Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,4,Mod(1,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("152.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.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: | \(8.96829032087\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 152.1 |
$q$-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 | ||||||||
\(3\) | −4.27492 | −0.822708 | −0.411354 | − | 0.911476i | \(-0.634944\pi\) | ||||
−0.411354 | + | 0.911476i | \(0.634944\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.27492 | 0.114032 | 0.0570160 | − | 0.998373i | \(-0.481841\pi\) | ||||
0.0570160 | + | 0.998373i | \(0.481841\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0997 | 0.653321 | 0.326660 | − | 0.945142i | \(-0.394077\pi\) | ||||
0.326660 | + | 0.945142i | \(0.394077\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.72508 | −0.323151 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.9244 | 0.518721 | 0.259360 | − | 0.965781i | \(-0.416488\pi\) | ||||
0.259360 | + | 0.965781i | \(0.416488\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −55.9244 | −1.19313 | −0.596563 | − | 0.802566i | \(-0.703468\pi\) | ||||
−0.596563 | + | 0.802566i | \(0.703468\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.45017 | −0.0938151 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −89.7492 | −1.28043 | −0.640217 | − | 0.768194i | \(-0.721155\pi\) | ||||
−0.640217 | + | 0.768194i | \(0.721155\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −51.7251 | −0.537492 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −135.072 | −1.22454 | −0.612272 | − | 0.790647i | \(-0.709744\pi\) | ||||
−0.612272 | + | 0.790647i | \(0.709744\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −123.375 | −0.986997 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 152.722 | 1.08857 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −102.474 | −0.656172 | −0.328086 | − | 0.944648i | \(-0.606404\pi\) | ||||
−0.328086 | + | 0.944648i | \(0.606404\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −103.698 | −0.600795 | −0.300398 | − | 0.953814i | \(-0.597119\pi\) | ||||
−0.300398 | + | 0.953814i | \(0.597119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −80.9003 | −0.426756 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.4261 | 0.0744995 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 29.6977 | 0.131953 | 0.0659766 | − | 0.997821i | \(-0.478984\pi\) | ||||
0.0659766 | + | 0.997821i | \(0.478984\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 239.072 | 0.981595 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 234.743 | 0.894162 | 0.447081 | − | 0.894494i | \(-0.352464\pi\) | ||||
0.447081 | + | 0.894494i | \(0.352464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −53.3231 | −0.189109 | −0.0945546 | − | 0.995520i | \(-0.530143\pi\) | ||||
−0.0945546 | + | 0.995520i | \(0.530143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.1238 | −0.0368496 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −33.3713 | −0.103568 | −0.0517841 | − | 0.998658i | \(-0.516491\pi\) | ||||
−0.0517841 | + | 0.998658i | \(0.516491\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −196.598 | −0.573172 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 383.670 | 1.05342 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 93.1752 | 0.241483 | 0.120742 | − | 0.992684i | \(-0.461473\pi\) | ||||
0.120742 | + | 0.992684i | \(0.461473\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 24.1271 | 0.0591508 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 81.2234 | 0.188742 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 637.320 | 1.40630 | 0.703152 | − | 0.711039i | \(-0.251775\pi\) | ||||
0.703152 | + | 0.711039i | \(0.251775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −125.571 | −0.263568 | −0.131784 | − | 0.991278i | \(-0.542071\pi\) | ||||
−0.131784 | + | 0.991278i | \(0.542071\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −105.571 | −0.211121 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −71.2990 | −0.136055 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 119.375 | 0.217671 | 0.108835 | − | 0.994060i | \(-0.465288\pi\) | ||||
0.108835 | + | 0.994060i | \(0.465288\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 577.423 | 1.00744 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 18.5083 | 0.0309370 | 0.0154685 | − | 0.999880i | \(-0.495076\pi\) | ||||
0.0154685 | + | 0.999880i | \(0.495076\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −394.794 | −0.632975 | −0.316487 | − | 0.948597i | \(-0.602503\pi\) | ||||
−0.316487 | + | 0.948597i | \(0.602503\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 527.416 | 0.812010 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 228.979 | 0.338891 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 303.341 | 0.432006 | 0.216003 | − | 0.976393i | \(-0.430698\pi\) | ||||
0.216003 | + | 0.976393i | \(0.430698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −417.296 | −0.572422 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −394.337 | −0.521496 | −0.260748 | − | 0.965407i | \(-0.583969\pi\) | ||||
−0.260748 | + | 0.965407i | \(0.583969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −114.423 | −0.146010 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 438.069 | 0.539838 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1021.88 | −1.21707 | −0.608536 | − | 0.793526i | \(-0.708243\pi\) | ||||
−0.608536 | + | 0.793526i | \(0.708243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −676.667 | −0.779494 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 443.299 | 0.494279 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.2234 | −0.0261607 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1322.82 | 1.38466 | 0.692330 | − | 0.721581i | \(-0.256584\pi\) | ||||
0.692330 | + | 0.721581i | \(0.256584\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −165.117 | −0.167625 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1923.06 | 1.89457 | 0.947285 | − | 0.320391i | \(-0.103814\pi\) | ||||
0.947285 | + | 0.320391i | \(0.103814\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 467.774 | 0.447487 | 0.223743 | − | 0.974648i | \(-0.428172\pi\) | ||||
0.223743 | + | 0.974648i | \(0.428172\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −65.9452 | −0.0612914 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 260.468 | 0.235330 | 0.117665 | − | 0.993053i | \(-0.462459\pi\) | ||||
