Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(127,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.b (of order \(2\), degree \(1\), not 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: | \(62.7794529086\) |
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: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.4 | ||
Root | \(-1.28897 + 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.127 |
Dual form | 2304.3.b.r.127.5 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | − 2.46308i | − 0.492615i | −0.969192 | − | 0.246308i | \(-0.920783\pi\) | ||||
0.969192 | − | 0.246308i | \(-0.0792173\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | −10.5830 | −0.962091 | −0.481046 | − | 0.876696i | \(-0.659743\pi\) | ||||
−0.481046 | + | 0.876696i | \(0.659743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.96663i | 0.689741i | 0.938650 | + | 0.344870i | \(0.112077\pi\) | ||||
−0.938650 | + | 0.344870i | \(0.887923\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.2399 | 0.955286 | 0.477643 | − | 0.878554i | \(-0.341491\pi\) | ||||
0.477643 | + | 0.878554i | \(0.341491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.96663 | 0.156138 | 0.0780692 | − | 0.996948i | \(-0.475124\pi\) | ||||
0.0780692 | + | 0.996948i | \(0.475124\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.46141i | 0.0635394i | 0.999495 | + | 0.0317697i | \(0.0101143\pi\) | ||||
−0.999495 | + | 0.0317697i | \(0.989886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.9333 | 0.757330 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 25.0905i | − 0.865189i | −0.901589 | − | 0.432595i | \(-0.857598\pi\) | ||||
0.901589 | − | 0.432595i | \(-0.142402\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.5167i | 0.339248i | 0.985509 | + | 0.169624i | \(0.0542553\pi\) | ||||
−0.985509 | + | 0.169624i | \(0.945745\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.5058 | 0.385881 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.9666i | 0.458558i | 0.973361 | + | 0.229279i | \(0.0736367\pi\) | ||||
−0.973361 | + | 0.229279i | \(0.926363\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −34.9666 | −0.813177 | −0.406589 | − | 0.913611i | \(-0.633282\pi\) | ||||
−0.406589 | + | 0.913611i | \(0.633282\pi\) | |||||||
\(44\) | 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 | ||||||||
\(53\) | 80.1976i | 1.51316i | 0.653900 | + | 0.756581i | \(0.273132\pi\) | ||||
−0.653900 | + | 0.756581i | \(0.726868\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26.0667i | 0.473941i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −66.4208 | −1.12578 | −0.562889 | − | 0.826533i | \(-0.690310\pi\) | ||||
−0.562889 | + | 0.826533i | \(0.690310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 0.966630i | − 0.0158464i | −0.999969 | − | 0.00792319i | \(-0.997478\pi\) | ||||
0.999969 | − | 0.00792319i | \(-0.00252206\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.0855 | 0.339777 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −113.800 | −1.69850 | −0.849252 | − | 0.527988i | \(-0.822947\pi\) | ||||
−0.849252 | + | 0.527988i | \(0.822947\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 90.5097i | 1.27478i | 0.770540 | + | 0.637392i | \(0.219987\pi\) | ||||
−0.770540 | + | 0.637392i | \(0.780013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −51.7998 | −0.709586 | −0.354793 | − | 0.934945i | \(-0.615449\pi\) | ||||
−0.354793 | + | 0.934945i | \(0.615449\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 58.0299i | − 0.753636i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80.4499i | 1.01835i | 0.860662 | + | 0.509177i | \(0.170050\pi\) | ||||
−0.860662 | + | 0.509177i | \(0.829950\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 79.9267 | 0.962972 | 0.481486 | − | 0.876454i | \(-0.340097\pi\) | ||||
0.481486 | + | 0.876454i | \(0.340097\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 40.0000i | − 0.470588i | ||||||||
\(86\) | 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 | ||||||||
\(91\) | −49.1669 | −0.540295 | ||||||||
\(92\) | 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 | ||||||||
\(101\) | 83.1204i | 0.822975i | 0.911415 | + | 0.411487i | \(0.134991\pi\) | ||||
