-0.773748\pi\) | ||||
−0.757846 | + | 0.652434i | \(0.773748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.32150 | −0.0444217 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.8463 | 0.699950 | 0.349975 | − | 0.936759i | \(-0.386190\pi\) | ||||
0.349975 | + | 0.936759i | \(0.386190\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 70.6086 | 2.36814 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.4433 | −0.986388 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.3618 | −0.647194 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.11760 | −0.0707045 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.172615 | 0.00575705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.6111 | −0.553396 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.97016 | −0.165396 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −50.8757 | −1.69116 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.4109 | −0.810552 | −0.405276 | − | 0.914194i | \(-0.632825\pi\) | ||||
−0.405276 | + | 0.914194i | \(0.632825\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.6796 | 0.752234 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.2744 | −0.804248 | −0.402124 | − | 0.915585i | \(-0.631728\pi\) | ||||
−0.402124 | + | 0.915585i | \(0.631728\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.4250 | −0.775255 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.00421 | 0.0331982 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.3601 | −0.408168 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.8568 | 1.05086 | 0.525429 | − | 0.850837i | \(-0.323905\pi\) | ||||
0.525429 | + | 0.850837i | \(0.323905\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.22050 | −0.106119 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.19656 | −0.302708 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.66129 | −0.0875026 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 49.5725 | 1.62817 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.2087 | −1.64730 | −0.823648 | − | 0.567102i | \(-0.808064\pi\) | ||||
−0.823648 | + | 0.567102i | \(0.808064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.75325 | 0.155614 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40.7005 | −1.33105 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.65600 | −0.152105 | −0.0760525 | − | 0.997104i | \(-0.524232\pi\) | ||||
−0.0760525 | + | 0.997104i | \(0.524232\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.35386 | −0.0441817 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.3973 | −0.762731 | −0.381366 | − | 0.924424i | \(-0.624546\pi\) | ||||
−0.381366 | + | 0.924424i | \(0.624546\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.0863 | 0.556407 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.85677 | 0.255581 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.4267 | 1.86612 | 0.933059 | − | 0.359724i | \(-0.117129\pi\) | ||||
0.933059 | + | 0.359724i | \(0.117129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.4611 | −1.54065 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.903827 | 0.0293086 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.9933 | −1.29551 | −0.647755 | − | 0.761849i | \(-0.724292\pi\) | ||||
−0.647755 | + | 0.761849i | \(0.724292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.7434 | 0.347648 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0245584 | −0.000793861 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.9112 | 0.739840 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.1726 | −0.618471 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.7434 | −0.603997 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.5254 | −0.918265 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.88240 | 0.124850 | 0.0624248 | − | 0.998050i | \(-0.480117\pi\) | ||||
0.0624248 | + | 0.998050i | \(0.480117\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.37483 | 0.0441203 | 0.0220602 | − | 0.999757i | \(-0.492977\pi\) | ||||
0.0220602 | + | 0.999757i | \(0.492977\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.1329 | −1.12631 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.442232 | 0.0141628 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.2541 | 0.647986 | 0.323993 | − | 0.946059i | \(-0.394975\pi\) | ||||
0.323993 | + | 0.946059i | \(0.394975\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.2860 | 1.44735 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.2222 | −1.06070 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.7606 | −0.407000 | −0.203500 | − | 0.979075i | \(-0.565232\pi\) | ||||
−0.203500 | + | 0.979075i | \(0.565232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0000 | −0.318626 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.02188 | 0.191679 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.7606 | −0.660149 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.9529 | 0.602060 | 0.301030 | − | 0.953615i | \(-0.402670\pi\) | ||||
0.301030 | + | 0.953615i | \(0.402670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.51698 | 0.0481400 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.70306 | 0.212501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.0649 | −0.382099 | −0.191049 | − | 0.981580i | \(-0.561189\pi\) | ||||
−0.191049 | + | 0.981580i | \(0.561189\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.75952 | 0.150585 |
(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 | 5776.2.a.bk.1.2 | 3 | ||
4.3 | odd | 2 | 2888.2.a.r.1.2 | 3 | |||
19.7 | even | 3 | 304.2.i.f.49.2 | 6 | |||
19.11 | even | 3 | 304.2.i.f.273.2 | 6 | |||
19.18 | odd | 2 | 5776.2.a.bq.1.2 | 3 | |||
57.11 | odd | 6 | 2736.2.s.y.577.3 | 6 | |||
57.26 | odd | 6 | 2736.2.s.y.1873.3 | 6 | |||
76.7 | odd | 6 | 152.2.i.c.49.2 | ✓ | 6 | ||
76.11 | odd | 6 | 152.2.i.c.121.2 | yes | 6 | ||
76.75 | even | 2 | 2888.2.a.n.1.2 | 3 | |||
152.11 | odd | 6 | 1216.2.i.n.577.2 | 6 | |||
152.45 | even | 6 | 1216.2.i.m.961.2 | 6 | |||
152.83 | odd | 6 | 1216.2.i.n.961.2 | 6 | |||
152.125 | even | 6 | 1216.2.i.m.577.2 | 6 | |||
228.11 | even | 6 | 1368.2.s.k.577.3 | 6 | |||
228.83 | even | 6 | 1368.2.s.k.505.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.i.c.49.2 | ✓ | 6 | 76.7 | odd | 6 | ||
152.2.i.c.121.2 | yes | 6 | 76.11 | odd | 6 | ||
304.2.i.f.49.2 | 6 | 19.7 | even | 3 | |||
304.2.i.f.273.2 | 6 | 19.11 | even | 3 | |||
1216.2.i.m.577.2 | 6 | 152.125 | even | 6 | |||
1216.2.i.m.961.2 | 6 | 152.45 | even | 6 | |||
1216.2.i.n.577.2 | 6 | 152.11 | odd | 6 | |||
1216.2.i.n.961.2 | 6 | 152.83 | odd | 6 | |||
1368.2.s.k.505.3 | 6 | 228.83 | even | 6 | |||
1368.2.s.k.577.3 | 6 | 228.11 | even | 6 | |||
2736.2.s.y.577.3 | 6 | 57.11 | odd | 6 | |||
2736.2.s.y.1873.3 | 6 | 57.26 | odd | 6 | |||
2888.2.a.n.1.2 | 3 | 76.75 | even | 2 | |||
2888.2.a.r.1.2 | 3 | 4.3 | odd | 2 | |||
5776.2.a.bk.1.2 | 3 | 1.1 | even | 1 | trivial | ||
5776.2.a.bq.1.2 | 3 | 19.18 | odd | 2 |