Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(63,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.63");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.d (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: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1871773696.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 31x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{38} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 63.4 | ||
Root | \(0.921201 + 0.921201i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.63 |
Dual form | 128.5.d.d.63.3 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −4.54118 | −0.504576 | −0.252288 | − | 0.967652i | \(-0.581183\pi\) | ||||
−0.252288 | + | 0.967652i | \(0.581183\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 16.8444i | 0.673776i | 0.941545 | + | 0.336888i | \(0.109374\pi\) | ||||
−0.941545 | + | 0.336888i | \(0.890626\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 40.7922i | − 0.832493i | −0.909252 | − | 0.416246i | \(-0.863345\pi\) | ||||
0.909252 | − | 0.416246i | \(-0.136655\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −60.3776 | −0.745403 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 104.133 | 0.860605 | 0.430303 | − | 0.902685i | \(-0.358407\pi\) | ||||
0.430303 | + | 0.902685i | \(0.358407\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 13.4668i | − 0.0796850i | −0.999206 | − | 0.0398425i | \(-0.987314\pi\) | ||||
0.999206 | − | 0.0398425i | \(-0.0126856\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 76.4936i | − 0.339971i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 73.3776 | 0.253902 | 0.126951 | − | 0.991909i | \(-0.459481\pi\) | ||||
0.126951 | + | 0.991909i | \(0.459481\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 502.501 | 1.39197 | 0.695985 | − | 0.718056i | \(-0.254968\pi\) | ||||
0.695985 | + | 0.718056i | \(0.254968\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 185.245i | 0.420056i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 973.921i | − 1.84106i | −0.390671 | − | 0.920530i | \(-0.627757\pi\) | ||||
0.390671 | − | 0.920530i | \(-0.372243\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 341.266 | 0.546025 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 642.022 | 0.880689 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1256.49i | − 1.49404i | −0.664801 | − | 0.747020i | \(-0.731484\pi\) | ||||
0.664801 | − | 0.747020i | \(-0.268516\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1086.12i | − 1.13019i | −0.825025 | − | 0.565097i | \(-0.808839\pi\) | ||||
0.825025 | − | 0.565097i | \(-0.191161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −472.888 | −0.434241 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 687.120 | 0.560914 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1953.73i | 1.42712i | 0.700592 | + | 0.713562i | \(0.252919\pi\) | ||||
−0.700592 | + | 0.713562i | \(0.747081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 61.1551i | 0.0402072i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −194.266 | −0.115566 | −0.0577828 | − | 0.998329i | \(-0.518403\pi\) | ||||
−0.0577828 | + | 0.998329i | \(0.518403\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1808.79 | 0.978254 | 0.489127 | − | 0.872212i | \(-0.337315\pi\) | ||||
0.489127 | + | 0.872212i | \(0.337315\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1017.03i | − 0.502235i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 627.155i | − 0.283909i | −0.989873 | − | 0.141954i | \(-0.954661\pi\) | ||||
0.989873 | − | 0.141954i | \(-0.0453386\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 737.000 | 0.306955 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −333.221 | −0.128113 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3011.33i | 1.07203i | 0.844208 | + | 0.536015i | \(0.180071\pi\) | ||||
−0.844208 | + | 0.536015i | \(0.819929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1754.06i | 0.579855i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2281.95 | −0.702355 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5696.96 | −1.63659 | −0.818294 | − | 0.574800i | \(-0.805080\pi\) | ||||
−0.818294 | + | 0.574800i | \(0.805080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 6076.93i | − 1.63314i | −0.577244 | − | 0.816572i | \(-0.695872\pi\) | ||||
0.577244 | − | 0.816572i | \(-0.304128\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2462.93i | 0.620543i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 226.840 | 0.0536899 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3518.77 | −0.783864 | −0.391932 | − | 0.919994i | \(-0.628193\pi\) | ||||
−0.391932 | + | 0.919994i | \(0.628193\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4422.76i | 0.928955i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3340.00i | 0.662567i | 0.943531 | + | 0.331283i | \(0.107482\pi\) | ||||
−0.943531 | + | 0.331283i | \(0.892518\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4810.79 | 0.902757 | 0.451378 | − | 0.892333i | \(-0.350932\pi\) | ||||
0.451378 | + | 0.892333i | \(0.350932\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1549.75 | −0.275511 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 4247.82i | − 0.716448i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5466.15i | 0.875845i | 0.899013 | + | 0.437923i | \(0.144286\pi\) | ||||
−0.899013 | + | 0.437923i | \(0.855714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1975.05 | 0.301029 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3945.61 | −0.572741 | −0.286370 | − | 0.958119i | \(-0.592449\pi\) | ||||
−0.286370 | + | 0.958119i | \(0.592449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1236.00i | 0.171073i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5705.94i | 0.753857i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −700.314 | −0.0884124 | −0.0442062 | − | 0.999022i | \(-0.514076\pi\) | ||||
−0.0442062 | + | 0.999022i | \(0.514076\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −549.339 | −0.0663372 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4932.25i | 0.570269i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8464.34i | 0.937877i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12767.9 | −1.35698 | −0.678492 | − | 0.734608i | \(-0.737366\pi\) | ||||
−0.678492 | + | 0.734608i | \(0.737366\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6287.32 | −0.641498 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 4197.02i | − 0.411432i | −0.978612 | − | 0.205716i | \(-0.934048\pi\) | ||||
0.978612 | − | 0.205716i | \(-0.0659524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 13201.4i | − 1.24436i | −0.782875 | − | 0.622179i | \(-0.786248\pi\) | ||||