0.117665 | + | 0.993053i | \(0.462459\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −511.856 | −0.449789 | −0.224894 | − | 0.974383i | \(-0.572204\pi\) | ||||
−0.224894 | + | 0.974383i | \(0.572204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −126.955 | −0.108559 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1453.48 | −1.21002 | −0.605008 | − | 0.796220i | \(-0.706830\pi\) | ||||
−0.605008 | + | 0.796220i | \(0.706830\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −172.206 | −0.139637 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 487.945 | 0.385560 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1085.94 | −0.836534 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −972.866 | −0.730929 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1003.50 | −0.735634 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −316.657 | −0.226581 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2166.29 | −1.51360 | −0.756799 | − | 0.653647i | \(-0.773238\pi\) | ||||
−0.756799 | + | 0.653647i | \(0.773238\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 227.952 | 0.155582 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 329.310 | 0.219633 | 0.109817 | − | 0.993952i | \(-0.464974\pi\) | ||||
0.109817 | + | 0.993952i | \(0.464974\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −229.894 | −0.149882 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 194.708 | 0.124132 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 736.919 | 0.459556 | 0.229778 | − | 0.973243i | \(-0.426200\pi\) | ||||
0.229778 | + | 0.973243i | \(0.426200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3041.10 | −1.85571 | −0.927853 | − | 0.372947i | \(-0.878347\pi\) | ||||
−0.927853 | + | 0.372947i | \(0.878347\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 142.659 | 0.0852063 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1058.34 | −0.618899 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −130.646 | −0.0748247 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 840.440 | 0.471553 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2156.31 | 1.18558 | 0.592790 | − | 0.805357i | \(-0.298026\pi\) | ||||
0.592790 | + | 0.805357i | \(0.298026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1816.60 | −0.979024 | −0.489512 | − | 0.871997i | \(-0.662825\pi\) | ||||
−0.489512 | + | 0.871997i | \(0.662825\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 783.069 | 0.413774 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −132.206 | −0.0685099 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1118.10 | −0.568368 | −0.284184 | − | 0.958770i | \(-0.591723\pi\) | ||||
−0.284184 | + | 0.958770i | \(0.591723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −398.316 | −0.198670 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1634.33 | −0.800020 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3304.95 | −1.58812 | −0.794060 | − | 0.607839i | \(-0.792037\pi\) | ||||
−0.794060 | + | 0.607839i | \(0.792037\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −103.141 | −0.0486638 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1750.74 | 0.811237 | 0.405618 | − | 0.914043i | \(-0.367056\pi\) | ||||
0.405618 | + | 0.914043i | \(0.367056\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 930.541 | 0.423551 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 165.777 | 0.0741360 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2698.18 | 1.18577 | 0.592887 | − | 0.805286i | \(-0.297988\pi\) | ||||
0.592887 | + | 0.805286i | \(0.297988\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1492.79 | −0.644825 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2724.49 | −1.15698 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3867.80 | 1.61505 | 0.807523 | − | 0.589836i | \(-0.200808\pi\) | ||||
0.807523 | + | 0.589836i | \(0.200808\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3858.74 | 1.58463 | 0.792315 | − | 0.610112i | \(-0.208875\pi\) | ||||
0.792315 | + | 0.610112i | \(0.208875\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 536.804 | 0.216840 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 37.8621 | 0.0150469 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1698.45 | −0.664187 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1847.88 | 0.711184 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4111.06 | 1.55741 | 0.778706 | − | 0.627389i | \(-0.215876\pi\) | ||||
0.778706 | + | 0.627389i | \(0.215876\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1825.36 | −0.680789 | −0.340395 | − | 0.940283i | \(-0.610561\pi\) | ||||
−0.340395 | + | 0.940283i | \(0.610561\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 304.797 | 0.111933 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −767.088 | −0.277425 | −0.138713 | − | 0.990333i | \(-0.544296\pi\) | ||||
−0.138713 | + | 0.990333i | \(0.544296\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3176.43 | 1.13151 | 0.565757 | − | 0.824572i | \(-0.308584\pi\) | ||||
0.565757 | + | 0.824572i | \(0.308584\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −510.316 | −0.179079 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1239.90 | −0.428691 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 299.277 | 0.101963 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1178.52 | 0.395713 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −359.564 | −0.119003 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2460.54 | 0.802797 | 0.401399 | − | 0.915903i | \(-0.368524\pi\) | ||||
0.401399 | + | 0.915903i | \(0.368524\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −79.1214 | −0.0254521 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −67.9825 | −0.0215645 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1254.71 | −0.392512 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1687.71 | 0.520753 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5019.17 | 1.52772 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3731.73 | 1.12061 | 0.560304 | − | 0.828287i | \(-0.310684\pi\) | ||||
0.560304 | + | 0.828287i | \(0.310684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1076.45 | 0.318949 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 653.188 | 0.190985 | 0.0954926 | − | 0.995430i | \(-0.469557\pi\) | ||||
0.0954926 | + | 0.995430i | \(0.469557\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 340.511 | 0.0982602 | 0.0491301 | − | 0.998792i | \(-0.484355\pi\) | ||||
