Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1932,2,Mod(1,1932)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1932.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1932.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: | \(15.4270976705\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1101.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.11903\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1932.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.11903 | −1.39487 | −0.697436 | − | 0.716647i | \(-0.745676\pi\) | ||||
−0.697436 | + | 0.716647i | \(0.745676\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.72833 | −1.03405 | −0.517026 | − | 0.855970i | \(-0.672961\pi\) | ||||
−0.517026 | + | 0.855970i | \(0.672961\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.11903 | −0.805329 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.39070 | 0.337294 | 0.168647 | − | 0.985677i | \(-0.446060\pi\) | ||||
0.168647 | + | 0.985677i | \(0.446060\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | 0.688247 | 0.344124 | − | 0.938924i | \(-0.388176\pi\) | ||||
0.344124 | + | 0.938924i | \(0.388176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.72833 | 0.945665 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.06596 | 1.49781 | 0.748905 | − | 0.662677i | \(-0.230580\pi\) | ||||
0.748905 | + | 0.662677i | \(0.230580\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.62875 | −1.01095 | −0.505477 | − | 0.862840i | \(-0.668683\pi\) | ||||
−0.505477 | + | 0.862840i | \(0.668683\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.11903 | 0.527212 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.82790 | 0.300505 | 0.150253 | − | 0.988648i | \(-0.451991\pi\) | ||||
0.150253 | + | 0.988648i | \(0.451991\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.72833 | −0.597010 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.01945 | 1.25243 | 0.626214 | − | 0.779651i | \(-0.284604\pi\) | ||||
0.626214 | + | 0.779651i | \(0.284604\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.50973 | 1.29772 | 0.648861 | − | 0.760907i | \(-0.275246\pi\) | ||||
0.648861 | + | 0.760907i | \(0.275246\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.11903 | −0.464957 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.39070 | 0.640449 | 0.320225 | − | 0.947342i | \(-0.396242\pi\) | ||||
0.320225 | + | 0.947342i | \(0.396242\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.39070 | 0.194737 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.72833 | 0.374765 | 0.187382 | − | 0.982287i | \(-0.440000\pi\) | ||||
0.187382 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.11903 | −0.420569 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.74778 | −0.748297 | −0.374149 | − | 0.927369i | \(-0.622065\pi\) | ||||
−0.374149 | + | 0.927369i | \(0.622065\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.90043 | 0.371361 | 0.185681 | − | 0.982610i | \(-0.440551\pi\) | ||||
0.185681 | + | 0.982610i | \(0.440551\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.6288 | 1.44237 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.337628 | −0.0412478 | −0.0206239 | − | 0.999787i | \(-0.506565\pi\) | ||||
−0.0206239 | + | 0.999787i | \(0.506565\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.29112 | 0.865297 | 0.432649 | − | 0.901563i | \(-0.357579\pi\) | ||||
0.432649 | + | 0.901563i | \(0.357579\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.60930 | −0.305396 | −0.152698 | − | 0.988273i | \(-0.548796\pi\) | ||||
−0.152698 | + | 0.988273i | \(0.548796\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.72833 | 0.545980 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8474 | −1.22042 | −0.610211 | − | 0.792239i | \(-0.708915\pi\) | ||||
−0.610211 | + | 0.792239i | \(0.708915\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0660 | 1.32441 | 0.662205 | − | 0.749322i | \(-0.269621\pi\) | ||||
0.662205 | + | 0.749322i | \(0.269621\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.33763 | −0.470482 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.06596 | 0.864761 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.9664 | 1.48043 | 0.740217 | − | 0.672368i | \(-0.234723\pi\) | ||||
0.740217 | + | 0.672368i | \(0.234723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.72833 | 0.390835 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.62875 | −0.583674 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.35708 | −0.960016 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.39070 | −0.344273 | −0.172137 | − | 0.985073i | \(-0.555067\pi\) | ||||
−0.172137 | + | 0.985073i | \(0.555067\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1850 | −1.01344 | −0.506722 | − | 0.862110i | \(-0.669143\pi\) | ||||
−0.506722 | + | 0.862110i | \(0.669143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.06596 | 0.696229 | 0.348115 | − | 0.937452i | \(-0.386822\pi\) | ||||
0.348115 | + | 0.937452i | \(0.386822\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.11903 | 0.304386 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.72833 | 0.553778 | 0.276889 | − | 0.960902i | \(-0.410697\pi\) | ||||
0.276889 | + | 0.960902i | \(0.410697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.5951 | 1.49374 | 0.746871 | − | 0.664968i | \(-0.231555\pi\) | ||||
0.746871 | + | 0.664968i | \(0.231555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.82790 | 0.173497 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3376 | 0.972482 | 0.486241 | − | 0.873825i | \(-0.338368\pi\) | ||||
0.486241 | + | 0.873825i | \(0.338368\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.11903 | −0.290851 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.72833 | −0.344684 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.39070 | −0.127485 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.01945 | 0.723090 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.847354 | 0.0757897 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.3571 | 1.45146 | 0.725728 | − | 0.687982i | \(-0.241503\pi\) | ||||