−0.911415 | + | 0.411487i | \(0.865009\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | −114.598 | −1.07101 | −0.535507 | − | 0.844531i | \(-0.679879\pi\) | ||||
−0.535507 | + | 0.844531i | \(0.679879\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 94.7664i | − 0.869417i | −0.900571 | − | 0.434708i | \(-0.856851\pi\) | ||||
0.900571 | − | 0.434708i | \(-0.143149\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 201.808 | 1.78591 | 0.892955 | − | 0.450146i | \(-0.148628\pi\) | ||||
0.892955 | + | 0.450146i | \(0.148628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.59955 | 0.0313005 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | − 108.211i | − 0.865687i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 171.417i | 1.34974i | 0.737938 | + | 0.674868i | \(0.235800\pi\) | ||||
−0.737938 | + | 0.674868i | \(0.764200\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 169.328 | 1.29258 | 0.646290 | − | 0.763092i | \(-0.276319\pi\) | ||||
0.646290 | + | 0.763092i | \(0.276319\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.2670i | 0.122308i | ||||||||
\(134\) | 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 | ||||||||
\(139\) | −209.800 | −1.50935 | −0.754675 | − | 0.656098i | \(-0.772206\pi\) | ||||
−0.754675 | + | 0.656098i | \(0.772206\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | − 51.7246i | − 0.347145i | −0.984821 | − | 0.173572i | \(-0.944469\pi\) | ||||
0.984821 | − | 0.173572i | \(-0.0555311\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 25.9034 | 0.167119 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 110.766i | 0.705519i | 0.935714 | + | 0.352759i | \(0.114757\pi\) | ||||
−0.935714 | + | 0.352759i | \(0.885243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.01335 | −0.0497724 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −276.766 | −1.69795 | −0.848977 | − | 0.528430i | \(-0.822781\pi\) | ||||
−0.848977 | + | 0.528430i | \(0.822781\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 80.2798i | 0.480717i | 0.970684 | + | 0.240359i | \(0.0772651\pi\) | ||||
−0.970684 | + | 0.240359i | \(0.922735\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 88.5996 | 0.524258 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 124.533i | − 0.719844i | −0.932982 | − | 0.359922i | \(-0.882803\pi\) | ||||
0.932982 | − | 0.359922i | \(-0.117197\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 103.817i | 0.593240i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 66.4208 | 0.371066 | 0.185533 | − | 0.982638i | \(-0.440599\pi\) | ||||
0.185533 | + | 0.982638i | \(0.440599\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 160.967i | − 0.889318i | −0.895700 | − | 0.444659i | \(-0.853325\pi\) | ||||
0.895700 | − | 0.444659i | \(-0.146675\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 41.7901 | 0.225892 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −171.867 | −0.919072 | ||||||||
\(188\) | 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 | ||||||||
\(197\) | 184.566i | 0.936885i | 0.883494 | + | 0.468442i | \(0.155185\pi\) | ||||
−0.883494 | + | 0.468442i | \(0.844815\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 137.579 | 0.677729 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 71.4661i | 0.348615i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.3959 | −0.150219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −197.933 | −0.938072 | −0.469036 | − | 0.883179i | \(-0.655399\pi\) | ||||
−0.469036 | + | 0.883179i | \(0.655399\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | 145.617i | 0.658900i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 99.6835i | 0.447011i | 0.974703 | + | 0.223506i | \(0.0717501\pi\) | ||||
−0.974703 | + | 0.223506i | \(0.928250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −243.409 | −1.07229 | −0.536143 | − | 0.844127i | \(-0.680119\pi\) | ||||
−0.536143 | + | 0.844127i | \(0.680119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 454.232i | 1.98355i | 0.128002 | + | 0.991774i | \(0.459144\pi\) | ||||
−0.128002 | + | 0.991774i | \(0.540856\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | −212.133 | −0.902696 | ||||||||
\(236\) | 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 | ||||||||
