Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.5490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3040) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.539189 | 0.311301 | 0.155650 | − | 0.987812i | \(-0.450253\pi\) | ||||
0.155650 | + | 0.987812i | \(0.450253\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.630898 | −0.238457 | −0.119228 | − | 0.992867i | \(-0.538042\pi\) | ||||
−0.119228 | + | 0.992867i | \(0.538042\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.70928 | −0.903092 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.70928 | −0.515366 | −0.257683 | − | 0.966230i | \(-0.582959\pi\) | ||||
−0.257683 | + | 0.966230i | \(0.582959\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.17009 | 0.879224 | 0.439612 | − | 0.898188i | \(-0.355116\pi\) | ||||
0.439612 | + | 0.898188i | \(0.355116\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.539189 | −0.139218 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41855 | 0.344049 | 0.172025 | − | 0.985093i | \(-0.444969\pi\) | ||||
0.172025 | + | 0.985093i | \(0.444969\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.340173 | −0.0742318 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.04945 | 0.844368 | 0.422184 | − | 0.906510i | \(-0.361264\pi\) | ||||
0.422184 | + | 0.906510i | \(0.361264\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.07838 | −0.592434 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.75872 | −0.697977 | −0.348989 | − | 0.937127i | \(-0.613475\pi\) | ||||
−0.348989 | + | 0.937127i | \(0.613475\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.41855 | −0.254779 | −0.127390 | − | 0.991853i | \(-0.540660\pi\) | ||||
−0.127390 | + | 0.991853i | \(0.540660\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.921622 | −0.160434 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.630898 | 0.106641 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.986669 | 0.162207 | 0.0811037 | − | 0.996706i | \(-0.474156\pi\) | ||||
0.0811037 | + | 0.996706i | \(0.474156\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.70928 | 0.273703 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.26180 | −1.44645 | −0.723225 | − | 0.690613i | \(-0.757341\pi\) | ||||
−0.723225 | + | 0.690613i | \(0.757341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.70928 | 0.870656 | 0.435328 | − | 0.900272i | \(-0.356632\pi\) | ||||
0.435328 | + | 0.900272i | \(0.356632\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.70928 | 0.403875 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.04945 | 0.590673 | 0.295336 | − | 0.955393i | \(-0.404568\pi\) | ||||
0.295336 | + | 0.955393i | \(0.404568\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.60197 | −0.943138 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.764867 | 0.107103 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.32684 | 1.00642 | 0.503210 | − | 0.864164i | \(-0.332152\pi\) | ||||
0.503210 | + | 0.864164i | \(0.332152\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.70928 | 0.230479 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.539189 | 0.0714173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.0205 | −1.69513 | −0.847564 | − | 0.530694i | \(-0.821931\pi\) | ||||
−0.847564 | + | 0.530694i | \(0.821931\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1278 | 1.68085 | 0.840423 | − | 0.541931i | \(-0.182307\pi\) | ||||
0.840423 | + | 0.541931i | \(0.182307\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.70928 | 0.215348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.17009 | −0.393201 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.14116 | 0.750262 | 0.375131 | − | 0.926972i | \(-0.377598\pi\) | ||||
0.375131 | + | 0.926972i | \(0.377598\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.18342 | 0.262853 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.94214 | −0.942559 | −0.471279 | − | 0.881984i | \(-0.656208\pi\) | ||||
−0.471279 | + | 0.881984i | \(0.656208\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.91548 | −1.16052 | −0.580260 | − | 0.814432i | \(-0.697049\pi\) | ||||
−0.580260 | + | 0.814432i | \(0.697049\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.539189 | 0.0622602 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.07838 | 0.122893 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.02052 | −0.564853 | −0.282426 | − | 0.959289i | \(-0.591139\pi\) | ||||
−0.282426 | + | 0.959289i | \(0.591139\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.46800 | 0.718667 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.86603 | 0.424352 | 0.212176 | − | 0.977231i | \(-0.431945\pi\) | ||||
0.212176 | + | 0.977231i | \(0.431945\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.41855 | −0.153863 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.02666 | −0.217281 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.60197 | 0.593807 | 0.296904 | − | 0.954907i | \(-0.404046\pi\) | ||||
0.296904 | + | 0.954907i | \(0.404046\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.764867 | −0.0793130 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.275126 | −0.0279348 | −0.0139674 | − | 0.999902i | \(-0.504446\pi\) | ||||
−0.0139674 | + | 0.999902i | \(0.504446\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.63090 | 0.465423 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.7298 | 1.66468 | 0.832338 | − | 0.554268i | \(-0.187002\pi\) | ||||
0.832338 | + | 0.554268i | \(0.187002\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.0628 | 1.68125 | 0.840623 | − | 0.541621i | \(-0.182189\pi\) | ||||
0.840623 | + | 0.541621i | \(0.182189\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.340173 | 0.0331975 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.77432 | −0.558225 | −0.279112 | − | 0.960258i | \(-0.590040\pi\) | ||||
−0.279112 | + | 0.960258i | \(0.590040\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.44521 | −0.138426 | −0.0692131 | − | 0.997602i | \(-0.522049\pi\) | ||||
−0.0692131 | + | 0.997602i | \(0.522049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.532001 | 0.0504953 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.93495 | −0.370169 | −0.185085 | − | 0.982723i | \(-0.559256\pi\) | ||||
