Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,3,Mod(593,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.593");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.q (of order \(6\), degree \(2\), 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: | \(35.3134422611\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1025.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.1025 |
Dual form | 1296.3.q.j.593.2 |
$q$-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 \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(5\) | 2.59808 | + | 1.50000i | 0.519615 | + | 0.300000i | 0.736777 | − | 0.676136i | \(-0.236347\pi\) |
−0.217162 | + | 0.976136i | \(0.569680\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 4.33013i | 0.357143 | + | 0.618590i | 0.987482 | − | 0.157730i | \(-0.0504176\pi\) |
−0.630339 | + | 0.776320i | \(0.717084\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.9904 | − | 7.50000i | 1.18094 | − | 0.681818i | 0.224711 | − | 0.974425i | \(-0.427856\pi\) |
0.956233 | + | 0.292607i | \(0.0945229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00000 | − | 8.66025i | 0.384615 | − | 0.666173i | −0.607100 | − | 0.794625i | \(-0.707667\pi\) |
0.991716 | + | 0.128452i | \(0.0410008\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.0000i | 1.05882i | 0.848365 | + | 0.529412i | \(0.177587\pi\) | ||||
−0.848365 | + | 0.529412i | \(0.822413\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.0000 | 0.842105 | 0.421053 | − | 0.907036i | \(-0.361661\pi\) | ||||
0.421053 | + | 0.907036i | \(0.361661\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10.3923 | − | 6.00000i | −0.451839 | − | 0.260870i | 0.256767 | − | 0.966473i | \(-0.417343\pi\) |
−0.708607 | + | 0.705604i | \(0.750676\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.00000 | − | 13.8564i | −0.320000 | − | 0.554256i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 25.9808 | − | 15.0000i | 0.895888 | − | 0.517241i | 0.0200244 | − | 0.999799i | \(-0.493626\pi\) |
0.875864 | + | 0.482558i | \(0.160292\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.500000 | + | 0.866025i | −0.0161290 | + | 0.0279363i | −0.873977 | − | 0.485967i | \(-0.838468\pi\) |
0.857848 | + | 0.513903i | \(0.171801\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.0000i | 0.428571i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 20.0000 | 0.540541 | 0.270270 | − | 0.962784i | \(-0.412887\pi\) | ||||
0.270270 | + | 0.962784i | \(0.412887\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −51.9615 | − | 30.0000i | −1.26735 | − | 0.731707i | −0.292868 | − | 0.956153i | \(-0.594610\pi\) |
−0.974487 | + | 0.224446i | \(0.927943\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 25.0000 | + | 43.3013i | 0.581395 | + | 1.00701i | 0.995314 | + | 0.0966925i | \(0.0308264\pi\) |
−0.413919 | + | 0.910314i | \(0.635840\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.19615 | − | 3.00000i | 0.110556 | − | 0.0638298i | −0.443702 | − | 0.896174i | \(-0.646335\pi\) |
0.554259 | + | 0.832345i | \(0.313002\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.0000 | − | 20.7846i | 0.244898 | − | 0.424176i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 27.0000i | − | 0.509434i | −0.967016 | − | 0.254717i | \(-0.918018\pi\) | ||
0.967016 | − | 0.254717i | \(-0.0819823\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 45.0000 | 0.818182 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −25.9808 | − | 15.0000i | −0.440352 | − | 0.254237i | 0.263395 | − | 0.964688i | \(-0.415158\pi\) |
−0.703747 | + | 0.710451i | \(0.748491\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38.0000 | + | 65.8179i | 0.622951 | + | 1.07898i | 0.988933 | + | 0.148361i | \(0.0473997\pi\) |
−0.365982 | + | 0.930622i | \(0.619267\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 25.9808 | − | 15.0000i | 0.399704 | − | 0.230769i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | + | 8.66025i | −0.0746269 | + | 0.129258i | −0.900924 | − | 0.433977i | \(-0.857110\pi\) |
0.826297 | + | 0.563235i | \(0.190443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 90.0000i | 1.26761i | 0.773495 | + | 0.633803i | \(0.218507\pi\) | ||||
−0.773495 | + | 0.633803i | \(0.781493\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 65.0000 | 0.890411 | 0.445205 | − | 0.895428i | \(-0.353131\pi\) | ||||
0.445205 | + | 0.895428i | \(0.353131\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 64.9519 | + | 37.5000i | 0.843531 | + | 0.487013i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.00000 | + | 12.1244i | 0.0886076 | + | 0.153473i | 0.906923 | − | 0.421297i | \(-0.138425\pi\) |
−0.818315 | + | 0.574770i | \(0.805092\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.59808 | + | 1.50000i | −0.0313021 | + | 0.0180723i | −0.515569 | − | 0.856848i | \(-0.672420\pi\) |
0.484267 | + | 0.874920i | \(0.339086\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −27.0000 | + | 46.7654i | −0.317647 | + | 0.550181i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 90.0000i | 1.01124i | 0.862757 | + | 0.505618i | \(0.168735\pi\) | ||||
−0.862757 | + | 0.505618i | \(0.831265\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 50.0000 | 0.549451 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 41.5692 | + | 24.0000i | 0.437571 | + | 0.252632i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 42.5000 | + | 73.6122i | 0.438144 | + | 0.758888i | 0.997546 | − | 0.0700082i | \(-0.0223025\pi\) |
−0.559402 | + | 0.828896i | \(0.688969\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −168.875 | + | 97.5000i | −1.67203 | + | 0.965347i | −0.705529 | + | 0.708681i | \(0.749291\pi\) |
−0.966500 | + | 0.256665i | \(0.917376\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 85.0000 | − | 147.224i | 0.825243 | − | 1.42936i | −0.0764909 | − | 0.997070i | \(-0.524372\pi\) |
0.901734 | − | 0.432292i | \(-0.142295\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 189.000i | − | 1.76636i | −0.469039 | − | 0.883178i | \(-0.655400\pi\) | ||