\(245\) | − 46.6340i | − 0.190343i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.6007i | 0.107695i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −131.733 | −0.524834 | −0.262417 | − | 0.964955i | \(-0.584520\pi\) | ||||
−0.262417 | + | 0.964955i | \(0.584520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 15.4661i | − 0.0611307i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −305.093 | −1.18713 | −0.593565 | − | 0.804786i | \(-0.702280\pi\) | ||||
−0.593565 | + | 0.804786i | \(0.702280\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −93.0334 | −0.359202 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 338.656i | − 1.28767i | −0.765166 | − | 0.643833i | \(-0.777343\pi\) | ||||
0.765166 | − | 0.643833i | \(-0.222657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 197.533 | 0.745407 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 271.234i | 1.00830i | 0.863615 | + | 0.504152i | \(0.168195\pi\) | ||||
−0.863615 | + | 0.504152i | \(0.831805\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 406.749i | 1.50092i | 0.660916 | + | 0.750460i | \(0.270168\pi\) | ||||
−0.660916 | + | 0.750460i | \(0.729832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −200.371 | −0.728621 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 249.234i | − 0.899760i | −0.893089 | − | 0.449880i | \(-0.851467\pi\) | ||||
0.893089 | − | 0.449880i | \(-0.148533\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −136.267 | −0.481509 | −0.240754 | − | 0.970586i | \(-0.577395\pi\) | ||||
−0.240754 | + | 0.970586i | \(0.577395\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | − 445.324i | − 1.51988i | −0.649996 | − | 0.759938i | \(-0.725229\pi\) | ||||
0.649996 | − | 0.759938i | \(-0.274771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 163.600i | 0.554575i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.1039 | −0.0438257 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 191.733i | − 0.636987i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.38088 | −0.00780617 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −329.533 | −1.07340 | −0.536698 | − | 0.843774i | \(-0.680329\pi\) | ||||
−0.536698 | + | 0.843774i | \(0.680329\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 359.116i | − 1.15471i | −0.816492 | − | 0.577357i | \(-0.804084\pi\) | ||||
0.816492 | − | 0.577357i | \(-0.195916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −147.666 | −0.471777 | −0.235889 | − | 0.971780i | \(-0.575800\pi\) | ||||
−0.235889 | + | 0.971780i | \(0.575800\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 233.663i | 0.737109i | 0.929606 | + | 0.368554i | \(0.120147\pi\) | ||||
−0.929606 | + | 0.368554i | \(0.879853\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 265.533i | 0.832391i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 48.1776 | 0.149157 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 169.768i | 0.522362i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 472.253 | 1.43542 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 163.600 | 0.494258 | 0.247129 | − | 0.968983i | \(-0.420513\pi\) | ||||
0.247129 | + | 0.968983i | \(0.420513\pi\) | |||||||
\(332\) | 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 | ||||||||
\(341\) | − 111.298i | − 0.326387i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 372.499i | 1.08600i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 584.282 | 1.68381 | 0.841905 | − | 0.539626i | \(-0.181435\pi\) | ||||
0.841905 | + | 0.539626i | \(0.181435\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 230.766i | 0.661222i | 0.943767 | + | 0.330611i | \(0.107255\pi\) | ||||
−0.943767 | + | 0.330611i | \(0.892745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −50.0166 | −0.141690 | −0.0708450 | − | 0.997487i | \(-0.522570\pi\) | ||||
−0.0708450 | + | 0.997487i | \(0.522570\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 222.932 | 0.627978 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 253.992i | − 0.707499i | −0.935340 | − | 0.353749i | \(-0.884907\pi\) | ||||
