Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,4,Mod(863,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.863");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(50.9776502450\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 863.8 | ||
Character | \(\chi\) | \(=\) | 864.863 |
Dual form | 864.4.c.b.863.17 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 8.99651i | − 0.804673i | −0.915492 | − | 0.402336i | \(-0.868198\pi\) | ||||
0.915492 | − | 0.402336i | \(-0.131802\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 35.3962i | 1.91121i | 0.294645 | + | 0.955607i | \(0.404799\pi\) | ||||
−0.294645 | + | 0.955607i | \(0.595201\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.88651 | −0.0791195 | −0.0395598 | − | 0.999217i | \(-0.512596\pi\) | ||||
−0.0395598 | + | 0.999217i | \(0.512596\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 47.2668 | 1.00842 | 0.504210 | − | 0.863581i | \(-0.331784\pi\) | ||||
0.504210 | + | 0.863581i | \(0.331784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.19790i | − 0.0456238i | −0.999740 | − | 0.0228119i | \(-0.992738\pi\) | ||||
0.999740 | − | 0.0228119i | \(-0.00726188\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 92.6761i | 1.11902i | 0.828824 | + | 0.559509i | \(0.189010\pi\) | ||||
−0.828824 | + | 0.559509i | \(0.810990\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −182.495 | −1.65447 | −0.827235 | − | 0.561855i | \(-0.810088\pi\) | ||||
−0.827235 | + | 0.561855i | \(0.810088\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.0628 | 0.352502 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 161.054i | − 1.03128i | −0.856806 | − | 0.515639i | \(-0.827555\pi\) | ||||
0.856806 | − | 0.515639i | \(-0.172445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.7511i | 0.0680825i | 0.999420 | + | 0.0340412i | \(0.0108378\pi\) | ||||
−0.999420 | + | 0.0340412i | \(0.989162\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 318.442 | 1.53790 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 71.1977 | 0.316347 | 0.158173 | − | 0.987411i | \(-0.449440\pi\) | ||||
0.158173 | + | 0.987411i | \(0.449440\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 111.322i | − 0.424040i | −0.977265 | − | 0.212020i | \(-0.931996\pi\) | ||||
0.977265 | − | 0.212020i | \(-0.0680042\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 30.0027i | 0.106404i | 0.998584 | + | 0.0532019i | \(0.0169427\pi\) | ||||
−0.998584 | + | 0.0532019i | \(0.983057\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −523.230 | −1.62385 | −0.811924 | − | 0.583763i | \(-0.801580\pi\) | ||||
−0.811924 | + | 0.583763i | \(0.801580\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −909.889 | −2.65274 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 683.907i | 1.77249i | 0.463219 | + | 0.886244i | \(0.346694\pi\) | ||||
−0.463219 | + | 0.886244i | \(0.653306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 25.9685i | 0.0636653i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 146.873 | 0.324089 | 0.162044 | − | 0.986783i | \(-0.448191\pi\) | ||||
0.162044 | + | 0.986783i | \(0.448191\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −717.089 | −1.50515 | −0.752573 | − | 0.658509i | \(-0.771187\pi\) | ||||
−0.752573 | + | 0.658509i | \(0.771187\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 425.237i | − 0.811448i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 228.684i | − 0.416988i | −0.978024 | − | 0.208494i | \(-0.933144\pi\) | ||||
0.978024 | − | 0.208494i | \(-0.0668562\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1042.11 | 1.74191 | 0.870955 | − | 0.491363i | \(-0.163501\pi\) | ||||
0.870955 | + | 0.491363i | \(0.163501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −676.843 | −1.08518 | −0.542592 | − | 0.839996i | \(-0.682557\pi\) | ||||
−0.542592 | + | 0.839996i | \(0.682557\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 102.171i | − 0.151214i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 865.762i | 1.23298i | 0.787361 | + | 0.616492i | \(0.211447\pi\) | ||||
−0.787361 | + | 0.616492i | \(0.788553\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −334.416 | −0.442251 | −0.221126 | − | 0.975245i | \(-0.570973\pi\) | ||||
−0.221126 | + | 0.975245i | \(0.570973\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.7699 | −0.0367122 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 598.589i | 0.712924i | 0.934310 | + | 0.356462i | \(0.116017\pi\) | ||||
−0.934310 | + | 0.356462i | \(0.883983\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1673.07i | 1.92731i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 833.762 | 0.900443 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1034.49 | 1.08286 | 0.541428 | − | 0.840747i | \(-0.317884\pi\) | ||||
0.541428 | + | 0.840747i | \(0.317884\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1563.41i | 1.54025i | 0.637892 | + | 0.770126i | \(0.279806\pi\) | ||||
−0.637892 | + | 0.770126i | \(0.720194\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 769.270i | 0.735907i | 0.929844 | + | 0.367954i | \(0.119941\pi\) | ||||