0.469039 | − | 0.883178i | \(-0.344600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 164.000 | 1.50459 | 0.752294 | − | 0.658828i | \(-0.228948\pi\) | ||||
0.752294 | + | 0.658828i | \(0.228948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.7846 | − | 12.0000i | −0.183935 | − | 0.106195i | 0.405205 | − | 0.914226i | \(-0.367200\pi\) |
−0.589140 | + | 0.808031i | \(0.700533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.0000 | − | 31.1769i | −0.156522 | − | 0.271104i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −77.9423 | + | 45.0000i | −0.654977 | + | 0.378151i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 52.0000 | − | 90.0666i | 0.429752 | − | 0.744352i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 123.000i | − | 0.984000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 205.000 | 1.61417 | 0.807087 | − | 0.590433i | \(-0.201043\pi\) | ||||
0.807087 | + | 0.590433i | \(0.201043\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.9904 | + | 7.50000i | 0.0991632 | + | 0.0572519i | 0.548761 | − | 0.835979i | \(-0.315100\pi\) |
−0.449598 | + | 0.893231i | \(0.648433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 40.0000 | + | 69.2820i | 0.300752 | + | 0.520918i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 119.512 | − | 69.0000i | 0.872347 | − | 0.503650i | 0.00421937 | − | 0.999991i | \(-0.498657\pi\) |
0.868127 | + | 0.496341i | \(0.165324\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.0000 | + | 24.2487i | −0.100719 | + | 0.174451i | −0.911981 | − | 0.410232i | \(-0.865448\pi\) |
0.811262 | + | 0.584683i | \(0.198781\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 150.000i | − | 1.04895i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 90.0000 | 0.620690 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 64.9519 | + | 37.5000i | 0.435919 | + | 0.251678i | 0.701865 | − | 0.712310i | \(-0.252351\pi\) |
−0.265946 | + | 0.963988i | \(0.585684\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 38.5000 | + | 66.6840i | 0.254967 | + | 0.441616i | 0.964887 | − | 0.262667i | \(-0.0846021\pi\) |
−0.709920 | + | 0.704283i | \(0.751269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.59808 | + | 1.50000i | −0.0167618 | + | 0.00967742i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 50.0000 | − | 86.6025i | 0.318471 | − | 0.551609i | −0.661698 | − | 0.749771i | \(-0.730164\pi\) |
0.980169 | + | 0.198162i | \(0.0634972\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 60.0000i | − | 0.372671i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −110.000 | −0.674847 | −0.337423 | − | 0.941353i | \(-0.609555\pi\) | ||||
−0.337423 | + | 0.941353i | \(0.609555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 67.5500 | + | 39.0000i | 0.404491 | + | 0.233533i | 0.688420 | − | 0.725312i | \(-0.258305\pi\) |
−0.283929 | + | 0.958845i | \(0.591638\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.5000 | + | 59.7558i | 0.204142 | + | 0.353584i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −153.286 | + | 88.5000i | −0.886049 | + | 0.511561i | −0.872648 | − | 0.488350i | \(-0.837599\pi\) |
−0.0134010 | + | 0.999910i | \(0.504266\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 40.0000 | − | 69.2820i | 0.228571 | − | 0.395897i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 225.000i | 1.25698i | 0.777816 | + | 0.628492i | \(0.216327\pi\) | ||||
−0.777816 | + | 0.628492i | \(0.783673\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −0.0883978 | −0.0441989 | − | 0.999023i | \(-0.514074\pi\) | ||||
−0.0441989 | + | 0.999023i | \(0.514074\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 51.9615 | + | 30.0000i | 0.280873 | + | 0.162162i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 135.000 | + | 233.827i | 0.721925 | + | 1.25041i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.9808 | + | 15.0000i | −0.136025 | + | 0.0785340i | −0.566468 | − | 0.824084i | \(-0.691691\pi\) |
0.430443 | + | 0.902618i | \(0.358357\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −107.500 | + | 186.195i | −0.556995 | + | 0.964743i | 0.440751 | + | 0.897630i | \(0.354712\pi\) |
−0.997745 | + | 0.0671137i | \(0.978621\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 207.000i | − | 1.05076i | −0.850867 | − | 0.525381i | \(-0.823923\pi\) | ||
0.850867 | − | 0.525381i | \(-0.176077\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 223.000 | 1.12060 | 0.560302 | − | 0.828289i | \(-0.310685\pi\) | ||||
0.560302 | + | 0.828289i | \(0.310685\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 129.904 | + | 75.0000i | 0.639920 | + | 0.369458i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −90.0000 | − | 155.885i | −0.439024 | − | 0.760413i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 207.846 | − | 120.000i | 0.994479 | − | 0.574163i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −158.000 | + | 273.664i | −0.748815 | + | 1.29699i | 0.199576 | + | 0.979882i | \(0.436044\pi\) |
−0.948391 | + | 0.317104i | \(0.897290\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 150.000i | 0.697674i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.00000 | −0.0230415 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 155.885 | + | 90.0000i | 0.705360 | + | 0.407240i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −65.0000 | − | 112.583i | −0.291480 | − | 0.504858i | 0.682680 | − | 0.730717i | \(-0.260814\pi\) |
−0.974160 | + | 0.225860i | \(0.927481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 36.3731 | − | 21.0000i | 0.160234 | − | 0.0925110i | −0.417739 | − | 0.908567i | \(-0.637177\pi\) |
0.577973 | + | 0.816056i | \(0.303844\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 113.000 | − | 195.722i | 0.493450 | − | 0.854680i | −0.506522 | − | 0.862227i | \(-0.669069\pi\) |
0.999972 | + | 0.00754710i | \(0.00240234\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 234.000i | 1.00429i | 0.864783 | + | 0.502146i | \(0.167456\pi\) | ||||
