Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.20087896.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 21x^{3} + 5x^{2} + 84x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.50582\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.89831 | −1.09546 | −0.547729 | − | 0.836656i | \(-0.684507\pi\) | ||||
−0.547729 | + | 0.836656i | \(0.684507\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.43123 | −1.03455 | −0.517277 | − | 0.855818i | \(-0.673054\pi\) | ||||
−0.517277 | + | 0.855818i | \(0.673054\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.72973 | −1.31179 | −0.655895 | − | 0.754852i | \(-0.727709\pi\) | ||||
−0.655895 | + | 0.754852i | \(0.727709\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.61639 | 0.634568 | 0.317284 | − | 0.948331i | \(-0.397229\pi\) | ||||
0.317284 | + | 0.948331i | \(0.397229\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.28192 | −0.523508 | −0.261754 | − | 0.965135i | \(-0.584301\pi\) | ||||
−0.261754 | + | 0.965135i | \(0.584301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.89831 | −0.632463 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.53292 | 0.470351 | 0.235176 | − | 0.971953i | \(-0.424433\pi\) | ||||
0.235176 | + | 0.971953i | \(0.424433\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.19681 | −1.11298 | −0.556490 | − | 0.830854i | \(-0.687852\pi\) | ||||
−0.556490 | + | 0.830854i | \(0.687852\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.43123 | −0.597300 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.89831 | −0.489904 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89831 | 0.805277 | 0.402638 | − | 0.915359i | \(-0.368093\pi\) | ||||
0.402638 | + | 0.915359i | \(0.368093\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.72973 | −0.757363 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4787 | 1.63650 | 0.818251 | − | 0.574861i | \(-0.194944\pi\) | ||||
0.818251 | + | 0.574861i | \(0.194944\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.01165 | 1.37426 | 0.687132 | − | 0.726533i | \(-0.258870\pi\) | ||||
0.687132 | + | 0.726533i | \(0.258870\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.28192 | 0.332852 | 0.166426 | − | 0.986054i | \(-0.446777\pi\) | ||||
0.166426 | + | 0.986054i | \(0.446777\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.40019 | 0.200027 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.61639 | 0.366368 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.682109 | 0.0936949 | 0.0468475 | − | 0.998902i | \(-0.485083\pi\) | ||||
0.0468475 | + | 0.998902i | \(0.485083\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.43123 | −0.462667 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.28192 | −0.302247 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.2753 | 1.85849 | 0.929246 | − | 0.369462i | \(-0.120458\pi\) | ||||
0.929246 | + | 0.369462i | \(0.120458\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.98342 | 0.638061 | 0.319031 | − | 0.947744i | \(-0.396643\pi\) | ||||
0.319031 | + | 0.947744i | \(0.396643\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.89831 | −0.365153 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.72973 | −0.586651 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.74900 | −0.213674 | −0.106837 | − | 0.994277i | \(-0.534072\pi\) | ||||
−0.106837 | + | 0.994277i | \(0.534072\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.32954 | 0.751178 | 0.375589 | − | 0.926786i | \(-0.377440\pi\) | ||||
0.375589 | + | 0.926786i | \(0.377440\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.51470 | −0.177282 | −0.0886410 | − | 0.996064i | \(-0.528252\pi\) | ||||
−0.0886410 | + | 0.996064i | \(0.528252\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.94476 | 1.13331 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.86234 | 0.434547 | 0.217273 | − | 0.976111i | \(-0.430284\pi\) | ||||
0.217273 | + | 0.976111i | \(0.430284\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.61639 | 0.506715 | 0.253357 | − | 0.967373i | \(-0.418465\pi\) | ||||
0.253357 | + | 0.967373i | \(0.418465\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.61639 | 0.283787 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.53292 | 0.271557 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.31015 | −0.668874 | −0.334437 | − | 0.942418i | \(-0.608546\pi\) | ||||
−0.334437 | + | 0.942418i | \(0.608546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.7082 | 1.43701 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.19681 | −0.642579 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.28192 | −0.234120 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.8741 | 1.81484 | 0.907420 | − | 0.420225i | \(-0.138049\pi\) | ||||
0.907420 | + | 0.420225i | \(0.138049\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.43123 | −0.344851 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.76570 | 0.374701 | 0.187351 | − | 0.982293i | \(-0.440010\pi\) | ||||
0.187351 | + | 0.982293i | \(0.440010\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.09512 | −0.896168 | −0.448084 | − | 0.893991i | \(-0.647894\pi\) | ||||
−0.448084 | + | 0.893991i | \(0.647894\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.89831 | −0.282846 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.31777 | −0.224067 | −0.112034 | − | 0.993704i | \(-0.535736\pi\) | ||||
−0.112034 | + | 0.993704i | \(0.535736\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.6463 | 1.21129 | 0.605646 | − | 0.795734i | \(-0.292915\pi\) | ||||
0.605646 | + | 0.795734i | \(0.292915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.89831 | 0.464927 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.11439 | 0.575193 | 0.287597 | − | 0.957752i | \(-0.407144\pi\) | ||||
0.287597 | + | 0.957752i | \(0.407144\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.72973 | −0.437263 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.58311 | −0.695142 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.773325 | 0.0703023 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.4787 | 0.944835 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.13273 | −0.366720 | −0.183360 | − | 0.983046i | \(-0.558697\pi\) | ||||