0.0491301 | + | 0.998792i | \(0.484355\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −978.867 | −0.278808 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3936.99 | −1.10696 | −0.553478 | − | 0.832864i | \(-0.686700\pi\) | ||||
−0.553478 | + | 0.832864i | \(0.686700\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −42.5456 | −0.0118101 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1296.76 | −0.355415 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4762.18 | 1.28887 | 0.644434 | − | 0.764660i | \(-0.277093\pi\) | ||||
0.644434 | + | 0.764660i | \(0.277093\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3893.55 | −1.04069 | −0.520343 | − | 0.853957i | \(-0.674196\pi\) | ||||
−0.520343 | + | 0.853957i | \(0.674196\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2339.58 | −0.617631 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −250.646 | −0.0653600 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1062.56 | 0.273722 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1685.76 | 0.429039 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1384.13 | 0.348069 | 0.174034 | − | 0.984740i | \(-0.444320\pi\) | ||||
0.174034 | + | 0.984740i | \(0.444320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2556.16 | −0.635196 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 489.148 | 0.120124 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4645.01 | −1.12742 | −0.563711 | − | 0.825972i | \(-0.690627\pi\) | ||||
−0.563711 | + | 0.825972i | \(0.690627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 359.332 | 0.0862078 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 894.096 | 0.212043 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2151.41 | −0.504416 | −0.252208 | − | 0.967673i | \(-0.581157\pi\) | ||||
−0.252208 | + | 0.967673i | \(0.581157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 118.791 | 0.0275368 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4368.47 | 1.00130 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5768.66 | −1.30752 | −0.653758 | − | 0.756704i | \(-0.726808\pi\) | ||||
−0.653758 | + | 0.756704i | \(0.726808\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6859.23 | −1.53752 | −0.768761 | − | 0.639537i | \(-0.779126\pi\) | ||||
−0.768761 | + | 0.639537i | \(0.779126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2892.70 | 0.641296 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2334.79 | −0.511976 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1237.24 | 0.268371 | 0.134185 | − | 0.990956i | \(-0.457158\pi\) | ||||
0.134185 | + | 0.990956i | \(0.457158\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 904.771 | 0.194148 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4355.21 | 0.924592 | 0.462296 | − | 0.886726i | \(-0.347026\pi\) | ||||
0.462296 | + | 0.886726i | \(0.347026\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3651.29 | −0.766949 | −0.383474 | − | 0.923551i | \(-0.625273\pi\) | ||||
−0.383474 | + | 0.923551i | \(0.625273\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 103.553 | 0.0215227 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2840.31 | 0.584174 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3141.91 | 0.639510 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5654.94 | −1.13917 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3391.25 | −0.676174 | −0.338087 | − | 0.941115i | \(-0.609780\pi\) | ||||
−0.338087 | + | 0.941115i | \(0.609780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 812.530 | 0.160364 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2890.17 | 0.564662 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7553.84 | 1.46104 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −645.192 | −0.123549 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8220.92 | −1.55868 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −160.092 | −0.0300552 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4343.35 | 0.807452 | 0.403726 | − | 0.914880i | \(-0.367715\pi\) | ||||
0.403726 | + | 0.914880i | \(0.367715\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1999.70 | −0.368151 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5671.28 | 1.03405 | 0.517024 | − | 0.855971i | \(-0.327040\pi\) | ||||
0.517024 | + | 0.855971i | \(0.327040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9449.71 | −1.70648 | −0.853241 | − | 0.521516i | \(-0.825367\pi\) | ||||
−0.853241 | + | 0.521516i | \(0.825367\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −134.594 | −0.0240746 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5390.75 | −0.955125 | −0.477562 | − | 0.878598i | \(-0.658480\pi\) | ||||
−0.477562 | + | 0.878598i | \(0.658480\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1939.27 | −0.340370 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1113.48 | −0.193608 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1705.23 | 0.293752 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6899.65 | 1.17761 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2188.14 | 0.370045 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −403.781 | −0.0676632 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9230.14 | −1.53273 | −0.766366 | − | 0.642404i | \(-0.777937\pi\) | ||||
−0.766366 | + | 0.642404i | \(0.777937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −259.115 | −0.0426408 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 152.193 | 0.0248214 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7815.90 | −1.26338 | −0.631690 | − | 0.775221i | \(-0.717638\pi\) | ||||
−0.631690 | + | 0.775221i | \(0.717638\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6213.50 | 0.995490 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1962.42 | −0.311645 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6528.96 | −1.02779 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 736.166 | 0.114881 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 680.076 | 0.105211 | 0.0526057 | − | 0.998615i | \(-0.483247\pi\) | ||||
0.0526057 | + | 0.998615i | \(0.483247\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3641.72 | 0.558558 | 0.279279 | − | 0.960210i | \(-0.409905\pi\) | ||||
0.279279 | + | 0.960210i | \(0.409905\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8540.88 | −1.29880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7885.46 | −1.18895 | −0.594477 | − | 0.804113i | \(-0.702641\pi\) | ||||
−0.594477 | + | 0.804113i | \(0.702641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.5965 | 0.00352781 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4642.28 | 0.688223 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2862.17 | −0.420779 | −0.210389 | − | 0.977618i | \(-0.567473\pi\) | ||||
