Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(127,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.g (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: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.4 | ||
Root | \(1.28897 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.127 |
Dual form | 1152.3.g.d.127.3 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −2.46308 | −0.492615 | −0.246308 | − | 0.969192i | \(-0.579217\pi\) | ||||
−0.246308 | + | 0.969192i | \(0.579217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.48331i | 0.783331i | 0.920108 | + | 0.391665i | \(0.128101\pi\) | ||||
−0.920108 | + | 0.391665i | \(0.871899\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 10.5830i | − 0.962091i | −0.876696 | − | 0.481046i | \(-0.840257\pi\) | ||||
0.876696 | − | 0.481046i | \(-0.159743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.96663 | 0.689741 | 0.344870 | − | 0.938650i | \(-0.387923\pi\) | ||||
0.344870 | + | 0.938650i | \(0.387923\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −16.2399 | −0.955286 | −0.477643 | − | 0.878554i | \(-0.658509\pi\) | ||||
−0.477643 | + | 0.878554i | \(0.658509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.96663i | 0.156138i | 0.996948 | + | 0.0780692i | \(0.0248755\pi\) | ||||
−0.996948 | + | 0.0780692i | \(0.975124\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.46141i | − 0.0635394i | −0.999495 | − | 0.0317697i | \(-0.989886\pi\) | ||||
0.999495 | − | 0.0317697i | \(-0.0101143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18.9333 | −0.757330 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 25.0905 | 0.865189 | 0.432595 | − | 0.901589i | \(-0.357598\pi\) | ||||
0.432595 | + | 0.901589i | \(0.357598\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 10.5167i | − 0.339248i | −0.985509 | − | 0.169624i | \(-0.945745\pi\) | ||||
0.985509 | − | 0.169624i | \(-0.0542553\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 13.5058i | − 0.385881i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −16.9666 | −0.458558 | −0.229279 | − | 0.973361i | \(-0.573637\pi\) | ||||
−0.229279 | + | 0.973361i | \(0.573637\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −29.0150 | −0.707682 | −0.353841 | − | 0.935306i | \(-0.615125\pi\) | ||||
−0.353841 | + | 0.935306i | \(0.615125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 34.9666i | 0.813177i | 0.913611 | + | 0.406589i | \(0.133282\pi\) | ||||
−0.913611 | + | 0.406589i | \(0.866718\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 86.1254i | − 1.83246i | −0.400657 | − | 0.916228i | \(-0.631218\pi\) | ||||
0.400657 | − | 0.916228i | \(-0.368782\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.9333 | 0.386393 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 80.1976 | 1.51316 | 0.756581 | − | 0.653900i | \(-0.226868\pi\) | ||||
0.756581 | + | 0.653900i | \(0.226868\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26.0667i | 0.473941i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 66.4208i | − 1.12578i | −0.826533 | − | 0.562889i | \(-0.809690\pi\) | ||||
0.826533 | − | 0.562889i | \(-0.190310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.966630 | −0.0158464 | −0.00792319 | − | 0.999969i | \(-0.502522\pi\) | ||||
−0.00792319 | + | 0.999969i | \(0.502522\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22.0855 | −0.339777 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 113.800i | − 1.69850i | −0.527988 | − | 0.849252i | \(-0.677053\pi\) | ||||
0.527988 | − | 0.849252i | \(-0.322947\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 90.5097i | − 1.27478i | −0.770540 | − | 0.637392i | \(-0.780013\pi\) | ||||
0.770540 | − | 0.637392i | \(-0.219987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 51.7998 | 0.709586 | 0.354793 | − | 0.934945i | \(-0.384551\pi\) | ||||
0.354793 | + | 0.934945i | \(0.384551\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 58.0299 | 0.753636 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 80.4499i | − 1.01835i | −0.860662 | − | 0.509177i | \(-0.829950\pi\) | ||||
0.860662 | − | 0.509177i | \(-0.170050\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 79.9267i | − 0.962972i | −0.876454 | − | 0.481486i | \(-0.840097\pi\) | ||||
0.876454 | − | 0.481486i | \(-0.159903\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 40.0000 | 0.470588 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −142.694 | −1.60330 | −0.801652 | − | 0.597791i | \(-0.796045\pi\) | ||||
−0.801652 | + | 0.597791i | \(0.796045\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49.1669i | 0.540295i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 7.30703i | − 0.0769161i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −45.8665 | −0.472851 | −0.236425 | − | 0.971650i | \(-0.575976\pi\) | ||||
−0.236425 | + | 0.971650i | \(0.575976\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 83.1204 | 0.822975 | 0.411487 | − | 0.911415i | \(-0.365009\pi\) | ||||
0.411487 | + | 0.911415i | \(0.365009\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 106.517i | 1.03414i | 0.855942 | + | 0.517071i | \(0.172978\pi\) | ||||
−0.855942 | + | 0.517071i | \(0.827022\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 114.598i | − 1.07101i | −0.844531 | − | 0.535507i | \(-0.820121\pi\) | ||||