−0.183360 | + | 0.983046i | \(0.558697\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.01165 | 0.793431 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.61370 | 0.573481 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.49812 | 0.384300 | 0.192150 | − | 0.981366i | \(-0.438454\pi\) | ||||
0.192150 | + | 0.981366i | \(0.438454\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.7606 | −1.25198 | −0.625991 | − | 0.779830i | \(-0.715305\pi\) | ||||
−0.625991 | + | 0.779830i | \(0.715305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.28192 | 0.192172 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.2288 | 1.35712 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.53292 | 0.210348 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.40019 | 0.115486 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.34776 | 0.765798 | 0.382899 | − | 0.923790i | \(-0.374926\pi\) | ||||
0.382899 | + | 0.923790i | \(0.374926\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.2267 | −0.994993 | −0.497496 | − | 0.867466i | \(-0.665747\pi\) | ||||
−0.497496 | + | 0.867466i | \(0.665747\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.61639 | 0.211523 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.19681 | −0.497740 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.334473 | 0.0266938 | 0.0133469 | − | 0.999911i | \(-0.495751\pi\) | ||||
0.0133469 | + | 0.999911i | \(0.495751\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.682109 | 0.0540948 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.89831 | −0.228419 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0952 | 0.947372 | 0.473686 | − | 0.880694i | \(-0.342923\pi\) | ||||
0.473686 | + | 0.880694i | \(0.342923\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.43123 | −0.267121 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.3346 | 1.49616 | 0.748078 | − | 0.663610i | \(-0.230977\pi\) | ||||
0.748078 | + | 0.663610i | \(0.230977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.37032 | 0.720794 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.28192 | −0.174503 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.203383 | −0.0154629 | −0.00773147 | − | 0.999970i | \(-0.502461\pi\) | ||||
−0.00773147 | + | 0.999970i | \(0.502461\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.89831 | −0.219092 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.2753 | 1.07300 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.62968 | 0.420782 | 0.210391 | − | 0.977617i | \(-0.432526\pi\) | ||||
0.210391 | + | 0.977617i | \(0.432526\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9282 | 1.10960 | 0.554801 | − | 0.831983i | \(-0.312794\pi\) | ||||
0.554801 | + | 0.831983i | \(0.312794\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.98342 | 0.368385 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.89831 | 0.360131 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.97743 | −0.656495 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.89831 | −0.210821 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.7414 | −1.13901 | −0.569503 | − | 0.821989i | \(-0.692864\pi\) | ||||
−0.569503 | + | 0.821989i | \(0.692864\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.3605 | 1.46558 | 0.732789 | − | 0.680456i | \(-0.238218\pi\) | ||||
0.732789 | + | 0.680456i | \(0.238218\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.72973 | −0.338703 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.16108 | −0.510206 | −0.255103 | − | 0.966914i | \(-0.582109\pi\) | ||||
−0.255103 | + | 0.966914i | \(0.582109\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.0951 | −1.49539 | −0.747697 | − | 0.664041i | \(-0.768840\pi\) | ||||
−0.747697 | + | 0.664041i | \(0.768840\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.74900 | −0.123365 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.34118 | −0.515250 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.4787 | 0.731866 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.82978 | 0.541597 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.76064 | 0.465422 | 0.232711 | − | 0.972546i | \(-0.425240\pi\) | ||||
0.232711 | + | 0.972546i | \(0.425240\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.32954 | 0.433693 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.01165 | 0.614589 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.9603 | 1.21922 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.51470 | −0.102354 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.3748 | −0.832420 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.58535 | 0.106163 | 0.0530816 | − | 0.998590i | \(-0.483096\pi\) | ||||
0.0530816 | + | 0.998590i | \(0.483096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.3279 | −0.950976 | −0.475488 | − | 0.879722i | \(-0.657728\pi\) | ||||
−0.475488 | + | 0.879722i | \(0.657728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.8200 | −1.11150 | −0.555749 | − | 0.831350i | \(-0.687569\pi\) | ||||
−0.555749 | + | 0.831350i | \(0.687569\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.94476 | 0.654317 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.2267 | −0.932020 | −0.466010 | − | 0.884779i | \(-0.654309\pi\) | ||||
−0.466010 | + | 0.884779i | \(0.654309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.28192 | 0.148856 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.86234 | 0.250886 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.6279 | −1.20494 | −0.602470 | − | 0.798142i | \(-0.705817\pi\) | ||||
−0.602470 | + | 0.798142i | \(0.705817\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3478 | 0.859805 | 0.429902 | − | 0.902875i | \(-0.358548\pi\) | ||||
0.429902 | + | 0.902875i | \(0.358548\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.40019 | 0.0894550 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.7929 | 0.686733 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.61639 | 0.292552 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7425 | −0.804302 | −0.402151 | − | 0.915573i | \(-0.631737\pi\) | ||||