0.782875 | − | 0.622179i | \(-0.213752\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3120.34 | −0.283024 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 179.932 | 0.0157160 | 0.00785800 | − | 0.999969i | \(-0.497499\pi\) | ||||
0.00785800 | + | 0.999969i | \(0.497499\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1774.81i | 0.149382i | 0.997207 | + | 0.0746909i | \(0.0237970\pi\) | ||||
−0.997207 | + | 0.0746909i | \(0.976203\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 8872.26i | − 0.720093i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16994.7 | 1.33093 | 0.665467 | − | 0.746427i | \(-0.268232\pi\) | ||||
0.665467 | + | 0.746427i | \(0.268232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16405.1 | 1.24046 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 813.092i | 0.0593975i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 2993.23i | − 0.211372i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3797.27 | −0.259359 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 882.197 | 0.0583117 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 16276.2i | 1.04168i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 22216.9i | − 1.37745i | −0.725024 | − | 0.688724i | \(-0.758171\pi\) | ||||
0.725024 | − | 0.688724i | \(-0.241829\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8214.06 | −0.493604 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15326.7 | 0.893113 | 0.446557 | − | 0.894755i | \(-0.352650\pi\) | ||||
0.446557 | + | 0.894755i | \(0.352650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 20498.1i | − 1.15881i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10814.5i | 0.593387i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4816.22 | 0.256605 | 0.128303 | − | 0.991735i | \(-0.459047\pi\) | ||||
0.128303 | + | 0.991735i | \(0.459047\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 26354.8 | 1.36405 | 0.682024 | − | 0.731330i | \(-0.261100\pi\) | ||||
0.682024 | + | 0.731330i | \(0.261100\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2848.02i | 0.143254i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1402.34i | − 0.0685773i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21164.8 | 1.00665 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3346.85 | −0.154882 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 35333.0i | − 1.59150i | −0.605622 | − | 0.795752i | \(-0.707076\pi\) | ||||
0.605622 | − | 0.795752i | \(-0.292924\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 35811.1i | − 1.57059i | −0.619120 | − | 0.785296i | \(-0.712511\pi\) | ||||
0.619120 | − | 0.785296i | \(-0.287489\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4430.37 | −0.189259 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18295.0 | 0.761498 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 27036.6i | 1.09687i | 0.836195 | + | 0.548433i | \(0.184775\pi\) | ||||
−0.836195 | + | 0.548433i | \(0.815225\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 13675.0i | − 0.540921i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −39728.3 | −1.53267 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15689.0 | 0.590499 | 0.295250 | − | 0.955420i | \(-0.404597\pi\) | ||||
0.295250 | + | 0.955420i | \(0.404597\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 7965.52i | − 0.292581i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10137.3i | 0.363487i | 0.983346 | + | 0.181743i | \(0.0581740\pi\) | ||||
−0.983346 | + | 0.181743i | \(0.941826\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28379.6 | 0.993650 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −30339.8 | −1.03758 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 39217.1i | 1.31034i | 0.755483 | + | 0.655169i | \(0.227402\pi\) | ||||
−0.755483 | + | 0.655169i | \(0.772598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 13921.0i | − 0.454562i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25871.0 | 0.825783 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −35042.8 | −1.09369 | −0.546843 | − | 0.837235i | \(-0.684171\pi\) | ||||
−0.546843 | + | 0.837235i | \(0.684171\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14059.3i | 0.429147i | 0.976708 | + | 0.214574i | \(0.0688362\pi\) | ||||
−0.976708 | + | 0.214574i | \(0.931164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27596.5i | 0.824045i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −32909.5 | −0.961562 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7641.05 | 0.218509 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 26189.5i | − 0.733167i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 45804.6i | 1.25558i | 0.778385 | + | 0.627788i | \(0.216039\pi\) | ||||
−0.778385 | + | 0.627788i | \(0.783961\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −40765.7 | −1.09441 | −0.547206 | − | 0.836998i | \(-0.684308\pi\) | ||||
−0.547206 | + | 0.836998i | \(0.684308\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1030.12 | −0.0270906 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 8098.75i | − 0.208682i | −0.994542 | − | 0.104341i | \(-0.966727\pi\) | ||||
0.994542 | − | 0.104341i | \(-0.0332734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 12023.2i | − 0.303609i | −0.988411 | − | 0.151805i | \(-0.951492\pi\) | ||||
0.988411 | − | 0.151805i | \(-0.0485085\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15979.4 | 0.395519 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −51254.9 | −1.24378 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 3272.29i | − 0.0778654i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 58803.1i | 1.37233i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 52327.1 | 1.19794 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 32994.3 | 0.741094 | 0.370547 | − | 0.928814i | \(-0.379170\pi\) | ||||
0.370547 | + | 0.928814i | \(0.379170\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 15167.6i | − 0.334315i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 30468.0i | 0.659125i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −44305.0 | −0.940878 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21846.7 | −0.455510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 988.160i | − 0.0202322i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8325.83i | 0.167424i | 0.996490 | + | 0.0837120i | \(0.0266776\pi\) | ||||
−0.996490 | + | 0.0837120i | \(0.973322\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20604.8 | −0.407009 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −98932.8 | −1.91994 | −0.959972 | − | 0.280096i | \(-0.909634\pi\) | ||||
−0.959972 | + | 0.280096i | \(0.909634\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 39028.4i | 0.744235i | 0.928186 | + | 0.372117i | \(0.121368\pi\) | ||||