0.725728 | + | 0.687982i | \(0.241503\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.50973 | 0.749240 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.45665 | −0.389380 | −0.194690 | − | 0.980865i | \(-0.562370\pi\) | ||||
−0.194690 | + | 0.980865i | \(0.562370\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | −0.260133 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.11903 | −0.268443 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.2575 | 1.73072 | 0.865358 | − | 0.501155i | \(-0.167091\pi\) | ||||
0.865358 | + | 0.501155i | \(0.167091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.77483 | −0.574634 | −0.287317 | − | 0.957836i | \(-0.592763\pi\) | ||||
−0.287317 | + | 0.957836i | \(0.592763\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.39070 | 0.369764 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.72833 | −0.311778 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −25.1579 | −2.08925 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.04650 | −0.167656 | −0.0838281 | − | 0.996480i | \(-0.526715\pi\) | ||||
−0.0838281 | + | 0.996480i | \(0.526715\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.17210 | −0.0953840 | −0.0476920 | − | 0.998862i | \(-0.515187\pi\) | ||||
−0.0476920 | + | 0.998862i | \(0.515187\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.39070 | 0.112431 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.5562 | 1.41015 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.0854 | −1.44337 | −0.721686 | − | 0.692220i | \(-0.756633\pi\) | ||||
−0.721686 | + | 0.692220i | \(0.756633\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.72833 | 0.216370 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2911 | −0.962715 | −0.481358 | − | 0.876524i | \(-0.659856\pi\) | ||||
−0.481358 | + | 0.876524i | \(0.659856\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.11903 | −0.242816 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.23805 | 0.0958034 | 0.0479017 | − | 0.998852i | \(-0.484747\pi\) | ||||
0.0479017 | + | 0.998852i | \(0.484747\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.900425 | 0.0692635 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | 0.229416 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.8668 | −0.902217 | −0.451108 | − | 0.892469i | \(-0.648971\pi\) | ||||
−0.451108 | + | 0.892469i | \(0.648971\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.72833 | −0.357428 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.74778 | −0.432030 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.68182 | −0.648910 | −0.324455 | − | 0.945901i | \(-0.605181\pi\) | ||||
−0.324455 | + | 0.945901i | \(0.605181\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.8668 | −1.47669 | −0.738344 | − | 0.674424i | \(-0.764392\pi\) | ||||
−0.738344 | + | 0.674424i | \(0.764392\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.90043 | 0.214406 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.70128 | −0.419166 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.39070 | 0.101698 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0854 | −1.16390 | −0.581950 | − | 0.813225i | \(-0.697710\pi\) | ||||
−0.581950 | + | 0.813225i | \(0.697710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.30401 | 0.669717 | 0.334859 | − | 0.942268i | \(-0.391311\pi\) | ||||
0.334859 | + | 0.942268i | \(0.391311\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.6288 | 0.832752 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.74778 | −0.338265 | −0.169133 | − | 0.985593i | \(-0.554097\pi\) | ||||
−0.169133 | + | 0.985593i | \(0.554097\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.31058 | 0.518233 | 0.259117 | − | 0.965846i | \(-0.416569\pi\) | ||||
0.259117 | + | 0.965846i | \(0.416569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.337628 | −0.0238145 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.06596 | −0.566119 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.0129 | −1.74698 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.00000 | 0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.800850 | −0.0551328 | −0.0275664 | − | 0.999620i | \(-0.508776\pi\) | ||||
−0.0275664 | + | 0.999620i | \(0.508776\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.29112 | 0.499580 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −26.5421 | −1.81015 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.62875 | 0.382105 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.60930 | −0.176320 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.18498 | −0.348780 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.2704 | 1.49134 | 0.745668 | − | 0.666318i | \(-0.232131\pi\) | ||||
0.745668 | + | 0.666318i | \(0.232131\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.72833 | 0.315222 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.5562 | 1.29799 | 0.648996 | − | 0.760792i | \(-0.275189\pi\) | ||||
0.648996 | + | 0.760792i | \(0.275189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.83447 | −0.187307 | −0.0936535 | − | 0.995605i | \(-0.529855\pi\) | ||||
−0.0936535 | + | 0.995605i | \(0.529855\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.77483 | 0.181785 | 0.0908926 | − | 0.995861i | \(-0.471028\pi\) | ||||
0.0908926 | + | 0.995861i | \(0.471028\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.6947 | −0.893344 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.8474 | −0.704611 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.536778 | −0.0347213 | −0.0173606 | − | 0.999849i | \(-0.505526\pi\) | ||||
−0.0173606 | + | 0.999849i | \(0.505526\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.9328 | 0.961904 | 0.480952 | − | 0.876747i | \(-0.340291\pi\) | ||||
0.480952 | + | 0.876747i | \(0.340291\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.11903 | −0.199267 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1850 | −0.711683 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0660 | 0.764649 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.9328 | −1.38438 | −0.692192 | − | 0.721714i | \(-0.743355\pi\) | ||||