−0.210389 | + | 0.977618i | \(0.567473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4158.92 | 0.601341 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −503.330 | −0.0721794 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9783.29 | −1.39151 | −0.695754 | − | 0.718280i | \(-0.744930\pi\) | ||||
−0.695754 | + | 0.718280i | \(0.744930\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2048.15 | −0.288949 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1127.39 | 0.157766 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6551.84 | 0.909495 | 0.454747 | − | 0.890621i | \(-0.349730\pi\) | ||||
0.454747 | + | 0.890621i | \(0.349730\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1353.68 | 0.186410 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5730.81 | 0.782896 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2228.78 | −0.302071 | −0.151035 | − | 0.988528i | \(-0.548261\pi\) | ||||
−0.151035 | + | 0.988528i | \(0.548261\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9260.71 | 1.24525 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5223.85 | −0.696935 | −0.348468 | − | 0.937321i | \(-0.613298\pi\) | ||||
−0.348468 | + | 0.937321i | \(0.613298\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 291.930 | 0.0386444 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 465.248 | 0.0611109 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7672.26 | −0.999998 | −0.499999 | − | 0.866026i | \(-0.666666\pi\) | ||||
−0.499999 | + | 0.866026i | \(0.666666\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12122.6 | 1.56795 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1407.77 | −0.180694 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 386.734 | 0.0492625 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13564.0 | −1.71475 | −0.857375 | − | 0.514692i | \(-0.827906\pi\) | ||||
−0.857375 | + | 0.514692i | \(0.827906\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 982.777 | 0.123309 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6488.39 | −0.808017 | −0.404009 | − | 0.914755i | \(-0.632383\pi\) | ||||
−0.404009 | + | 0.914755i | \(0.632383\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5799.23 | 0.716825 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −532.017 | −0.0652745 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 562.011 | 0.0684469 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14696.2 | 1.77672 | 0.888360 | − | 0.459147i | \(-0.151845\pi\) | ||||
0.888360 | + | 0.459147i | \(0.151845\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3150.27 | −0.378081 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7711.36 | 0.918768 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −502.747 | −0.0594672 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13000.5 | 1.52670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9492.08 | 1.10673 | 0.553363 | − | 0.832940i | \(-0.313344\pi\) | ||||
0.553363 | + | 0.832940i | \(0.313344\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13028.4 | −1.50823 | −0.754116 | − | 0.656741i | \(-0.771935\pi\) | ||||
−0.754116 | + | 0.656741i | \(0.771935\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 291.167 | 0.0334682 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11072.8 | 1.26378 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1519.36 | −0.172195 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4524.30 | 0.509174 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5404.99 | −0.604058 | −0.302029 | − | 0.953299i | \(-0.597664\pi\) | ||||
−0.302029 | + | 0.953299i | \(0.597664\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16745.4 | 1.85850 | 0.929252 | − | 0.369448i | \(-0.120453\pi\) | ||||
0.929252 | + | 0.369448i | \(0.120453\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 558.502 | 0.0615589 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2566.37 | 0.280930 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13422.6 | 1.45928 | 0.729641 | − | 0.683831i | \(-0.239687\pi\) | ||||
0.729641 | + | 0.683831i | \(0.239687\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1715.33 | 0.185221 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14048.7 | −1.50672 | −0.753358 | − | 0.657611i | \(-0.771567\pi\) | ||||
−0.753358 | + | 0.657611i | \(0.771567\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1302.82 | −0.138785 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9218.03 | −0.975387 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9841.11 | 1.03437 | 0.517183 | − | 0.855875i | \(-0.326980\pi\) | ||||
0.517183 | + | 0.855875i | \(0.326980\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4442.37 | 0.463820 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7765.81 | 0.805451 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −862.694 | −0.0888873 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4443.15 | 0.454796 | 0.227398 | − | 0.973802i | \(-0.426978\pi\) | ||||
0.227398 | + | 0.973802i | \(0.426978\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13706.7 | −1.39384 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12288.1 | −1.24146 | −0.620728 | − | 0.784026i | \(-0.713163\pi\) | ||||
−0.620728 | + | 0.784026i | \(0.713163\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4814.38 | 0.483246 | 0.241623 | − | 0.970370i | \(-0.422320\pi\) | ||||
0.241623 | + | 0.970370i | \(0.422320\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 565.170 | 0.0563637 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9863.03 | 0.977316 | 0.488658 | − | 0.872475i | \(-0.337487\pi\) | ||||
0.488658 | + | 0.872475i | \(0.337487\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1444.39 | 0.142209 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4779.77 | 0.467601 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1009.11 | −0.0980949 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2344.12 | 0.226433 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −812.962 | −0.0780356 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12743.3 | 1.21557 | 0.607785 | − | 0.794102i | \(-0.292058\pi\) | ||||
0.607785 | + | 0.794102i | \(0.292058\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1660.83 | −0.157437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6986.62 | 0.658183 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1686.48 | 0.157896 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4200.07 | −0.390807 | −0.195404 | − | 0.980723i | \(-0.562602\pi\) | ||||
