Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(863,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.863");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.s (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: | \(20.6972242039\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1727.4 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.1727 |
Dual form | 2592.2.s.b.863.4 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||||||
\(5\) | 1.67303 | − | 0.965926i | 0.748203 | − | 0.431975i | −0.0768413 | − | 0.997043i | \(-0.524483\pi\) |
0.825044 | + | 0.565068i | \(0.191150\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.633975 | − | 0.366025i | −0.239620 | − | 0.138345i | 0.375382 | − | 0.926870i | \(-0.377511\pi\) |
−0.615002 | + | 0.788526i | \(0.710845\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.63896 | + | 4.57081i | −0.795676 | + | 1.37815i | 0.126733 | + | 0.991937i | \(0.459551\pi\) |
−0.922409 | + | 0.386214i | \(0.873783\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.23205 | − | 3.86603i | −0.619060 | − | 1.07224i | −0.989658 | − | 0.143449i | \(-0.954181\pi\) |
0.370598 | − | 0.928793i | \(-0.379153\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.896575i | − | 0.217451i | −0.994072 | − | 0.108726i | \(-0.965323\pi\) | ||
0.994072 | − | 0.108726i | \(-0.0346770\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26795i | 0.290887i | 0.989367 | + | 0.145444i | \(0.0464610\pi\) | ||||
−0.989367 | + | 0.145444i | \(0.953539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.707107 | − | 1.22474i | −0.147442 | − | 0.255377i | 0.782839 | − | 0.622224i | \(-0.213771\pi\) |
−0.930281 | + | 0.366847i | \(0.880437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.633975 | + | 1.09808i | −0.126795 | + | 0.219615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.69093 | − | 2.70831i | −0.871084 | − | 0.502920i | −0.00337538 | − | 0.999994i | \(-0.501074\pi\) |
−0.867708 | + | 0.497074i | \(0.834408\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.46410 | + | 3.73205i | −1.16099 | + | 0.670296i | −0.951540 | − | 0.307524i | \(-0.900500\pi\) |
−0.209447 | + | 0.977820i | \(0.567166\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41421 | −0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.73205 | −1.27114 | −0.635571 | − | 0.772043i | \(-0.719235\pi\) | ||||
−0.635571 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.328169 | + | 0.189469i | −0.0512514 | + | 0.0295900i | −0.525407 | − | 0.850851i | \(-0.676087\pi\) |
0.474155 | + | 0.880441i | \(0.342754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.56218 | + | 4.36603i | 1.15322 | + | 0.665813i | 0.949670 | − | 0.313252i | \(-0.101418\pi\) |
0.203551 | + | 0.979064i | \(0.434752\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.31079 | − | 4.00240i | 0.337063 | − | 0.583811i | −0.646816 | − | 0.762646i | \(-0.723900\pi\) |
0.983879 | + | 0.178836i | \(0.0572331\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.23205 | − | 5.59808i | −0.461722 | − | 0.799725i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.44949i | 0.336463i | 0.985747 | + | 0.168232i | \(0.0538057\pi\) | ||||
−0.985747 | + | 0.168232i | \(0.946194\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.1962i | 1.37485i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.41662 | − | 9.38186i | −0.705184 | − | 1.22141i | −0.966625 | − | 0.256194i | \(-0.917531\pi\) |
0.261442 | − | 0.965219i | \(-0.415802\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.598076 | − | 1.03590i | 0.0765758 | − | 0.132633i | −0.825195 | − | 0.564848i | \(-0.808935\pi\) |
0.901770 | + | 0.432215i | \(0.142268\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.46859 | − | 4.31199i | −0.926364 | − | 0.534837i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3660 | + | 6.56218i | −1.38858 | + | 0.801698i | −0.993155 | − | 0.116800i | \(-0.962736\pi\) |
−0.395426 | + | 0.918498i | \(0.629403\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.2827 | 1.57637 | 0.788185 | − | 0.615439i | \(-0.211021\pi\) | ||||
0.788185 | + | 0.615439i | \(0.211021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.7321 | −1.60721 | −0.803607 | − | 0.595160i | \(-0.797089\pi\) | ||||
−0.803607 | + | 0.595160i | \(0.797089\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.34607 | − | 1.93185i | 0.381320 | − | 0.220155i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.3660 | − | 8.29423i | −1.61630 | − | 0.933174i | −0.987865 | − | 0.155315i | \(-0.950361\pi\) |
−0.628439 | − | 0.777859i | \(-0.716306\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.27792 | + | 9.14162i | −0.579327 | + | 1.00342i | 0.416230 | + | 0.909259i | \(0.363351\pi\) |