−0.864783 | + | 0.502146i | \(0.832544\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.0000 | 0.0765957 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −103.923 | − | 60.0000i | −0.434824 | − | 0.251046i | 0.266575 | − | 0.963814i | \(-0.414108\pi\) |
−0.701400 | + | 0.712768i | \(0.747441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.00000 | − | 12.1244i | −0.0290456 | − | 0.0503085i | 0.851137 | − | 0.524943i | \(-0.175913\pi\) |
−0.880183 | + | 0.474635i | \(0.842580\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 62.3538 | − | 36.0000i | 0.254505 | − | 0.146939i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 80.0000 | − | 138.564i | 0.323887 | − | 0.560988i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 90.0000i | − | 0.358566i | −0.983798 | − | 0.179283i | \(-0.942622\pi\) | ||
0.983798 | − | 0.179283i | \(-0.0573777\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −180.000 | −0.711462 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −379.319 | − | 219.000i | −1.47595 | − | 0.852140i | −0.476318 | − | 0.879273i | \(-0.658029\pi\) |
−0.999632 | + | 0.0271330i | \(0.991362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 50.0000 | + | 86.6025i | 0.193050 | + | 0.334373i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 239.023 | − | 138.000i | 0.908833 | − | 0.524715i | 0.0287773 | − | 0.999586i | \(-0.490839\pi\) |
0.880055 | + | 0.474871i | \(0.157505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 40.5000 | − | 70.1481i | 0.152830 | − | 0.264710i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 270.000i | 1.00372i | 0.864950 | + | 0.501859i | \(0.167350\pi\) | ||||
−0.864950 | + | 0.501859i | \(0.832650\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −299.000 | −1.10332 | −0.551661 | − | 0.834069i | \(-0.686006\pi\) | ||||
−0.551661 | + | 0.834069i | \(0.686006\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −207.846 | − | 120.000i | −0.755804 | − | 0.436364i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −70.0000 | − | 121.244i | −0.252708 | − | 0.437702i | 0.711563 | − | 0.702623i | \(-0.247988\pi\) |
−0.964270 | + | 0.264920i | \(0.914654\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −129.904 | + | 75.0000i | −0.462291 | + | 0.266904i | −0.713007 | − | 0.701157i | \(-0.752667\pi\) |
0.250716 | + | 0.968061i | \(0.419334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −140.000 | + | 242.487i | −0.494700 | + | 0.856845i | −0.999981 | − | 0.00610955i | \(-0.998055\pi\) |
0.505282 | + | 0.862954i | \(0.331389\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 300.000i | − | 1.04530i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −35.0000 | −0.121107 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −223.435 | − | 129.000i | −0.762575 | − | 0.440273i | 0.0676443 | − | 0.997709i | \(-0.478452\pi\) |
−0.830220 | + | 0.557436i | \(0.811785\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −45.0000 | − | 77.9423i | −0.152542 | − | 0.264211i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −103.923 | + | 60.0000i | −0.347569 | + | 0.200669i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −125.000 | + | 216.506i | −0.415282 | + | 0.719290i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 228.000i | 0.747541i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −290.000 | −0.944625 | −0.472313 | − | 0.881431i | \(-0.656581\pi\) | ||||
−0.472313 | + | 0.881431i | \(0.656581\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −415.692 | − | 240.000i | −1.33663 | − | 0.771704i | −0.350325 | − | 0.936628i | \(-0.613929\pi\) |
−0.986306 | + | 0.164924i | \(0.947262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −92.5000 | − | 160.215i | −0.295527 | − | 0.511868i | 0.679580 | − | 0.733601i | \(-0.262162\pi\) |
−0.975107 | + | 0.221733i | \(0.928829\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 158.483 | − | 91.5000i | 0.499945 | − | 0.288644i | −0.228746 | − | 0.973486i | \(-0.573462\pi\) |
0.728691 | + | 0.684843i | \(0.240129\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 225.000 | − | 389.711i | 0.705329 | − | 1.22167i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 288.000i | 0.891641i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −160.000 | −0.492308 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.9808 | + | 15.0000i | 0.0789689 | + | 0.0455927i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −119.000 | − | 206.114i | −0.359517 | − | 0.622701i | 0.628363 | − | 0.777920i | \(-0.283725\pi\) |
−0.987880 | + | 0.155219i | \(0.950392\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.9808 | + | 15.0000i | −0.0775545 | + | 0.0447761i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | − | 8.66025i | 0.0148368 | − | 0.0256981i | −0.858512 | − | 0.512794i | \(-0.828610\pi\) |
0.873348 | + | 0.487096i | \(0.161944\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0000i | 0.0439883i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 365.000 | 1.06414 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 59.7558 | + | 34.5000i | 0.172207 | + | 0.0994236i | 0.583626 | − | 0.812023i | \(-0.301633\pi\) |
−0.411419 | + | 0.911446i | \(0.634967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 128.000 | + | 221.703i | 0.366762 | + | 0.635251i | 0.989057 | − | 0.147532i | \(-0.0471329\pi\) |
−0.622295 | + | 0.782783i | \(0.713800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −394.908 | + | 228.000i | −1.11872 | + | 0.645892i | −0.941073 | − | 0.338202i | \(-0.890181\pi\) |
−0.177645 | + | 0.984095i | \(0.556848\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −135.000 | + | 233.827i | −0.380282 | + | 0.658667i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 450.000i | 1.25348i | 0.779228 | + | 0.626741i | \(0.215612\pi\) | ||||
−0.779228 | + | 0.626741i | \(0.784388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −105.000 | −0.290859 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 168.875 | + | 97.5000i | 0.462671 | + | 0.267123i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −312.500 | − | 541.266i | −0.851499 | − | 1.47484i | −0.879856 | − | 0.475241i | \(-0.842361\pi\) |