0.844531 | − | 0.535507i | \(-0.179879\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −94.7664 | −0.869417 | −0.434708 | − | 0.900571i | \(-0.643149\pi\) | ||||
−0.434708 | + | 0.900571i | \(0.643149\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −201.808 | −1.78591 | −0.892955 | − | 0.450146i | \(-0.851372\pi\) | ||||
−0.892955 | + | 0.450146i | \(0.851372\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.59955i | 0.0313005i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 89.0483i | − 0.748305i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.0743802 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 108.211 | 0.865687 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 171.417i | − 1.34974i | −0.737938 | − | 0.674868i | \(-0.764200\pi\) | ||||
0.737938 | − | 0.674868i | \(-0.235800\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 169.328i | − 1.29258i | −0.763092 | − | 0.646290i | \(-0.776319\pi\) | ||||
0.763092 | − | 0.646290i | \(-0.223681\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.2670 | −0.122308 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.38088 | −0.0173787 | −0.00868935 | − | 0.999962i | \(-0.502766\pi\) | ||||
−0.00868935 | + | 0.999962i | \(0.502766\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 209.800i | 1.50935i | 0.656098 | + | 0.754675i | \(0.272206\pi\) | ||||
−0.656098 | + | 0.754675i | \(0.727794\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 94.8939i | − 0.663594i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −61.7998 | −0.426205 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −51.7246 | −0.347145 | −0.173572 | − | 0.984821i | \(-0.555531\pi\) | ||||
−0.173572 | + | 0.984821i | \(0.555531\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 227.150i | 1.50430i | 0.658991 | + | 0.752151i | \(0.270984\pi\) | ||||
−0.658991 | + | 0.752151i | \(0.729016\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.9034i | 0.167119i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 110.766 | 0.705519 | 0.352759 | − | 0.935714i | \(-0.385243\pi\) | ||||
0.352759 | + | 0.935714i | \(0.385243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.01335 | 0.0497724 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 276.766i | − 1.69795i | −0.528430 | − | 0.848977i | \(-0.677219\pi\) | ||||
0.528430 | − | 0.848977i | \(-0.322781\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 80.2798i | − 0.480717i | −0.970684 | − | 0.240359i | \(-0.922735\pi\) | ||||
0.970684 | − | 0.240359i | \(-0.0772651\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −88.5996 | −0.524258 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 124.533 | 0.719844 | 0.359922 | − | 0.932982i | \(-0.382803\pi\) | ||||
0.359922 | + | 0.932982i | \(0.382803\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 103.817i | − 0.593240i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 66.4208i | − 0.371066i | −0.982638 | − | 0.185533i | \(-0.940599\pi\) | ||||
0.982638 | − | 0.185533i | \(-0.0594012\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 160.967 | 0.889318 | 0.444659 | − | 0.895700i | \(-0.353325\pi\) | ||||
0.444659 | + | 0.895700i | \(0.353325\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 41.7901 | 0.225892 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 171.867i | 0.919072i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 83.2026i | − 0.435616i | −0.975992 | − | 0.217808i | \(-0.930109\pi\) | ||||
0.975992 | − | 0.217808i | \(-0.0698906\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 131.666 | 0.682209 | 0.341104 | − | 0.940025i | \(-0.389199\pi\) | ||||
0.341104 | + | 0.940025i | \(0.389199\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 184.566 | 0.936885 | 0.468442 | − | 0.883494i | \(-0.344815\pi\) | ||||
0.468442 | + | 0.883494i | \(0.344815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 168.717i | 0.847824i | 0.905703 | + | 0.423912i | \(0.139343\pi\) | ||||
−0.905703 | + | 0.423912i | \(0.860657\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 137.579i | 0.677729i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 71.4661 | 0.348615 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31.3959 | 0.150219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 197.933i | − 0.938072i | −0.883179 | − | 0.469036i | \(-0.844601\pi\) | ||||
0.883179 | − | 0.469036i | \(-0.155399\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 86.1254i | − 0.400583i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 57.6663 | 0.265743 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −145.617 | −0.658900 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 99.6835i | − 0.447011i | −0.974703 | − | 0.223506i | \(-0.928250\pi\) | ||||
0.974703 | − | 0.223506i | \(-0.0717501\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 243.409i | 1.07229i | 0.844127 | + | 0.536143i | \(0.180119\pi\) | ||||
−0.844127 | + | 0.536143i | \(0.819881\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −454.232 | −1.98355 | −0.991774 | − | 0.128002i | \(-0.959144\pi\) | ||||
−0.991774 | + | 0.128002i | \(0.959144\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −77.7346 | −0.333625 | −0.166812 | − | 0.985989i | \(-0.553347\pi\) | ||||