−0.928186 | + | 0.372117i | \(0.878632\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19290.1i | 0.361502i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 47062.2 | 0.866882 | 0.433441 | − | 0.901182i | \(-0.357299\pi\) | ||||
0.433441 | + | 0.901182i | \(0.357299\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10564.0 | 0.191291 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 24822.8i | − 0.441930i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18051.8i | 0.316028i | 0.987437 | + | 0.158014i | \(0.0505091\pi\) | ||||
−0.987437 | + | 0.158014i | \(0.949491\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 87375.0 | 1.50437 | 0.752183 | − | 0.658955i | \(-0.229001\pi\) | ||||
0.752183 | + | 0.658955i | \(0.229001\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −60972.8 | −1.03258 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12414.3i | 0.206819i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 6767.07i | − 0.110919i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17917.8 | 0.288991 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14707.9 | −0.233456 | −0.116728 | − | 0.993164i | \(-0.537240\pi\) | ||||
−0.116728 | + | 0.993164i | \(0.537240\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 101418.i | − 1.58443i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 5612.92i | − 0.0863194i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −105989. | −1.60470 | −0.802351 | − | 0.596852i | \(-0.796418\pi\) | ||||
−0.802351 | + | 0.596852i | \(0.796418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 79697.0 | 1.18807 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 75863.8i | 1.11366i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 2401.32i | − 0.0347166i | −0.999849 | − | 0.0173583i | \(-0.994474\pi\) | ||||
0.999849 | − | 0.0173583i | \(-0.00552560\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −50724.1 | −0.722309 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3180.26 | 0.0446108 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 17257.4i | − 0.238490i | −0.992865 | − | 0.119245i | \(-0.961953\pi\) | ||||
0.992865 | − | 0.119245i | \(-0.0380474\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 119967.i | − 1.63351i | −0.576982 | − | 0.816757i | \(-0.695770\pi\) | ||||
0.576982 | − | 0.816757i | \(-0.304230\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2494.65 | 0.0334722 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 35537.1 | 0.469912 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 101645.i | 1.32473i | 0.749183 | + | 0.662363i | \(0.230446\pi\) | ||||
−0.749183 | + | 0.662363i | \(0.769554\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 65577.1i | 0.842450i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12028.5 | 0.152335 | 0.0761675 | − | 0.997095i | \(-0.475732\pi\) | ||||
0.0761675 | + | 0.997095i | \(0.475732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 98095.9 | 1.22484 | 0.612418 | − | 0.790534i | \(-0.290197\pi\) | ||||
0.612418 | + | 0.790534i | \(0.290197\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 38438.1i | − 0.473230i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7924.52i | 0.0962076i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −78136.7 | −0.935534 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 57981.2 | 0.684701 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2060.54i | 0.0240019i | 0.999928 | + | 0.0120010i | \(0.00382012\pi\) | ||||
−0.999928 | + | 0.0120010i | \(0.996180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 95962.0i | − 1.10269i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 66855.8 | 0.757925 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13115.6 | −0.146705 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 73784.5i | − 0.814390i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19059.5i | 0.207599i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 102362. | 1.10037 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 76322.7 | 0.809798 | 0.404899 | − | 0.914361i | \(-0.367307\pi\) | ||||
0.404899 | + | 0.914361i | \(0.367307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 59949.9i | 0.627873i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 93007.1i | − 0.961602i | −0.876830 | − | 0.480801i | \(-0.840346\pi\) | ||||
0.876830 | − | 0.480801i | \(-0.159654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −44008.6 | −0.449210 | −0.224605 | − | 0.974450i | \(-0.572109\pi\) | ||||
−0.224605 | + | 0.974450i | \(0.572109\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −41486.7 | −0.418107 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 110474.i | 1.09936i | 0.835375 | + | 0.549680i | \(0.185250\pi\) | ||||
−0.835375 | + | 0.549680i | \(0.814750\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 130842.i | − 1.28578i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −817.107 | −0.00792992 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36872.4 | 0.353424 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4595.75i | − 0.0435100i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 8059.72i | − 0.0753745i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25583.0 | −0.236352 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 210881. | 1.92478 | 0.962390 | − | 0.271673i | \(-0.0875769\pi\) | ||||
0.962390 | + | 0.271673i | \(0.0875769\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 117962.i | − 1.06378i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 59271.5i | − 0.528149i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 46756.0 | 0.411697 | 0.205848 | − | 0.978584i | \(-0.434005\pi\) | ||||
0.205848 | + | 0.978584i | \(0.434005\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −77176.1 | −0.671558 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 113101.i | − 0.972650i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 128006.i | − 1.08803i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −74498.7 | −0.625908 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −41355.2 | −0.343456 | −0.171728 | − | 0.985144i | \(-0.554935\pi\) | ||||
−0.171728 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 60146.7i | − 0.493812i | −0.969039 | − | 0.246906i | \(-0.920586\pi\) | ||||
0.969039 | − | 0.246906i | \(-0.0794138\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 8645.96i | − 0.0701777i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12988.7 | −0.104236 | −0.0521178 | − | 0.998641i | \(-0.516597\pi\) | ||||
−0.0521178 | + | 0.998641i | \(0.516597\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −56260.3 | −0.446422 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13592.8i | 0.106653i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 191555.i | 1.48630i | 0.669127 | + | 0.743148i | \(0.266668\pi\) | ||||