0.935340 | − | 0.353749i | \(-0.115093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −352.199 | −0.975621 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 127.587i | 0.349553i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 348.682i | − 0.950088i | −0.879962 | − | 0.475044i | \(-0.842432\pi\) | ||||
0.879962 | − | 0.475044i | \(-0.157568\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −439.749 | −1.18531 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 646.499i | − 1.73324i | −0.498967 | − | 0.866621i | \(-0.666287\pi\) | ||||
0.498967 | − | 0.866621i | \(-0.333713\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 224.977 | 0.596756 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −274.433 | −0.724097 | −0.362048 | − | 0.932159i | \(-0.617922\pi\) | ||||
−0.362048 | + | 0.932159i | \(0.617922\pi\) | |||||||
\(380\) | 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 | ||||||||
\(389\) | − 412.679i | − 1.06087i | −0.847725 | − | 0.530436i | \(-0.822028\pi\) | ||||
0.847725 | − | 0.530436i | \(-0.177972\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.7330i | 0.0606983i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 198.154 | 0.501656 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 384.700i | − 0.969017i | −0.874787 | − | 0.484508i | \(-0.838999\pi\) | ||||
0.874787 | − | 0.484508i | \(-0.161001\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −561.466 | −1.40016 | −0.700082 | − | 0.714063i | \(-0.746853\pi\) | ||||
−0.700082 | + | 0.714063i | \(0.746853\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −94.2992 | −0.233993 | ||||||||
\(404\) | 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 | \(-0.399772\pi\) | ||||
0.309698 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 364.206i | − 0.881856i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 196.865i | − 0.474374i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −622.985 | −1.48684 | −0.743418 | − | 0.668827i | \(-0.766797\pi\) | ||||
−0.743418 | + | 0.668827i | \(0.766797\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 487.300i | 1.15748i | 0.815511 | + | 0.578741i | \(0.196456\pi\) | ||||
−0.815511 | + | 0.578741i | \(0.803544\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 307.473 | 0.723467 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.30033 | 0.0124130 | ||||||||
\(428\) | 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 | ||||||||
\(437\) | 4.33545i | 0.00992094i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | −104.722 | −0.236392 | −0.118196 | − | 0.992990i | \(-0.537711\pi\) | ||||
−0.118196 | + | 0.992990i | \(0.537711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 351.466i | 0.789811i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 219.132 | 0.488043 | 0.244022 | − | 0.969770i | \(-0.421533\pi\) | ||||
0.244022 | + | 0.969770i | \(0.421533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 307.066 | 0.680855 | ||||||||
\(452\) | 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 | \(-0.483834\pi\) | ||||
0.0507664 | + | 0.998711i | \(0.483834\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 517.377i | 1.12229i | 0.827717 | + | 0.561146i | \(0.189639\pi\) | ||||
−0.827717 | + | 0.561146i | \(0.810361\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 111.016i | 0.239776i | 0.992787 | + | 0.119888i | \(0.0382535\pi\) | ||||
−0.992787 | + | 0.119888i | \(0.961747\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 233.934 | 0.500930 | 0.250465 | − | 0.968126i | \(-0.419416\pi\) | ||||
0.250465 | + | 0.968126i | \(0.419416\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 624.000i | − 1.33049i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 370.052 | 0.782351 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 56.1680 | 0.118248 | ||||||||
\(476\) | 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 | ||||||||
\(485\) | 112.973i | 0.232933i | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 423.320 | 0.862159 | 0.431080 | − | 0.902314i | \(-0.358133\pi\) | ||||
0.431080 | + | 0.902314i | \(0.358133\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 407.466i | − 0.826503i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −496.293 | −0.998577 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −126.932 | −0.254373 | −0.127187 | − | 0.991879i | \(-0.540595\pi\) | ||||