−0.402151 | + | 0.915573i | \(0.631737\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.43123 | −0.215719 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.61639 | 0.163845 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.1079 | −1.06716 | −0.533582 | − | 0.845748i | \(-0.679154\pi\) | ||||
−0.533582 | + | 0.845748i | \(0.679154\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.1968 | −0.882147 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.53292 | 0.156784 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.141565 | −0.00872927 | −0.00436463 | − | 0.999990i | \(-0.501389\pi\) | ||||
−0.00436463 | + | 0.999990i | \(0.501389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.682109 | 0.0419016 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.31015 | −0.386175 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.69376 | −0.591039 | −0.295519 | − | 0.955337i | \(-0.595493\pi\) | ||||
−0.295519 | + | 0.955337i | \(0.595493\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.59981 | −0.461655 | −0.230828 | − | 0.972995i | \(-0.574143\pi\) | ||||
−0.230828 | + | 0.972995i | \(0.574143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.7082 | 0.829659 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.43123 | −0.206911 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2383 | −1.15592 | −0.577959 | − | 0.816066i | \(-0.696151\pi\) | ||||
−0.577959 | + | 0.816066i | \(0.696151\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.19681 | −0.370993 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3887 | 0.619737 | 0.309868 | − | 0.950779i | \(-0.399715\pi\) | ||||
0.309868 | + | 0.950779i | \(0.399715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.1095 | 1.19538 | 0.597691 | − | 0.801726i | \(-0.296085\pi\) | ||||
0.597691 | + | 0.801726i | \(0.296085\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.28192 | −0.135169 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.3706 | −1.79272 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.1545 | −0.597324 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.8741 | 1.04780 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.27935 | 0.308423 | 0.154211 | − | 0.988038i | \(-0.450716\pi\) | ||||
0.154211 | + | 0.988038i | \(0.450716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.2753 | 0.831143 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.43123 | −0.199100 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.72973 | −0.273527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.1185 | −1.50545 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.76570 | 0.216334 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.98342 | 0.285350 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.7414 | 0.670116 | 0.335058 | − | 0.942198i | \(-0.391244\pi\) | ||||
0.335058 | + | 0.942198i | \(0.391244\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.09512 | −0.517403 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.7039 | 1.34412 | 0.672062 | − | 0.740495i | \(-0.265409\pi\) | ||||
0.672062 | + | 0.740495i | \(0.265409\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6446 | 0.714716 | 0.357358 | − | 0.933967i | \(-0.383678\pi\) | ||||
0.357358 | + | 0.933967i | \(0.383678\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.89831 | −0.163301 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.1079 | −1.18554 | −0.592770 | − | 0.805372i | \(-0.701966\pi\) | ||||
−0.592770 | + | 0.805372i | \(0.701966\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.69102 | −0.486604 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.31777 | −0.129365 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.97039 | −0.332201 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.72973 | −0.262358 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.6463 | 0.699340 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.61370 | −0.364625 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0266 | 0.551111 | 0.275556 | − | 0.961285i | \(-0.411138\pi\) | ||||
0.275556 | + | 0.961285i | \(0.411138\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.89831 | 0.268426 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.74900 | −0.0955580 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.08359 | 0.494815 | 0.247407 | − | 0.968912i | \(-0.420421\pi\) | ||||
0.247407 | + | 0.968912i | \(0.420421\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.11439 | 0.332088 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.2627 | 1.15144 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.2300 | 0.876336 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.7541 | 1.00677 | 0.503386 | − | 0.864062i | \(-0.332088\pi\) | ||||
0.503386 | + | 0.864062i | \(0.332088\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.9276 | −0.691998 | −0.345999 | − | 0.938235i | \(-0.612460\pi\) | ||||
−0.345999 | + | 0.938235i | \(0.612460\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.72973 | −0.252454 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.5712 | 0.722320 | 0.361160 | − | 0.932504i | \(-0.382381\pi\) | ||||
0.361160 | + | 0.932504i | \(0.382381\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.32954 | 0.335937 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.58311 | −0.401341 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.3346 | 1.44267 | 0.721333 | − | 0.692589i | \(-0.243530\pi\) | ||||
0.721333 | + | 0.692589i | \(0.243530\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7929 | −0.725940 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.773325 | 0.0405891 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.51470 | −0.0792830 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.0591 | −0.733881 | −0.366941 | − | 0.930244i | \(-0.619595\pi\) | ||||
−0.366941 | + | 0.930244i | \(0.619595\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.4787 | 0.545501 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.97696 | −0.102639 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.6590 | 0.810790 | 0.405395 | − | 0.914142i | \(-0.367134\pi\) | ||||