−0.669127 | + | 0.743148i | \(0.733332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 122187. | 0.937582 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17244.1 | 0.130866 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 81034.9i | 0.608256i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 163572.i | 1.21444i | 0.794532 | + | 0.607222i | \(0.207716\pi\) | ||||
−0.794532 | + | 0.607222i | \(0.792284\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11729.3 | 0.0861430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 122839. | 0.892458 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 55059.2i | 0.395742i | 0.980228 | + | 0.197871i | \(0.0634028\pi\) | ||||
−0.980228 | + | 0.197871i | \(0.936597\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 73913.1i | − 0.525605i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16920.8 | −0.119053 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −108892. | −0.758083 | −0.379041 | − | 0.925380i | \(-0.623746\pi\) | ||||
−0.379041 | + | 0.925380i | \(0.623746\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 100891.i | 0.695027i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 169594.i | 1.15615i | 0.815985 | + | 0.578073i | \(0.196195\pi\) | ||||
−0.815985 | + | 0.578073i | \(0.803805\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 71552.0 | 0.482726 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −109211. | −0.729194 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 183067.i | − 1.20979i | −0.796304 | − | 0.604896i | \(-0.793215\pi\) | ||||
0.796304 | − | 0.604896i | \(-0.206785\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 71464.0i | − 0.467449i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −69601.4 | −0.450644 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −92074.1 | −0.590124 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 145471.i | 0.922984i | 0.887144 | + | 0.461492i | \(0.152686\pi\) | ||||
−0.887144 | + | 0.461492i | \(0.847314\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 93085.7i | 0.584706i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −188314. | −1.17110 | −0.585550 | − | 0.810636i | \(-0.699121\pi\) | ||||
−0.585550 | + | 0.810636i | \(0.699121\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14626.5 | −0.0900595 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 33268.5i | 0.202826i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 203448.i | 1.22819i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 88454.1 | 0.528776 | 0.264388 | − | 0.964416i | \(-0.414830\pi\) | ||||
0.264388 | + | 0.964416i | \(0.414830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21871.4 | −0.129477 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 232391.i | 1.36245i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 66461.5i | − 0.385899i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −119682. | −0.688266 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −146392. | −0.833851 | −0.416925 | − | 0.908941i | \(-0.636892\pi\) | ||||
−0.416925 | + | 0.908941i | \(0.636892\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 127042.i | − 0.716774i | −0.933573 | − | 0.358387i | \(-0.883327\pi\) | ||||
0.933573 | − | 0.358387i | \(-0.116673\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 37866.1i | 0.211626i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25041.3 | 0.138637 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −247891. | −1.35958 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6368.28i | 0.0346025i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 113658.i | − 0.611850i | −0.952056 | − | 0.305925i | \(-0.901034\pi\) | ||||
0.952056 | − | 0.305925i | \(-0.0989656\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9580.62 | −0.0510996 | −0.0255498 | − | 0.999674i | \(-0.508134\pi\) | ||||
−0.0255498 | + | 0.999674i | \(0.508134\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −96113.3 | −0.507931 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 489397.i | − 2.56270i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 310714.i | 1.61225i | 0.591747 | + | 0.806123i | \(0.298438\pi\) | ||||
−0.591747 | + | 0.806123i | \(0.701562\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −44498.3 | −0.228805 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −89033.9 | −0.453678 | −0.226839 | − | 0.973932i | \(-0.572839\pi\) | ||||
−0.226839 | + | 0.973932i | \(0.572839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 11796.4i | − 0.0595702i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 160454.i | 0.803035i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 282195. | 1.39977 | 0.699885 | − | 0.714256i | \(-0.253235\pi\) | ||||
0.699885 | + | 0.714256i | \(0.253235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20229.5 | −0.0994564 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 162625.i | 0.792484i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 9253.28i | − 0.0446965i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −100299. | −0.480246 | −0.240123 | − | 0.970742i | \(-0.577188\pi\) | ||||
−0.240123 | + | 0.970742i | \(0.577188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 47110.1 | 0.223608 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 309619.i | 1.45689i | 0.685106 | + | 0.728443i | \(0.259756\pi\) | ||||
−0.685106 | + | 0.728443i | \(0.740244\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15604.3i | 0.0727917i | 0.999337 | + | 0.0363959i | \(0.0115877\pi\) | ||||
−0.999337 | + | 0.0363959i | \(0.988412\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −83080.9 | −0.384234 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −137144. | −0.628844 | −0.314422 | − | 0.949283i | \(-0.601811\pi\) | ||||
−0.314422 | + | 0.949283i | \(0.601811\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 143538.i | 0.652561i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 122778.i | − 0.553452i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 188355. | 0.841891 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 171487. | 0.760051 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 181817.i | − 0.799095i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16795.8i | 0.0732031i | 0.999330 | + | 0.0366016i | \(0.0116532\pi\) | ||||
−0.999330 | + | 0.0366016i | \(0.988347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26310.5 | 0.113720 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 180414. | 0.773349 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 215067.i | − 0.914303i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 119105.i | 0.502194i | 0.967962 | + | 0.251097i | \(0.0807913\pi\) | ||||