0.0283570 | − | 0.999598i | \(-0.490972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 116.913 | − | 67.5000i | 0.315131 | − | 0.181941i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −85.0000 | + | 147.224i | −0.227882 | + | 0.394703i | −0.957180 | − | 0.289493i | \(-0.906513\pi\) |
0.729298 | + | 0.684196i | \(0.239847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 300.000i | − | 0.795756i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −704.000 | −1.85752 | −0.928760 | − | 0.370682i | \(-0.879124\pi\) | ||||
−0.928760 | + | 0.370682i | \(0.879124\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 535.204 | + | 309.000i | 1.39740 | + | 0.806789i | 0.994120 | − | 0.108288i | \(-0.0345370\pi\) |
0.403279 | + | 0.915077i | \(0.367870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 112.500 | + | 194.856i | 0.292208 | + | 0.506119i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 454.663 | − | 262.500i | 1.16880 | − | 0.674807i | 0.215403 | − | 0.976525i | \(-0.430893\pi\) |
0.953397 | + | 0.301718i | \(0.0975601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 108.000 | − | 187.061i | 0.276215 | − | 0.478418i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 42.0000i | 0.106329i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −70.0000 | −0.176322 | −0.0881612 | − | 0.996106i | \(-0.528099\pi\) | ||||
−0.0881612 | + | 0.996106i | \(0.528099\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 103.923 | + | 60.0000i | 0.259160 | + | 0.149626i | 0.623951 | − | 0.781463i | \(-0.285526\pi\) |
−0.364791 | + | 0.931089i | \(0.618860\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.00000 | + | 8.66025i | 0.0124069 | + | 0.0214895i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 259.808 | − | 150.000i | 0.638348 | − | 0.368550i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −134.500 | + | 232.961i | −0.328851 | + | 0.569586i | −0.982284 | − | 0.187398i | \(-0.939995\pi\) |
0.653433 | + | 0.756984i | \(0.273328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 150.000i | − | 0.363196i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.00000 | −0.0216867 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −181.865 | − | 105.000i | −0.434046 | − | 0.250597i | 0.267023 | − | 0.963690i | \(-0.413960\pi\) |
−0.701069 | + | 0.713094i | \(0.747293\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −322.000 | − | 557.720i | −0.764846 | − | 1.32475i | −0.940328 | − | 0.340269i | \(-0.889482\pi\) |
0.175483 | − | 0.984483i | \(-0.443851\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 249.415 | − | 144.000i | 0.586860 | − | 0.338824i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −190.000 | + | 329.090i | −0.444965 | + | 0.770702i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 270.000i | − | 0.626450i | −0.949679 | − | 0.313225i | \(-0.898591\pi\) | ||
0.949679 | − | 0.313225i | \(-0.101409\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −565.000 | −1.30485 | −0.652425 | − | 0.757853i | \(-0.726248\pi\) | ||||
−0.652425 | + | 0.757853i | \(0.726248\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −166.277 | − | 96.0000i | −0.380496 | − | 0.219680i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −105.500 | − | 182.731i | −0.240319 | − | 0.416245i | 0.720486 | − | 0.693469i | \(-0.243919\pi\) |
−0.960805 | + | 0.277225i | \(0.910585\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −431.281 | + | 249.000i | −0.973545 | + | 0.562077i | −0.900315 | − | 0.435238i | \(-0.856664\pi\) |
−0.0732302 | + | 0.997315i | \(0.523331\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −135.000 | + | 233.827i | −0.303371 | + | 0.525454i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 360.000i | − | 0.801782i | −0.916126 | − | 0.400891i | \(-0.868701\pi\) | ||
0.916126 | − | 0.400891i | \(-0.131299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −900.000 | −1.99557 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 129.904 | + | 75.0000i | 0.285503 | + | 0.164835i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −182.500 | − | 316.099i | −0.399344 | − | 0.691683i | 0.594301 | − | 0.804242i | \(-0.297429\pi\) |
−0.993645 | + | 0.112559i | \(0.964095\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −90.9327 | + | 52.5000i | −0.197251 | + | 0.113883i | −0.595373 | − | 0.803450i | \(-0.702996\pi\) |
0.398122 | + | 0.917333i | \(0.369662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 107.500 | − | 186.195i | 0.232181 | − | 0.402150i | −0.726268 | − | 0.687411i | \(-0.758747\pi\) |
0.958450 | + | 0.285261i | \(0.0920804\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 63.0000i | − | 0.134904i | −0.997723 | − | 0.0674518i | \(-0.978513\pi\) | ||
0.997723 | − | 0.0674518i | \(-0.0214869\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −50.0000 | −0.106610 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 649.519 | + | 375.000i | 1.37319 | + | 0.792812i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −128.000 | − | 221.703i | −0.269474 | − | 0.466742i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −649.519 | + | 375.000i | −1.35599 | + | 0.782881i | −0.989081 | − | 0.147376i | \(-0.952917\pi\) |
−0.366909 | + | 0.930257i | \(0.619584\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 100.000 | − | 173.205i | 0.207900 | − | 0.360094i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 255.000i | 0.525773i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −110.000 | −0.225873 | −0.112936 | − | 0.993602i | \(-0.536026\pi\) | ||||
−0.112936 | + | 0.993602i | \(0.536026\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 558.586 | + | 322.500i | 1.13765 | + | 0.656823i | 0.945848 | − | 0.324611i | \(-0.105233\pi\) |
0.191803 | + | 0.981433i | \(0.438567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 270.000 | + | 467.654i | 0.547667 | + | 0.948588i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −389.711 | + | 225.000i | −0.784128 | + | 0.452716i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −383.000 | + | 663.375i | −0.767535 | + | 1.32941i | 0.171361 | + | 0.985208i | \(0.445184\pi\) |