−0.995557 | + | 0.0941638i | \(0.969982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.866025 | − | 1.50000i | −0.0939336 | − | 0.162698i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.9372i | 1.58334i | 0.610951 | + | 0.791669i | \(0.290787\pi\) | ||||
−0.610951 | + | 0.791669i | \(0.709213\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.26795i | 0.342574i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.22474 | + | 2.12132i | 0.125656 | + | 0.217643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.19615 | − | 5.53590i | 0.324520 | − | 0.562085i | −0.656895 | − | 0.753982i | \(-0.728131\pi\) |
0.981415 | + | 0.191897i | \(0.0614639\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.46739 | + | 3.15660i | 0.544025 | + | 0.314093i | 0.746709 | − | 0.665151i | \(-0.231633\pi\) |
−0.202683 | + | 0.979244i | \(0.564966\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.46410 | − | 2.00000i | 0.341328 | − | 0.197066i | −0.319531 | − | 0.947576i | \(-0.603525\pi\) |
0.660859 | + | 0.750510i | \(0.270192\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.79315 | 0.173350 | 0.0866752 | − | 0.996237i | \(-0.472376\pi\) | ||||
0.0866752 | + | 0.996237i | \(0.472376\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.92820 | 0.376254 | 0.188127 | − | 0.982145i | \(-0.439758\pi\) | ||||
0.188127 | + | 0.982145i | \(0.439758\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.5068 | − | 10.1075i | 1.64690 | − | 0.950838i | 0.668605 | − | 0.743617i | \(-0.266892\pi\) |
0.978294 | − | 0.207221i | \(-0.0664418\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.36603 | − | 1.36603i | −0.220633 | − | 0.127383i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.328169 | + | 0.568406i | −0.0300832 | + | 0.0521057i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.42820 | − | 14.5981i | −0.766200 | − | 1.32710i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1087i | 1.08304i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.1244i | 1.87448i | 0.348680 | + | 0.937242i | \(0.386630\pi\) | ||||
−0.348680 | + | 0.937242i | \(0.613370\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0507680 | + | 0.0879327i | 0.00443562 | + | 0.00768272i | 0.868235 | − | 0.496154i | \(-0.165255\pi\) |
−0.863799 | + | 0.503836i | \(0.831921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.464102 | − | 0.803848i | 0.0402427 | − | 0.0697024i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.21046 | + | 2.43091i | 0.359723 | + | 0.207686i | 0.668959 | − | 0.743299i | \(-0.266740\pi\) |
−0.309236 | + | 0.950985i | \(0.600073\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7321 | + | 6.19615i | −0.910281 | + | 0.525551i | −0.880521 | − | 0.474006i | \(-0.842807\pi\) |
−0.0297592 | + | 0.999557i | \(0.509474\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.5612 | 1.97028 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4641 | −0.868996 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.58510 | − | 0.915158i | 0.129856 | − | 0.0749727i | −0.433665 | − | 0.901074i | \(-0.642780\pi\) |
0.563521 | + | 0.826102i | \(0.309446\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.928203 | + | 0.535898i | 0.0755361 | + | 0.0436108i | 0.537292 | − | 0.843396i | \(-0.319447\pi\) |
−0.461756 | + | 0.887007i | \(0.652781\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.20977 | + | 12.4877i | −0.579103 | + | 1.00304i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.33013 | − | 9.23205i | −0.425390 | − | 0.736798i | 0.571066 | − | 0.820904i | \(-0.306530\pi\) |
−0.996457 | + | 0.0841060i | \(0.973197\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.03528i | 0.0815912i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.60770i | 0.125924i | 0.998016 | + | 0.0629622i | \(0.0200548\pi\) | ||||
−0.998016 | + | 0.0629622i | \(0.979945\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.32868 | − | 9.22955i | −0.412346 | − | 0.714204i | 0.582800 | − | 0.812616i | \(-0.301957\pi\) |
−0.995146 | + | 0.0984115i | \(0.968624\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.46410 | + | 6.00000i | −0.266469 | + | 0.461538i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.58991 | − | 5.53674i | −0.729107 | − | 0.420950i | 0.0889883 | − | 0.996033i | \(-0.471637\pi\) |
−0.818095 | + | 0.575082i | \(0.804970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.803848 | − | 0.464102i | 0.0607652 | − | 0.0350828i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.8695 | −1.63461 | −0.817303 | − | 0.576208i | \(-0.804532\pi\) | ||||
−0.817303 | + | 0.576208i | \(0.804532\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.3205 | −1.73340 | −0.866700 | − | 0.498830i | \(-0.833763\pi\) | ||||