−0.929844 | + | 0.367954i | \(0.880059\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1577.71 | −1.42545 | −0.712725 | − | 0.701443i | \(-0.752539\pi\) | ||||
−0.712725 | + | 0.701443i | \(0.752539\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 371.530 | 0.326478 | 0.163239 | − | 0.986587i | \(-0.447806\pi\) | ||||
0.163239 | + | 0.986587i | \(0.447806\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1713.42i | − 1.42642i | −0.700952 | − | 0.713208i | \(-0.747241\pi\) | ||||
0.700952 | − | 0.713208i | \(-0.252759\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1641.82i | 1.33131i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 113.193 | 0.0871967 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1322.67 | −0.993740 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1520.98i | − 1.08832i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2035.62i | 1.42230i | 0.703040 | + | 0.711150i | \(0.251826\pi\) | ||||
−0.703040 | + | 0.711150i | \(0.748174\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 31.6824 | 0.0211305 | 0.0105653 | − | 0.999944i | \(-0.496637\pi\) | ||||
0.0105653 | + | 0.999944i | \(0.496637\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3280.38 | −2.13868 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1032.16i | 0.643676i | 0.946795 | + | 0.321838i | \(0.104301\pi\) | ||||
−0.946795 | + | 0.321838i | \(0.895699\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1315.52i | 0.802743i | 0.915915 | + | 0.401371i | \(0.131466\pi\) | ||||
−0.915915 | + | 0.401371i | \(0.868534\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −136.436 | −0.0797857 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1448.93 | −0.829841 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1824.84i | 1.00334i | 0.865060 | + | 0.501668i | \(0.167280\pi\) | ||||
−0.865060 | + | 0.501668i | \(0.832720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 247.339i | − 0.133299i | −0.997776 | − | 0.0666497i | \(-0.978769\pi\) | ||||
0.997776 | − | 0.0666497i | \(-0.0212310\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 105.719 | 0.0547841 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1889.16 | −0.960329 | −0.480164 | − | 0.877179i | \(-0.659423\pi\) | ||||
−0.480164 | + | 0.877179i | \(0.659423\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 6459.62i | − 3.16205i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1966.48i | − 0.944950i | −0.881344 | − | 0.472475i | \(-0.843361\pi\) | ||||
0.881344 | − | 0.472475i | \(-0.156639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −443.537 | −0.205520 | −0.102760 | − | 0.994706i | \(-0.532767\pi\) | ||||
−0.102760 | + | 0.994706i | \(0.532767\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.1537 | 0.0169111 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3105.57i | 1.36481i | 0.730975 | + | 0.682404i | \(0.239066\pi\) | ||||
−0.730975 | + | 0.682404i | \(0.760934\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1559.65i | 0.673707i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1973.24 | −0.823947 | −0.411974 | − | 0.911196i | \(-0.635160\pi\) | ||||
−0.411974 | + | 0.911196i | \(0.635160\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3126.34 | −1.28386 | −0.641932 | − | 0.766762i | \(-0.721867\pi\) | ||||
−0.641932 | + | 0.766762i | \(0.721867\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 640.531i | − 0.254555i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.23075i | 0.00360973i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3230.96 | −1.22400 | −0.612000 | − | 0.790857i | \(-0.709635\pi\) | ||||
−0.612000 | + | 0.790857i | \(0.709635\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −707.651 | −0.263927 | −0.131963 | − | 0.991255i | \(-0.542128\pi\) | ||||
−0.131963 | + | 0.991255i | \(0.542128\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2826.44i | 1.02221i | 0.859518 | + | 0.511106i | \(0.170764\pi\) | ||||
−0.859518 | + | 0.511106i | \(0.829236\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 2702.47i | − 0.962678i | −0.876534 | − | 0.481339i | \(-0.840151\pi\) | ||||
0.876534 | − | 0.481339i | \(-0.159849\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5700.71 | 1.97099 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1001.51 | −0.341213 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 267.510i | − 0.0885362i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 231.147i | − 0.0754161i | −0.999289 | − | 0.0377080i | \(-0.987994\pi\) | ||||
0.999289 | − | 0.0377080i | \(-0.0120057\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 269.919 | 0.0856202 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −415.943 | −0.130120 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 151.154i | − 0.0460079i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 784.305i | − 0.235520i | −0.993042 | − | 0.117760i | \(-0.962429\pi\) | ||||
0.993042 | − | 0.117760i | \(-0.0375714\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1070.17 | 0.312907 | 0.156453 | − | 0.987685i | \(-0.449994\pi\) | ||||