−0.195404 | + | 0.980723i | \(0.562602\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14128.4 | 1.30656 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11292.3 | −1.03791 | −0.518955 | − | 0.854802i | \(-0.673679\pi\) | ||||
−0.518955 | + | 0.854802i | \(0.673679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9196.98 | 0.840185 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −210.511 | −0.0191146 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 223.944 | 0.0202118 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12126.6 | −1.08790 | −0.543948 | − | 0.839119i | \(-0.683071\pi\) | ||||
−0.543948 | + | 0.839119i | \(0.683071\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7484.28 | −0.667411 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2033.61 | −0.180267 | −0.0901336 | − | 0.995930i | \(-0.528729\pi\) | ||||
−0.0901336 | + | 0.995930i | \(0.528729\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2451.74 | 0.216042 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3977.98 | −0.348459 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1367.41 | −0.119076 | −0.0595379 | − | 0.998226i | \(-0.518963\pi\) | ||||
−0.0595379 | + | 0.998226i | \(0.518963\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4776.88 | −0.413535 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2901.71 | −0.249734 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 596.373 | 0.0510279 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −631.532 | −0.0537229 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11534.5 | −0.975545 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9613.98 | −0.808438 | −0.404219 | − | 0.914662i | \(-0.632457\pi\) | ||||
−0.404219 | + | 0.914662i | \(0.632457\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8185.79 | −0.684397 | −0.342199 | − | 0.939628i | \(-0.611172\pi\) | ||||
−0.342199 | + | 0.939628i | \(0.611172\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6381.56 | 0.530503 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9306.78 | 0.769278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6077.52 | 0.499508 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5560.67 | −0.454449 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13127.8 | −1.06685 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 332.075 | 0.0268352 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16534.5 | −1.32871 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3720.50 | −0.297316 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1869.73 | −0.148587 | −0.0742937 | − | 0.997236i | \(-0.523670\pi\) | ||||
−0.0742937 | + | 0.997236i | \(0.523670\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16495.8 | −1.30369 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −652.575 | −0.0512903 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4024.62 | 0.314589 | 0.157295 | − | 0.987552i | \(-0.449723\pi\) | ||||
0.157295 | + | 0.987552i | \(0.449723\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1095.61 | 0.0851724 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1947.01 | 0.150536 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3670.32 | 0.282239 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −161.857 | −0.0123792 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15750.7 | −1.19816 | −0.599082 | − | 0.800688i | \(-0.704468\pi\) | ||||
−0.599082 | + | 0.800688i | \(0.704468\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2982.06 | 0.225631 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7260.74 | 0.546432 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −641.091 | −0.0479907 | −0.0239954 | − | 0.999712i | \(-0.507639\pi\) | ||||
−0.0239954 | + | 0.999712i | \(0.507639\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1853.06 | −0.137981 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5049.14 | −0.373975 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18392.3 | −1.35509 | −0.677544 | − | 0.735482i | \(-0.736956\pi\) | ||||
−0.677544 | + | 0.735482i | \(0.736956\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1400.26 | 0.102625 | 0.0513126 | − | 0.998683i | \(-0.483660\pi\) | ||||
0.0513126 | + | 0.998683i | \(0.483660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17574.4 | −1.28130 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16664.5 | 1.20862 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23464.7 | 1.69298 | 0.846489 | − | 0.532406i | \(-0.178712\pi\) | ||||
0.846489 | + | 0.532406i | \(0.178712\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7803.26 | 0.560091 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4771.35 | −0.340704 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1763.29 | 0.125262 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 622.090 | 0.0439662 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1336.76 | −0.0939934 | −0.0469967 | − | 0.998895i | \(-0.514965\pi\) | ||||
−0.0469967 | + | 0.998895i | \(0.514965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1970.26 | 0.137832 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3279.24 | 0.228240 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14890.5 | −1.03116 | −0.515581 | − | 0.856841i | \(-0.672424\pi\) | ||||
−0.515581 | + | 0.856841i | \(0.672424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1384.48 | −0.0953917 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13579.0 | −0.930906 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22648.7 | 1.54491 | 0.772456 | − | 0.635068i | \(-0.219028\pi\) | ||||
0.772456 | + | 0.635068i | \(0.219028\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8930.64 | 0.606137 | 0.303069 | − | 0.952969i | \(-0.401989\pi\) | ||||
0.303069 | + | 0.952969i | \(0.401989\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1041.55 | −0.0703405 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1240.32 | −0.0833493 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5611.75 | −0.375245 | −0.187623 | − | 0.982241i | \(-0.560078\pi\) | ||||
−0.187623 | + | 0.982241i | \(0.560078\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5300.49 | 0.352687 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1866.27 | 0.123570 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16212.8 | −1.06823 | −0.534117 | − | 0.845410i | \(-0.679356\pi\) | ||||
−0.534117 | + | 0.845410i | \(0.679356\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1279.39 | −0.0838859 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26562.7 | −1.73318 | −0.866592 | − | 0.499017i | \(-0.833694\pi\) | ||||