−0.967962 | + | 0.251097i | \(0.919209\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −71246.5 | −0.297952 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 379148. | 1.57270 | 0.786349 | − | 0.617783i | \(-0.211969\pi\) | ||||
0.786349 | + | 0.617783i | \(0.211969\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 92198.1i | − 0.379340i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 105906.i | − 0.432226i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 136246. | 0.551582 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −54844.8 | −0.220260 | −0.110130 | − | 0.993917i | \(-0.535127\pi\) | ||||
−0.110130 | + | 0.993917i | \(0.535127\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 46035.3i | − 0.183407i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 146931.i | − 0.580732i | −0.956916 | − | 0.290366i | \(-0.906223\pi\) | ||||
0.956916 | − | 0.290366i | \(-0.0937771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 70696.4 | 0.277213 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −128877. | −0.501372 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 156866.i | 0.605470i | 0.953075 | + | 0.302735i | \(0.0978997\pi\) | ||||
−0.953075 | + | 0.302735i | \(0.902100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 196243.i | − 0.751539i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 322617. | 1.22589 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 222370. | 0.838419 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 65307.6i | − 0.244333i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 178092.i | − 0.661165i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −433939. | −1.59865 | −0.799325 | − | 0.600899i | \(-0.794809\pi\) | ||||
−0.799325 | + | 0.600899i | \(0.794809\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −244305. | −0.893161 | −0.446580 | − | 0.894744i | \(-0.647358\pi\) | ||||
−0.446580 | + | 0.894744i | \(0.647358\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 63217.7i | 0.229361i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 79696.6i | − 0.286958i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −668681. | −2.38950 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 343969. | 1.21992 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2616.13i | 0.00920885i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3030.86i | 0.0105891i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 159136. | 0.551848 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 76746.2 | 0.264167 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 263893.i | − 0.901642i | −0.892614 | − | 0.450821i | \(-0.851131\pi\) | ||||
0.892614 | − | 0.450821i | \(-0.148869\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 63845.8i | − 0.216537i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29895.5 | −0.100650 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5684.58 | 0.0189987 | 0.00949935 | − | 0.999955i | \(-0.496976\pi\) | ||||
0.00949935 | + | 0.999955i | \(0.496976\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 366911.i | 1.21735i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 631387.i | − 2.07966i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 222976. | 0.729135 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 149448. | 0.485181 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 229010.i | 0.738150i | 0.929400 | + | 0.369075i | \(0.120325\pi\) | ||||
−0.929400 | + | 0.369075i | \(0.879675\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 24358.6i | − 0.0779522i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34699.4 | −0.110255 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8586.54 | −0.0270895 | −0.0135448 | − | 0.999908i | \(-0.504312\pi\) | ||||
−0.0135448 | + | 0.999908i | \(0.504312\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 286266.i | 0.896752i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 80566.5i | − 0.250604i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 58381.6 | 0.180323 | 0.0901616 | − | 0.995927i | \(-0.471262\pi\) | ||||
0.0901616 | + | 0.995927i | \(0.471262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 512966. | 1.57332 | 0.786658 | − | 0.617389i | \(-0.211809\pi\) | ||||
0.786658 | + | 0.617389i | \(0.211809\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 208007.i | − 0.633533i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 332366.i | − 1.00527i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 457649. | 1.37461 | 0.687307 | − | 0.726367i | \(-0.258793\pi\) | ||||
0.687307 | + | 0.726367i | \(0.258793\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 185125. | 0.552214 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 160950.i | 0.476803i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 313580.i | 0.922595i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13696.1 | −0.0400206 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −76953.3 | −0.223332 | −0.111666 | − | 0.993746i | \(-0.535619\pi\) | ||||
−0.111666 | + | 0.993746i | \(0.535619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 545775.i | − 1.57320i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36777.9i | 0.105296i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −559786. | −1.59189 | −0.795944 | − | 0.605370i | \(-0.793025\pi\) | ||||
−0.795944 | + | 0.605370i | \(0.793025\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 50419.2 | 0.142417 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 54599.8i | 0.153194i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 209237.i | − 0.583157i | −0.956547 | − | 0.291579i | \(-0.905820\pi\) | ||||
0.956547 | − | 0.291579i | \(-0.0941805\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2016.35 | 0.00558236 | 0.00279118 | − | 0.999996i | \(-0.499112\pi\) | ||||
0.00279118 | + | 0.999996i | \(0.499112\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 212455. | 0.584295 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 63962.8i | − 0.174750i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 648350.i | 1.75967i | 0.475275 | + | 0.879837i | \(0.342349\pi\) | ||||
−0.475275 | + | 0.879837i | \(0.657651\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 232758. | 0.627581 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8445.75 | −0.0226233 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 303258.i | 0.807033i | 0.914972 | + | 0.403516i | \(0.132212\pi\) | ||||
−0.914972 | + | 0.403516i | \(0.867788\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14860.1i | 0.0392890i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 174055. | 0.457210 | 0.228605 | − | 0.973519i | \(-0.426584\pi\) | ||||
0.228605 | + | 0.973519i | \(0.426584\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −577628. | −1.50753 | −0.753767 | − | 0.657142i | \(-0.771765\pi\) | ||||