0.405395 | + | 0.914142i | \(0.367134\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.9800 | −0.617002 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −38.5121 | −1.97824 | −0.989118 | − | 0.147124i | \(-0.952998\pi\) | ||||
−0.989118 | + | 0.147124i | \(0.952998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.13273 | −0.211726 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.61627 | −0.0825875 | −0.0412938 | − | 0.999147i | \(-0.513148\pi\) | ||||
−0.0412938 | + | 0.999147i | \(0.513148\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.94476 | 0.506832 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.01165 | 0.458088 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.1844 | 1.27690 | 0.638449 | − | 0.769664i | \(-0.279576\pi\) | ||||
0.638449 | + | 0.769664i | \(0.279576\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.61639 | 0.132317 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.86234 | 0.194335 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.3065 | −1.11953 | −0.559766 | − | 0.828651i | \(-0.689109\pi\) | ||||
−0.559766 | + | 0.828651i | \(0.689109\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.61370 | 0.331099 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.4014 | −1.86774 | −0.933868 | − | 0.357618i | \(-0.883589\pi\) | ||||
−0.933868 | + | 0.357618i | \(0.883589\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.3092 | 1.46000 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.8072 | −0.833103 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.1869 | 1.59154 | 0.795771 | − | 0.605598i | \(-0.207066\pi\) | ||||
0.795771 | + | 0.605598i | \(0.207066\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.49812 | 0.221876 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −41.3743 | −2.03590 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.61639 | 0.226610 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.7606 | −0.722832 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0012 | 0.635149 | 0.317574 | − | 0.948233i | \(-0.397132\pi\) | ||||
0.317574 | + | 0.948233i | \(0.397132\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4064 | 0.799601 | 0.399800 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399800 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.28192 | 0.110951 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.61639 | 0.126914 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.4435 | −0.698969 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.2288 | 0.783533 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.7581 | 0.759040 | 0.379520 | − | 0.925184i | \(-0.376089\pi\) | ||||
0.379520 | + | 0.925184i | \(0.376089\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.9101 | 1.00487 | 0.502437 | − | 0.864614i | \(-0.332437\pi\) | ||||
0.502437 | + | 0.864614i | \(0.332437\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.53292 | 0.121444 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.28192 | −0.109159 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.85307 | 0.470261 | 0.235131 | − | 0.971964i | \(-0.424448\pi\) | ||||
0.235131 | + | 0.971964i | \(0.424448\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.40019 | 0.0666758 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.2069 | 1.05508 | 0.527542 | − | 0.849529i | \(-0.323114\pi\) | ||||
0.527542 | + | 0.849529i | \(0.323114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.31015 | −0.299130 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.34776 | 0.442134 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.6783 | −1.77815 | −0.889075 | − | 0.457761i | \(-0.848652\pi\) | ||||
−0.889075 | + | 0.457761i | \(0.848652\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −35.9549 | −1.69305 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.2267 | −0.574459 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.7082 | 0.642651 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8116 | 0.599299 | 0.299650 | − | 0.954049i | \(-0.403130\pi\) | ||||
0.299650 | + | 0.954049i | \(0.403130\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.61639 | 0.122123 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.8610 | 1.20446 | 0.602232 | − | 0.798321i | \(-0.294278\pi\) | ||||
0.602232 | + | 0.798321i | \(0.294278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.8999 | 0.506564 | 0.253282 | − | 0.967393i | \(-0.418490\pi\) | ||||
0.253282 | + | 0.967393i | \(0.418490\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.19681 | −0.287370 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.8757 | −0.734642 | −0.367321 | − | 0.930094i | \(-0.619725\pi\) | ||||
−0.367321 | + | 0.930094i | \(0.619725\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.06914 | 0.234071 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.334473 | 0.0154117 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.9210 | −1.42175 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.28192 | −0.104702 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.682109 | 0.0312316 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.0129 | −0.594576 | −0.297288 | − | 0.954788i | \(-0.596082\pi\) | ||||
−0.297288 | + | 0.954788i | \(0.596082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.1677 | −1.05635 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.89831 | −0.131878 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.8741 | 0.811621 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.56865 | 0.0710824 | 0.0355412 | − | 0.999368i | \(-0.488685\pi\) | ||||
0.0355412 | + | 0.999368i | \(0.488685\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.0952 | 0.546966 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.9382 | −0.629021 | −0.314511 | − | 0.949254i | \(-0.601840\pi\) | ||||
−0.314511 | + | 0.949254i | \(0.601840\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.62711 | 0.298470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.43123 | −0.154222 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.3449 | −0.822883 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.56103 | −0.338478 | −0.169239 | − | 0.985575i | \(-0.554131\pi\) | ||||