−0.866592 | + | 0.499017i | \(0.833694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 816.376 | 0.0530096 | 0.0265048 | − | 0.999649i | \(-0.491562\pi\) | ||||
0.0265048 | + | 0.999649i | \(0.491562\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20628.5 | −1.33300 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12364.5 | −0.795139 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15018.1 | 0.961159 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1537.11 | 0.0979045 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2665.34 | −0.168957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29218.6 | 1.84338 | 0.921690 | − | 0.387928i | \(-0.126809\pi\) | ||||
0.921690 | + | 0.387928i | \(0.126809\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10518.6 | −0.660468 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2761.84 | −0.172599 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10994.6 | 0.683867 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −161.486 | −0.00999734 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4831.98 | −0.297740 | −0.148870 | − | 0.988857i | \(-0.547564\pi\) | ||||
−0.148870 | + | 0.988857i | \(0.547564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25259.5 | 1.54920 | 0.774602 | − | 0.632449i | \(-0.217950\pi\) | ||||
0.774602 | + | 0.632449i | \(0.217950\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 290.620 | 0.0177413 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11004.6 | 0.668676 | 0.334338 | − | 0.942453i | \(-0.391487\pi\) | ||||
0.334338 | + | 0.942453i | \(0.391487\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12060.9 | 0.729479 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5363.77 | 0.322923 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5034.69 | 0.301720 | 0.150860 | − | 0.988555i | \(-0.451796\pi\) | ||||
0.150860 | + | 0.988555i | \(0.451796\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 419.843 | 0.0250452 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3444.61 | 0.204547 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5027.20 | −0.297165 | −0.148583 | − | 0.988900i | \(-0.547471\pi\) | ||||
−0.148583 | + | 0.988900i | \(0.547471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28126.0 | −1.65503 | −0.827515 | − | 0.561444i | \(-0.810246\pi\) | ||||
−0.827515 | + | 0.561444i | \(0.810246\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21456.5 | −1.25687 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −293.095 | −0.0170914 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13841.4 | 0.803512 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15952.9 | −0.921933 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2376.35 | −0.136718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15864.9 | 0.908689 | 0.454344 | − | 0.890826i | \(-0.349874\pi\) | ||||
0.454344 | + | 0.890826i | \(0.349874\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18842.0 | −1.07441 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15911.8 | 0.903308 | 0.451654 | − | 0.892193i | \(-0.350834\pi\) | ||||
0.451654 | + | 0.892193i | \(0.350834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16005.7 | 0.904626 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2792.33 | −0.157125 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30172.0 | −1.69033 | −0.845167 | − | 0.534502i | \(-0.820499\pi\) | ||||
−0.845167 | + | 0.534502i | \(0.820499\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 939.510 | 0.0524042 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1455.65 | −0.0808394 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5210.77 | −0.288120 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14213.9 | −0.782522 | −0.391261 | − | 0.920280i | \(-0.627961\pi\) | ||||
−0.391261 | + | 0.920280i | \(0.627961\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1997.86 | −0.109513 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3877.16 | −0.211610 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21067.9 | −1.14491 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16830.3 | 0.910703 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25215.2 | 1.35858 | 0.679292 | − | 0.733869i | \(-0.262287\pi\) | ||||
0.679292 | + | 0.733869i | \(0.262287\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −564.256 | −0.0302721 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 181.879 | 0.00971625 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23268.4 | 1.23776 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34384.4 | 1.82134 | 0.910672 | − | 0.413130i | \(-0.135564\pi\) | ||||
0.910672 | + | 0.413130i | \(0.135564\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2646.67 | −0.139603 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14006.7 | 0.735700 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1349.29 | −0.0705744 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20357.9 | −1.06036 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4418.46 | 0.229180 | 0.114590 | − | 0.993413i | \(-0.463445\pi\) | ||||
0.114590 | + | 0.993413i | \(0.463445\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5659.91 | 0.292353 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16644.6 | 0.856181 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12642.7 | 0.647640 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 805.044 | 0.0410694 | 0.0205347 | − | 0.999789i | \(-0.493463\pi\) | ||||
0.0205347 | + | 0.999789i | \(0.493463\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21268.5 | 1.08055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4785.70 | 0.242142 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1662.37 | −0.0837668 | −0.0418834 | − | 0.999123i | \(-0.513336\pi\) | ||||
−0.0418834 | + | 0.999123i | \(0.513336\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1071.49 | 0.0537722 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2259.09 | 0.112910 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3145.59 | 0.156580 | 0.0782899 | − | 0.996931i | \(-0.475054\pi\) | ||||
0.0782899 | + | 0.996931i | \(0.475054\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4542.37 | −0.225193 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35469.5 | 1.75134 | 0.875672 | − | 0.482906i | \(-0.160419\pi\) | ||||