−0.753767 | + | 0.657142i | \(0.771765\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 625279.i | − 1.62140i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28567.3i | 0.0736027i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −60871.5 | −0.155831 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −237627. | −0.604450 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 143360.i | 0.362349i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 166511.i | − 0.418200i | −0.977894 | − | 0.209100i | \(-0.932947\pi\) | ||||
0.977894 | − | 0.209100i | \(-0.0670533\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −149833. | −0.373939 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 374230. | 0.928092 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 9925.01i | − 0.0244598i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 201661.i | − 0.493879i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 515858. | 1.25549 | 0.627746 | − | 0.778418i | \(-0.283978\pi\) | ||||
0.627746 | + | 0.778418i | \(0.283978\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −585939. | −1.41720 | −0.708599 | − | 0.705611i | \(-0.750673\pi\) | ||||
−0.708599 | + | 0.705611i | \(0.750673\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 138361.i | − 0.332579i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 734055.i | 1.75356i | 0.480895 | + | 0.876778i | \(0.340312\pi\) | ||||
−0.480895 | + | 0.876778i | \(0.659688\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −593243. | −1.40846 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 201197. | 0.474745 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 78218.9i | − 0.183436i | −0.995785 | − | 0.0917181i | \(-0.970764\pi\) | ||||
0.995785 | − | 0.0917181i | \(-0.0292359\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 258169.i | 0.601759i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −290464. | −0.672918 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4105.91 | 0.00945450 | 0.00472725 | − | 0.999989i | \(-0.498495\pi\) | ||||
0.00472725 | + | 0.999989i | \(0.498495\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 478700.i | 1.09562i | 0.836602 | + | 0.547811i | \(0.184539\pi\) | ||||
−0.836602 | + | 0.547811i | \(0.815461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4487.42i | 0.0102087i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 345279. | 0.780776 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.22372e6 | −2.75062 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 37809.1i | − 0.0844782i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 632810.i | − 1.40549i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 292887. | 0.646651 | 0.323326 | − | 0.946288i | \(-0.395199\pi\) | ||||
0.323326 | + | 0.946288i | \(0.395199\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 219100. | 0.480878 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 358940.i | − 0.783149i | −0.920146 | − | 0.391575i | \(-0.871930\pi\) | ||||
0.920146 | − | 0.391575i | \(-0.128070\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 520828.i | 1.12968i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 449272. | 0.968758 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −166893. | −0.357765 | −0.178883 | − | 0.983870i | \(-0.557248\pi\) | ||||
−0.178883 | + | 0.983870i | \(0.557248\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 81126.4i | 0.172895i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 177235.i | − 0.375523i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40552.9 | 0.0854248 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −102959. | −0.215629 | −0.107814 | − | 0.994171i | \(-0.534385\pi\) | ||||
−0.107814 | + | 0.994171i | \(0.534385\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 256473.i | 0.534042i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 443930.i | 0.919063i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14254.8 | −0.0293423 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −213718. | −0.437408 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 196855.i | 0.400599i | 0.979735 | + | 0.200299i | \(0.0641915\pi\) | ||||
−0.979735 | + | 0.200299i | \(0.935808\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 981753.i | 1.98651i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −47973.3 | −0.0965209 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −171206. | −0.342515 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 621291.i | 1.23595i | 0.786196 | + | 0.617977i | \(0.212048\pi\) | ||||
−0.786196 | + | 0.617977i | \(0.787952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 330033.i | − 0.652857i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.05779e6 | −2.08075 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23621.6 | 0.0462058 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 81976.7i | − 0.159460i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 699397.i | 1.35290i | 0.736488 | + | 0.676450i | \(0.236483\pi\) | ||||
−0.736488 | + | 0.676450i | \(0.763517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −538513. | −1.03592 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −396786. | −0.759067 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 428796.i | − 0.815784i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 526955.i | 0.997022i | 0.866883 | + | 0.498511i | \(0.166120\pi\) | ||||
−0.866883 | + | 0.498511i | \(0.833880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 116910. | 0.219987 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 132725. | 0.248381 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 13466.6i | − 0.0250640i | −0.999921 | − | 0.0125320i | \(-0.996011\pi\) | ||||
0.999921 | − | 0.0125320i | \(-0.00398917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 56375.8i | − 0.104356i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −366420. | −0.674597 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −352928. | −0.646245 | −0.323122 | − | 0.946357i | \(-0.604733\pi\) | ||||
−0.323122 | + | 0.946357i | \(0.604733\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30730.5i | 0.0559672i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 539226.i | − 0.976772i | −0.872628 | − | 0.488386i | \(-0.837586\pi\) | ||||
0.872628 | − | 0.488386i | \(-0.162414\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 595164. | 1.07232 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 238227. | 0.426923 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 7339.83i | − 0.0130835i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 301606.i | − 0.534762i | −0.963591 | − | 0.267381i | \(-0.913842\pi\) | ||||