0.156453 | + | 0.987685i | \(0.449994\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4827.56 | 1.39308 | 0.696538 | − | 0.717520i | \(-0.254723\pi\) | ||||
0.696538 | + | 0.717520i | \(0.254723\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 2689.22i | − 0.756124i | −0.925780 | − | 0.378062i | \(-0.876591\pi\) | ||||
0.925780 | − | 0.378062i | \(-0.123409\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4707.24i | 1.30667i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1031.51 | 0.279175 | 0.139587 | − | 0.990210i | \(-0.455422\pi\) | ||||
0.139587 | + | 0.990210i | \(0.455422\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2351.47 | −0.628513 | −0.314256 | − | 0.949338i | \(-0.601755\pi\) | ||||
−0.314256 | + | 0.949338i | \(0.601755\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8185.83i | 2.13459i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4380.51i | 1.12844i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5723.75 | 1.43936 | 0.719681 | − | 0.694305i | \(-0.244288\pi\) | ||||
0.719681 | + | 0.694305i | \(0.244288\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 526.773 | 0.130901 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 5348.44i | − 1.29816i | −0.760721 | − | 0.649079i | \(-0.775154\pi\) | ||||
0.760721 | − | 0.649079i | \(-0.224846\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2520.13i | 0.604606i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7061.50 | −1.65563 | −0.827815 | − | 0.561000i | \(-0.810417\pi\) | ||||
−0.827815 | + | 0.561000i | \(0.810417\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6152.78 | 1.42627 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2946.25i | 0.667792i | 0.942610 | + | 0.333896i | \(0.108363\pi\) | ||||
−0.942610 | + | 0.333896i | \(0.891637\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2048.60i | 0.459201i | 0.973285 | + | 0.229600i | \(0.0737419\pi\) | ||||
−0.973285 | + | 0.229600i | \(0.926258\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −127.187 | −0.0278898 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8653.43 | 1.87702 | 0.938509 | − | 0.345254i | \(-0.112207\pi\) | ||||
0.938509 | + | 0.345254i | \(0.112207\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2228.69i | 0.473141i | 0.971614 | + | 0.236570i | \(0.0760233\pi\) | ||||
−0.971614 | + | 0.236570i | \(0.923977\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3226.05i | − 0.677628i | −0.940853 | − | 0.338814i | \(-0.889974\pi\) | ||||
0.940853 | − | 0.338814i | \(-0.110026\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3940.39 | 0.810431 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4902.77 | 0.997918 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3044.49i | − 0.607034i | −0.952826 | − | 0.303517i | \(-0.901839\pi\) | ||||
0.952826 | − | 0.303517i | \(-0.0981610\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 1321.34i | − 0.260785i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8625.96 | −1.66840 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1061.98 | −0.203360 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6451.30i | 1.21115i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7394.12i | − 1.37461i | −0.726370 | − | 0.687304i | \(-0.758794\pi\) | ||||
0.726370 | − | 0.687304i | \(-0.241206\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8469.46 | 1.54424 | 0.772121 | − | 0.635476i | \(-0.219196\pi\) | ||||
0.772121 | + | 0.635476i | \(0.219196\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6394.80 | −1.15481 | −0.577405 | − | 0.816458i | \(-0.695934\pi\) | ||||
−0.577405 | + | 0.816458i | \(0.695934\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3234.14i | 0.573021i | 0.958077 | + | 0.286510i | \(0.0924953\pi\) | ||||
−0.958077 | + | 0.286510i | \(0.907505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 464.885i | 0.0815942i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 296.369 | 0.0510538 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2082.71 | 0.355470 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 18520.3i | − 3.10352i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 7913.16i | − 1.31404i | −0.753874 | − | 0.657019i | \(-0.771817\pi\) | ||||
0.753874 | − | 0.657019i | \(-0.228183\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2057.36 | −0.335539 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 638.612 | 0.103227 | 0.0516134 | − | 0.998667i | \(-0.483564\pi\) | ||||
0.0516134 | + | 0.998667i | \(0.483564\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 33.9196i | − 0.00538665i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 20065.7i | − 3.15873i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2900.91 | −0.448786 | −0.224393 | − | 0.974499i | \(-0.572040\pi\) | ||||
−0.224393 | + | 0.974499i | \(0.572040\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11177.2 | 1.71432 | 0.857162 | − | 0.515047i | \(-0.172225\pi\) | ||||
0.857162 | + | 0.515047i | \(0.172225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 4077.91i | − 0.614859i | −0.951571 | − | 0.307430i | \(-0.900531\pi\) | ||||