−0.185085 | + | 0.982723i | \(0.559256\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.04945 | −0.377613 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.58864 | −0.794020 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.894960 | −0.0820409 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.07838 | −0.734398 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.99386 | −0.450281 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.71646 | 0.862197 | 0.431098 | − | 0.902305i | \(-0.358126\pi\) | ||||
0.431098 | + | 0.902305i | \(0.358126\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.07838 | 0.271036 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6537 | 1.28030 | 0.640149 | − | 0.768251i | \(-0.278873\pi\) | ||||
0.640149 | + | 0.768251i | \(0.278873\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.630898 | −0.0547058 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.07838 | 0.264945 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.52359 | 0.728219 | 0.364110 | − | 0.931356i | \(-0.381373\pi\) | ||||
0.364110 | + | 0.931356i | \(0.381373\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.3896 | 1.89906 | 0.949531 | − | 0.313672i | \(-0.101559\pi\) | ||||
0.949531 | + | 0.313672i | \(0.101559\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.18342 | 0.183877 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.41855 | −0.453122 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.75872 | 0.312145 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.55971 | −0.293600 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.38962 | −0.523458 | −0.261729 | − | 0.965141i | \(-0.584293\pi\) | ||||
−0.261729 | + | 0.965141i | \(0.584293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.18342 | 0.340442 | 0.170221 | − | 0.985406i | \(-0.445552\pi\) | ||||
0.170221 | + | 0.985406i | \(0.445552\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.84324 | −0.310708 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.41855 | 0.113941 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3607 | 1.22592 | 0.612958 | − | 0.790115i | \(-0.289979\pi\) | ||||
0.612958 | + | 0.790115i | \(0.289979\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.95055 | 0.313299 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.55479 | −0.201345 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.1217 | 1.73270 | 0.866352 | − | 0.499434i | \(-0.166459\pi\) | ||||
0.866352 | + | 0.499434i | \(0.166459\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.921622 | 0.0717482 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.03612 | −0.0801772 | −0.0400886 | − | 0.999196i | \(-0.512764\pi\) | ||||
−0.0400886 | + | 0.999196i | \(0.512764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.95055 | −0.226966 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.70928 | −0.207183 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.6153 | 0.959123 | 0.479562 | − | 0.877508i | \(-0.340796\pi\) | ||||
0.479562 | + | 0.877508i | \(0.340796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.630898 | −0.0476914 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.02052 | −0.527695 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.4908 | 1.75578 | 0.877892 | − | 0.478859i | \(-0.158949\pi\) | ||||
0.877892 | + | 0.478859i | \(0.158949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.36069 | −0.249798 | −0.124899 | − | 0.992169i | \(-0.539861\pi\) | ||||
−0.124899 | + | 0.992169i | \(0.539861\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.07838 | 0.523249 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.986669 | −0.0725413 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.42469 | −0.177311 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.94214 | 0.141270 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.4596 | 1.55276 | 0.776381 | − | 0.630264i | \(-0.217053\pi\) | ||||
0.776381 | + | 0.630264i | \(0.217053\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0856 | 0.941920 | 0.470960 | − | 0.882155i | \(-0.343908\pi\) | ||||
0.470960 | + | 0.882155i | \(0.343908\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.70928 | −0.122404 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.49693 | 0.177899 | 0.0889494 | − | 0.996036i | \(-0.471649\pi\) | ||||
0.0889494 | + | 0.996036i | \(0.471649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6803 | 0.898886 | 0.449443 | − | 0.893309i | \(-0.351623\pi\) | ||||
0.449443 | + | 0.893309i | \(0.351623\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.31124 | 0.233557 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.37137 | 0.166438 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.26180 | 0.646872 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.9711 | −0.762542 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.70928 | −0.118233 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8638 | 1.16095 | 0.580475 | − | 0.814278i | \(-0.302867\pi\) | ||||
0.580475 | + | 0.814278i | \(0.302867\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.28231 | −0.293419 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.70928 | −0.389369 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.894960 | 0.0607539 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.34632 | −0.361271 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.49693 | 0.302496 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.22568 | 0.550832 | 0.275416 | − | 0.961325i | \(-0.411184\pi\) | ||||
0.275416 | + | 0.961325i | \(0.411184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.70928 | −0.180618 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.19287 | −0.610152 | −0.305076 | − | 0.952328i | \(-0.598682\pi\) | ||||
−0.305076 | + | 0.952328i | \(0.598682\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.68261 | −0.243354 | −0.121677 | − | 0.992570i | \(-0.538827\pi\) | ||||
−0.121677 | + | 0.992570i | \(0.538827\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.581449 | 0.0382566 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.17727 | 0.470199 | 0.235099 | − | 0.971971i | \(-0.424458\pi\) | ||||
0.235099 | + | 0.971971i | \(0.424458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.04945 | −0.264157 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.70701 | −0.175839 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.1256 | 0.654968 | 0.327484 | − | 0.944857i | \(-0.393799\pi\) | ||||