0.875672 | + | 0.482906i | \(0.160419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2749.11 | 0.135194 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3440.63 | 0.168522 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3151.57 | 0.153746 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29978.8 | −1.45665 | −0.728324 | − | 0.685233i | \(-0.759700\pi\) | ||||
−0.728324 | + | 0.685233i | \(0.759700\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5917.02 | −0.286359 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2316.01 | −0.111640 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33882.6 | −1.62680 | −0.813398 | − | 0.581707i | \(-0.802385\pi\) | ||||
−0.813398 | + | 0.581707i | \(0.802385\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10927.4 | 0.522581 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9023.05 | 0.429810 | 0.214905 | − | 0.976635i | \(-0.431056\pi\) | ||||
0.214905 | + | 0.976635i | \(0.431056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6193.29 | −0.293856 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 998.348 | 0.0471835 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35641.7 | −1.67790 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −773.311 | −0.0362631 | −0.0181315 | − | 0.999836i | \(-0.505772\pi\) | ||||
−0.0181315 | + | 0.999836i | \(0.505772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19857.0 | 0.927540 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19778.7 | 0.920299 | 0.460150 | − | 0.887841i | \(-0.347796\pi\) | ||||
0.460150 | + | 0.887841i | \(0.347796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12793.7 | 0.592983 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1536.12 | −0.0709238 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4460.11 | −0.205135 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 350.258 | 0.0160477 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15650.0 | −0.714288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1425.48 | −0.0648122 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32308.3 | 1.46336 | 0.731681 | − | 0.681648i | \(-0.238736\pi\) | ||||
0.731681 | + | 0.681648i | \(0.238736\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9197.09 | 0.414987 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17586.6 | −0.790528 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7022.46 | 0.314470 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −507.821 | −0.0226548 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40290.5 | 1.79067 | 0.895335 | − | 0.445394i | \(-0.146936\pi\) | ||||
0.895335 | + | 0.445394i | \(0.146936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2995.04 | 0.132612 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8916.02 | 0.393298 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7471.25 | −0.328337 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2083.64 | −0.0912279 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24660.6 | 1.07570 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16600.1 | −0.721417 | −0.360709 | − | 0.932679i | \(-0.617465\pi\) | ||||
−0.360709 | + | 0.932679i | \(0.617465\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9586.41 | 0.415073 | 0.207537 | − | 0.978227i | \(-0.433455\pi\) | ||||
0.207537 | + | 0.978227i | \(0.433455\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29322.6 | 1.26493 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4213.54 | −0.181097 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1013.14 | 0.0433846 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5903.98 | 0.251894 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33381.4 | −1.41902 | −0.709512 | − | 0.704693i | \(-0.751085\pi\) | ||||
−0.709512 | + | 0.704693i | \(0.751085\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3953.76 | −0.167460 | −0.0837299 | − | 0.996488i | \(-0.526683\pi\) | ||||
−0.0837299 | + | 0.996488i | \(0.526683\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9981.04 | 0.421207 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33403.5 | −1.40454 | −0.702270 | − | 0.711910i | \(-0.747830\pi\) | ||||
−0.702270 | + | 0.711910i | \(0.747830\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41612.3 | 1.74337 | 0.871686 | − | 0.490065i | \(-0.163027\pi\) | ||||
0.871686 | + | 0.490065i | \(0.163027\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5289.11 | −0.220791 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17644.5 | 0.733909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2232.05 | 0.0925070 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15836.9 | −0.654006 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10843.5 | 0.446199 | 0.223099 | − | 0.974796i | \(-0.428383\pi\) | ||||
0.223099 | + | 0.974796i | \(0.428383\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13888.0 | −0.569438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18618.2 | −0.760669 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1186.36 | 0.0482984 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11771.4 | −0.477531 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15609.0 | 0.630975 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4011.33 | −0.161583 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13530.7 | 0.543119 | 0.271560 | − | 0.962422i | \(-0.412461\pi\) | ||||
0.271560 | + | 0.962422i | \(0.412461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 211.351 | 0.00845388 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3510.58 | −0.139929 | −0.0699645 | − | 0.997549i | \(-0.522289\pi\) | ||||
−0.0699645 | + | 0.997549i | \(0.522289\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4945.74 | −0.196445 | −0.0982226 | − | 0.995164i | \(-0.531316\pi\) | ||||
−0.0982226 | + | 0.995164i | \(0.531316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12142.1 | −0.480605 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38957.6 | −1.53665 | −0.768326 | − | 0.640059i | \(-0.778910\pi\) | ||||
−0.768326 | + | 0.640059i | \(0.778910\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3439.96 | 0.135216 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13431.4 | −0.526130 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5740.54 | 0.224090 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6675.95 | −0.259708 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11541.7 | −0.447454 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3831.45 | −0.148030 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 544.671 | 0.0209718 | 0.0104859 | − | 0.999945i | \(-0.496662\pi\) | ||||