0.951571 | − | 0.307430i | \(-0.0994688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 9375.35i | − 1.40167i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10771.0 | 1.58349 | 0.791744 | − | 0.610853i | \(-0.209173\pi\) | ||||
0.791744 | + | 0.610853i | \(0.209173\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1729.86 | −0.252202 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6089.22i | 0.873218i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 11402.5i | − 1.62181i | −0.585178 | − | 0.810905i | \(-0.698975\pi\) | ||||
0.585178 | − | 0.810905i | \(-0.301025\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24207.7 | −3.38760 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9787.33 | −1.35863 | −0.679315 | − | 0.733847i | \(-0.737723\pi\) | ||||
−0.679315 | + | 0.733847i | \(0.737723\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 7612.53i | − 1.03996i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14341.9i | 1.94378i | 0.235438 | + | 0.971889i | \(0.424348\pi\) | ||||
−0.235438 | + | 0.971889i | \(0.575652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4395.34 | −0.586400 | −0.293200 | − | 0.956051i | \(-0.594720\pi\) | ||||
−0.293200 | + | 0.956051i | \(0.594720\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −919.185 | −0.121678 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5527.39i | 0.720436i | 0.932868 | + | 0.360218i | \(0.117298\pi\) | ||||
−0.932868 | + | 0.360218i | \(0.882702\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 583.600i | 0.0754832i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7788.84 | 0.992149 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2814.85 | 0.355852 | 0.177926 | − | 0.984044i | \(-0.443061\pi\) | ||||
0.177926 | + | 0.984044i | \(0.443061\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9331.30i | 1.16205i | 0.813885 | + | 0.581026i | \(0.197349\pi\) | ||||
−0.813885 | + | 0.581026i | \(0.802651\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 555.437i | 0.0686557i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −205.513 | −0.0250292 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12861.5 | 1.55492 | 0.777458 | − | 0.628935i | \(-0.216509\pi\) | ||||
0.777458 | + | 0.628935i | \(0.216509\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5198.74i | 0.619403i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3008.57i | 0.355868i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6006.40 | 0.700314 | 0.350157 | − | 0.936691i | \(-0.386128\pi\) | ||||
0.350157 | + | 0.936691i | \(0.386128\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3455.89 | 0.400071 | 0.200035 | − | 0.979789i | \(-0.435894\pi\) | ||||
0.200035 | + | 0.979789i | \(0.435894\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 140.908i | − 0.0160825i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 25382.2i | − 2.87665i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11022.5 | −1.23187 | −0.615935 | − | 0.787797i | \(-0.711221\pi\) | ||||
−0.615935 | + | 0.787797i | \(0.711221\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11314.1 | 1.25571 | 0.627856 | − | 0.778330i | \(-0.283933\pi\) | ||||
0.627856 | + | 0.778330i | \(0.283933\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 16912.9i | − 1.85138i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14000.0i | 1.52205i | 0.648720 | + | 0.761027i | \(0.275305\pi\) | ||||
−0.648720 | + | 0.761027i | \(0.724695\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9289.05 | 0.996244 | 0.498122 | − | 0.867107i | \(-0.334023\pi\) | ||||
0.498122 | + | 0.867107i | \(0.334023\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5385.21 | 0.573671 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 14592.2i | − 1.53374i | −0.641804 | − | 0.766869i | \(-0.721814\pi\) | ||||
0.641804 | − | 0.766869i | \(-0.278186\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 321.333i | 0.0335498i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15051.8 | 1.55085 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6034.71 | 0.617707 | 0.308853 | − | 0.951110i | \(-0.400055\pi\) | ||||
0.308853 | + | 0.951110i | \(0.400055\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14113.8i | 1.42591i | 0.701211 | + | 0.712953i | \(0.252643\pi\) | ||||
−0.701211 | + | 0.712953i | \(0.747357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 615.069i | 0.0617380i | 0.999523 | + | 0.0308690i | \(0.00982746\pi\) | ||||
−0.999523 | + | 0.0308690i | \(0.990173\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7925.30 | 0.785309 | 0.392655 | − | 0.919686i | \(-0.371557\pi\) | ||||
0.392655 | + | 0.919686i | \(0.371557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8094.54 | 0.796954 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 86.6029i | − 0.00841862i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4083.56i | 0.394456i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12221.7 | −1.16581 | −0.582904 | − | 0.812541i | \(-0.698084\pi\) | ||||
−0.582904 | + | 0.812541i | \(0.698084\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3365.29 | 0.319010 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 9306.84i | − 0.871344i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 4058.84i | − 0.377667i | −0.982009 | − | 0.188833i | \(-0.939529\pi\) | ||||