−0.166812 | + | 0.985989i | \(0.553347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 212.133i | 0.902696i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 348.886i | 1.45977i | 0.683568 | + | 0.729887i | \(0.260427\pi\) | ||||
−0.683568 | + | 0.729887i | \(0.739573\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 75.7998 | 0.314522 | 0.157261 | − | 0.987557i | \(-0.449734\pi\) | ||||
0.157261 | + | 0.987557i | \(0.449734\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −46.6340 | −0.190343 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.6007i | 0.107695i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 131.733i | − 0.524834i | −0.964955 | − | 0.262417i | \(-0.915480\pi\) | ||||
0.964955 | − | 0.262417i | \(-0.0845197\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.4661 | −0.0611307 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 305.093 | 1.18713 | 0.593565 | − | 0.804786i | \(-0.297720\pi\) | ||||
0.593565 | + | 0.804786i | \(0.297720\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 93.0334i | − 0.359202i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 338.656i | 1.28767i | 0.765166 | + | 0.643833i | \(0.222657\pi\) | ||||
−0.765166 | + | 0.643833i | \(0.777343\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −197.533 | −0.745407 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −271.234 | −1.00830 | −0.504152 | − | 0.863615i | \(-0.668195\pi\) | ||||
−0.504152 | + | 0.863615i | \(0.668195\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 406.749i | − 1.50092i | −0.660916 | − | 0.750460i | \(-0.729832\pi\) | ||||
0.660916 | − | 0.750460i | \(-0.270168\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 200.371i | 0.728621i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 249.234 | 0.899760 | 0.449880 | − | 0.893089i | \(-0.351467\pi\) | ||||
0.449880 | + | 0.893089i | \(0.351467\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 56.9461 | 0.202655 | 0.101328 | − | 0.994853i | \(-0.467691\pi\) | ||||
0.101328 | + | 0.994853i | \(0.467691\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 136.267i | 0.481509i | 0.970586 | + | 0.240754i | \(0.0773948\pi\) | ||||
−0.970586 | + | 0.240754i | \(0.922605\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 159.098i | − 0.554349i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −25.2670 | −0.0874289 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −445.324 | −1.51988 | −0.759938 | − | 0.649996i | \(-0.774771\pi\) | ||||
−0.759938 | + | 0.649996i | \(0.774771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 163.600i | 0.554575i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 13.1039i | − 0.0438257i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −191.733 | −0.636987 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.38088 | 0.00780617 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 329.533i | − 1.07340i | −0.843774 | − | 0.536698i | \(-0.819671\pi\) | ||||
0.843774 | − | 0.536698i | \(-0.180329\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 359.116i | 1.15471i | 0.816492 | + | 0.577357i | \(0.195916\pi\) | ||||
−0.816492 | + | 0.577357i | \(0.804084\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 147.666 | 0.471777 | 0.235889 | − | 0.971780i | \(-0.424200\pi\) | ||||
0.235889 | + | 0.971780i | \(0.424200\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −233.663 | −0.737109 | −0.368554 | − | 0.929606i | \(-0.620147\pi\) | ||||
−0.368554 | + | 0.929606i | \(0.620147\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 265.533i | − 0.832391i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 48.1776i | − 0.149157i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −169.768 | −0.522362 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 472.253 | 1.43542 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 163.600i | − 0.494258i | −0.968983 | − | 0.247129i | \(-0.920513\pi\) | ||||
0.968983 | − | 0.247129i | \(-0.0794872\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 280.297i | 0.836709i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.9333 | −0.106627 | −0.0533134 | − | 0.998578i | \(-0.516978\pi\) | ||||
−0.0533134 | + | 0.998578i | \(0.516978\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −111.298 | −0.326387 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 372.499i | 1.08600i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 584.282i | 1.68381i | 0.539626 | + | 0.841905i | \(0.318565\pi\) | ||||
−0.539626 | + | 0.841905i | \(0.681435\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 230.766 | 0.661222 | 0.330611 | − | 0.943767i | \(-0.392745\pi\) | ||||
0.330611 | + | 0.943767i | \(0.392745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 50.0166 | 0.141690 | 0.0708450 | − | 0.997487i | \(-0.477430\pi\) | ||||
0.0708450 | + | 0.997487i | \(0.477430\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 222.932i | 0.627978i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 253.992i | 0.707499i | 0.935340 | + | 0.353749i | \(0.115093\pi\) | ||||