0.0104859 | + | 0.999945i | \(0.496662\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14497.3 | 0.556294 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19771.1 | −0.756079 | −0.378040 | − | 0.925789i | \(-0.623402\pi\) | ||||
−0.378040 | + | 0.925789i | \(0.623402\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12249.6 | −0.466854 | −0.233427 | − | 0.972374i | \(-0.574994\pi\) | ||||
−0.233427 | + | 0.972374i | \(0.574994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3473.50 | −0.131933 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21817.3 | −0.825877 | −0.412938 | − | 0.910759i | \(-0.635497\pi\) | ||||
−0.412938 | + | 0.910759i | \(0.635497\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26211.4 | −0.988866 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7897.08 | −0.296927 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 634.054 | 0.0237602 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4931.13 | 0.184167 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32292.0 | −1.20201 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10626.3 | 0.394225 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8362.40 | −0.309203 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2758.14 | 0.101645 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4919.58 | 0.180699 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35592.0 | −1.30299 | −0.651496 | − | 0.758652i | \(-0.725858\pi\) | ||||
−0.651496 | + | 0.758652i | \(0.725858\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16778.9 | −0.612233 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 952.654 | 0.0346464 | 0.0173232 | − | 0.999850i | \(-0.494486\pi\) | ||||
0.0173232 | + | 0.999850i | \(0.494486\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7462.60 | −0.270511 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 684.381 | 0.0247267 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3984.54 | 0.143491 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42326.8 | −1.51929 | −0.759647 | − | 0.650335i | \(-0.774628\pi\) | ||||
−0.759647 | + | 0.650335i | \(0.774628\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18567.4 | −0.664298 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1035.06 | −0.0369118 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3663.94 | −0.130237 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4081.37 | −0.144606 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27446.4 | −0.969309 | −0.484654 | − | 0.874706i | \(-0.661055\pi\) | ||||
−0.484654 | + | 0.874706i | \(0.661055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3735.36 | 0.131495 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24244.3 | −0.850720 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2165.38 | −0.0757387 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15560.3 | 0.542511 | 0.271256 | − | 0.962507i | \(-0.412561\pi\) | ||||
0.271256 | + | 0.962507i | \(0.412561\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40396.7 | 1.40394 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17725.4 | 0.614060 | 0.307030 | − | 0.951700i | \(-0.400665\pi\) | ||||
0.307030 | + | 0.951700i | \(0.400665\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31707.2 | −1.09494 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2355.90 | 0.0810977 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −588.382 | −0.0201899 | −0.0100950 | − | 0.999949i | \(-0.503213\pi\) | ||||
−0.0100950 | + | 0.999949i | \(0.503213\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22078.6 | 0.755219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23045.0 | 0.785789 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28644.2 | 0.973638 | 0.486819 | − | 0.873503i | \(-0.338157\pi\) | ||||
0.486819 | + | 0.873503i | \(0.338157\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5241.26 | 0.177595 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8290.20 | 0.280025 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8916.47 | 0.300238 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19037.8 | −0.639045 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2272.60 | −0.0760473 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2327.18 | −0.0776318 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44523.4 | 1.48064 | 0.740318 | − | 0.672257i | \(-0.234675\pi\) | ||||
0.740318 | + | 0.672257i | \(0.234675\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7289.74 | −0.241672 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18242.7 | 0.602922 | 0.301461 | − | 0.953478i | \(-0.402526\pi\) | ||||
0.301461 | + | 0.953478i | \(0.402526\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36796.4 | −1.21237 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −29495.4 | −0.968831 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23434.6 | 0.767390 | 0.383695 | − | 0.923460i | \(-0.374651\pi\) | ||||
0.383695 | + | 0.923460i | \(0.374651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19338.6 | −0.631321 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4465.99 | 0.145350 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −59519.4 | −1.93121 | −0.965603 | − | 0.260022i | \(-0.916270\pi\) | ||||
−0.965603 | + | 0.260022i | \(0.916270\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −977.974 | −0.0316354 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1726.13 | 0.0556671 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7202.47 | 0.231573 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8466.93 | 0.271404 | 0.135702 | − | 0.990750i | \(-0.456671\pi\) | ||||
0.135702 | + | 0.990750i | \(0.456671\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39458.1 | 1.26099 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4049.69 | 0.129029 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27474.3 | 0.872738 | 0.436369 | − | 0.899768i | \(-0.356264\pi\) | ||||
0.436369 | + | 0.899768i | \(0.356264\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4535.48 | 0.143640 |
(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 | 152.4.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1368.4.a.a.1.1 | 2 | |||
4.3 | odd | 2 | 304.4.a.e.1.2 | 2 | |||
8.3 | odd | 2 | 1216.4.a.k.1.1 | 2 | |||
8.5 | even | 2 | 1216.4.a.m.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.4.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
304.4.a.e.1.2 | 2 | 4.3 | odd | 2 | |||
1216.4.a.k.1.1 | 2 | 8.3 | odd | 2 | |||
1216.4.a.m.1.2 | 2 | 8.5 | even | 2 | |||
1368.4.a.a.1.1 | 2 | 3.2 | odd | 2 |