0.982009 | − | 0.188833i | \(-0.0604706\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4906.51 | 0.450973 | 0.225486 | − | 0.974246i | \(-0.427603\pi\) | ||||
0.225486 | + | 0.974246i | \(0.427603\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −515.035 | −0.0470508 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 36886.7i | 3.32916i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7905.92i | 0.709254i | 0.935008 | + | 0.354627i | \(0.115392\pi\) | ||||
−0.935008 | + | 0.354627i | \(0.884608\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16309.7 | −1.44575 | −0.722876 | − | 0.690977i | \(-0.757180\pi\) | ||||
−0.722876 | + | 0.690977i | \(0.757180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14065.3 | 1.23940 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10047.1i | 0.874915i | 0.899239 | + | 0.437458i | \(0.144121\pi\) | ||||
−0.899239 | + | 0.437458i | \(0.855879\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 23957.6i | − 2.07402i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6920.75 | 0.592164 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1510.31 | 0.128478 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 1449.81i | − 0.121914i | −0.998140 | − | 0.0609572i | \(-0.980585\pi\) | ||||
0.998140 | − | 0.0609572i | \(-0.0194153\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 191.955i | 0.0160489i | 0.999968 | + | 0.00802447i | \(0.00255430\pi\) | ||||
−0.999968 | + | 0.00802447i | \(0.997446\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.5788 | 0.00310618 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21137.4 | 1.73727 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5261.86i | − 0.427610i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14193.9i | 1.14702i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2626.40 | 0.209883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3901.48 | −0.310051 | −0.155026 | − | 0.987910i | \(-0.549546\pi\) | ||||
−0.155026 | + | 0.987910i | \(0.549546\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 3342.47i | − 0.262708i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15716.7i | 1.22851i | 0.789107 | + | 0.614256i | \(0.210544\pi\) | ||||
−0.789107 | + | 0.614256i | \(0.789456\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14925.9 | 1.15402 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30644.7 | −2.35650 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 20798.3i | − 1.58214i | −0.611725 | − | 0.791071i | \(-0.709524\pi\) | ||||
0.611725 | − | 0.791071i | \(-0.290476\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1418.13i | 0.107300i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11103.8 | 0.831203 | 0.415602 | − | 0.909547i | \(-0.363571\pi\) | ||||
0.415602 | + | 0.909547i | \(0.363571\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15414.8 | −1.14780 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14825.2i | 1.09228i | 0.837694 | + | 0.546139i | \(0.183903\pi\) | ||||
−0.837694 | + | 0.546139i | \(0.816097\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 14831.3i | − 1.08699i | −0.839412 | − | 0.543495i | \(-0.817101\pi\) | ||||
0.839412 | − | 0.543495i | \(-0.182899\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8041.23 | −0.583204 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25829.0 | −1.86356 | −0.931780 | − | 0.363024i | \(-0.881744\pi\) | ||||
−0.931780 | + | 0.363024i | \(0.881744\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 11837.0i | − 0.845237i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1974.10i | − 0.140238i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4780.76 | −0.336155 | −0.168078 | − | 0.985774i | \(-0.553756\pi\) | ||||
−0.168078 | + | 0.985774i | \(0.553756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1089.04 | −0.0761856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4513.09i | 0.312530i | 0.987715 | + | 0.156265i | \(0.0499455\pi\) | ||||
−0.987715 | + | 0.156265i | \(0.950055\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1018.34i | − 0.0701648i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4646.83 | 0.316968 | 0.158484 | − | 0.987362i | \(-0.449339\pi\) | ||||
0.158484 | + | 0.987362i | \(0.449339\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1610.99 | 0.109341 | 0.0546703 | − | 0.998504i | \(-0.482589\pi\) | ||||
0.0546703 | + | 0.998504i | \(0.482589\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11899.4i | 0.799635i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10227.7i | 0.683906i | 0.939717 | + | 0.341953i | \(0.111088\pi\) | ||||
−0.939717 | + | 0.341953i | \(0.888912\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24731.4 | −1.63752 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11957.6 | −0.787869 | −0.393934 | − | 0.919139i | \(-0.628886\pi\) | ||||
−0.393934 | + | 0.919139i | \(0.628886\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 11950.8i | − 0.779777i | −0.920862 | − | 0.389889i | \(-0.872514\pi\) | ||||