−0.692192 | + | 0.721714i | \(0.743355\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00000 | 0.0628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.33763 | −0.271633 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.0854 | −0.753867 | −0.376934 | − | 0.926240i | \(-0.623021\pi\) | ||||
−0.376934 | + | 0.926240i | \(0.623021\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.82790 | −0.113580 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.06596 | 0.499270 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.01945 | 0.124525 | 0.0622624 | − | 0.998060i | \(-0.480168\pi\) | ||||
0.0622624 | + | 0.998060i | \(0.480168\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.50973 | −0.522748 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.9664 | 0.854729 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.5292 | −1.19071 | −0.595357 | − | 0.803461i | \(-0.702990\pi\) | ||||
−0.595357 | + | 0.803461i | \(0.702990\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.5615 | 0.945295 | 0.472647 | − | 0.881252i | \(-0.343298\pi\) | ||||
0.472647 | + | 0.881252i | \(0.343298\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.72833 | 0.225649 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.72833 | 0.285129 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.35708 | 0.502128 | 0.251064 | − | 0.967970i | \(-0.419219\pi\) | ||||
0.251064 | + | 0.967970i | \(0.419219\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.62875 | −0.336985 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.0195 | 1.13461 | 0.567303 | − | 0.823509i | \(-0.307987\pi\) | ||||
0.567303 | + | 0.823509i | \(0.307987\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.35708 | −0.556221 | −0.278110 | − | 0.960549i | \(-0.589708\pi\) | ||||
−0.278110 | + | 0.960549i | \(0.589708\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.35708 | −0.554266 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.01945 | −0.473373 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0660 | −0.886233 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.39070 | −0.198766 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.4761 | 0.728862 | 0.364431 | − | 0.931230i | \(-0.381264\pi\) | ||||
0.364431 | + | 0.931230i | \(0.381264\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.9275 | 1.04378 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.72833 | −0.215615 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.50973 | −0.490492 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.1850 | −0.585112 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.04650 | −0.518001 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.7607 | 1.58438 | 0.792192 | − | 0.610271i | \(-0.208940\pi\) | ||||
0.792192 | + | 0.610271i | \(0.208940\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.06596 | 0.401968 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.5757 | 1.56367 | 0.781837 | − | 0.623483i | \(-0.214283\pi\) | ||||
0.781837 | + | 0.623483i | \(0.214283\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.75435 | 0.438302 | 0.219151 | − | 0.975691i | \(-0.429671\pi\) | ||||
0.219151 | + | 0.975691i | \(0.429671\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.11903 | 0.175737 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.3960 | 1.20172 | 0.600859 | − | 0.799355i | \(-0.294825\pi\) | ||||
0.600859 | + | 0.799355i | \(0.294825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.06596 | 0.451607 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.72833 | 0.319724 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.17210 | 0.232142 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.6288 | −0.977867 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.5951 | 0.862413 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.39070 | −0.242067 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0182 | 1.43009 | 0.715044 | − | 0.699080i | \(-0.246407\pi\) | ||||
0.715044 | + | 0.699080i | \(0.246407\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.82790 | 0.100168 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.05307 | 0.0575354 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.09197 | −0.277378 | −0.138689 | − | 0.990336i | \(-0.544289\pi\) | ||||
−0.138689 | + | 0.990336i | \(0.544289\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.3376 | 0.561463 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.62875 | −0.304814 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.11903 | −0.167923 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.30401 | −0.338417 | −0.169208 | − | 0.985580i | \(-0.554121\pi\) | ||||
−0.169208 | + | 0.985580i | \(0.554121\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.9199 | −1.76216 | −0.881080 | − | 0.472967i | \(-0.843183\pi\) | ||||
−0.881080 | + | 0.472967i | \(0.843183\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.72833 | −0.199003 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.5226 | −0.613287 | −0.306643 | − | 0.951824i | \(-0.599206\pi\) | ||||
−0.306643 | + | 0.951824i | \(0.599206\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.7412 | −1.20698 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.39070 | −0.0736036 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.05179 | 0.372179 | 0.186090 | − | 0.982533i | \(-0.440419\pi\) | ||||
0.186090 | + | 0.982533i | \(0.440419\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.13848 | 0.425987 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1385 | 0.790222 | 0.395111 | − | 0.918633i | \(-0.370706\pi\) | ||||
0.395111 | + | 0.918633i | \(0.370706\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.01945 | 0.417476 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.72833 | −0.141648 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.17210 | −0.319579 | −0.159790 | − | 0.987151i | \(-0.551082\pi\) | ||||
−0.159790 | + | 0.987151i | \(0.551082\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.847354 | 0.0437572 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.0725 | −1.54881 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3442 | 0.531346 | 0.265673 | − | 0.964063i | \(-0.414406\pi\) | ||||