−0.127187 | + | 0.991879i | \(0.540595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 274.452i | 0.545630i | 0.962067 | + | 0.272815i | \(0.0879547\pi\) | ||||
−0.962067 | + | 0.272815i | \(0.912045\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 204.732 | 0.405410 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 750.416i | 1.47429i | 0.675732 | + | 0.737147i | \(0.263828\pi\) | ||||
−0.675732 | + | 0.737147i | \(0.736172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 284.034i | − 0.555840i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 262.359 | 0.509434 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 911.466i | 1.76299i | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 184.366 | 0.352516 | 0.176258 | − | 0.984344i | \(-0.443601\pi\) | ||||
0.176258 | + | 0.984344i | \(0.443601\pi\) | |||||||
\(524\) | 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 | ||||||||
\(533\) | − 260.167i | − 0.488117i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 282.265i | 0.527598i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −200.371 | −0.371745 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 432.967i | 0.800308i | 0.916448 | + | 0.400154i | \(0.131043\pi\) | ||||
−0.916448 | + | 0.400154i | \(0.868957\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −233.417 | −0.428288 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 557.567 | 1.01932 | 0.509659 | − | 0.860376i | \(-0.329771\pi\) | ||||
0.509659 | + | 0.860376i | \(0.329771\pi\) | |||||||
\(548\) | 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 | ||||||||
\(557\) | − 656.984i | − 1.17950i | −0.807584 | − | 0.589752i | \(-0.799226\pi\) | ||||
0.807584 | − | 0.589752i | \(-0.200774\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 313.533i | − 0.560882i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 204.706 | 0.363599 | 0.181799 | − | 0.983336i | \(-0.441808\pi\) | ||||
0.181799 | + | 0.983336i | \(0.441808\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 497.068i | − 0.879766i | ||||||||
\(566\) | 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 | ||||||||
\(571\) | 832.198 | 1.45744 | 0.728720 | − | 0.684812i | \(-0.240116\pi\) | ||||
0.728720 | + | 0.684812i | \(0.240116\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | 438.263i | 0.754325i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 848.732i | − 1.45580i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −84.6640 | −0.144232 | −0.0721159 | − | 0.997396i | \(-0.522975\pi\) | ||||
−0.0721159 | + | 0.997396i | \(0.522975\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.1991i | 0.0529696i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 923.717 | 1.55770 | 0.778851 | − | 0.627209i | \(-0.215803\pi\) | ||||
0.778851 | + | 0.627209i | \(0.215803\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 219.333 | 0.368626 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 538.674i | − 0.899288i | −0.893208 | − | 0.449644i | \(-0.851551\pi\) | ||||
0.893208 | − | 0.449644i | \(-0.148449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 164.334 | 0.273434 | 0.136717 | − | 0.990610i | \(-0.456345\pi\) | ||||
0.136717 | + | 0.990610i | \(0.456345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.1677i | 0.0366408i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 368.984i | − 0.607881i | −0.952691 | − | 0.303941i | \(-0.901698\pi\) | ||||
0.952691 | − | 0.303941i | \(-0.0983024\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 772.255 | 1.26392 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 968.433i | 1.57982i | 0.613220 | + | 0.789912i | \(0.289874\pi\) | ||||
−0.613220 | + | 0.789912i | \(0.710126\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 1066.80 | 1.72342 | 0.861711 | − | 0.507399i | \(-0.169393\pi\) | ||||
0.861711 | + | 0.507399i | \(0.169393\pi\) | |||||||
\(620\) | 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 | ||||||||
\(629\) | 275.536i | 0.438054i | ||||||||
\(630\) | 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 | ||||||||
\(635\) | 422.212 | 0.664901 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 169.768i | 0.266511i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 603.043 | 0.940784 | 0.470392 | − | 0.882458i | \(-0.344113\pi\) | ||||