0.327484 | + | 0.944857i | \(0.393799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.3607 | −1.63363 | −0.816813 | − | 0.576903i | \(-0.804261\pi\) | ||||
−0.816813 | + | 0.576903i | \(0.804261\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.7226 | 0.816156 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.60197 | 0.421784 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.17009 | 0.201708 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.08452 | 0.132101 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.26180 | −0.584599 | −0.292300 | − | 0.956327i | \(-0.594420\pi\) | ||||
−0.292300 | + | 0.956327i | \(0.594420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.92162 | −0.435159 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.764867 | −0.0478978 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.34736 | −0.395937 | −0.197969 | − | 0.980208i | \(-0.563434\pi\) | ||||
−0.197969 | + | 0.980208i | \(0.563434\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.622487 | −0.0386795 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.1834 | 0.630338 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.79380 | 0.110610 | 0.0553051 | − | 0.998470i | \(-0.482387\pi\) | ||||
0.0553051 | + | 0.998470i | \(0.482387\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.32684 | −0.450084 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.02052 | 0.184853 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.70701 | 0.408933 | 0.204467 | − | 0.978874i | \(-0.434454\pi\) | ||||
0.204467 | + | 0.978874i | \(0.434454\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.8143 | −0.778414 | −0.389207 | − | 0.921150i | \(-0.627251\pi\) | ||||
−0.389207 | + | 0.921150i | \(0.627251\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.07838 | −0.0652664 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.70928 | −0.103073 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.15676 | −0.249755 | −0.124878 | − | 0.992172i | \(-0.539854\pi\) | ||||
−0.124878 | + | 0.992172i | \(0.539854\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.84324 | 0.230089 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.0928 | −1.73553 | −0.867764 | − | 0.496976i | \(-0.834444\pi\) | ||||
−0.867764 | + | 0.496976i | \(0.834444\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1340 | 0.721290 | 0.360645 | − | 0.932703i | \(-0.382557\pi\) | ||||
0.360645 | + | 0.932703i | \(0.382557\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.539189 | −0.0319388 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.84324 | 0.344916 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9877 | −0.881630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.148345 | −0.00869614 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.9227 | −0.696530 | −0.348265 | − | 0.937396i | \(-0.613229\pi\) | ||||
−0.348265 | + | 0.937396i | \(0.613229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.0205 | 0.758084 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.26180 | 0.305320 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.8371 | 0.742389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.60197 | −0.207614 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.02052 | 0.518215 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.1278 | −0.751697 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.02174 | 0.172460 | 0.0862299 | − | 0.996275i | \(-0.472518\pi\) | ||||
0.0862299 | + | 0.996275i | \(0.472518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.20006 | 0.523373 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.3835 | 1.55277 | 0.776387 | − | 0.630256i | \(-0.217050\pi\) | ||||
0.776387 | + | 0.630256i | \(0.217050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1773 | 0.857870 | 0.428935 | − | 0.903335i | \(-0.358889\pi\) | ||||
0.428935 | + | 0.903335i | \(0.358889\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.70928 | −0.0963068 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.6092 | −0.764366 | −0.382183 | − | 0.924087i | \(-0.624828\pi\) | ||||
−0.382183 | + | 0.924087i | \(0.624828\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.42469 | 0.359714 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.11345 | −0.173776 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.41855 | 0.0789303 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.17009 | 0.175845 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.779243 | −0.0430922 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.55479 | −0.140850 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.92162 | −0.380447 | −0.190223 | − | 0.981741i | \(-0.560921\pi\) | ||||
−0.190223 | + | 0.981741i | \(0.560921\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.67316 | −0.146488 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.14116 | −0.335527 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.6875 | 1.23587 | 0.617934 | − | 0.786230i | \(-0.287970\pi\) | ||||
0.617934 | + | 0.786230i | \(0.287970\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.12168 | −0.115234 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.42469 | 0.131305 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.58145 | 0.463355 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.18342 | −0.117551 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.8287 | 1.54761 | 0.773803 | − | 0.633427i | \(-0.218352\pi\) | ||||
0.773803 | + | 0.633427i | \(0.218352\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.2823 | −0.550400 | −0.275200 | − | 0.961387i | \(-0.588744\pi\) | ||||
−0.275200 | + | 0.961387i | \(0.588744\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.75872 | −0.520882 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.6163 | −1.15052 | −0.575261 | − | 0.817970i | \(-0.695099\pi\) | ||||
−0.575261 | + | 0.817970i | \(0.695099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.94214 | 0.421525 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.482553 | −0.0255394 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0700 | −0.795362 | −0.397681 | − | 0.917524i | \(-0.630185\pi\) | ||||
−0.397681 | + | 0.917524i | \(0.630185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.35577 | −0.228619 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.91548 | 0.519000 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.3256 | −1.53078 | −0.765392 | − | 0.643564i | \(-0.777455\pi\) | ||||