0.265673 | + | 0.964063i | \(0.414406\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.3571 | 0.837999 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.1979 | 1.23645 | 0.618227 | − | 0.786000i | \(-0.287851\pi\) | ||||
0.618227 | + | 0.786000i | \(0.287851\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.11903 | 0.158960 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.50973 | 0.432574 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.1243 | −1.78087 | −0.890437 | − | 0.455107i | \(-0.849601\pi\) | ||||
−0.890437 | + | 0.455107i | \(0.849601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.39070 | 0.0703307 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.45665 | −0.224808 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.8332 | 1.70233 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.6753 | −1.13804 | −0.569019 | − | 0.822324i | \(-0.692677\pi\) | ||||
−0.569019 | + | 0.822324i | \(0.692677\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.00000 | −0.150188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.6275 | 1.62934 | 0.814669 | − | 0.579926i | \(-0.196919\pi\) | ||||
0.814669 | + | 0.579926i | \(0.196919\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.9858 | 1.04538 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.11903 | −0.154986 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.82790 | 0.0906057 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.6288 | −1.86062 | −0.930311 | − | 0.366772i | \(-0.880463\pi\) | ||||
−0.930311 | + | 0.366772i | \(0.880463\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.2575 | 0.999229 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.74778 | 0.282830 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.6340 | −1.84738 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.77483 | −0.331765 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.5951 | −1.25040 | −0.625202 | − | 0.780463i | \(-0.714983\pi\) | ||||
−0.625202 | + | 0.780463i | \(0.714983\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.3363 | −1.86840 | −0.934200 | − | 0.356751i | \(-0.883885\pi\) | ||||
−0.934200 | + | 0.356751i | \(0.883885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.39070 | 0.213483 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.57568 | 0.318967 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.90043 | −0.140361 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.72833 | −0.180005 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1385 | −0.536522 | −0.268261 | − | 0.963346i | \(-0.586449\pi\) | ||||
−0.268261 | + | 0.963346i | \(0.586449\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.70231 | −0.0818077 | −0.0409039 | − | 0.999163i | \(-0.513024\pi\) | ||||
−0.0409039 | + | 0.999163i | \(0.513024\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.1579 | −1.20623 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.00000 | 0.143509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.45794 | −0.0695836 | −0.0347918 | − | 0.999395i | \(-0.511077\pi\) | ||||
−0.0347918 | + | 0.999395i | \(0.511077\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.1256 | −0.718639 | −0.359319 | − | 0.933215i | \(-0.616991\pi\) | ||||
−0.359319 | + | 0.933215i | \(0.616991\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −43.5615 | −2.06501 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.04650 | −0.0967963 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.0323 | −0.567841 | −0.283921 | − | 0.958848i | \(-0.591635\pi\) | ||||
−0.283921 | + | 0.958848i | \(0.591635\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.01945 | 0.377621 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.17210 | −0.0550700 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.6288 | −0.545164 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.7270 | −1.76480 | −0.882398 | − | 0.470503i | \(-0.844072\pi\) | ||||
−0.882398 | + | 0.470503i | \(0.844072\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.39070 | 0.0649123 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.0518 | 0.607882 | 0.303941 | − | 0.952691i | \(-0.401697\pi\) | ||||
0.303941 | + | 0.952691i | \(0.401697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.30529 | 0.246558 | 0.123279 | − | 0.992372i | \(-0.460659\pi\) | ||||
0.123279 | + | 0.992372i | \(0.460659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.5562 | 0.814151 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.58985 | −0.166118 | −0.0830592 | − | 0.996545i | \(-0.526469\pi\) | ||||
−0.0830592 | + | 0.996545i | \(0.526469\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.337628 | 0.0155902 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.0854 | −0.833332 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.50973 | 0.391278 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.1850 | 0.650852 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.72833 | 0.124922 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.69599 | 0.168874 | 0.0844371 | − | 0.996429i | \(-0.473091\pi\) | ||||
0.0844371 | + | 0.996429i | \(0.473091\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.81502 | −0.310738 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.5757 | 0.480217 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.32346 | −0.422486 | −0.211243 | − | 0.977434i | \(-0.567751\pi\) | ||||
−0.211243 | + | 0.977434i | \(0.567751\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.2911 | −0.555824 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.2044 | 1.27285 | 0.636424 | − | 0.771339i | \(-0.280413\pi\) | ||||
0.636424 | + | 0.771339i | \(0.280413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.2173 | 0.505203 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.11903 | −0.140190 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.29112 | −0.327052 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.88097 | −0.218502 | −0.109251 | − | 0.994014i | \(-0.534845\pi\) | ||||