0.470392 | + | 0.882458i | \(0.344113\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 352.633 | 0.548418 | 0.274209 | − | 0.961670i | \(-0.411584\pi\) | ||||
0.274209 | + | 0.961670i | \(0.411584\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 897.790i | 1.38762i | 0.720158 | + | 0.693810i | \(0.244069\pi\) | ||||
−0.720158 | + | 0.693810i | \(0.755931\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 702.932 | 1.08310 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 169.459i | − 0.259508i | −0.991546 | − | 0.129754i | \(-0.958581\pi\) | ||||
0.991546 | − | 0.129754i | \(-0.0414188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 417.068i | − 0.636745i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.4864 | −0.0553663 | −0.0276832 | − | 0.999617i | \(-0.508813\pi\) | ||||
−0.0276832 | + | 0.999617i | \(0.508813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1038.77i | − 1.57151i | −0.618539 | − | 0.785754i | \(-0.712275\pi\) | ||||
0.618539 | − | 0.785754i | \(-0.287725\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 40.0668 | 0.0602508 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.6674 | 0.0549736 | ||||||||
\(668\) | 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 | ||||||||
\(677\) | 296.455i | 0.437895i | 0.975737 | + | 0.218948i | \(0.0702624\pi\) | ||||
−0.975737 | + | 0.218948i | \(0.929738\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 251.501i | − 0.370398i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1169.67 | −1.71255 | −0.856275 | − | 0.516520i | \(-0.827227\pi\) | ||||
−0.856275 | + | 0.516520i | \(0.827227\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.86429i | 0.00856101i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −719.102 | −1.04369 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1242.70 | 1.79841 | 0.899204 | − | 0.437530i | \(-0.144147\pi\) | ||||
0.899204 | + | 0.437530i | \(0.144147\pi\) | |||||||
\(692\) | 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 | ||||||||
\(701\) | − 1362.28i | − 1.94333i | −0.236358 | − | 0.971666i | \(-0.575954\pi\) | ||||
0.236358 | − | 0.971666i | \(-0.424046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.3337i | 0.0715984i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −455.776 | −0.644661 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1261.97i | 1.77992i | 0.456036 | + | 0.889962i | \(0.349269\pi\) | ||||
−0.456036 | + | 0.889962i | \(0.650731\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.3692 | −0.0215556 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −233.731 | −0.326896 | ||||||||
\(716\) | 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 | ||||||||
\(725\) | − 475.045i | − 0.655234i | ||||||||
\(726\) | 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 | ||||||||
\(731\) | −567.853 | −0.776817 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 165.699i | − 0.226055i | −0.993592 | − | 0.113028i | \(-0.963945\pi\) | ||||
0.993592 | − | 0.113028i | \(-0.0360549\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1204.34 | 1.63412 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −248.999 | −0.336940 | −0.168470 | − | 0.985707i | \(-0.553883\pi\) | ||||
−0.168470 | + | 0.985707i | \(0.553883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 538.674i | 0.724998i | 0.931984 | + | 0.362499i | \(0.118076\pi\) | ||||
−0.931984 | + | 0.362499i | \(0.881924\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −127.402 | −0.171009 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 628.380i | − 0.838958i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 979.882i | − 1.30477i | −0.757888 | − | 0.652385i | \(-0.773769\pi\) | ||||
0.757888 | − | 0.652385i | \(-0.226231\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 559.487 | 0.741042 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1151.90i | − 1.52166i | −0.648950 | − | 0.760831i | \(-0.724791\pi\) | ||||
0.648950 | − | 0.760831i | \(-0.275209\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 519.634 | 0.681041 | ||||||||
\(764\) | 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 | ||||||||