−0.935340 | + | 0.353749i | \(0.884907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 352.199 | 0.975621 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −127.587 | −0.349553 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 348.682i | 0.950088i | 0.879962 | + | 0.475044i | \(0.157568\pi\) | ||||
−0.879962 | + | 0.475044i | \(0.842432\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 439.749i | 1.18531i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 646.499 | 1.73324 | 0.866621 | − | 0.498967i | \(-0.166287\pi\) | ||||
0.866621 | + | 0.498967i | \(0.166287\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 224.977 | 0.596756 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 274.433i | 0.724097i | 0.932159 | + | 0.362048i | \(0.117922\pi\) | ||||
−0.932159 | + | 0.362048i | \(0.882078\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 272.990i | 0.712769i | 0.934339 | + | 0.356384i | \(0.115991\pi\) | ||||
−0.934339 | + | 0.356384i | \(0.884009\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −142.932 | −0.371252 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −412.679 | −1.06087 | −0.530436 | − | 0.847725i | \(-0.677972\pi\) | ||||
−0.530436 | + | 0.847725i | \(0.677972\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.7330i | 0.0606983i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 198.154i | 0.501656i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −384.700 | −0.969017 | −0.484508 | − | 0.874787i | \(-0.661001\pi\) | ||||
−0.484508 | + | 0.874787i | \(0.661001\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 561.466 | 1.40016 | 0.700082 | − | 0.714063i | \(-0.253147\pi\) | ||||
0.700082 | + | 0.714063i | \(0.253147\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 94.2992i | − 0.233993i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 179.558i | 0.441174i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −253.333 | −0.619395 | −0.309698 | − | 0.950835i | \(-0.600228\pi\) | ||||
−0.309698 | + | 0.950835i | \(0.600228\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 364.206 | 0.881856 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 196.865i | 0.474374i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 622.985i | 1.48684i | 0.668827 | + | 0.743418i | \(0.266797\pi\) | ||||
−0.668827 | + | 0.743418i | \(0.733203\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −487.300 | −1.15748 | −0.578741 | − | 0.815511i | \(-0.696456\pi\) | ||||
−0.578741 | + | 0.815511i | \(0.696456\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 307.473 | 0.723467 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.30033i | − 0.0124130i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 176.635i | − 0.409826i | −0.978780 | − | 0.204913i | \(-0.934309\pi\) | ||||
0.978780 | − | 0.204913i | \(-0.0656912\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −257.066 | −0.593685 | −0.296843 | − | 0.954926i | \(-0.595934\pi\) | ||||
−0.296843 | + | 0.954926i | \(0.595934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.33545 | 0.00992094 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 638.482i | − 1.45440i | −0.686425 | − | 0.727201i | \(-0.740821\pi\) | ||||
0.686425 | − | 0.727201i | \(-0.259179\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 104.722i | − 0.236392i | −0.992990 | − | 0.118196i | \(-0.962289\pi\) | ||||
0.992990 | − | 0.118196i | \(-0.0377112\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 351.466 | 0.789811 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −219.132 | −0.488043 | −0.244022 | − | 0.969770i | \(-0.578467\pi\) | ||||
−0.244022 | + | 0.969770i | \(0.578467\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 307.066i | 0.680855i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 121.102i | − 0.266158i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −46.4004 | −0.101533 | −0.0507664 | − | 0.998711i | \(-0.516166\pi\) | ||||
−0.0507664 | + | 0.998711i | \(0.516166\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −517.377 | −1.12229 | −0.561146 | − | 0.827717i | \(-0.689639\pi\) | ||||
−0.561146 | + | 0.827717i | \(0.689639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 111.016i | − 0.239776i | −0.992787 | − | 0.119888i | \(-0.961747\pi\) | ||||
0.992787 | − | 0.119888i | \(-0.0382535\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 233.934i | − 0.500930i | −0.968126 | − | 0.250465i | \(-0.919416\pi\) | ||||
0.968126 | − | 0.250465i | \(-0.0805835\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 624.000 | 1.33049 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 370.052 | 0.782351 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 56.1680i | − 0.118248i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 610.185i | 1.27387i | 0.770916 | + | 0.636937i | \(0.219799\pi\) | ||||
−0.770916 | + | 0.636937i | \(0.780201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −152.133 | −0.316286 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 112.973 | 0.232933 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 104.183i | − 0.213928i | −0.994263 | − | 0.106964i | \(-0.965887\pi\) | ||||
0.994263 | − | 0.106964i | \(-0.0341130\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 423.320i | 0.862159i | 0.902314 | + | 0.431080i | \(0.141867\pi\) | ||||