−0.109251 | + | 0.994014i | \(0.534845\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.23805 | 0.0553121 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.9393 | 0.532348 | 0.266174 | − | 0.963925i | \(-0.414240\pi\) | ||||
0.266174 | + | 0.963925i | \(0.414240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.7672 | 1.41362 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.900425 | 0.0399893 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.60930 | −0.337276 | −0.168638 | − | 0.985678i | \(-0.553937\pi\) | ||||
−0.168638 | + | 0.985678i | \(0.553937\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.60930 | 0.115429 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.00000 | 0.132453 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.0389 | −0.971150 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.39070 | 0.193103 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.8668 | −0.520895 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.6017 | 1.12163 | 0.560815 | − | 0.827941i | \(-0.310488\pi\) | ||||
0.560815 | + | 0.827941i | \(0.310488\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.93404 | −0.303205 | −0.151602 | − | 0.988442i | \(-0.548443\pi\) | ||||
−0.151602 | + | 0.988442i | \(0.548443\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.72833 | −0.206361 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.82790 | −0.340989 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.74778 | −0.249432 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.8991 | −1.29508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.8668 | −0.772449 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.68182 | −0.374648 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7801 | 1.36633 | 0.683167 | − | 0.730262i | \(-0.260602\pi\) | ||||
0.683167 | + | 0.730262i | \(0.260602\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.8668 | −0.852566 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −48.6416 | −2.08358 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.5951 | 0.837827 | 0.418914 | − | 0.908026i | \(-0.362411\pi\) | ||||
0.418914 | + | 0.908026i | \(0.362411\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.90043 | 0.123787 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.1979 | 1.03086 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.8474 | 0.461276 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.70128 | −0.242006 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.58225 | −0.363642 | −0.181821 | − | 0.983332i | \(-0.558199\pi\) | ||||
−0.181821 | + | 0.983332i | \(0.558199\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.7270 | −1.34191 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.39070 | 0.0587154 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.18498 | −0.218521 | −0.109260 | − | 0.994013i | \(-0.534848\pi\) | ||||
−0.109260 | + | 0.994013i | \(0.534848\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.2433 | −1.35649 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.41015 | 0.394494 | 0.197247 | − | 0.980354i | \(-0.436800\pi\) | ||||
0.197247 | + | 0.980354i | \(0.436800\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.1526 | 1.13630 | 0.568151 | − | 0.822924i | \(-0.307659\pi\) | ||||
0.568151 | + | 0.822924i | \(0.307659\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.0854 | −0.671978 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.72833 | 0.197185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.9522 | 0.788991 | 0.394495 | − | 0.918898i | \(-0.370919\pi\) | ||||
0.394495 | + | 0.918898i | \(0.370919\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.30401 | 0.386661 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0660 | −0.500580 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.72833 | 0.112996 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.6288 | 0.480790 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.6624 | 0.935376 | 0.467688 | − | 0.883894i | \(-0.345087\pi\) | ||||
0.467688 | + | 0.883894i | \(0.345087\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.8863 | −0.695786 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.74778 | −0.195298 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.4567 | −0.716859 | −0.358429 | − | 0.933557i | \(-0.616688\pi\) | ||||
−0.358429 | + | 0.933557i | \(0.616688\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.33763 | 0.177825 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.31058 | 0.299202 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.0311 | 1.71734 | 0.858671 | − | 0.512527i | \(-0.171291\pi\) | ||||
0.858671 | + | 0.512527i | \(0.171291\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.7207 | −1.08996 | −0.544981 | − | 0.838449i | \(-0.683463\pi\) | ||||
−0.544981 | + | 0.838449i | \(0.683463\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.337628 | −0.0137493 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.1903 | 1.26806 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.310576 | 0.0126059 | 0.00630295 | − | 0.999980i | \(-0.497994\pi\) | ||||
0.00630295 | + | 0.999980i | \(0.497994\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.06596 | −0.326849 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.3700 | −0.662258 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.28456 | −0.213441 | −0.106721 | − | 0.994289i | \(-0.534035\pi\) | ||||
−0.106721 | + | 0.994289i | \(0.534035\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25.0129 | −1.00862 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.47082 | 0.179989 | 0.0899943 | − | 0.995942i | \(-0.471315\pi\) | ||||
0.0899943 | + | 0.995942i | \(0.471315\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.8345 | −0.636441 | −0.318221 | − | 0.948017i | \(-0.603085\pi\) | ||||
−0.318221 | + | 0.948017i | \(0.603085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.9664 | −0.559551 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.2846 | −1.05138 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.00000 | 0.119808 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.54206 | 0.101359 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8279 | 1.18743 | 0.593715 | − | 0.804675i | \(-0.297661\pi\) | ||||