0.920862 | − | 0.389889i | \(-0.127486\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5595.35i | − 0.363322i | −0.983361 | − | 0.181661i | \(-0.941853\pi\) | ||||
0.983361 | − | 0.181661i | \(-0.0581473\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21187.7 | −1.36255 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8175.63 | −0.523240 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 227.683i | − 0.0144329i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 19082.2i | − 1.20389i | −0.798539 | − | 0.601943i | \(-0.794393\pi\) | ||||
0.798539 | − | 0.601943i | \(-0.205607\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18313.5 | 1.14449 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −43007.6 | −2.67507 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 27622.7i | − 1.70208i | −0.525105 | − | 0.851038i | \(-0.675974\pi\) | ||||
0.525105 | − | 0.851038i | \(-0.324026\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 19288.6i | − 1.18300i | −0.806306 | − | 0.591498i | \(-0.798537\pi\) | ||||
0.806306 | − | 0.591498i | \(-0.201463\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11188.6 | 0.679861 | 0.339931 | − | 0.940450i | \(-0.389596\pi\) | ||||
0.339931 | + | 0.940450i | \(0.389596\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −423.950 | −0.0256417 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 14406.5i | − 0.863356i | −0.902028 | − | 0.431678i | \(-0.857922\pi\) | ||||
0.902028 | − | 0.431678i | \(-0.142078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 285.031i | − 0.0170032i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27480.4 | −1.62441 | −0.812205 | − | 0.583373i | \(-0.801733\pi\) | ||||
−0.812205 | + | 0.583373i | \(0.801733\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24268.4 | 1.42804 | 0.714019 | − | 0.700127i | \(-0.246873\pi\) | ||||
0.714019 | + | 0.700127i | \(0.246873\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 29512.0i | 1.72094i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29391.6i | 1.70622i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2069.88 | 0.119086 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15316.2 | −0.877261 | −0.438631 | − | 0.898667i | \(-0.644536\pi\) | ||||
−0.438631 | + | 0.898667i | \(0.644536\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3781.94i | − 0.214700i | −0.994221 | − | 0.107350i | \(-0.965763\pi\) | ||||
0.994221 | − | 0.107350i | \(-0.0342365\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36617.1i | 2.06957i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24496.7 | 1.37238 | 0.686192 | − | 0.727420i | \(-0.259281\pi\) | ||||
0.686192 | + | 0.727420i | \(0.259281\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9285.87 | 0.517948 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32326.1i | 1.78741i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21646.8i | 1.19172i | 0.803087 | + | 0.595862i | \(0.203190\pi\) | ||||
−0.803087 | + | 0.595862i | \(0.796810\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11835.1 | 0.645945 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −355.998 | −0.0193463 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 22628.9i | − 1.21923i | −0.792696 | − | 0.609617i | \(-0.791323\pi\) | ||||
0.792696 | − | 0.609617i | \(-0.208677\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6598.32i | 0.353998i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −55338.8 | −2.94375 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14610.9 | 0.773940 | 0.386970 | − | 0.922092i | \(-0.373522\pi\) | ||||
0.386970 | + | 0.922092i | \(0.373522\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2144.51i | − 0.112640i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1227.45i | 0.0642014i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12211.2 | 0.633381 | 0.316690 | − | 0.948529i | \(-0.397428\pi\) | ||||
0.316690 | + | 0.948529i | \(0.397428\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27229.2 | −1.40648 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 7096.50i | − 0.363528i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13197.1i | 0.673250i | 0.941639 | + | 0.336625i | \(0.109285\pi\) | ||||
−0.941639 | + | 0.336625i | \(0.890715\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 95.9454 | 0.00485454 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22565.2 | 1.13706 | 0.568531 | − | 0.822662i | \(-0.307512\pi\) | ||||
0.568531 | + | 0.822662i | \(0.307512\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 660.098i | 0.0329919i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25340.2i | 1.26137i | 0.776038 | + | 0.630686i | \(0.217226\pi\) | ||||
−0.776038 | + | 0.630686i | \(0.782774\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4341.02 | −0.214343 | −0.107171 | − | 0.994241i | \(-0.534179\pi\) | ||||
−0.107171 | + | 0.994241i | \(0.534179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16417.2 | 0.807356 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 55845.0i | − 2.72434i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30349.5i | 1.47466i | 0.675534 | + | 0.737328i | \(0.263913\pi\) | ||||