−0.902314 | + | 0.431080i | \(0.858133\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −407.466 | −0.826503 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 496.293 | 0.998577 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 126.932i | − 0.254373i | −0.991879 | − | 0.127187i | \(-0.959405\pi\) | ||||
0.991879 | − | 0.127187i | \(-0.0405947\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 274.452i | − 0.545630i | −0.962067 | − | 0.272815i | \(-0.912045\pi\) | ||||
0.962067 | − | 0.272815i | \(-0.0879547\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −204.732 | −0.405410 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −750.416 | −1.47429 | −0.737147 | − | 0.675732i | \(-0.763828\pi\) | ||||
−0.737147 | + | 0.675732i | \(0.763828\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 284.034i | 0.555840i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 262.359i | − 0.509434i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −911.466 | −1.76299 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −822.387 | −1.57848 | −0.789239 | − | 0.614086i | \(-0.789525\pi\) | ||||
−0.789239 | + | 0.614086i | \(0.789525\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 184.366i | − 0.352516i | −0.984344 | − | 0.176258i | \(-0.943601\pi\) | ||||
0.984344 | − | 0.176258i | \(-0.0563993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 170.789i | 0.324079i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 526.864 | 0.995963 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −260.167 | −0.488117 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 282.265i | 0.527598i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 200.371i | − 0.371745i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 432.967 | 0.800308 | 0.400154 | − | 0.916448i | \(-0.368957\pi\) | ||||
0.400154 | + | 0.916448i | \(0.368957\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 233.417 | 0.428288 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 557.567i | 1.01932i | 0.860376 | + | 0.509659i | \(0.170229\pi\) | ||||
−0.860376 | + | 0.509659i | \(0.829771\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 74.4342i | 0.135089i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 441.132 | 0.797708 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 656.984 | 1.17950 | 0.589752 | − | 0.807584i | \(-0.299226\pi\) | ||||
0.589752 | + | 0.807584i | \(0.299226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 313.533i | 0.560882i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 204.706i | − 0.363599i | −0.983336 | − | 0.181799i | \(-0.941808\pi\) | ||||
0.983336 | − | 0.181799i | \(-0.0581922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 497.068 | 0.879766 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −251.611 | −0.442199 | −0.221100 | − | 0.975251i | \(-0.570965\pi\) | ||||
−0.221100 | + | 0.975251i | \(0.570965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 832.198i | − 1.45744i | −0.684812 | − | 0.728720i | \(-0.740116\pi\) | ||||
0.684812 | − | 0.728720i | \(-0.259884\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.6692i | 0.0481203i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 539.132 | 0.934372 | 0.467186 | − | 0.884159i | \(-0.345268\pi\) | ||||
0.467186 | + | 0.884159i | \(0.345268\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 438.263 | 0.754325 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 848.732i | − 1.45580i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 84.6640i | − 0.144232i | −0.997396 | − | 0.0721159i | \(-0.977025\pi\) | ||||
0.997396 | − | 0.0721159i | \(-0.0229751\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.1991 | 0.0529696 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −923.717 | −1.55770 | −0.778851 | − | 0.627209i | \(-0.784197\pi\) | ||||
−0.778851 | + | 0.627209i | \(0.784197\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 219.333i | 0.368626i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 538.674i | 0.899288i | 0.893208 | + | 0.449644i | \(0.148449\pi\) | ||||
−0.893208 | + | 0.449644i | \(0.851551\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −164.334 | −0.273434 | −0.136717 | − | 0.990610i | \(-0.543655\pi\) | ||||
−0.136717 | + | 0.990610i | \(0.543655\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.1677 | −0.0366408 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 368.984i | 0.607881i | 0.952691 | + | 0.303941i | \(0.0983024\pi\) | ||||
−0.952691 | + | 0.303941i | \(0.901698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 772.255i | − 1.26392i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −968.433 | −1.57982 | −0.789912 | − | 0.613220i | \(-0.789874\pi\) | ||||
−0.789912 | + | 0.613220i | \(0.789874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −53.2682 | −0.0863342 | −0.0431671 | − | 0.999068i | \(-0.513745\pi\) | ||||
−0.0431671 | + | 0.999068i | \(0.513745\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1066.80i | − 1.72342i | −0.507399 | − | 0.861711i | \(-0.669393\pi\) | ||||
0.507399 | − | 0.861711i | \(-0.330607\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 782.436i | − 1.25592i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 206.800 | 0.330880 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 275.536 | 0.438054 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 468.049i | − 0.741758i | −0.928681 | − | 0.370879i | \(-0.879056\pi\) | ||||