−0.169239 | + | 0.985575i | \(0.554131\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.3346 | 0.863807 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.34118 | −0.327327 | −0.163664 | − | 0.986516i | \(-0.552331\pi\) | ||||
−0.163664 | + | 0.986516i | \(0.552331\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.76570 | 0.167571 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.37032 | 0.416151 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.74619 | 0.121723 | 0.0608614 | − | 0.998146i | \(-0.480615\pi\) | ||||
0.0608614 | + | 0.998146i | \(0.480615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.39006 | 0.194205 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.28192 | −0.100749 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.09512 | −0.400779 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.82978 | −0.344353 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.203383 | −0.00892753 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.4971 | −0.635128 | −0.317564 | − | 0.948237i | \(-0.602865\pi\) | ||||
−0.317564 | + | 0.948237i | \(0.602865\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.4286 | 1.72409 | 0.862045 | − | 0.506832i | \(-0.169183\pi\) | ||||
0.862045 | + | 0.506832i | \(0.169183\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.89831 | −0.126493 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.2133 | −0.706261 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.2753 | 0.619497 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.5615 | −2.14675 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.31777 | −0.100206 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.62968 | 0.242938 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.80438 | −0.206939 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.74393 | −0.289944 | −0.144972 | − | 0.989436i | \(-0.546309\pi\) | ||||
−0.144972 | + | 0.989436i | \(0.546309\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.9282 | 0.640629 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.6463 | 0.541706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.7249 | 1.09992 | 0.549959 | − | 0.835192i | \(-0.314643\pi\) | ||||
0.549959 | + | 0.835192i | \(0.314643\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.98342 | 0.212687 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.77991 | −0.246233 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1942 | −0.476027 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.89831 | 0.207922 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.3374 | −1.62441 | −0.812204 | − | 0.583373i | \(-0.801733\pi\) | ||||
−0.812204 | + | 0.583373i | \(0.801733\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.6226 | −1.80275 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.97743 | −0.379027 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.8757 | 1.34340 | 0.671701 | − | 0.740822i | \(-0.265564\pi\) | ||||
0.671701 | + | 0.740822i | \(0.265564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.11439 | 0.257234 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.89831 | −0.121718 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.4249 | 1.73662 | 0.868311 | − | 0.496020i | \(-0.165206\pi\) | ||||
0.868311 | + | 0.496020i | \(0.165206\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.5674 | 1.86509 | 0.932544 | − | 0.361057i | \(-0.117584\pi\) | ||||
0.932544 | + | 0.361057i | \(0.117584\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.7414 | −0.657605 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.1418 | 1.25482 | 0.627410 | − | 0.778689i | \(-0.284115\pi\) | ||||
0.627410 | + | 0.778689i | \(0.284115\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.3605 | 0.846152 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.3797 | −0.555084 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.34047 | −0.0969325 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.72973 | −0.195550 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.5215 | 0.640642 | 0.320321 | − | 0.947309i | \(-0.396209\pi\) | ||||
0.320321 | + | 0.947309i | \(0.396209\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.1406 | 0.582654 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.16108 | −0.294567 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.4042 | −1.04323 | −0.521613 | − | 0.853182i | \(-0.674669\pi\) | ||||
−0.521613 | + | 0.853182i | \(0.674669\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.58311 | −0.310877 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.0951 | −0.863366 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.3721 | 0.791522 | 0.395761 | − | 0.918353i | \(-0.370481\pi\) | ||||
0.395761 | + | 0.918353i | \(0.370481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.62687 | 0.270316 | 0.135158 | − | 0.990824i | \(-0.456846\pi\) | ||||
0.135158 | + | 0.990824i | \(0.456846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.74900 | −0.0712247 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.773325 | 0.0314401 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.99895 | −0.243490 | −0.121745 | − | 0.992561i | \(-0.538849\pi\) | ||||
−0.121745 | + | 0.992561i | \(0.538849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.34118 | −0.297480 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.7929 | −0.436632 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.5640 | 0.547843 | 0.273922 | − | 0.961752i | \(-0.411679\pi\) | ||||
0.273922 | + | 0.961752i | \(0.411679\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.4787 | 0.422543 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.9089 | −1.12357 | −0.561785 | − | 0.827283i | \(-0.689885\pi\) | ||||
−0.561785 | + | 0.827283i | \(0.689885\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7482 | −0.954521 | −0.477260 | − | 0.878762i | \(-0.658370\pi\) | ||||