−0.866700 | + | 0.498830i | \(0.833763\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.9360 | + | 7.46859i | −0.951072 | + | 0.549101i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.09808 | + | 2.36603i | 0.299681 | + | 0.173021i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.2277 | − | 17.7148i | 0.740048 | − | 1.28180i | −0.212425 | − | 0.977177i | \(-0.568136\pi\) |
0.952473 | − | 0.304623i | \(-0.0985305\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.23205 | + | 7.33013i | 0.304630 | + | 0.527634i | 0.977179 | − | 0.212418i | \(-0.0681340\pi\) |
−0.672549 | + | 0.740052i | \(0.734801\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.76079i | − | 0.695428i | −0.937601 | − | 0.347714i | \(-0.886958\pi\) | ||
0.937601 | − | 0.347714i | \(-0.113042\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000i | 0.567105i | 0.958957 | + | 0.283552i | \(0.0915130\pi\) | ||||
−0.958957 | + | 0.283552i | \(0.908487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.98262 | + | 3.43400i | 0.139153 | + | 0.241019i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.366025 | + | 0.633975i | −0.0255643 | + | 0.0442787i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.79555 | − | 3.34607i | −0.400887 | − | 0.231452i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.5622 | + | 9.56218i | −1.14019 | + | 0.658287i | −0.946477 | − | 0.322771i | \(-0.895386\pi\) |
−0.193710 | + | 0.981059i | \(0.562052\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.8690 | 1.15046 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.46410 | 0.370927 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.46618 | + | 2.00120i | −0.233161 | + | 0.134615i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.9545 | + | 8.63397i | 1.00143 | + | 0.578174i | 0.908670 | − | 0.417515i | \(-0.137099\pi\) |
0.0927563 | + | 0.995689i | \(0.470432\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.67475 | + | 15.0251i | −0.575763 | + | 0.997251i | 0.420195 | + | 0.907434i | \(0.361962\pi\) |
−0.995958 | + | 0.0898175i | \(0.971372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.50000 | − | 9.52628i | −0.363450 | − | 0.629514i | 0.625076 | − | 0.780564i | \(-0.285068\pi\) |
−0.988526 | + | 0.151050i | \(0.951735\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.8009i | − | 1.23169i | −0.787869 | − | 0.615843i | \(-0.788815\pi\) | ||
0.787869 | − | 0.615843i | \(-0.211185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 8.92820i | − | 0.582412i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.52056 | − | 16.4901i | −0.615834 | − | 1.06666i | −0.990238 | − | 0.139390i | \(-0.955486\pi\) |
0.374404 | − | 0.927266i | \(-0.377847\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.06218 | − | 13.9641i | 0.519331 | − | 0.899507i | −0.480417 | − | 0.877040i | \(-0.659515\pi\) |
0.999748 | − | 0.0224667i | \(-0.00715197\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.8147 | − | 6.24384i | −0.690923 | − | 0.398904i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.90192 | − | 2.83013i | 0.311902 | − | 0.180077i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.8386 | −1.50468 | −0.752338 | − | 0.658777i | \(-0.771074\pi\) | ||||
−0.752338 | + | 0.658777i | \(0.771074\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.46410 | 0.469264 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.688524 | − | 0.397520i | 0.0429490 | − | 0.0247966i | −0.478372 | − | 0.878157i | \(-0.658773\pi\) |
0.521321 | + | 0.853361i | \(0.325440\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.90192 | + | 2.83013i | 0.304591 | + | 0.175856i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.72500 | − | 6.45189i | 0.229694 | − | 0.397841i | −0.728024 | − | 0.685552i | \(-0.759561\pi\) |
0.957717 | + | 0.287711i | \(0.0928943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.36603 | + | 4.09808i | 0.145344 | + | 0.251743i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.7661i | 1.38807i | 0.719939 | + | 0.694037i | \(0.244170\pi\) | ||||
−0.719939 | + | 0.694037i | \(0.755830\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.2679i | − | 0.805971i | −0.915206 | − | 0.402985i | \(-0.867973\pi\) | ||
0.915206 | − | 0.402985i | \(-0.132027\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.34607 | − | 5.79555i | −0.201775 | − | 0.349485i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.535898 | + | 0.928203i | −0.0321990 | + | 0.0557703i | −0.881676 | − | 0.471856i | \(-0.843584\pi\) |
0.849477 | + | 0.527626i | \(0.176918\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.91808 | − | 5.72620i | −0.591663 | − | 0.341597i | 0.174092 | − | 0.984729i | \(-0.444301\pi\) |
−0.765755 | + | 0.643133i | \(0.777634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.7321 | + | 9.66025i | −0.994617 | + | 0.574242i | −0.906651 | − | 0.421881i | \(-0.861370\pi\) |