−0.765392 | + | 0.643564i | \(0.777455\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 25.0928 | 1.30628 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.62249 | −0.239988 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.0917087 | −0.00474850 | −0.00237425 | − | 0.999997i | \(-0.500756\pi\) | ||||
−0.00237425 | + | 0.999997i | \(0.500756\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.539189 | −0.0278436 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.9155 | −0.613678 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1506 | −0.572768 | −0.286384 | − | 0.958115i | \(-0.592453\pi\) | ||||
−0.286384 | + | 0.958115i | \(0.592453\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.23901 | 0.268403 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.9060 | −0.761662 | −0.380831 | − | 0.924645i | \(-0.624362\pi\) | ||||
−0.380831 | + | 0.924645i | \(0.624362\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.07838 | −0.0549592 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.4680 | −0.786283 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.71154 | −0.137481 | −0.0687403 | − | 0.997635i | \(-0.521898\pi\) | ||||
−0.0687403 | + | 0.997635i | \(0.521898\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.74435 | 0.290504 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.90110 | 0.398558 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.02052 | 0.252610 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.3340 | −1.67299 | −0.836494 | − | 0.547977i | \(-0.815398\pi\) | ||||
−0.836494 | + | 0.547977i | \(0.815398\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.340173 | −0.0170299 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.88882 | 0.393949 | 0.196974 | − | 0.980409i | \(-0.436888\pi\) | ||||
0.196974 | + | 0.980409i | \(0.436888\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.49693 | −0.224008 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.46800 | −0.321397 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.68649 | −0.0835962 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.97334 | −0.0975753 | −0.0487876 | − | 0.998809i | \(-0.515536\pi\) | ||||
−0.0487876 | + | 0.998809i | \(0.515536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.59583 | 0.226695 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.21461 | 0.404215 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.86603 | −0.189776 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0722 | 0.591180 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.9627 | 0.828680 | 0.414340 | − | 0.910122i | \(-0.364012\pi\) | ||||
0.414340 | + | 0.910122i | \(0.364012\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.366835 | 0.0178784 | 0.00893922 | − | 0.999960i | \(-0.497155\pi\) | ||||
0.00893922 | + | 0.999960i | \(0.497155\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.9711 | −0.533432 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.41855 | 0.0688098 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.28231 | −0.400809 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.92162 | −0.141057 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.39803 | −0.404519 | −0.202259 | − | 0.979332i | \(-0.564828\pi\) | ||||
−0.202259 | + | 0.979332i | \(0.564828\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.2690 | 1.50269 | 0.751346 | − | 0.659909i | \(-0.229405\pi\) | ||||
0.751346 | + | 0.659909i | \(0.229405\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.02666 | 0.0971710 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.04945 | 0.193711 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.0784 | 0.910561 | 0.455281 | − | 0.890348i | \(-0.349539\pi\) | ||||
0.455281 | + | 0.890348i | \(0.349539\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.8865 | 0.851740 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.04945 | −0.382441 | −0.191220 | − | 0.981547i | \(-0.561245\pi\) | ||||
−0.191220 | + | 0.981547i | \(0.561245\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.60197 | −0.265559 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.44521 | −0.162953 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.92162 | −0.326652 | −0.163326 | − | 0.986572i | \(-0.552222\pi\) | ||||
−0.163326 | + | 0.986572i | \(0.552222\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.8310 | 0.745451 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.25565 | 0.105980 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.00000 | 0.0937614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.6803 | 0.686718 | 0.343359 | − | 0.939204i | \(-0.388435\pi\) | ||||
0.343359 | + | 0.939204i | \(0.388435\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.36683 | −0.203826 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.1506 | 1.54398 | 0.771989 | − | 0.635636i | \(-0.219262\pi\) | ||||
0.771989 | + | 0.635636i | \(0.219262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.5197 | 0.860684 | 0.430342 | − | 0.902666i | \(-0.358393\pi\) | ||||
0.430342 | + | 0.902666i | \(0.358393\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.764867 | 0.0354698 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.5669 | −1.09055 | −0.545273 | − | 0.838259i | \(-0.683574\pi\) | ||||
−0.545273 | + | 0.838259i | \(0.683574\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.87444 | −0.178905 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.28231 | 0.381629 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.75872 | −0.448707 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.8504 | −0.908889 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.2907 | 0.470195 | 0.235098 | − | 0.971972i | \(-0.424459\pi\) | ||||
0.235098 | + | 0.971972i | \(0.424459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.12783 | 0.142617 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.37751 | −0.0626790 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.275126 | 0.0124928 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.9926 | 1.31378 | 0.656891 | − | 0.753986i | \(-0.271871\pi\) | ||||
0.656891 | + | 0.753986i | \(0.271871\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.9278 | 0.539392 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.5692 | −0.838015 | −0.419007 | − | 0.907983i | \(-0.637622\pi\) | ||||