0.928681 | − | 0.370879i | \(-0.120944\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 422.212i | 0.664901i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 169.768 | 0.266511 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −603.043 | −0.940784 | −0.470392 | − | 0.882458i | \(-0.655887\pi\) | ||||
−0.470392 | + | 0.882458i | \(0.655887\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 352.633i | 0.548418i | 0.961670 | + | 0.274209i | \(0.0884160\pi\) | ||||
−0.961670 | + | 0.274209i | \(0.911584\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 897.790i | − 1.38762i | −0.720158 | − | 0.693810i | \(-0.755931\pi\) | ||||
0.720158 | − | 0.693810i | \(-0.244069\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −702.932 | −1.08310 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 169.459 | 0.259508 | 0.129754 | − | 0.991546i | \(-0.458581\pi\) | ||||
0.129754 | + | 0.991546i | \(0.458581\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 417.068i | 0.636745i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.4864i | 0.0553663i | 0.999617 | + | 0.0276832i | \(0.00881295\pi\) | ||||
−0.999617 | + | 0.0276832i | \(0.991187\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1038.77 | 1.57151 | 0.785754 | − | 0.618539i | \(-0.212275\pi\) | ||||
0.785754 | + | 0.618539i | \(0.212275\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 40.0668 | 0.0602508 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 36.6674i | − 0.0549736i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.2298i | 0.0152457i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −593.600 | −0.882020 | −0.441010 | − | 0.897502i | \(-0.645380\pi\) | ||||
−0.441010 | + | 0.897502i | \(0.645380\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 296.455 | 0.437895 | 0.218948 | − | 0.975737i | \(-0.429738\pi\) | ||||
0.218948 | + | 0.975737i | \(0.429738\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 251.501i | − 0.370398i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1169.67i | − 1.71255i | −0.516520 | − | 0.856275i | \(-0.672773\pi\) | ||||
0.516520 | − | 0.856275i | \(-0.327227\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.86429 | 0.00856101 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 719.102 | 1.04369 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1242.70i | 1.79841i | 0.437530 | + | 0.899204i | \(0.355853\pi\) | ||||
−0.437530 | + | 0.899204i | \(0.644147\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 516.753i | − 0.743529i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 471.199 | 0.676039 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1362.28 | 1.94333 | 0.971666 | − | 0.236358i | \(-0.0759538\pi\) | ||||
0.971666 | + | 0.236358i | \(0.0759538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 50.3337i | − 0.0715984i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 455.776i | 0.644661i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1261.97 | −1.77992 | −0.889962 | − | 0.456036i | \(-0.849269\pi\) | ||||
−0.889962 | + | 0.456036i | \(0.849269\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.3692 | −0.0215556 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 233.731i | 0.326896i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 951.764i | − 1.32373i | −0.749622 | − | 0.661867i | \(-0.769765\pi\) | ||||
0.749622 | − | 0.661867i | \(-0.230235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −584.065 | −0.810076 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −475.045 | −0.655234 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 982.383i | − 1.35128i | −0.737230 | − | 0.675642i | \(-0.763867\pi\) | ||||
0.737230 | − | 0.675642i | \(-0.236133\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 567.853i | − 0.776817i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −165.699 | −0.226055 | −0.113028 | − | 0.993592i | \(-0.536055\pi\) | ||||
−0.113028 | + | 0.993592i | \(0.536055\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1204.34 | −1.63412 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 248.999i | − 0.336940i | −0.985707 | − | 0.168470i | \(-0.946117\pi\) | ||||
0.985707 | − | 0.168470i | \(-0.0538827\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 538.674i | − 0.724998i | −0.931984 | − | 0.362499i | \(-0.881924\pi\) | ||||
0.931984 | − | 0.362499i | \(-0.118076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 127.402 | 0.171009 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 628.380 | 0.838958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 979.882i | 1.30477i | 0.757888 | + | 0.652385i | \(0.226231\pi\) | ||||
−0.757888 | + | 0.652385i | \(0.773769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 559.487i | − 0.741042i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1151.90 | 1.52166 | 0.760831 | − | 0.648950i | \(-0.224791\pi\) | ||||
0.760831 | + | 0.648950i | \(0.224791\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −268.064 | −0.352253 | −0.176126 | − | 0.984368i | \(-0.556357\pi\) | ||||