−0.477260 | + | 0.878762i | \(0.658370\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.2887 | 0.732723 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.82978 | 0.312691 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.8159 | 0.511003 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5108 | 0.537857 | 0.268928 | − | 0.963160i | \(-0.413330\pi\) | ||||
0.268928 | + | 0.963160i | \(0.413330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.76064 | 0.268711 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.13273 | −0.164002 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.62252 | −0.262394 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.32954 | 0.250393 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.5556 | −1.52286 | −0.761428 | − | 0.648250i | \(-0.775501\pi\) | ||||
−0.761428 | + | 0.648250i | \(0.775501\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.3848 | 0.803897 | 0.401949 | − | 0.915662i | \(-0.368333\pi\) | ||||
0.401949 | + | 0.915662i | \(0.368333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.01165 | 0.354833 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.3710 | 0.525670 | 0.262835 | − | 0.964841i | \(-0.415342\pi\) | ||||
0.262835 | + | 0.964841i | \(0.415342\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.9820 | −1.92271 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.9603 | 0.703918 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.63699 | −0.259726 | −0.129863 | − | 0.991532i | \(-0.541454\pi\) | ||||
−0.129863 | + | 0.991532i | \(0.541454\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.51470 | −0.0590940 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.2897 | 0.985146 | 0.492573 | − | 0.870271i | \(-0.336056\pi\) | ||||
0.492573 | + | 0.870271i | \(0.336056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.8292 | 0.460101 | 0.230051 | − | 0.973179i | \(-0.426111\pi\) | ||||
0.230051 | + | 0.973179i | \(0.426111\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.3748 | −0.480598 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.61370 | 0.256468 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.53292 | 0.0980750 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.58535 | 0.0612933 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.0992 | −0.660109 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2819 | 0.473433 | 0.236717 | − | 0.971579i | \(-0.423929\pi\) | ||||
0.236717 | + | 0.971579i | \(0.423929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.8065 | 0.684360 | 0.342180 | − | 0.939635i | \(-0.388835\pi\) | ||||
0.342180 | + | 0.939635i | \(0.388835\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −51.8047 | −1.98808 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.3279 | −0.549046 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.3678 | 1.58289 | 0.791447 | − | 0.611238i | \(-0.209328\pi\) | ||||
0.791447 | + | 0.611238i | \(0.209328\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.49812 | 0.171864 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.8200 | −0.641724 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.22619 | −0.122908 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.6530 | 1.66064 | 0.830319 | − | 0.557289i | \(-0.188158\pi\) | ||||
0.830319 | + | 0.557289i | \(0.188158\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.94476 | 0.377770 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.7606 | −0.559903 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.4164 | 1.03847 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.2267 | −0.538102 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.2396 | −1.63314 | −0.816569 | − | 0.577248i | \(-0.804127\pi\) | ||||
−0.816569 | + | 0.577248i | \(0.804127\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.1775 | −0.421569 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.28192 | 0.0859420 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.9142 | −0.410469 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 50.2595 | 1.88754 | 0.943768 | − | 0.330609i | \(-0.107254\pi\) | ||||
0.943768 | + | 0.330609i | \(0.107254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.86234 | 0.144849 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.19681 | −0.232072 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.2288 | 0.606922 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.6279 | −0.695672 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.8254 | −1.41065 | −0.705325 | − | 0.708884i | \(-0.749199\pi\) | ||||
−0.705325 | + | 0.708884i | \(0.749199\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.3605 | 0.981715 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.3478 | 0.496408 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.53292 | 0.0940703 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.9548 | 1.14805 | 0.574024 | − | 0.818838i | \(-0.305381\pi\) | ||||
0.574024 | + | 0.818838i | \(0.305381\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.5780 | 0.872063 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.9781 | 1.58743 | 0.793715 | − | 0.608289i | \(-0.208144\pi\) | ||||
0.793715 | + | 0.608289i | \(0.208144\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.40019 | 0.0516468 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.00121 | 0.221057 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.0322 | −0.442612 | −0.221306 | − | 0.975204i | \(-0.571032\pi\) | ||||
−0.221306 | + | 0.975204i | \(0.571032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.7929 | 0.396485 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.8686 | −0.435415 | −0.217708 | − | 0.976014i | \(-0.569858\pi\) | ||||
−0.217708 | + | 0.976014i | \(0.569858\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.34776 | 0.342475 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.61639 | 0.168905 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.71761 | 0.245456 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.7022 | −1.59472 | −0.797358 | − | 0.603506i | \(-0.793770\pi\) | ||||