−0.419007 | + | 0.907983i | \(0.637622\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.33194 | −0.240139 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.63090 | −0.208143 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.01068 | 0.224760 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.7671 | 0.884898 | 0.442449 | − | 0.896794i | \(-0.354110\pi\) | ||||
0.442449 | + | 0.896794i | \(0.354110\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.558663 | −0.0249592 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.8287 | −0.928705 | −0.464353 | − | 0.885650i | \(-0.653713\pi\) | ||||
−0.464353 | + | 0.885650i | \(0.653713\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.7298 | −0.744466 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.59090 | −0.0706546 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.5380 | −1.08763 | −0.543813 | − | 0.839206i | \(-0.683020\pi\) | ||||
−0.543813 | + | 0.839206i | \(0.683020\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.25565 | 0.276734 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.07838 | −0.135914 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.0628 | −0.751876 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.92162 | −0.304413 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.80203 | 0.298576 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.58145 | −0.288339 | −0.144169 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144169 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.6586 | 1.20943 | 0.604713 | − | 0.796443i | \(-0.293288\pi\) | ||||
0.604713 | + | 0.796443i | \(0.293288\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.340173 | −0.0148464 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.01229 | −0.0876566 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.60197 | −0.287042 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35.2762 | 1.53086 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.3607 | −1.27175 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.77432 | 0.249646 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.6660 | 0.546577 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.2846 | 0.486061 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.9444 | 0.728497 | 0.364249 | − | 0.931302i | \(-0.381326\pi\) | ||||
0.364249 | + | 0.931302i | \(0.381326\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.81205 | −0.0777624 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.44521 | 0.0619061 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.4608 | −0.661057 | −0.330528 | − | 0.943796i | \(-0.607227\pi\) | ||||
−0.330528 | + | 0.943796i | \(0.607227\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −35.5669 | −1.51796 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.75872 | −0.160127 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.16743 | 0.134693 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.532001 | −0.0225822 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.3012 | −1.70762 | −0.853809 | − | 0.520587i | \(-0.825713\pi\) | ||||
−0.853809 | + | 0.520587i | \(0.825713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.0989 | 0.765502 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.30737 | −0.0551971 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.2134 | −0.767603 | −0.383801 | − | 0.923416i | \(-0.625385\pi\) | ||||
−0.383801 | + | 0.923416i | \(0.625385\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.93495 | 0.165545 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.08065 | −0.171371 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.13009 | −0.173143 | −0.0865713 | − | 0.996246i | \(-0.527591\pi\) | ||||
−0.0865713 | + | 0.996246i | \(0.527591\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.2267 | −1.05571 | −0.527853 | − | 0.849336i | \(-0.677003\pi\) | ||||
−0.527853 | + | 0.849336i | \(0.677003\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.5708 | 0.483376 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.04945 | 0.168874 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.7480 | 1.44658 | 0.723290 | − | 0.690544i | \(-0.242629\pi\) | ||||
0.723290 | + | 0.690544i | \(0.242629\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.05559 | 0.293220 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.43907 | −0.101190 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.5236 | −0.518674 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.58864 | 0.355096 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.91935 | −0.326867 | −0.163433 | − | 0.986554i | \(-0.552257\pi\) | ||||
−0.163433 | + | 0.986554i | \(0.552257\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.41855 | −0.0584504 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.34632 | 0.0553800 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.837101 | 0.0343756 | 0.0171878 | − | 0.999852i | \(-0.494529\pi\) | ||||
0.0171878 | + | 0.999852i | \(0.494529\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.894960 | 0.0366898 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.83710 | 0.279824 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.9216 | 1.01827 | 0.509135 | − | 0.860687i | \(-0.329965\pi\) | ||||
0.509135 | + | 0.860687i | \(0.329965\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.7275 | −0.723121 | −0.361560 | − | 0.932349i | \(-0.617756\pi\) | ||||
−0.361560 | + | 0.932349i | \(0.617756\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.6381 | −0.677555 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.07838 | 0.328433 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.40749 | −0.381838 | −0.190919 | − | 0.981606i | \(-0.561147\pi\) | ||||
−0.190919 | + | 0.981606i | \(0.561147\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.27862 | 0.0518121 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.8371 | 0.519334 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.3919 | −0.621673 | −0.310836 | − | 0.950463i | \(-0.600609\pi\) | ||||
−0.310836 | + | 0.950463i | \(0.600609\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.99386 | 0.201372 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.28846 | 0.212905 | 0.106453 | − | 0.994318i | \(-0.466051\pi\) | ||||
0.106453 | + | 0.994318i | \(0.466051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.9132 | 1.16212 | 0.581060 | − | 0.813861i | \(-0.302638\pi\) | ||||