−0.675534 | + | 0.737328i | \(0.736087\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2225.19 | −0.107262 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.5144 | −0.00213726 | −0.00106863 | − | 0.999999i | \(-0.500340\pi\) | ||||
−0.00106863 | + | 0.999999i | \(0.500340\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12698.4i | 0.604885i | 0.953168 | + | 0.302442i | \(0.0978020\pi\) | ||||
−0.953168 | + | 0.302442i | \(0.902198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13150.7i | 0.623969i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6942.22 | 0.326817 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3620.32 | −0.169769 | −0.0848843 | − | 0.996391i | \(-0.527052\pi\) | ||||
−0.0848843 | + | 0.996391i | \(0.527052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30688.4i | 1.42792i | 0.700184 | + | 0.713962i | \(0.253101\pi\) | ||||
−0.700184 | + | 0.713962i | \(0.746899\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 517.785i | 0.0239992i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10316.9 | 0.474509 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3008.06 | −0.137819 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16995.9i | 0.772750i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26627.7i | 1.20607i | 0.797715 | + | 0.603035i | \(0.206042\pi\) | ||||
−0.797715 | + | 0.603035i | \(0.793958\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 60648.6 | 2.72619 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33894.5 | −1.51782 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 11706.4i | − 0.520279i | −0.965571 | − | 0.260139i | \(-0.916232\pi\) | ||||
0.965571 | − | 0.260139i | \(-0.0837685\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1673.23i | 0.0740861i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1953.71 | 0.0858593 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −58114.1 | −2.54441 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34745.1i | 1.50998i | 0.655736 | + | 0.754990i | \(0.272358\pi\) | ||||
−0.655736 | + | 0.754990i | \(0.727642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5538.24i | 0.239795i | 0.992786 | + | 0.119898i | \(0.0382567\pi\) | ||||
−0.992786 | + | 0.119898i | \(0.961743\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17691.5 | −0.760375 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2780.53 | −0.119068 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1271.12i | − 0.0540347i | −0.999635 | − | 0.0270174i | \(-0.991399\pi\) | ||||
0.999635 | − | 0.0270174i | \(-0.00860094\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36457.6i | 1.54414i | 0.635535 | + | 0.772072i | \(0.280780\pi\) | ||||
−0.635535 | + | 0.772072i | \(0.719220\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10229.2 | −0.430115 | −0.215058 | − | 0.976601i | \(-0.568994\pi\) | ||||
−0.215058 | + | 0.976601i | \(0.568994\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11008.2 | −0.461196 | −0.230598 | − | 0.973049i | \(-0.574068\pi\) | ||||
−0.230598 | + | 0.973049i | \(0.574068\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2909.73i | 0.121028i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3990.29i | 0.165377i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9498.63 | −0.390857 | −0.195429 | − | 0.980718i | \(-0.562610\pi\) | ||||
−0.195429 | + | 0.980718i | \(0.562610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1549.53 | −0.0635338 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 334.254i | − 0.0136079i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 46817.4i | − 1.89925i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12993.2 | −0.523386 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18750.8 | −0.752655 | −0.376328 | − | 0.926487i | \(-0.622813\pi\) | ||||
−0.376328 | + | 0.926487i | \(0.622813\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37740.6i | 1.50431i | 0.658985 | + | 0.752156i | \(0.270986\pi\) | ||||
−0.658985 | + | 0.752156i | \(0.729014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 21464.7i | − 0.852579i | −0.904587 | − | 0.426290i | \(-0.859820\pi\) | ||||
0.904587 | − | 0.426290i | \(-0.140180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29001.8 | −1.14396 | −0.571978 | − | 0.820269i | \(-0.693824\pi\) | ||||
−0.571978 | + | 0.820269i | \(0.693824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27939.3 | 1.09822 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2499.03i | − 0.0975532i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 10809.2i | − 0.420499i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 53836.7 | 2.08001 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15055.6 | 0.579695 | 0.289848 | − | 0.957073i | \(-0.406395\pi\) | ||||
0.289848 | + | 0.957073i | \(0.406395\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6679.13i | 0.255421i | 0.991812 | + | 0.127710i | \(0.0407628\pi\) | ||||
−0.991812 | + | 0.127710i | \(0.959237\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14960.3i | 0.570165i | 0.958503 | + | 0.285083i | \(0.0920210\pi\) | ||||