−0.938896 | + | 0.344201i | \(0.888150\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 828.000i | − | 1.64612i | −0.567952 | − | 0.823062i | \(-0.692264\pi\) | ||
0.567952 | − | 0.823062i | \(-0.307736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −585.000 | −1.15842 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −480.644 | − | 277.500i | −0.944291 | − | 0.545187i | −0.0529881 | − | 0.998595i | \(-0.516875\pi\) |
−0.891303 | + | 0.453409i | \(0.850208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 162.500 | + | 281.458i | 0.318004 | + | 0.550799i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 441.673 | − | 255.000i | 0.857617 | − | 0.495146i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.0000 | − | 77.9423i | 0.0870406 | − | 0.150759i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 450.000i | − | 0.863724i | −0.901940 | − | 0.431862i | \(-0.857857\pi\) | ||
0.901940 | − | 0.431862i | \(-0.142143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 250.000 | 0.478011 | 0.239006 | − | 0.971018i | \(-0.423179\pi\) | ||||
0.239006 | + | 0.971018i | \(0.423179\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.5885 | − | 9.00000i | −0.0295796 | − | 0.0170778i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −192.500 | − | 333.420i | −0.363894 | − | 0.630283i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −519.615 | + | 300.000i | −0.974888 | + | 0.562852i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 283.500 | − | 491.036i | 0.529907 | − | 0.917825i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 360.000i | − | 0.667904i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −268.000 | −0.495379 | −0.247689 | − | 0.968839i | \(-0.579671\pi\) | ||||
−0.247689 | + | 0.968839i | \(0.579671\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 426.084 | + | 246.000i | 0.781806 | + | 0.451376i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 205.000 | + | 355.070i | 0.374771 | + | 0.649123i | 0.990293 | − | 0.138997i | \(-0.0443878\pi\) |
−0.615521 | + | 0.788120i | \(0.711055\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 415.692 | − | 240.000i | 0.754432 | − | 0.435572i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.0000 | + | 60.6218i | −0.0632911 | + | 0.109623i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 639.000i | 1.14722i | 0.819130 | + | 0.573609i | \(0.194457\pi\) | ||||
−0.819130 | + | 0.573609i | \(0.805543\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 500.000 | 0.894454 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −174.071 | − | 100.500i | −0.309185 | − | 0.178508i | 0.337377 | − | 0.941370i | \(-0.390460\pi\) |
−0.646562 | + | 0.762862i | \(0.723794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.0000 | − | 62.3538i | −0.0637168 | − | 0.110361i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −207.846 | + | 120.000i | −0.365283 | + | 0.210896i | −0.671396 | − | 0.741099i | \(-0.734305\pi\) |
0.306113 | + | 0.951995i | \(0.400972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −473.000 | + | 819.260i | −0.828371 | + | 1.43478i | 0.0709440 | + | 0.997480i | \(0.477399\pi\) |
−0.899315 | + | 0.437301i | \(0.855934\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 192.000i | 0.333913i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 830.000 | 1.43847 | 0.719237 | − | 0.694764i | \(-0.244491\pi\) | ||||
0.719237 | + | 0.694764i | \(0.244491\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.9904 | − | 7.50000i | −0.0223587 | − | 0.0129088i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −202.500 | − | 350.740i | −0.347341 | − | 0.601613i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −392.310 | + | 226.500i | −0.668330 | + | 0.385860i | −0.795443 | − | 0.606028i | \(-0.792762\pi\) |
0.127114 | + | 0.991888i | \(0.459429\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | + | 13.8564i | −0.0135823 | + | 0.0235253i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 702.000i | − | 1.18381i | −0.806007 | − | 0.591906i | \(-0.798376\pi\) | ||
0.806007 | − | 0.591906i | \(-0.201624\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −270.000 | −0.453782 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −961.288 | − | 555.000i | −1.60482 | − | 0.926544i | −0.990504 | − | 0.137486i | \(-0.956098\pi\) |
−0.614318 | − | 0.789059i | \(-0.710569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −434.500 | − | 752.576i | −0.722962 | − | 1.25221i | −0.959807 | − | 0.280659i | \(-0.909447\pi\) |
0.236846 | − | 0.971547i | \(-0.423886\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 270.200 | − | 156.000i | 0.446611 | − | 0.257851i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 265.000 | − | 458.993i | 0.436573 | − | 0.756167i | −0.560849 | − | 0.827918i | \(-0.689525\pi\) |
0.997423 | + | 0.0717508i | \(0.0228586\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 60.0000i | − | 0.0981997i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −70.0000 | −0.114192 | −0.0570962 | − | 0.998369i | \(-0.518184\pi\) | ||||
−0.0570962 | + | 0.998369i | \(0.518184\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 478.046 | + | 276.000i | 0.774791 | + | 0.447326i | 0.834581 | − | 0.550885i | \(-0.185710\pi\) |
−0.0597901 | + | 0.998211i | \(0.519043\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 331.000 | + | 573.309i | 0.534733 | + | 0.926185i | 0.999176 | + | 0.0405823i | \(0.0129213\pi\) |
−0.464443 | + | 0.885603i | \(0.653745\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −389.711 | + | 225.000i | −0.625540 | + | 0.361156i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.5000 | + | 26.8468i | −0.0248000 | + | 0.0429549i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 360.000i | 0.572337i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 331.000 | 0.524564 | 0.262282 | − | 0.964991i | \(-0.415525\pi\) | ||||