0.593715 | + | 0.804675i | \(0.297661\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.800850 | −0.0318309 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −51.0182 | −2.02459 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.72833 | −0.147722 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.29112 | 0.288432 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.0712 | −0.516283 | −0.258141 | − | 0.966107i | \(-0.583110\pi\) | ||||
−0.258141 | + | 0.966107i | \(0.583110\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.9845 | −1.18248 | −0.591238 | − | 0.806497i | \(-0.701360\pi\) | ||||
−0.591238 | + | 0.806497i | \(0.701360\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −26.5421 | −1.04509 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0323 | −0.708924 | −0.354462 | − | 0.935070i | \(-0.615336\pi\) | ||||
−0.354462 | + | 0.935070i | \(0.615336\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.74778 | −0.225620 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.62875 | 0.220608 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.749062 | −0.0293131 | −0.0146565 | − | 0.999893i | \(-0.504665\pi\) | ||||
−0.0146565 | + | 0.999893i | \(0.504665\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.9004 | 0.543135 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.60930 | −0.101799 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.8474 | 0.967915 | 0.483958 | − | 0.875091i | \(-0.339199\pi\) | ||||
0.483958 | + | 0.875091i | \(0.339199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.8461 | 0.927505 | 0.463752 | − | 0.885965i | \(-0.346503\pi\) | ||||
0.463752 | + | 0.885965i | \(0.346503\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.18498 | −0.201368 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.35708 | 0.362852 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.06596 | 0.312315 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.2704 | 0.861023 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.90043 | 0.111970 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.31161 | 0.320389 | 0.160194 | − | 0.987085i | \(-0.448788\pi\) | ||||
0.160194 | + | 0.987085i | \(0.448788\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.72833 | 0.181993 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.9275 | −0.535276 | −0.267638 | − | 0.963519i | \(-0.586243\pi\) | ||||
−0.267638 | + | 0.963519i | \(0.586243\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.39070 | 0.130123 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.5562 | 0.749396 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.2651 | −0.545839 | −0.272920 | − | 0.962037i | \(-0.587989\pi\) | ||||
−0.272920 | + | 0.962037i | \(0.587989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −63.1837 | −2.41413 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.83447 | −0.108142 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.1721 | −0.387526 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.1850 | −0.958082 | −0.479041 | − | 0.877793i | \(-0.659015\pi\) | ||||
−0.479041 | + | 0.877793i | \(0.659015\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.00000 | −0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.1309 | 0.801540 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.1526 | 0.422437 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.77483 | 0.104954 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.1114 | −0.721829 | −0.360914 | − | 0.932599i | \(-0.617535\pi\) | ||||
−0.360914 | + | 0.932599i | \(0.617535\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.48371 | 0.206822 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.6947 | −0.515773 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.1850 | 0.383046 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.7735 | 1.15572 | 0.577862 | − | 0.816134i | \(-0.303887\pi\) | ||||
0.577862 | + | 0.816134i | \(0.303887\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.8474 | −0.406808 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.62875 | −0.210798 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.6288 | 0.434891 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.536778 | −0.0200463 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.67654 | −0.0998181 | −0.0499090 | − | 0.998754i | \(-0.515893\pi\) | ||||
−0.0499090 | + | 0.998754i | \(0.515893\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.06596 | −0.263150 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.9328 | 0.555355 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.1385 | 1.41643 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.3505 | 1.12564 | 0.562819 | − | 0.826580i | \(-0.309717\pi\) | ||||
0.562819 | + | 0.826580i | \(0.309717\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.8345 | 0.437714 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.01945 | 0.259269 | 0.129635 | − | 0.991562i | \(-0.458620\pi\) | ||||
0.129635 | + | 0.991562i | \(0.458620\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.11903 | −0.115047 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.337628 | −0.0124367 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.9509 | −1.87426 | −0.937130 | − | 0.348980i | \(-0.886528\pi\) | ||||
−0.937130 | + | 0.348980i | \(0.886528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.1850 | −0.410891 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.39727 | −0.308066 | −0.154033 | − | 0.988066i | \(-0.549226\pi\) | ||||
−0.154033 | + | 0.988066i | \(0.549226\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.38310 | 0.233859 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0660 | 0.441470 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.72833 | −0.209309 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.2057 | 0.737317 | 0.368659 | − | 0.929565i | \(-0.379817\pi\) | ||||