\(773\) | 1118.14i | 1.44649i | 0.690592 | + | 0.723245i | \(0.257350\pi\) | ||||
−0.690592 | + | 0.723245i | \(0.742650\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 199.115i | 0.256923i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −86.0767 | −0.110496 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 957.864i | − 1.22646i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 272.826 | 0.347549 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 711.832 | 0.904488 | 0.452244 | − | 0.891894i | \(-0.350624\pi\) | ||||
0.452244 | + | 0.891894i | \(0.350624\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | 209.033i | 0.262274i | 0.991364 | + | 0.131137i | \(0.0418628\pi\) | ||||
−0.991364 | + | 0.131137i | \(0.958137\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1398.67i | − 1.75052i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 548.197 | 0.682687 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.7375i | 0.0245186i | ||||||||
\(806\) | 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 | ||||||||
\(811\) | −171.432 | −0.211383 | −0.105691 | − | 0.994399i | \(-0.533706\pi\) | ||||
−0.105691 | + | 0.994399i | \(0.533706\pi\) | |||||||
\(812\) | 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 | ||||||||
\(821\) | 1134.49i | 1.38184i | 0.722931 | + | 0.690921i | \(0.242795\pi\) | ||||
−0.722931 | + | 0.690921i | \(0.757205\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | −1177.33 | −1.42362 | −0.711809 | − | 0.702373i | \(-0.752124\pi\) | ||||
−0.711809 | + | 0.702373i | \(0.752124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1278.56i | 1.54230i | 0.636656 | + | 0.771148i | \(0.280317\pi\) | ||||
−0.636656 | + | 0.771148i | \(0.719683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 307.473 | 0.369116 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 197.735 | 0.236809 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1015.97i | − 1.21093i | −0.795873 | − | 0.605464i | \(-0.792988\pi\) | ||||
0.795873 | − | 0.605464i | \(-0.207012\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 211.467 | 0.251447 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 218.227i | − 0.258257i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 49.3498i | − 0.0582643i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.7951 | −0.0291365 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1509.43i | − 1.76956i | −0.466012 | − | 0.884778i | \(-0.654310\pi\) | ||||
0.466012 | − | 0.884778i | \(-0.345690\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | 989.231 | 1.15161 | 0.575804 | − | 0.817588i | \(-0.304689\pi\) | ||||
0.575804 | + | 0.817588i | \(0.304689\pi\) | |||||||
\(860\) | 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 | ||||||||
\(869\) | − 851.402i | − 0.979749i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1020.40i | − 1.17153i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 593.355 | 0.678120 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 591.899i | − 0.674913i | −0.941341 | − | 0.337457i | \(-0.890433\pi\) | ||||
0.941341 | − | 0.337457i | \(-0.109567\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 797.050 | 0.904711 | 0.452355 | − | 0.891838i | \(-0.350584\pi\) | ||||
0.452355 | + | 0.891838i | \(0.350584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 276.964 | 0.313663 | 0.156831 | − | 0.987625i | \(-0.449872\pi\) | ||||
0.156831 | + | 0.987625i | \(0.449872\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 910.845i | − 1.02688i | −0.858125 | − | 0.513441i | \(-0.828370\pi\) | ||||
0.858125 | − | 0.513441i | \(-0.171630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −939.931 | −1.05729 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 255.502i | − 0.286117i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 163.600i | − 0.182793i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 263.869 | 0.293514 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1302.40i | 1.44550i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −396.473 | −0.438092 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1472.83 | 1.62385 | 0.811924 | − | 0.583763i | \(-0.198420\pi\) | ||||
0.811924 | + | 0.583763i | \(0.198420\pi\) | |||||||