0.581060 | + | 0.813861i | \(0.302638\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.4657 | −0.500233 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.53427 | −0.141597 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.921622 | −0.0368060 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.39964 | 0.0558073 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.38962 | 0.254367 | 0.127183 | − | 0.991879i | \(-0.459406\pi\) | ||||
0.127183 | + | 0.991879i | \(0.459406\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.09275 | 0.361405 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.71646 | −0.385586 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.9288 | −0.829230 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.5174 | 0.851217 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.04718 | 0.0413612 | 0.0206806 | − | 0.999786i | \(-0.493417\pi\) | ||||
0.0206806 | + | 0.999786i | \(0.493417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.46800 | −0.294509 | −0.147255 | − | 0.989099i | \(-0.547044\pi\) | ||||
−0.147255 | + | 0.989099i | \(0.547044\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.07838 | −0.121211 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.70313 | −0.106271 | −0.0531355 | − | 0.998587i | \(-0.516922\pi\) | ||||
−0.0531355 | + | 0.998587i | \(0.516922\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.2557 | 0.873611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.482553 | 0.0189127 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.4329 | 0.838735 | 0.419368 | − | 0.907817i | \(-0.362252\pi\) | ||||
0.419368 | + | 0.907817i | \(0.362252\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.6537 | −0.572567 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.8638 | 1.04806 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.8576 | 0.773543 | 0.386772 | − | 0.922176i | \(-0.373590\pi\) | ||||
0.386772 | + | 0.922176i | \(0.373590\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.83710 | 0.110350 | 0.0551752 | − | 0.998477i | \(-0.482428\pi\) | ||||
0.0551752 | + | 0.998477i | \(0.482428\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.42469 | 0.0941673 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.630898 | 0.0244652 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.2208 | −0.589350 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.43519 | 0.171475 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.4391 | −0.866251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0338 | 0.926437 | 0.463218 | − | 0.886244i | \(-0.346695\pi\) | ||||
0.463218 | + | 0.886244i | \(0.346695\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.07838 | −0.118487 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.4114 | −0.746039 | −0.373020 | − | 0.927823i | \(-0.621678\pi\) | ||||
−0.373020 | + | 0.927823i | \(0.621678\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.173576 | 0.00666125 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.95669 | −0.189941 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.821503 | 0.0314339 | 0.0157170 | − | 0.999876i | \(-0.494997\pi\) | ||||
0.0157170 | + | 0.999876i | \(0.494997\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.52359 | −0.325670 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.98562 | −0.0757563 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.2267 | 0.884868 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.54638 | −0.172952 | −0.0864762 | − | 0.996254i | \(-0.527561\pi\) | ||||
−0.0864762 | + | 0.996254i | \(0.527561\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.92162 | −0.110983 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.3896 | −0.849287 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.1383 | −0.497650 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.86991 | 0.146373 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.6453 | −0.477605 | −0.238803 | − | 0.971068i | \(-0.576755\pi\) | ||||
−0.238803 | + | 0.971068i | \(0.576755\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.986669 | 0.0372129 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.18342 | −0.0822323 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.5548 | −0.396954 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.8059 | 0.480936 | 0.240468 | − | 0.970657i | \(-0.422699\pi\) | ||||
0.240468 | + | 0.970657i | \(0.422699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6020 | 0.510114 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.74435 | −0.215128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.41855 | 0.202642 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.45959 | 0.203892 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.90707 | 0.0711217 | 0.0355608 | − | 0.999368i | \(-0.488678\pi\) | ||||
0.0355608 | + | 0.999368i | \(0.488678\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7649 | −0.400905 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.6742 | −0.508549 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.75872 | −0.139595 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9239 | −0.961464 | −0.480732 | − | 0.876868i | \(-0.659629\pi\) | ||||
−0.480732 | + | 0.876868i | \(0.659629\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.5441 | −0.464597 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.09890 | 0.299549 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.1605 | −1.44642 | −0.723212 | − | 0.690626i | \(-0.757335\pi\) | ||||
−0.723212 | + | 0.690626i | \(0.757335\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.55971 | 0.131302 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.4969 | −0.386659 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.31351 | 0.305817 | 0.152909 | − | 0.988240i | \(-0.451136\pi\) | ||||
0.152909 | + | 0.988240i | \(0.451136\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.70928 | 0.0627918 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.5597 | 1.74480 | 0.872398 | − | 0.488796i | \(-0.162564\pi\) | ||||
0.872398 | + | 0.488796i | \(0.162564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.38962 | 0.234098 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.4741 | −0.383229 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.64301 | 0.133113 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.8622 | 0.870742 | 0.435371 | − | 0.900251i | \(-0.356617\pi\) | ||||