0.368659 | + | 0.929565i | \(0.379817\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.9328 | −0.799274 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.65580 | 0.133048 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.2951 | 1.86435 | 0.932177 | − | 0.362004i | \(-0.117907\pi\) | ||||
0.932177 | + | 0.362004i | \(0.117907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.00000 | 0.0362977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.5032 | 0.924489 | 0.462244 | − | 0.886753i | \(-0.347044\pi\) | ||||
0.462244 | + | 0.886753i | \(0.347044\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.5951 | −0.564582 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.33763 | −0.156827 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.4296 | 0.773778 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.3700 | 0.446072 | 0.223036 | − | 0.974810i | \(-0.428403\pi\) | ||||
0.223036 | + | 0.974810i | \(0.428403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0854 | −0.435245 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.503158 | −0.0180974 | −0.00904868 | − | 0.999959i | \(-0.502880\pi\) | ||||
−0.00904868 | + | 0.999959i | \(0.502880\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.6146 | −0.956024 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.82790 | −0.0655756 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0584 | 0.861980 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.29112 | 0.260897 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.06596 | 0.288254 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.4089 | 2.01332 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.4903 | 0.730399 | 0.365200 | − | 0.930929i | \(-0.381001\pi\) | ||||
0.365200 | + | 0.930929i | \(0.381001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.01945 | 0.0718944 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.3376 | −0.367564 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.8137 | −0.384007 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.50973 | −0.301809 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.3636 | −0.402521 | −0.201261 | − | 0.979538i | \(-0.564504\pi\) | ||||
−0.201261 | + | 0.979538i | \(0.564504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.10614 | 0.216020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.9664 | 0.493478 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.60930 | −0.0920802 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.11903 | 0.109931 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.5292 | −0.687460 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.4425 | 0.648403 | 0.324202 | − | 0.945988i | \(-0.394904\pi\) | ||||
0.324202 | + | 0.945988i | \(0.394904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.1243 | 0.812004 | 0.406002 | − | 0.913872i | \(-0.366923\pi\) | ||||
0.406002 | + | 0.913872i | \(0.366923\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.5615 | 0.545766 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.3363 | 1.34286 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.5292 | 0.893153 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.72833 | 0.130278 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.4089 | −1.13108 | −0.565539 | − | 0.824722i | \(-0.691332\pi\) | ||||
−0.565539 | + | 0.824722i | \(0.691332\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.92748 | −0.171761 | −0.0858805 | − | 0.996305i | \(-0.527370\pi\) | ||||
−0.0858805 | + | 0.996305i | \(0.527370\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.72833 | 0.164619 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.635320 | 0.0220922 | 0.0110461 | − | 0.999939i | \(-0.496484\pi\) | ||||
0.0110461 | + | 0.999939i | \(0.496484\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.1438 | 0.838548 | 0.419274 | − | 0.907860i | \(-0.362285\pi\) | ||||
0.419274 | + | 0.907860i | \(0.362285\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.35708 | 0.289904 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.39070 | 0.0481849 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.86152 | −0.133633 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.62875 | −0.194558 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.5939 | 1.50503 | 0.752513 | − | 0.658577i | \(-0.228841\pi\) | ||||
0.752513 | + | 0.658577i | \(0.228841\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.0596 | 1.24344 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.0195 | 0.655065 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.80845 | −0.0966136 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0000 | 0.343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.35708 | −0.321134 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.82790 | 0.0626597 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.7531 | 1.53232 | 0.766158 | − | 0.642652i | \(-0.222166\pi\) | ||||
0.766158 | + | 0.642652i | \(0.222166\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.35708 | −0.320005 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.5704 | 0.395237 | 0.197619 | − | 0.980279i | \(-0.436679\pi\) | ||||
0.197619 | + | 0.980279i | \(0.436679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.2575 | −1.47593 | −0.737964 | − | 0.674841i | \(-0.764212\pi\) | ||||
−0.737964 | + | 0.674841i | \(0.764212\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.01945 | −0.273302 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.9805 | 0.578025 | 0.289012 | − | 0.957325i | \(-0.406673\pi\) | ||||
0.289012 | + | 0.957325i | \(0.406673\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.0129 | 1.25848 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.0660 | −0.511667 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.8474 | −0.367971 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.25879 | 0.0426524 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.39070 | −0.114758 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.847354 | −0.0286458 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.4491 | 0.386607 | 0.193304 | − | 0.981139i | \(-0.438080\pi\) | ||||
0.193304 | + | 0.981139i | \(0.438080\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.4761 | 0.420809 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.0584 | −0.709474 | −0.354737 | − | 0.934966i | \(-0.615430\pi\) | ||||