−0.176126 | + | 0.984368i | \(0.556357\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 519.634i | − 0.681041i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 595.571i | − 0.776494i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 428.467 | 0.557174 | 0.278587 | − | 0.960411i | \(-0.410134\pi\) | ||||
0.278587 | + | 0.960411i | \(0.410134\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1118.14 | 1.44649 | 0.723245 | − | 0.690592i | \(-0.242650\pi\) | ||||
0.723245 | + | 0.690592i | \(0.242650\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 199.115i | 0.256923i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 86.0767i | − 0.110496i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −957.864 | −1.22646 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −272.826 | −0.347549 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 711.832i | 0.904488i | 0.891894 | + | 0.452244i | \(0.149376\pi\) | ||||
−0.891894 | + | 0.452244i | \(0.850624\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1106.58i | − 1.39896i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.66741 | −0.0109299 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −209.033 | −0.262274 | −0.131137 | − | 0.991364i | \(-0.541863\pi\) | ||||
−0.131137 | + | 0.991364i | \(0.541863\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1398.67i | 1.75052i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 548.197i | − 0.682687i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.7375 | −0.0245186 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −581.170 | −0.718381 | −0.359190 | − | 0.933264i | \(-0.616947\pi\) | ||||
−0.359190 | + | 0.933264i | \(0.616947\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 171.432i | 0.211383i | 0.994399 | + | 0.105691i | \(0.0337056\pi\) | ||||
−0.994399 | + | 0.105691i | \(0.966294\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 681.697i | 0.836437i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −103.733 | −0.126968 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1134.49 | 1.38184 | 0.690921 | − | 0.722931i | \(-0.257205\pi\) | ||||
0.690921 | + | 0.722931i | \(0.257205\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 379.249i | − 0.460812i | −0.973095 | − | 0.230406i | \(-0.925995\pi\) | ||||
0.973095 | − | 0.230406i | \(-0.0740055\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1177.33i | − 1.42362i | −0.702373 | − | 0.711809i | \(-0.747876\pi\) | ||||
0.702373 | − | 0.711809i | \(-0.252124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1278.56 | 1.54230 | 0.771148 | − | 0.636656i | \(-0.219683\pi\) | ||||
0.771148 | + | 0.636656i | \(0.219683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −307.473 | −0.369116 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 197.735i | 0.236809i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1015.97i | 1.21093i | 0.795873 | + | 0.605464i | \(0.207012\pi\) | ||||
−0.795873 | + | 0.605464i | \(0.792988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −211.467 | −0.251447 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 218.227 | 0.258257 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 49.3498i | 0.0582643i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.7951i | 0.0291365i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1509.43 | 1.76956 | 0.884778 | − | 0.466012i | \(-0.154310\pi\) | ||||
0.884778 | + | 0.466012i | \(0.154310\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −844.260 | −0.985134 | −0.492567 | − | 0.870275i | \(-0.663941\pi\) | ||||
−0.492567 | + | 0.870275i | \(0.663941\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 989.231i | − 1.15161i | −0.817588 | − | 0.575804i | \(-0.804689\pi\) | ||||
0.817588 | − | 0.575804i | \(-0.195311\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1680.23i | − 1.94696i | −0.228774 | − | 0.973480i | \(-0.573472\pi\) | ||||
0.228774 | − | 0.973480i | \(-0.426528\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −306.734 | −0.354606 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −851.402 | −0.979749 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1020.40i | − 1.17153i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 593.355i | 0.678120i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −591.899 | −0.674913 | −0.337457 | − | 0.941341i | \(-0.609567\pi\) | ||||
−0.337457 | + | 0.941341i | \(0.609567\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −797.050 | −0.904711 | −0.452355 | − | 0.891838i | \(-0.649416\pi\) | ||||
−0.452355 | + | 0.891838i | \(0.649416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 276.964i | 0.313663i | 0.987625 | + | 0.156831i | \(0.0501280\pi\) | ||||
−0.987625 | + | 0.156831i | \(0.949872\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 910.845i | 1.02688i | 0.858125 | + | 0.513441i | \(0.171630\pi\) | ||||
−0.858125 | + | 0.513441i | \(0.828370\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 939.931 | 1.05729 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 255.502 | 0.286117 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 163.600i | 0.182793i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 263.869i | − 0.293514i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1302.40 | −1.44550 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −396.473 | −0.438092 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1472.83i | − 1.62385i | −0.583763 | − | 0.811924i | \(-0.698420\pi\) | ||||