0.262282 | + | 0.964991i | \(0.415525\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 532.606 | + | 307.500i | 0.838749 | + | 0.484252i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −120.000 | − | 207.846i | −0.188383 | − | 0.326289i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −51.9615 | + | 30.0000i | −0.0810632 | + | 0.0468019i | −0.539984 | − | 0.841675i | \(-0.681570\pi\) |
0.458920 | + | 0.888477i | \(0.348236\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 220.000 | − | 381.051i | 0.342146 | − | 0.592615i | −0.642685 | − | 0.766131i | \(-0.722180\pi\) |
0.984831 | + | 0.173516i | \(0.0555129\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 972.000i | 1.50232i | 0.660121 | + | 0.751159i | \(0.270505\pi\) | ||||
−0.660121 | + | 0.751159i | \(0.729495\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −450.000 | −0.693374 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −418.290 | − | 241.500i | −0.640567 | − | 0.369832i | 0.144266 | − | 0.989539i | \(-0.453918\pi\) |
−0.784833 | + | 0.619707i | \(0.787251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.5000 | + | 38.9711i | 0.0343511 | + | 0.0594979i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 714.471 | − | 412.500i | 1.08417 | − | 0.625948i | 0.152155 | − | 0.988357i | \(-0.451379\pi\) |
0.932019 | + | 0.362408i | \(0.118045\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 464.000 | − | 803.672i | 0.701967 | − | 1.21584i | −0.265808 | − | 0.964026i | \(-0.585639\pi\) |
0.967775 | − | 0.251816i | \(-0.0810278\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 240.000i | 0.360902i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −360.000 | −0.539730 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 987.269 | + | 570.000i | 1.47134 | + | 0.849478i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 492.500 | + | 853.035i | 0.731798 | + | 1.26751i | 0.956114 | + | 0.292995i | \(0.0946518\pi\) |
−0.224316 | + | 0.974516i | \(0.572015\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 306.573 | − | 177.000i | 0.452840 | − | 0.261448i | −0.256189 | − | 0.966627i | \(-0.582467\pi\) |
0.709029 | + | 0.705179i | \(0.249133\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −212.500 | + | 368.061i | −0.312960 | + | 0.542063i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 198.000i | − | 0.289898i | −0.989439 | − | 0.144949i | \(-0.953698\pi\) | ||
0.989439 | − | 0.144949i | \(-0.0463017\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 414.000 | 0.604380 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −233.827 | − | 135.000i | −0.339371 | − | 0.195936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −218.000 | − | 377.587i | −0.315485 | − | 0.546436i | 0.664056 | − | 0.747683i | \(-0.268834\pi\) |
−0.979540 | + | 0.201247i | \(0.935500\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −72.7461 | + | 42.0000i | −0.104671 | + | 0.0604317i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 540.000 | − | 935.307i | 0.774749 | − | 1.34190i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 135.000i | 0.192582i | 0.995353 | + | 0.0962910i | \(0.0306979\pi\) | ||||
−0.995353 | + | 0.0962910i | \(0.969302\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 320.000 | 0.455192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −844.375 | − | 487.500i | −1.19431 | − | 0.689533i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0000 | − | 27.7128i | −0.0225670 | − | 0.0390872i | 0.854521 | − | 0.519416i | \(-0.173851\pi\) |
−0.877088 | + | 0.480329i | \(0.840517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.3923 | − | 6.00000i | 0.0145755 | − | 0.00841515i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 225.000 | − | 389.711i | 0.314685 | − | 0.545051i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 900.000i | 1.25174i | 0.779928 | + | 0.625869i | \(0.215256\pi\) | ||||
−0.779928 | + | 0.625869i | \(0.784744\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 850.000 | 1.17892 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −415.692 | − | 240.000i | −0.573369 | − | 0.331034i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −87.5000 | − | 151.554i | −0.120358 | − | 0.208466i | 0.799551 | − | 0.600598i | \(-0.205071\pi\) |
−0.919909 | + | 0.392133i | \(0.871737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −779.423 | + | 450.000i | −1.06624 | + | 0.615595i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −580.000 | + | 1004.59i | −0.791269 | + | 1.37052i | 0.133913 | + | 0.990993i | \(0.457246\pi\) |
−0.925182 | + | 0.379525i | \(0.876088\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 150.000i | 0.203528i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1006.00 | 1.36130 | 0.680650 | − | 0.732609i | \(-0.261698\pi\) | ||||
0.680650 | + | 0.732609i | \(0.261698\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 98.7269 | + | 57.0000i | 0.132876 | + | 0.0767160i | 0.564965 | − | 0.825115i | \(-0.308890\pi\) |
−0.432088 | + | 0.901831i | \(0.642223\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 112.500 | + | 194.856i | 0.151007 | + | 0.261551i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 818.394 | − | 472.500i | 1.09265 | − | 0.630841i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 179.500 | − | 310.903i | 0.239015 | − | 0.413986i | −0.721417 | − | 0.692501i | \(-0.756509\pi\) |
0.960432 | + | 0.278515i | \(0.0898423\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 231.000i | 0.305960i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −430.000 | −0.568032 | −0.284016 | − | 0.958820i | \(-0.591667\pi\) | ||||
−0.284016 | + | 0.958820i | \(0.591667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1143.15 | − | 660.000i | −1.50217 | − | 0.867280i | −0.999997 | − | 0.00251446i | \(-0.999200\pi\) |
−0.502176 | − | 0.864765i | \(-0.667467\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 410.000 | + | 710.141i | 0.537353 | + | 0.930722i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −259.808 | + | 150.000i | −0.338732 | + | 0.195567i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −629.500 | + | 1090.33i | −0.818596 | + | 1.41785i | 0.0881215 | + | 0.996110i | \(0.471914\pi\) |