0.963591 | − | 0.267381i | \(-0.0861582\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 66791.4 | 0.117796 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 603217. | 1.05823 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 402304.i | − 0.702042i | −0.936368 | − | 0.351021i | \(-0.885835\pi\) | ||||
0.936368 | − | 0.351021i | \(-0.114165\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 460556.i | 0.799464i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 622961. | 1.07570 | 0.537851 | − | 0.843040i | \(-0.319236\pi\) | ||||
0.537851 | + | 0.843040i | \(0.319236\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 72398.1 | 0.124359 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 74627.0i | − 0.127518i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 76719.7i | 0.130412i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 563590. | 0.953039 | 0.476520 | − | 0.879164i | \(-0.341898\pi\) | ||||
0.476520 | + | 0.879164i | \(0.341898\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 481316. | 0.809694 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 510328.i | − 0.854063i | −0.904237 | − | 0.427032i | \(-0.859559\pi\) | ||||
0.904237 | − | 0.427032i | \(-0.140441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 370654.i | − 0.617114i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −361919. | −0.599472 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −97618.9 | −0.160864 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 347805.i | 0.570208i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 806693.i | − 1.31578i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −455416. | −0.739042 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −970831. | −1.56745 | −0.783726 | − | 0.621107i | \(-0.786683\pi\) | ||||
−0.783726 | + | 0.621107i | \(0.786683\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10904.8i | 0.0175172i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 693250.i | − 1.10799i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −81836.6 | −0.130137 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 230348. | 0.364460 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.12132e6i | 1.76528i | 0.470051 | + | 0.882639i | \(0.344235\pi\) | ||||
−0.470051 | + | 0.882639i | \(0.655765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 46019.1i | − 0.0720850i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 42283.3 | 0.0659028 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 500963. | 0.776917 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 669200.i | − 1.03268i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 78368.9i | 0.120336i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 533014. | 0.814406 | 0.407203 | − | 0.913338i | \(-0.366504\pi\) | ||||
0.407203 | + | 0.913338i | \(0.366504\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 736257. | 1.11941 | 0.559703 | − | 0.828693i | \(-0.310915\pi\) | ||||
0.559703 | + | 0.828693i | \(0.310915\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 544792.i | 0.824232i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 264271.i | 0.397864i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 908921. | 1.36170 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 33167.8 | 0.0494480 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 221216.i | − 0.328194i | −0.986444 | − | 0.164097i | \(-0.947529\pi\) | ||||
0.986444 | − | 0.164097i | \(-0.0524711\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 427766.i | − 0.631548i | −0.948834 | − | 0.315774i | \(-0.897736\pi\) | ||||
0.948834 | − | 0.315774i | \(-0.102264\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −161381. | −0.237106 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −87673.4 | −0.128191 | −0.0640954 | − | 0.997944i | \(-0.520416\pi\) | ||||
−0.0640954 | + | 0.997944i | \(0.520416\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 442564.i | − 0.643971i | −0.946745 | − | 0.321986i | \(-0.895650\pi\) | ||||
0.946745 | − | 0.321986i | \(-0.104350\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 461588.i | − 0.668425i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 54079.3 | 0.0779366 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −170757. | −0.244909 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 697310.i | − 0.995349i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 705591.i | − 1.00237i | −0.865339 | − | 0.501186i | \(-0.832897\pi\) | ||||
0.865339 | − | 0.501186i | \(-0.167103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −871481. | −1.23216 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −54623.8 | −0.0768646 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 478038.i | 0.669498i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 154899.i | 0.215914i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −445472. | −0.618023 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.90278e6 | 2.62742 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.11225e6i | − 1.52864i | −0.644837 | − | 0.764320i | \(-0.723075\pi\) | ||||
0.644837 | − | 0.764320i | \(-0.276925\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 511057.i | − 0.699096i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −119068. | −0.162119 | −0.0810597 | − | 0.996709i | \(-0.525830\pi\) | ||||
−0.0810597 | + | 0.996709i | \(0.525830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −78675.9 | −0.106624 | −0.0533120 | − | 0.998578i | \(-0.516978\pi\) | ||||
−0.0533120 | + | 0.998578i | \(0.516978\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 35986.7i | − 0.0485440i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 92999.5i | − 0.124870i | −0.998049 | − | 0.0624351i | \(-0.980113\pi\) | ||||
0.998049 | − | 0.0624351i | \(-0.0198866\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −660589. | −0.882874 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 354833. | 0.472048 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 569208.i | 0.753757i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 47386.4i | 0.0624622i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 770893. | 1.01150 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 663940. | 0.867187 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 861315.i | 1.11986i | 0.828541 | + | 0.559929i | \(0.189171\pi\) | ||||
−0.828541 | + | 0.559929i | \(0.810829\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 9357.30i | − 0.0121108i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.03692e6 | 1.33596 | 0.667981 | − | 0.744178i | \(-0.267159\pi\) | ||||
0.667981 | + | 0.744178i | \(0.267159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.07531e6 | 1.37915 | 0.689577 | − | 0.724212i | \(-0.257797\pi\) | ||||
0.689577 | + | 0.724212i | \(0.257797\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 435781.i | 0.556393i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 97396.5i | − 0.123793i | −0.998083 | − | 0.0618965i | \(-0.980285\pi\) | ||||