−0.797358 | + | 0.603506i | \(0.793770\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.7425 | −0.464364 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.2267 | −0.444974 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.3155 | −1.35625 | −0.678127 | − | 0.734945i | \(-0.737208\pi\) | ||||
−0.678127 | + | 0.734945i | \(0.737208\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.43123 | −0.124546 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.45167 | −0.342623 | −0.171311 | − | 0.985217i | \(-0.554800\pi\) | ||||
−0.171311 | + | 0.985217i | \(0.554800\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.6528 | −1.32692 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.61639 | 0.0945958 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −67.5185 | −2.43795 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.74724 | −0.171190 | −0.0855949 | − | 0.996330i | \(-0.527279\pi\) | ||||
−0.0855949 | + | 0.996330i | \(0.527279\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.1079 | −0.616127 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.1841 | 0.402265 | 0.201133 | − | 0.979564i | \(-0.435538\pi\) | ||||
0.201133 | + | 0.979564i | \(0.435538\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.19681 | −0.222596 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.1968 | −0.509308 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.9116 | −0.856722 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.7181 | −0.777134 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.53292 | 0.0905192 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.334473 | 0.0119378 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.9780 | 1.13989 | 0.569947 | − | 0.821682i | \(-0.306964\pi\) | ||||
0.569947 | + | 0.821682i | \(0.306964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.141565 | −0.00503985 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.7214 | −0.630100 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.5702 | −0.837003 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.682109 | 0.0241919 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.5354 | 1.43584 | 0.717919 | − | 0.696126i | \(-0.245095\pi\) | ||||
0.717919 | + | 0.696126i | \(0.245095\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.97039 | 0.211217 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.31015 | −0.222958 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.19728 | 0.183408 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.89831 | −0.102152 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.69376 | −0.341236 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.1178 | −0.601829 | −0.300915 | − | 0.953651i | \(-0.597292\pi\) | ||||
−0.300915 | + | 0.953651i | \(0.597292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.6198 | −1.04009 | −0.520046 | − | 0.854138i | \(-0.674085\pi\) | ||||
−0.520046 | + | 0.854138i | \(0.674085\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.59981 | −0.266537 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0952 | 0.423678 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.5638 | −0.719438 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.7082 | 0.479004 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.1958 | −0.984039 | −0.492020 | − | 0.870584i | \(-0.663741\pi\) | ||||
−0.492020 | + | 0.870584i | \(0.663741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.1535 | −1.43452 | −0.717260 | − | 0.696806i | \(-0.754604\pi\) | ||||
−0.717260 | + | 0.696806i | \(0.754604\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.43123 | −0.119460 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.8433 | −0.516152 | −0.258076 | − | 0.966125i | \(-0.583089\pi\) | ||||
−0.258076 | + | 0.966125i | \(0.583089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.1778 | 1.29124 | 0.645619 | − | 0.763660i | \(-0.276599\pi\) | ||||
0.645619 | + | 0.763660i | \(0.276599\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.2383 | −0.667370 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.66345 | 0.126931 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.3346 | 0.669102 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.19681 | −0.214193 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.4131 | 1.22260 | 0.611299 | − | 0.791400i | \(-0.290647\pi\) | ||||
0.611299 | + | 0.791400i | \(0.290647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.5843 | −0.778770 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.3887 | 0.357805 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.37032 | 0.322349 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.24134 | −0.0770132 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.1095 | 0.690155 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.89831 | 0.167912 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.58863 | 0.259830 | 0.129915 | − | 0.991525i | \(-0.458530\pi\) | ||||
0.129915 | + | 0.991525i | \(0.458530\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.28192 | −0.0780399 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.3219 | −0.489227 | −0.244614 | − | 0.969621i | \(-0.578661\pi\) | ||||
−0.244614 | + | 0.969621i | \(0.578661\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.9977 | 1.74002 | 0.870010 | − | 0.493035i | \(-0.164113\pi\) | ||||
0.870010 | + | 0.493035i | \(0.164113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.3706 | −1.03503 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.4463 | 1.54701 | 0.773505 | − | 0.633790i | \(-0.218502\pi\) | ||||
0.773505 | + | 0.633790i | \(0.218502\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.203383 | −0.00691524 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.1545 | −0.344865 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.2526 | −0.449562 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.27229 | 0.280296 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.8741 | 0.604947 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.89831 | −0.0979807 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.8832 | −0.435036 | −0.217518 | − | 0.976056i | \(-0.569796\pi\) | ||||