−0.906717 | + | 0.421739i | \(0.861420\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 522.000i | − | 0.675291i | −0.941273 | − | 0.337646i | \(-0.890369\pi\) | ||
0.941273 | − | 0.337646i | \(-0.109631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.0000 | 0.0206452 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −831.384 | − | 480.000i | −1.06725 | − | 0.616175i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 675.000 | + | 1169.13i | 0.864277 | + | 1.49697i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 259.808 | − | 150.000i | 0.330965 | − | 0.191083i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −230.000 | + | 398.372i | −0.292249 | + | 0.506190i | −0.974341 | − | 0.225076i | \(-0.927737\pi\) |
0.682092 | + | 0.731266i | \(0.261070\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 120.000i | − | 0.151707i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 760.000 | 0.958386 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 205.248 | + | 118.500i | 0.257526 | + | 0.148683i | 0.623205 | − | 0.782058i | \(-0.285830\pi\) |
−0.365680 | + | 0.930741i | \(0.619163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.0000 | + | 93.5307i | 0.0675845 | + | 0.117060i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 844.375 | − | 487.500i | 1.05153 | − | 0.607098i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 90.0000 | − | 155.885i | 0.111801 | − | 0.193645i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 810.000i | 1.00124i | 0.865668 | + | 0.500618i | \(0.166894\pi\) | ||||
−0.865668 | + | 0.500618i | \(0.833106\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −272.000 | −0.335388 | −0.167694 | − | 0.985839i | \(-0.553632\pi\) | ||||
−0.167694 | + | 0.985839i | \(0.553632\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −285.788 | − | 165.000i | −0.350661 | − | 0.202454i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 400.000 | + | 692.820i | 0.489596 | + | 0.848005i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 337.750 | − | 195.000i | 0.411388 | − | 0.237515i | −0.279998 | − | 0.960001i | \(-0.590334\pi\) |
0.691386 | + | 0.722485i | \(0.257000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 602.500 | − | 1043.56i | 0.732078 | − | 1.26800i | −0.223916 | − | 0.974608i | \(-0.571884\pi\) |
0.955994 | − | 0.293387i | \(-0.0947826\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.0000i | − | 0.0217654i | −0.999941 | − | 0.0108827i | \(-0.996536\pi\) | ||
0.999941 | − | 0.0108827i | \(-0.00346414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1442.00 | 1.73945 | 0.869723 | − | 0.493541i | \(-0.164298\pi\) | ||||
0.869723 | + | 0.493541i | \(0.164298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 374.123 | + | 216.000i | 0.449127 | + | 0.259304i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 117.000 | + | 202.650i | 0.140120 | + | 0.242695i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1376.98 | − | 795.000i | 1.64122 | − | 0.947557i | 0.660814 | − | 0.750550i | \(-0.270211\pi\) |
0.980402 | − | 0.197007i | \(-0.0631222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.5000 | − | 51.0955i | 0.0350773 | − | 0.0607556i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 207.000i | 0.244970i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 520.000 | 0.613932 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −207.846 | − | 120.000i | −0.244237 | − | 0.141011i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −295.000 | − | 510.955i | −0.345838 | − | 0.599009i | 0.639667 | − | 0.768652i | \(-0.279072\pi\) |
−0.985506 | + | 0.169642i | \(0.945739\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1127.57 | + | 651.000i | −1.31571 | + | 0.759627i | −0.983036 | − | 0.183415i | \(-0.941285\pi\) |
−0.332676 | + | 0.943041i | \(0.607952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −158.000 | + | 273.664i | −0.183935 | + | 0.318584i | −0.943217 | − | 0.332177i | \(-0.892217\pi\) |
0.759282 | + | 0.650761i | \(0.225550\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1188.00i | − | 1.37659i | −0.725429 | − | 0.688297i | \(-0.758359\pi\) | ||
0.725429 | − | 0.688297i | \(-0.241641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −531.000 | −0.613873 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 181.865 | + | 105.000i | 0.209281 | + | 0.120829i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.0000 | + | 86.6025i | 0.0574053 | + | 0.0994289i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 532.606 | − | 307.500i | 0.608692 | − | 0.351429i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 275.000 | − | 476.314i | 0.313569 | − | 0.543117i | −0.665563 | − | 0.746341i | \(-0.731809\pi\) |
0.979132 | + | 0.203224i | \(0.0651420\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 90.0000i | − | 0.102157i | −0.998695 | − | 0.0510783i | \(-0.983734\pi\) | ||
0.998695 | − | 0.0510783i | \(-0.0162658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 880.000 | 0.996602 | 0.498301 | − | 0.867004i | \(-0.333957\pi\) | ||||
0.498301 | + | 0.867004i | \(0.333957\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −244.219 | − | 141.000i | −0.275332 | − | 0.158963i | 0.355976 | − | 0.934495i | \(-0.384148\pi\) |
−0.631308 | + | 0.775532i | \(0.717482\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 512.500 | + | 887.676i | 0.576490 | + | 0.998511i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 83.1384 | − | 48.0000i | 0.0931002 | − | 0.0537514i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −337.500 | + | 584.567i | −0.377095 | + | 0.653148i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.0000i | 0.0333704i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 486.000 | 0.539401 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41.5692 | − | 24.0000i | −0.0459328 | − | 0.0265193i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −650.000 | − | 1125.83i | −0.716648 | − | 1.24127i | −0.962320 | − | 0.271918i | \(-0.912342\pi\) |