0.435371 | + | 0.900251i | \(0.356617\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.99386 | −0.181986 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.18342 | −0.152250 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.3402 | −1.61157 | −0.805785 | − | 0.592208i | \(-0.798257\pi\) | ||||
−0.805785 | + | 0.592208i | \(0.798257\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.73206 | −0.135465 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.577574 | 0.0209370 | 0.0104685 | − | 0.999945i | \(-0.496668\pi\) | ||||
0.0104685 | + | 0.999945i | \(0.496668\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.911781 | 0.0330087 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.84324 | 0.138953 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41.2762 | −1.49040 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.7938 | 0.785904 | 0.392952 | − | 0.919559i | \(-0.371454\pi\) | ||||
0.392952 | + | 0.919559i | \(0.371454\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.42243 | −0.123256 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.4135 | 1.56147 | 0.780737 | − | 0.624860i | \(-0.214844\pi\) | ||||
0.780737 | + | 0.624860i | \(0.214844\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.41855 | −0.0509558 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.335638 | −0.0120410 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.26180 | −0.331838 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.5753 | 0.485763 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.5708 | 0.413506 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.3607 | −0.548247 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.2134 | 0.506653 | 0.253326 | − | 0.967381i | \(-0.418475\pi\) | ||||
0.253326 | + | 0.967381i | \(0.418475\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.967195 | 0.0344331 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.48255 | 0.0882694 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.6163 | 1.47784 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.95055 | −0.140112 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.0482 | 0.780988 | 0.390494 | − | 0.920605i | \(-0.372304\pi\) | ||||
0.390494 | + | 0.920605i | \(0.372304\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.74435 | 0.203220 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.1773 | −0.536263 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.9483 | 0.598092 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.55479 | 0.0900444 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.61634 | 0.127301 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.49854 | 0.263635 | 0.131817 | − | 0.991274i | \(-0.457919\pi\) | ||||
0.131817 | + | 0.991274i | \(0.457919\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.4063 | 1.52420 | 0.762100 | − | 0.647459i | \(-0.224168\pi\) | ||||
0.762100 | + | 0.647459i | \(0.224168\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.90934 | −0.242321 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.1217 | −0.774889 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.70928 | 0.199742 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.41855 | 0.189339 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.7115 | 0.932239 | 0.466120 | − | 0.884722i | \(-0.345652\pi\) | ||||
0.466120 | + | 0.884722i | \(0.345652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.2206 | −0.774561 | −0.387280 | − | 0.921962i | \(-0.626585\pi\) | ||||
−0.387280 | + | 0.921962i | \(0.626585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.921622 | −0.0320868 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.7431 | −1.10382 | −0.551908 | − | 0.833905i | \(-0.686100\pi\) | ||||
−0.551908 | + | 0.833905i | \(0.686100\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.9093 | −1.42084 | −0.710420 | − | 0.703778i | \(-0.751495\pi\) | ||||
−0.710420 | + | 0.703778i | \(0.751495\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.24128 | −0.0777490 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.36523 | −0.324486 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.03612 | 0.0358563 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.36683 | 0.150940 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.3980 | 0.497075 | 0.248538 | − | 0.968622i | \(-0.420050\pi\) | ||||
0.248538 | + | 0.968622i | \(0.420050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.8720 | −0.512827 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.6865 | −0.540271 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.95055 | 0.101502 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.09663 | 0.175122 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.54250 | 0.224538 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.99547 | 0.136963 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.1399 | 0.826536 | 0.413268 | − | 0.910610i | \(-0.364387\pi\) | ||||
0.413268 | + | 0.910610i | \(0.364387\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.70928 | 0.0926553 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.4089 | 1.61946 | 0.809729 | − | 0.586804i | \(-0.199614\pi\) | ||||
0.809729 | + | 0.586804i | \(0.199614\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.9504 | −1.32897 | −0.664485 | − | 0.747302i | \(-0.731349\pi\) | ||||
−0.664485 | + | 0.747302i | \(0.731349\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.15061 | 0.107373 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.5392 | −0.699162 | −0.349581 | − | 0.936906i | \(-0.613676\pi\) | ||||
−0.349581 | + | 0.936906i | \(0.613676\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.6153 | −0.428933 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.08121 | −0.274452 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.58145 | 0.291106 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.4680 | 0.659648 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.745393 | 0.0252277 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.630898 | 0.0213282 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.56198 | −0.0865118 | −0.0432559 | − | 0.999064i | \(-0.513773\pi\) | ||||