0.998083 | − | 0.0618965i | \(-0.0197149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −906273. | −1.14672 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 205668. | 0.259067 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 315146.i | − 0.395193i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 590276.i | − 0.736900i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 59560.2 | 0.0740238 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.36469e6 | −1.68855 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 220965.i | 0.272191i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 335069.i | 0.410922i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −236820. | −0.289149 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 172583. | 0.209790 | 0.104895 | − | 0.994483i | \(-0.466549\pi\) | ||||
0.104895 | + | 0.994483i | \(0.466549\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 253406.i | 0.306683i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.07491e6i | − 1.29519i | −0.761983 | − | 0.647597i | \(-0.775774\pi\) | ||||
0.761983 | − | 0.647597i | \(-0.224226\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −410869. | −0.492904 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −464846. | −0.555222 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 625210.i | − 0.743510i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 763121.i | 0.903571i | 0.892127 | + | 0.451785i | \(0.149213\pi\) | ||||
−0.892127 | + | 0.451785i | \(0.850787\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −346595. | −0.408605 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44979.0 | 0.0527966 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 666742.i | 0.779246i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 797069.i | 0.927548i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −742596. | −0.860441 | −0.430220 | − | 0.902724i | \(-0.641564\pi\) | ||||
−0.430220 | + | 0.902724i | \(0.641564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 370344. | 0.427273 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 422362.i | 0.485201i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 128709.i | 0.147226i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.57493e6 | 1.79383 | 0.896915 | − | 0.442204i | \(-0.145803\pi\) | ||||
0.896915 | + | 0.442204i | \(0.145803\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 199851. | 0.226661 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43641.7i | 0.0492859i | 0.999696 | + | 0.0246429i | \(0.00784489\pi\) | ||||
−0.999696 | + | 0.0246429i | \(0.992155\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 189200.i | 0.212763i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 441146. | 0.493991 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.56638e6 | −1.74661 | −0.873307 | − | 0.487170i | \(-0.838029\pi\) | ||||
−0.873307 | + | 0.487170i | \(0.838029\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 64785.8i | − 0.0719362i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 501681.i | − 0.554711i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 280777. | 0.309154 | 0.154577 | − | 0.987981i | \(-0.450598\pi\) | ||||
0.154577 | + | 0.987981i | \(0.450598\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −771552. | −0.845977 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 594178.i | 0.648773i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 196464.i | − 0.213622i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −256127. | −0.277337 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10863.9 | −0.0117148 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 686675.i | − 0.737389i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 273606.i | 0.292599i | 0.989240 | + | 0.146299i | \(0.0467363\pi\) | ||||
−0.989240 | + | 0.146299i | \(0.953264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −167444. | −0.178329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −813827. | −0.863164 | −0.431582 | − | 0.902074i | \(-0.642045\pi\) | ||||
−0.431582 | + | 0.902074i | \(0.642045\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.07507e6i | − 1.13556i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20870.1i | 0.0219541i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 195689. | 0.205011 | 0.102506 | − | 0.994732i | \(-0.467314\pi\) | ||||
0.102506 | + | 0.994732i | \(0.467314\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −72926.0 | −0.0760881 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 107159.i | − 0.111350i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.01172e6i | 1.04701i | 0.852022 | + | 0.523506i | \(0.175376\pi\) | ||||
−0.852022 | + | 0.523506i | \(0.824624\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 136419. | 0.140605 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 116177. | 0.119258 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.76162e6i | − 1.80103i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 419686.i | − 0.427344i | −0.976905 | − | 0.213672i | \(-0.931458\pi\) | ||||
0.976905 | − | 0.213672i | \(-0.0685424\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −957648. | −0.971198 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 202524. | 0.204565 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 499410.i | − 0.502420i | −0.967933 | − | 0.251210i | \(-0.919172\pi\) | ||||
0.967933 | − | 0.251210i | \(-0.0808285\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.25434e6i | 1.25685i |
(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 | 128.5.d.d.63.4 | yes | 8 | |
3.2 | odd | 2 | 1152.5.b.l.703.3 | 8 | |||
4.3 | odd | 2 | inner | 128.5.d.d.63.6 | yes | 8 | |
8.3 | odd | 2 | inner | 128.5.d.d.63.3 | ✓ | 8 | |
8.5 | even | 2 | inner | 128.5.d.d.63.5 | yes | 8 | |
12.11 | even | 2 | 1152.5.b.l.703.4 | 8 | |||
16.3 | odd | 4 | 256.5.c.g.255.3 | 4 | |||
16.5 | even | 4 | 256.5.c.k.255.3 | 4 | |||
16.11 | odd | 4 | 256.5.c.k.255.2 | 4 | |||
16.13 | even | 4 | 256.5.c.g.255.2 | 4 | |||
24.5 | odd | 2 | 1152.5.b.l.703.5 | 8 | |||
24.11 | even | 2 | 1152.5.b.l.703.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.5.d.d.63.3 | ✓ | 8 | 8.3 | odd | 2 | inner | |
128.5.d.d.63.4 | yes | 8 | 1.1 | even | 1 | trivial | |
128.5.d.d.63.5 | yes | 8 | 8.5 | even | 2 | inner | |
128.5.d.d.63.6 | yes | 8 | 4.3 | odd | 2 | inner | |
256.5.c.g.255.2 | 4 | 16.13 | even | 4 | |||
256.5.c.g.255.3 | 4 | 16.3 | odd | 4 | |||
256.5.c.k.255.2 | 4 | 16.11 | odd | 4 | |||
256.5.c.k.255.3 | 4 | 16.5 | even | 4 | |||
1152.5.b.l.703.3 | 8 | 3.2 | odd | 2 | |||
1152.5.b.l.703.4 | 8 | 12.11 | even | 2 | |||
1152.5.b.l.703.5 | 8 | 24.5 | odd | 2 | |||
1152.5.b.l.703.6 | 8 | 24.11 | even | 2 |