0.245672 | − | 0.969353i | \(-0.420991\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −181.865 | + | 105.000i | −0.199633 | + | 0.115258i | −0.596484 | − | 0.802625i | \(-0.703436\pi\) |
0.396851 | + | 0.917883i | \(0.370103\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.5000 | + | 38.9711i | −0.0246440 | + | 0.0426847i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 75.0000i | 0.0817884i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −137.000 | −0.149075 | −0.0745375 | − | 0.997218i | \(-0.523748\pi\) | ||||
−0.0745375 | + | 0.997218i | \(0.523748\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 779.423 | + | 450.000i | 0.844445 | + | 0.487541i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −160.000 | − | 277.128i | −0.172973 | − | 0.299598i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 571.577 | − | 330.000i | 0.615260 | − | 0.355221i | −0.159761 | − | 0.987156i | \(-0.551072\pi\) |
0.775021 | + | 0.631935i | \(0.217739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 192.000 | − | 332.554i | 0.206230 | − | 0.357201i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 810.000i | 0.866310i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 605.000 | 0.645678 | 0.322839 | − | 0.946454i | \(-0.395363\pi\) | ||||
0.322839 | + | 0.946454i | \(0.395363\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1389.97 | + | 802.500i | 1.47712 | + | 0.852816i | 0.999666 | − | 0.0258401i | \(-0.00822609\pi\) |
0.477455 | + | 0.878656i | \(0.341559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 360.000 | + | 623.538i | 0.381760 | + | 0.661228i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −470.252 | + | 271.500i | −0.496570 | + | 0.286695i | −0.727296 | − | 0.686324i | \(-0.759223\pi\) |
0.230726 | + | 0.973019i | \(0.425890\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 325.000 | − | 562.917i | 0.342466 | − | 0.593168i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 144.000i | 0.151102i | 0.997142 | + | 0.0755509i | \(0.0240715\pi\) | ||||
−0.997142 | + | 0.0755509i | \(0.975928\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −90.0000 | −0.0942408 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 597.558 | + | 345.000i | 0.623105 | + | 0.359750i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 480.000 | + | 831.384i | 0.499480 | + | 0.865124i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −558.586 | + | 322.500i | −0.578846 | + | 0.334197i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 422.500 | − | 731.791i | 0.436918 | − | 0.756765i | −0.560532 | − | 0.828133i | \(-0.689403\pi\) |
0.997450 | + | 0.0713682i | \(0.0227365\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 405.000i | − | 0.417096i | −0.978012 | − | 0.208548i | \(-0.933126\pi\) | ||
0.978012 | − | 0.208548i | \(-0.0668737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −140.000 | −0.143885 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 213.042 | + | 123.000i | 0.218058 | + | 0.125896i | 0.605051 | − | 0.796187i | \(-0.293153\pi\) |
−0.386993 | + | 0.922083i | \(0.626486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 675.000 | + | 1169.13i | 0.689479 | + | 1.19421i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −898.934 | + | 519.000i | −0.914481 | + | 0.527976i | −0.881870 | − | 0.471493i | \(-0.843715\pi\) |
−0.0326105 | + | 0.999468i | \(0.510382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 310.500 | − | 537.802i | 0.315228 | − | 0.545992i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 600.000i | − | 0.606673i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1501.00 | 1.51463 | 0.757316 | − | 0.653049i | \(-0.226510\pi\) | ||||
0.757316 | + | 0.653049i | \(0.226510\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 579.371 | + | 334.500i | 0.582282 | + | 0.336181i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −385.000 | − | 666.840i | −0.386158 | − | 0.668846i | 0.605771 | − | 0.795639i | \(-0.292865\pi\) |
−0.991929 | + | 0.126793i | \(0.959532\pi\) | |||||||
\(998\) | 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 | 1296.3.q.j.1025.2 | 4 | ||
3.2 | odd | 2 | inner | 1296.3.q.j.1025.1 | 4 | ||
4.3 | odd | 2 | 81.3.d.b.53.2 | 4 | |||
9.2 | odd | 6 | inner | 1296.3.q.j.593.2 | 4 | ||
9.4 | even | 3 | 432.3.e.c.161.1 | 2 | |||
9.5 | odd | 6 | 432.3.e.c.161.2 | 2 | |||
9.7 | even | 3 | inner | 1296.3.q.j.593.1 | 4 | ||
12.11 | even | 2 | 81.3.d.b.53.1 | 4 | |||
36.7 | odd | 6 | 81.3.d.b.26.1 | 4 | |||
36.11 | even | 6 | 81.3.d.b.26.2 | 4 | |||
36.23 | even | 6 | 27.3.b.b.26.1 | ✓ | 2 | ||
36.31 | odd | 6 | 27.3.b.b.26.2 | yes | 2 | ||
72.5 | odd | 6 | 1728.3.e.g.1025.1 | 2 | |||
72.13 | even | 6 | 1728.3.e.g.1025.2 | 2 | |||
72.59 | even | 6 | 1728.3.e.m.1025.1 | 2 | |||
72.67 | odd | 6 | 1728.3.e.m.1025.2 | 2 | |||
180.23 | odd | 12 | 675.3.d.a.674.1 | 2 | |||
180.59 | even | 6 | 675.3.c.h.26.2 | 2 | |||
180.67 | even | 12 | 675.3.d.a.674.2 | 2 | |||
180.103 | even | 12 | 675.3.d.d.674.1 | 2 | |||
180.139 | odd | 6 | 675.3.c.h.26.1 | 2 | |||
180.167 | odd | 12 | 675.3.d.d.674.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.3.b.b.26.1 | ✓ | 2 | 36.23 | even | 6 | ||
27.3.b.b.26.2 | yes | 2 | 36.31 | odd | 6 | ||
81.3.d.b.26.1 | 4 | 36.7 | odd | 6 | |||
81.3.d.b.26.2 | 4 | 36.11 | even | 6 | |||
81.3.d.b.53.1 | 4 | 12.11 | even | 2 | |||
81.3.d.b.53.2 | 4 | 4.3 | odd | 2 | |||
432.3.e.c.161.1 | 2 | 9.4 | even | 3 | |||
432.3.e.c.161.2 | 2 | 9.5 | odd | 6 | |||
675.3.c.h.26.1 | 2 | 180.139 | odd | 6 | |||
675.3.c.h.26.2 | 2 | 180.59 | even | 6 | |||
675.3.d.a.674.1 | 2 | 180.23 | odd | 12 | |||
675.3.d.a.674.2 | 2 | 180.67 | even | 12 | |||
675.3.d.d.674.1 | 2 | 180.103 | even | 12 | |||
675.3.d.d.674.2 | 2 | 180.167 | odd | 12 | |||
1296.3.q.j.593.1 | 4 | 9.7 | even | 3 | inner | ||
1296.3.q.j.593.2 | 4 | 9.2 | odd | 6 | inner | ||
1296.3.q.j.1025.1 | 4 | 3.2 | odd | 2 | inner | ||
1296.3.q.j.1025.2 | 4 | 1.1 | even | 1 | trivial | ||
1728.3.e.g.1025.1 | 2 | 72.5 | odd | 6 | |||
1728.3.e.g.1025.2 | 2 | 72.13 | even | 6 | |||
1728.3.e.m.1025.1 | 2 | 72.59 | even | 6 | |||
1728.3.e.m.1025.2 | 2 | 72.67 | odd | 6 |