−0.217518 | + | 0.976056i | \(0.569796\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.27935 | 0.178068 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.0480 | −1.11342 | −0.556708 | − | 0.830709i | \(-0.687936\pi\) | ||||
−0.556708 | + | 0.830709i | \(0.687936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.94710 | 0.267441 | 0.133721 | − | 0.991019i | \(-0.457308\pi\) | ||||
0.133721 | + | 0.991019i | \(0.457308\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.2753 | 0.479860 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.5314 | −1.19303 | −0.596514 | − | 0.802603i | \(-0.703448\pi\) | ||||
−0.596514 | + | 0.802603i | \(0.703448\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.9779 | 0.401727 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.43123 | −0.114950 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.20715 | −0.174251 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.62968 | 0.188179 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.72973 | −0.157921 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.6960 | −0.523491 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.78466 | 0.0594558 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.1185 | −0.869170 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.9282 | 0.496229 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.2938 | 1.83600 | 0.918001 | − | 0.396579i | \(-0.129803\pi\) | ||||
0.918001 | + | 0.396579i | \(0.129803\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.76570 | 0.124900 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.6203 | −1.34581 | −0.672905 | − | 0.739729i | \(-0.734954\pi\) | ||||
−0.672905 | + | 0.739729i | \(0.734954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.8399 | −0.524224 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.98342 | 0.164747 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0994 | 1.32276 | 0.661378 | − | 0.750052i | \(-0.269972\pi\) | ||||
0.661378 | + | 0.750052i | \(0.269972\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.7414 | 0.386891 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.9370 | −0.985388 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.89831 | 0.161055 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.09512 | −0.298723 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.3976 | 0.702034 | 0.351017 | − | 0.936369i | \(-0.385836\pi\) | ||||
0.351017 | + | 0.936369i | \(0.385836\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.19512 | −0.104716 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.7039 | 0.776030 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.97743 | −0.293593 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.0879 | −1.57096 | −0.785481 | − | 0.618886i | \(-0.787584\pi\) | ||||
−0.785481 | + | 0.618886i | \(0.787584\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.6446 | 0.412642 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.9704 | 1.17260 | 0.586301 | − | 0.810094i | \(-0.300584\pi\) | ||||
0.586301 | + | 0.810094i | \(0.300584\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.4787 | 0.341234 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.89831 | −0.0942820 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.1568 | −1.23993 | −0.619965 | − | 0.784629i | \(-0.712853\pi\) | ||||
−0.619965 | + | 0.784629i | \(0.712853\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.16411 | 0.232557 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.1079 | −0.684472 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.7187 | 0.638751 | 0.319375 | − | 0.947628i | \(-0.396527\pi\) | ||||
0.319375 | + | 0.947628i | \(0.396527\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.7414 | −0.509379 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.69102 | −0.280941 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.0369 | −0.420984 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.40043 | 0.238724 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.31777 | −0.0746891 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.3605 | 0.655426 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.9496 | 1.60627 | 0.803135 | − | 0.595797i | \(-0.203164\pi\) | ||||
0.803135 | + | 0.595797i | \(0.203164\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.97039 | −0.191797 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.4016 | 1.32864 | 0.664321 | − | 0.747448i | \(-0.268721\pi\) | ||||
0.664321 | + | 0.747448i | \(0.268721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.7809 | 1.37149 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.72973 | −0.151473 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.7018 | 1.11021 | 0.555104 | − | 0.831781i | \(-0.312679\pi\) | ||||
0.555104 | + | 0.831781i | \(0.312679\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.6515 | 0.691986 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.6463 | 0.403764 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.8239 | 0.983131 | 0.491565 | − | 0.870841i | \(-0.336425\pi\) | ||||
0.491565 | + | 0.870841i | \(0.336425\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.16108 | −0.228171 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.61370 | −0.210516 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.01165 | 0.286554 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.53774 | −0.0488478 | −0.0244239 | − | 0.999702i | \(-0.507775\pi\) | ||||
−0.0244239 | + | 0.999702i | \(0.507775\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.0266 | 0.318184 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0951 | −0.668760 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.8478 | −1.70538 | −0.852688 | − | 0.522420i | \(-0.825029\pi\) | ||||
−0.852688 | + | 0.522420i | \(0.825029\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.89831 | 0.154976 |
(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 | 5520.2.a.cc.1.1 | 5 | ||
4.3 | odd | 2 | 2760.2.a.w.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 8280.2.a.br.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.w.1.5 | ✓ | 5 | 4.3 | odd | 2 | ||
5520.2.a.cc.1.1 | 5 | 1.1 | even | 1 | trivial | ||
8280.2.a.br.1.5 | 5 | 12.11 | even | 2 |