−0.958503 | + | 0.285083i | \(0.907979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13974.6 | −0.528997 | −0.264498 | − | 0.964386i | \(-0.585206\pi\) | ||||
−0.264498 | + | 0.964386i | \(0.585206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −72053.2 | −2.71832 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 48490.9i | − 1.81712i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17752.2i | 0.663008i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1892.56 | 0.0702119 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2187.06 | 0.0808675 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28126.2i | 1.03309i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 15103.3i | − 0.552919i | −0.961026 | − | 0.276459i | \(-0.910839\pi\) | ||||
0.961026 | − | 0.276459i | \(-0.0891611\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7158.99 | −0.260360 | −0.130180 | − | 0.991490i | \(-0.541556\pi\) | ||||
−0.130180 | + | 0.991490i | \(0.541556\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 965.293 | 0.0349907 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1121.43i | 0.0403850i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 6718.51i | − 0.241157i | −0.992704 | − | 0.120578i | \(-0.961525\pi\) | ||||
0.992704 | − | 0.120578i | \(-0.0384749\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 49257.2 | 1.75658 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3137.17 | 0.111513 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 52525.0i | − 1.85499i | −0.373832 | − | 0.927497i | \(-0.621956\pi\) | ||||
0.373832 | − | 0.927497i | \(-0.378044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 84324.9i | − 2.96846i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 83.0446 | 0.00290465 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14330.5 | 0.499635 | 0.249818 | − | 0.968293i | \(-0.419629\pi\) | ||||
0.249818 | + | 0.968293i | \(0.419629\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8295.24i | 0.287372i | 0.989623 | + | 0.143686i | \(0.0458956\pi\) | ||||
−0.989623 | + | 0.143686i | \(0.954104\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20315.8i | 0.701562i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39543.2 | 1.35690 | 0.678449 | − | 0.734647i | \(-0.262652\pi\) | ||||
0.678449 | + | 0.734647i | \(0.262652\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31992.2 | −1.09432 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2750.61i | 0.0934954i | 0.998907 | + | 0.0467477i | \(0.0148857\pi\) | ||||
−0.998907 | + | 0.0467477i | \(0.985114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29067.4i | 0.984920i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36534.6 | −1.23020 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29652.9 | 0.995365 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6366.39i | 0.212375i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 13315.8i | − 0.442821i | −0.975181 | − | 0.221411i | \(-0.928934\pi\) | ||||
0.975181 | − | 0.221411i | \(-0.0710661\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13075.9 | −0.432158 | −0.216079 | − | 0.976376i | \(-0.569327\pi\) | ||||
−0.216079 | + | 0.976376i | \(0.569327\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46564.5 | −1.53421 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 4325.21i | − 0.141633i | −0.997489 | − | 0.0708167i | \(-0.977439\pi\) | ||||
0.997489 | − | 0.0708167i | \(-0.0225605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1727.83i | − 0.0564062i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4345.41 | −0.140994 | −0.0704970 | − | 0.997512i | \(-0.522459\pi\) | ||||
−0.0704970 | + | 0.997512i | \(0.522459\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25428.1 | 0.822546 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 5475.34i | − 0.176042i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 15332.7i | − 0.491484i | −0.969335 | − | 0.245742i | \(-0.920968\pi\) | ||||
0.969335 | − | 0.245742i | \(-0.0790316\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24312.8 | −0.774641 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58134.3 | 1.84667 | 0.923335 | − | 0.383995i | \(-0.125452\pi\) | ||||
0.923335 | + | 0.383995i | \(0.125452\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 864.4.c.b.863.8 | yes | 24 | |
3.2 | odd | 2 | inner | 864.4.c.b.863.18 | yes | 24 | |
4.3 | odd | 2 | inner | 864.4.c.b.863.7 | ✓ | 24 | |
8.3 | odd | 2 | 1728.4.c.k.1727.17 | 24 | |||
8.5 | even | 2 | 1728.4.c.k.1727.18 | 24 | |||
12.11 | even | 2 | inner | 864.4.c.b.863.17 | yes | 24 | |
24.5 | odd | 2 | 1728.4.c.k.1727.8 | 24 | |||
24.11 | even | 2 | 1728.4.c.k.1727.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.4.c.b.863.7 | ✓ | 24 | 4.3 | odd | 2 | inner | |
864.4.c.b.863.8 | yes | 24 | 1.1 | even | 1 | trivial | |
864.4.c.b.863.17 | yes | 24 | 12.11 | even | 2 | inner | |
864.4.c.b.863.18 | yes | 24 | 3.2 | odd | 2 | inner | |
1728.4.c.k.1727.7 | 24 | 24.11 | even | 2 | |||
1728.4.c.k.1727.8 | 24 | 24.5 | odd | 2 | |||
1728.4.c.k.1727.17 | 24 | 8.3 | odd | 2 | |||
1728.4.c.k.1727.18 | 24 | 8.5 | even | 2 |