\(908\) | 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 | ||||||||
\(917\) | 928.479i | 1.01252i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | −811.567 | −0.879270 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 321.234i | 0.347280i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −762.190 | −0.820441 | −0.410220 | − | 0.911986i | \(-0.634548\pi\) | ||||
−0.410220 | + | 0.911986i | \(0.634548\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 56.1680 | 0.0603308 | ||||||||
\(932\) | 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 | \(-0.520964\pi\) | ||||
−0.0658137 | + | 0.997832i | \(0.520964\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 735.638i | 0.781762i | 0.920441 | + | 0.390881i | \(0.127830\pi\) | ||||
−0.920441 | + | 0.390881i | \(0.872170\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 42.4027i | − 0.0449657i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 549.610 | 0.580370 | 0.290185 | − | 0.956971i | \(-0.406283\pi\) | ||||
0.290185 | + | 0.956971i | \(0.406283\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 464.469i | − 0.489430i | ||||||||
\(950\) | 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 | ||||||||
\(955\) | −204.934 | −0.214591 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | − 324.304i | − 0.336066i | ||||||||
\(966\) | 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 | ||||||||
\(971\) | −1248.49 | −1.28578 | −0.642889 | − | 0.765959i | \(-0.722264\pi\) | ||||
−0.642889 | + | 0.765959i | \(0.722264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1150.40i | − 1.18232i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 126.028 | 0.128995 | 0.0644973 | − | 0.997918i | \(-0.479456\pi\) | ||||
0.0644973 | + | 0.997918i | \(0.479456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1510.13 | 1.54252 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1018.89i | 1.03651i | 0.855226 | + | 0.518256i | \(0.173419\pi\) | ||||
−0.855226 | + | 0.518256i | \(0.826581\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 454.601 | 0.461524 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 51.1005i | − 0.0516688i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 859.981i | 0.867791i | 0.900963 | + | 0.433895i | \(0.142861\pi\) | ||||
−0.900963 | + | 0.433895i | \(0.857139\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 415.562 | 0.417651 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1104.43i | 1.10776i | 0.832598 | + | 0.553878i | \(0.186853\pi\) | ||||
−0.832598 | + | 0.553878i | \(0.813147\pi\) | |||||||
\(998\) | 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 | 2304.3.b.r.127.4 | 8 | ||
3.2 | odd | 2 | inner | 2304.3.b.r.127.6 | 8 | ||
4.3 | odd | 2 | 2304.3.b.s.127.3 | 8 | |||
8.3 | odd | 2 | inner | 2304.3.b.r.127.5 | 8 | ||
8.5 | even | 2 | 2304.3.b.s.127.6 | 8 | |||
12.11 | even | 2 | 2304.3.b.s.127.5 | 8 | |||
16.3 | odd | 4 | 1152.3.g.e.127.4 | yes | 8 | ||
16.5 | even | 4 | 1152.3.g.d.127.5 | yes | 8 | ||
16.11 | odd | 4 | 1152.3.g.d.127.6 | yes | 8 | ||
16.13 | even | 4 | 1152.3.g.e.127.3 | yes | 8 | ||
24.5 | odd | 2 | 2304.3.b.s.127.4 | 8 | |||
24.11 | even | 2 | inner | 2304.3.b.r.127.3 | 8 | ||
48.5 | odd | 4 | 1152.3.g.d.127.3 | ✓ | 8 | ||
48.11 | even | 4 | 1152.3.g.d.127.4 | yes | 8 | ||
48.29 | odd | 4 | 1152.3.g.e.127.5 | yes | 8 | ||
48.35 | even | 4 | 1152.3.g.e.127.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.g.d.127.3 | ✓ | 8 | 48.5 | odd | 4 | ||
1152.3.g.d.127.4 | yes | 8 | 48.11 | even | 4 | ||
1152.3.g.d.127.5 | yes | 8 | 16.5 | even | 4 | ||
1152.3.g.d.127.6 | yes | 8 | 16.11 | odd | 4 | ||
1152.3.g.e.127.3 | yes | 8 | 16.13 | even | 4 | ||
1152.3.g.e.127.4 | yes | 8 | 16.3 | odd | 4 | ||
1152.3.g.e.127.5 | yes | 8 | 48.29 | odd | 4 | ||
1152.3.g.e.127.6 | yes | 8 | 48.35 | even | 4 | ||
2304.3.b.r.127.3 | 8 | 24.11 | even | 2 | inner | ||
2304.3.b.r.127.4 | 8 | 1.1 | even | 1 | trivial | ||
2304.3.b.r.127.5 | 8 | 8.3 | odd | 2 | inner | ||
2304.3.b.r.127.6 | 8 | 3.2 | odd | 2 | inner | ||
2304.3.b.s.127.3 | 8 | 4.3 | odd | 2 | |||
2304.3.b.s.127.4 | 8 | 24.5 | odd | 2 | |||
2304.3.b.s.127.5 | 8 | 12.11 | even | 2 | |||
2304.3.b.s.127.6 | 8 | 8.5 | even | 2 |