0.583763 | − | 0.811924i | \(-0.301580\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 36.5352i | − 0.0401045i | −0.999799 | − | 0.0200522i | \(-0.993617\pi\) | ||||
0.999799 | − | 0.0200522i | \(-0.00638325\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −845.864 | −0.926467 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 928.479 | 1.01252 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 467.150i | 0.508324i | 0.967162 | + | 0.254162i | \(0.0817996\pi\) | ||||
−0.967162 | + | 0.254162i | \(0.918200\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 811.567i | − 0.879270i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 321.234 | 0.347280 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 762.190 | 0.820441 | 0.410220 | − | 0.911986i | \(-0.365452\pi\) | ||||
0.410220 | + | 0.911986i | \(0.365452\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 56.1680i | 0.0603308i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 423.320i | − 0.452749i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 123.335 | 0.131627 | 0.0658137 | − | 0.997832i | \(-0.479036\pi\) | ||||
0.0658137 | + | 0.997832i | \(0.479036\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −735.638 | −0.781762 | −0.390881 | − | 0.920441i | \(-0.627830\pi\) | ||||
−0.390881 | + | 0.920441i | \(0.627830\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.4027i | 0.0449657i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 549.610i | − 0.580370i | −0.956971 | − | 0.290185i | \(-0.906283\pi\) | ||||
0.956971 | − | 0.290185i | \(-0.0937168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 464.469 | 0.489430 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1217.33 | −1.27737 | −0.638684 | − | 0.769469i | \(-0.720521\pi\) | ||||
−0.638684 | + | 0.769469i | \(0.720521\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 204.934i | 0.214591i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 13.0551i | − 0.0136133i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 850.399 | 0.884911 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −324.304 | −0.336066 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 514.616i | − 0.532178i | −0.963949 | − | 0.266089i | \(-0.914269\pi\) | ||||
0.963949 | − | 0.266089i | \(-0.0857314\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1248.49i | − 1.28578i | −0.765959 | − | 0.642889i | \(-0.777736\pi\) | ||||
0.765959 | − | 0.642889i | \(-0.222264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1150.40 | −1.18232 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −126.028 | −0.128995 | −0.0644973 | − | 0.997918i | \(-0.520544\pi\) | ||||
−0.0644973 | + | 0.997918i | \(0.520544\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1510.13i | 1.54252i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1018.89i | − 1.03651i | −0.855226 | − | 0.518256i | \(-0.826581\pi\) | ||||
0.855226 | − | 0.518256i | \(-0.173419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −454.601 | −0.461524 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51.1005 | 0.0516688 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 859.981i | − 0.867791i | −0.900963 | − | 0.433895i | \(-0.857139\pi\) | ||||
0.900963 | − | 0.433895i | \(-0.142861\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 415.562i | − 0.417651i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1104.43 | −1.10776 | −0.553878 | − | 0.832598i | \(-0.686853\pi\) | ||||
−0.553878 | + | 0.832598i | \(0.686853\pi\) | |||||||
\(998\) | 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 | 1152.3.g.d.127.4 | yes | 8 | |
3.2 | odd | 2 | inner | 1152.3.g.d.127.6 | yes | 8 | |
4.3 | odd | 2 | inner | 1152.3.g.d.127.3 | ✓ | 8 | |
8.3 | odd | 2 | 1152.3.g.e.127.5 | yes | 8 | ||
8.5 | even | 2 | 1152.3.g.e.127.6 | yes | 8 | ||
12.11 | even | 2 | inner | 1152.3.g.d.127.5 | yes | 8 | |
16.3 | odd | 4 | 2304.3.b.r.127.6 | 8 | |||
16.5 | even | 4 | 2304.3.b.r.127.3 | 8 | |||
16.11 | odd | 4 | 2304.3.b.s.127.4 | 8 | |||
16.13 | even | 4 | 2304.3.b.s.127.5 | 8 | |||
24.5 | odd | 2 | 1152.3.g.e.127.4 | yes | 8 | ||
24.11 | even | 2 | 1152.3.g.e.127.3 | yes | 8 | ||
48.5 | odd | 4 | 2304.3.b.r.127.5 | 8 | |||
48.11 | even | 4 | 2304.3.b.s.127.6 | 8 | |||
48.29 | odd | 4 | 2304.3.b.s.127.3 | 8 | |||
48.35 | even | 4 | 2304.3.b.r.127.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.g.d.127.3 | ✓ | 8 | 4.3 | odd | 2 | inner | |
1152.3.g.d.127.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1152.3.g.d.127.5 | yes | 8 | 12.11 | even | 2 | inner | |
1152.3.g.d.127.6 | yes | 8 | 3.2 | odd | 2 | inner | |
1152.3.g.e.127.3 | yes | 8 | 24.11 | even | 2 | ||
1152.3.g.e.127.4 | yes | 8 | 24.5 | odd | 2 | ||
1152.3.g.e.127.5 | yes | 8 | 8.3 | odd | 2 | ||
1152.3.g.e.127.6 | yes | 8 | 8.5 | even | 2 | ||
2304.3.b.r.127.3 | 8 | 16.5 | even | 4 | |||
2304.3.b.r.127.4 | 8 | 48.35 | even | 4 | |||
2304.3.b.r.127.5 | 8 | 48.5 | odd | 4 | |||
2304.3.b.r.127.6 | 8 | 16.3 | odd | 4 | |||
2304.3.b.s.127.3 | 8 | 48.29 | odd | 4 | |||
2304.3.b.s.127.4 | 8 | 16.11 | odd | 4 | |||
2304.3.b.s.127.5 | 8 | 16.13 | even | 4 | |||
2304.3.b.s.127.6 | 8 | 48.11 | even | 4 |