−0.354737 | + | 0.934966i | \(0.615430\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.4966 | 0.420544 | 0.210272 | − | 0.977643i | \(-0.432565\pi\) | ||||
0.210272 | + | 0.977643i | \(0.432565\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.9275 | 0.602626 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −57.3169 | −1.92451 | −0.962256 | − | 0.272144i | \(-0.912267\pi\) | ||||
−0.962256 | + | 0.272144i | \(0.912267\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.3571 | −0.548599 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.1721 | 0.440787 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.0788 | 0.905146 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.72833 | −0.124485 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.4013 | −1.51422 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.79428 | 0.126406 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.50973 | −0.283186 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 61.9651 | 2.05979 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.5562 | 1.51267 | 0.756335 | − | 0.654185i | \(-0.226988\pi\) | ||||
0.756335 | + | 0.654185i | \(0.226988\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.1850 | −0.337815 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.9328 | 0.527876 | 0.263938 | − | 0.964540i | \(-0.414979\pi\) | ||||
0.263938 | + | 0.964540i | \(0.414979\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0660 | 0.399325 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.04650 | −0.299068 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.45665 | 0.147172 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.1243 | −1.15864 | −0.579322 | − | 0.815099i | \(-0.696683\pi\) | ||||
−0.579322 | + | 0.815099i | \(0.696683\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.7607 | 0.914745 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.1837 | −0.894762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.64292 | 0.284177 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.06596 | 0.232076 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.2704 | −0.993139 | −0.496570 | − | 0.867997i | \(-0.665407\pi\) | ||||
−0.496570 | + | 0.867997i | \(0.665407\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.00000 | 0.0983210 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.5757 | 0.902787 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.33763 | −0.141856 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.8266 | 0.811050 | 0.405525 | − | 0.914084i | \(-0.367089\pi\) | ||||
0.405525 | + | 0.914084i | \(0.367089\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.75435 | 0.253054 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.60170 | −0.247808 | −0.123904 | − | 0.992294i | \(-0.539542\pi\) | ||||
−0.123904 | + | 0.992294i | \(0.539542\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.01945 | 0.261149 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.11903 | 0.101462 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.8592 | −0.742824 | −0.371412 | − | 0.928468i | \(-0.621126\pi\) | ||||
−0.371412 | + | 0.928468i | \(0.621126\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.72833 | 0.315795 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.3960 | 0.693812 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.3828 | −1.11377 | −0.556885 | − | 0.830590i | \(-0.688004\pi\) | ||||
−0.556885 | + | 0.830590i | \(0.688004\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.1708 | 1.62349 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.06596 | 0.260735 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.2575 | −0.654149 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.682856 | 0.0220276 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.72833 | 0.184593 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.0195 | −0.934169 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.74249 | 0.152508 | 0.0762542 | − | 0.997088i | \(-0.475704\pi\) | ||||
0.0762542 | + | 0.997088i | \(0.475704\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.17210 | 0.134027 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.2691 | 1.67740 | 0.838698 | − | 0.544597i | \(-0.183317\pi\) | ||||
0.838698 | + | 0.544597i | \(0.183317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.77483 | 0.217191 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.6288 | −0.564572 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.1385 | 1.06019 | 0.530097 | − | 0.847937i | \(-0.322156\pi\) | ||||
0.530097 | + | 0.847937i | \(0.322156\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.9664 | 0.446367 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.5951 | 0.497914 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.5357 | 0.750674 | 0.375337 | − | 0.926888i | \(-0.377527\pi\) | ||||
0.375337 | + | 0.926888i | \(0.377527\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.8085 | 0.471836 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.39070 | −0.139757 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.50973 | 0.270594 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.4890 | −0.333194 | −0.166597 | − | 0.986025i | \(-0.553278\pi\) | ||||
−0.166597 | + | 0.986025i | \(0.553278\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.0182 | 0.825662 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.8019 | −0.722868 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.0182 | −1.36240 | −0.681200 | − | 0.732098i | \(-0.738541\pi\) | ||||
−0.681200 | + | 0.732098i | \(0.738541\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.82790 | 0.0578323 |
(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 | 1932.2.a.j.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 5796.2.a.o.1.3 | 3 | |||
4.3 | odd | 2 | 7728.2.a.br.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.a.j.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5796.2.a.o.1.3 | 3 | 3.2 | odd | 2 | |||
7728.2.a.br.1.1 | 3 | 4.3 | odd | 2 |