−0.0432559 | + | 0.999064i | \(0.513773\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.42857 | −0.216830 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.0289 | −0.843246 | −0.421623 | − | 0.906771i | \(-0.638539\pi\) | ||||
−0.421623 | + | 0.906771i | \(0.638539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.2411 | 1.92632 | 0.963158 | − | 0.268936i | \(-0.0866719\pi\) | ||||
0.963158 | + | 0.268936i | \(0.0866719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.02052 | 0.235992 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.0049 | −1.04104 | −0.520522 | − | 0.853848i | \(-0.674263\pi\) | ||||
−0.520522 | + | 0.853848i | \(0.674263\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.13009 | −0.205597 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.0556 | −0.370376 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.04945 | 0.135510 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.4908 | −0.785210 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.92162 | 0.231106 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.33194 | 0.177830 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.3935 | 0.346258 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.94214 | −0.0646304 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.36069 | 0.111713 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.9783 | −0.829389 | −0.414695 | − | 0.909961i | \(-0.636112\pi\) | ||||
−0.414695 | + | 0.909961i | \(0.636112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −45.3256 | −1.50336 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.4678 | −1.80460 | −0.902300 | − | 0.431109i | \(-0.858122\pi\) | ||||
−0.902300 | + | 0.431109i | \(0.858122\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.60811 | −0.218697 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.07838 | −0.234004 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.24497 | −0.305296 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.7998 | −0.653134 | −0.326567 | − | 0.945174i | \(-0.605892\pi\) | ||||
−0.326567 | + | 0.945174i | \(0.605892\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.62929 | 0.0536869 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.1773 | −0.828720 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.986669 | 0.0324415 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −46.2278 | −1.51832 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.78992 | −0.255579 | −0.127790 | − | 0.991801i | \(-0.540788\pi\) | ||||
−0.127790 | + | 0.991801i | \(0.540788\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.60197 | −0.216371 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.7649 | 0.483380 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.42469 | 0.0792960 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.88058 | 0.0941046 | 0.0470523 | − | 0.998892i | \(-0.485017\pi\) | ||||
0.0470523 | + | 0.998892i | \(0.485017\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.18342 | 0.267056 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.6163 | 1.74784 | 0.873921 | − | 0.486067i | \(-0.161569\pi\) | ||||
0.873921 | + | 0.486067i | \(0.161569\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37.5052 | −1.22134 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.94214 | −0.0631779 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.7708 | 0.869935 | 0.434968 | − | 0.900446i | \(-0.356760\pi\) | ||||
0.434968 | + | 0.900446i | \(0.356760\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.4329 | −1.02036 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.33791 | −0.237948 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.1061 | 0.521727 | 0.260864 | − | 0.965376i | \(-0.415993\pi\) | ||||
0.260864 | + | 0.965376i | \(0.415993\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.4596 | −0.694416 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.46412 | 0.111979 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.37751 | −0.173649 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9877 | −0.935088 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.6442 | 0.504128 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.0856 | −0.421239 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.8537 | 0.574138 | 0.287069 | − | 0.957910i | \(-0.407319\pi\) | ||||
0.287069 | + | 0.957910i | \(0.407319\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.764867 | 0.0245711 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −58.1978 | −1.86766 | −0.933828 | − | 0.357722i | \(-0.883553\pi\) | ||||
−0.933828 | + | 0.357722i | \(0.883553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.1256 | −0.452845 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.70928 | 0.0547406 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.7766 | 0.408759 | 0.204380 | − | 0.978892i | \(-0.434482\pi\) | ||||
0.204380 | + | 0.978892i | \(0.434482\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.57531 | −0.306028 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.91548 | 0.125012 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.0833 | 1.27846 | 0.639229 | − | 0.769016i | \(-0.279253\pi\) | ||||
0.639229 | + | 0.769016i | \(0.279253\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.49693 | −0.0795588 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.37751 | −0.0438467 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.1194 | 0.735155 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.5318 | 0.874577 | 0.437289 | − | 0.899321i | \(-0.355939\pi\) | ||||
0.437289 | + | 0.899321i | \(0.355939\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.73206 | −0.118433 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.6803 | −0.401994 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.1399 | −0.637838 | −0.318919 | − | 0.947782i | \(-0.603320\pi\) | ||||
−0.318919 | + | 0.947782i | \(0.603320\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.03734 | −0.0960972 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6080.2.a.bu.1.2 | 3 | ||
4.3 | odd | 2 | 6080.2.a.bt.1.2 | 3 | |||
8.3 | odd | 2 | 3040.2.a.l.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 3040.2.a.m.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3040.2.a.l.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
3040.2.a.m.1.2 | yes | 3 | 8.5 | even | 2 | ||
6080.2.a.bt.1.2 | 3 | 4.3 | odd | 2 | |||
6080.2.a.bu.1.2 | 3 | 1.1 | even | 1 | trivial |