−0.0879660 | + | 0.996123i | \(0.528037\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.277401 | 0.0163745 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1962 | 0.952715 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.6126 | − | 11.9007i | 1.20420 | − | 0.695246i | 0.242715 | − | 0.970098i | \(-0.421962\pi\) |
0.961487 | + | 0.274852i | \(0.0886287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.1244 | − | 10.4641i | −1.05524 | − | 0.609244i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.15660 | + | 5.46739i | −0.182551 | + | 0.316187i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.19615 | − | 5.53590i | −0.184223 | − | 0.319084i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.31079i | − | 0.132315i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.0000i | − | 1.02731i | −0.857996 | − | 0.513657i | \(-0.828290\pi\) | ||
0.857996 | − | 0.513657i | \(-0.171710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1087 | + | 20.9730i | 0.686624 | + | 1.18927i | 0.972923 | + | 0.231128i | \(0.0742415\pi\) |
−0.286299 | + | 0.958140i | \(0.592425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.1603 | + | 24.5263i | −0.800385 | + | 1.38631i | 0.118978 | + | 0.992897i | \(0.462038\pi\) |
−0.919363 | + | 0.393410i | \(0.871295\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.33178 | + | 3.65565i | 0.355628 | + | 0.205322i | 0.667161 | − | 0.744913i | \(-0.267509\pi\) |
−0.311533 | + | 0.950235i | \(0.600843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.7583 | − | 14.2942i | 1.38620 | − | 0.800323i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.13681 | 0.0632539 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.66025 | 0.313974 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.92996 | + | 1.69161i | −0.161534 | + | 0.0932618i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.75833 | − | 3.90192i | −0.371471 | − | 0.214469i | 0.302630 | − | 0.953108i | \(-0.402135\pi\) |
−0.674101 | + | 0.738639i | \(0.735469\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.6772 | + | 21.9575i | −0.692627 | + | 1.19967i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.46410 | + | 4.26795i | 0.134228 | + | 0.232490i | 0.925302 | − | 0.379230i | \(-0.123811\pi\) |
−0.791074 | + | 0.611720i | \(0.790478\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 39.3949i | − | 2.13335i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.85641i | 0.532196i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.88160 | + | 11.9193i | 0.369424 | + | 0.639860i | 0.989476 | − | 0.144700i | \(-0.0462218\pi\) |
−0.620052 | + | 0.784561i | \(0.712888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.07180 | − | 1.85641i | 0.0573720 | − | 0.0993712i | −0.835913 | − | 0.548862i | \(-0.815061\pi\) |
0.893285 | + | 0.449491i | \(0.148395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.2311 | + | 13.9898i | 1.28969 | + | 0.744604i | 0.978599 | − | 0.205776i | \(-0.0659719\pi\) |
0.311092 | + | 0.950380i | \(0.399305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.2224 | − | 12.8301i | 1.17944 | − | 0.680952i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.44949 | 0.129279 | 0.0646396 | − | 0.997909i | \(-0.479410\pi\) | ||||
0.0646396 | + | 0.997909i | \(0.479410\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3923 | 0.915384 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.9742 | + | 13.2641i | −1.20252 | + | 0.694277i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.8564 | − | 6.26795i | −0.566700 | − | 0.327184i | 0.189130 | − | 0.981952i | \(-0.439433\pi\) |
−0.755830 | + | 0.654768i | \(0.772766\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.896575 | − | 1.55291i | 0.0465479 | − | 0.0806233i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1244 | + | 27.9282i | 0.834887 | + | 1.44607i | 0.894122 | + | 0.447823i | \(0.147801\pi\) |
−0.0592345 | + | 0.998244i | \(0.518866\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.1803i | 1.24535i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14.3923i | − | 0.739283i | −0.929174 | − | 0.369642i | \(-0.879480\pi\) | ||
0.929174 | − | 0.369642i | \(-0.120520\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.60849 | + | 16.6424i | 0.490971 | + | 0.850387i | 0.999946 | − | 0.0103947i | \(-0.00330879\pi\) |
−0.508975 | + | 0.860781i | \(0.669975\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.73205 | − | 6.46410i | 0.190203 | − | 0.329441i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.29392 | + | 5.36585i | 0.471221 | + | 0.272059i | 0.716751 | − | 0.697330i | \(-0.245629\pi\) |
−0.245530 | + | 0.969389i | \(0.578962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.09808 | + | 0.633975i | −0.0555321 | + | 0.0320615i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −32.0464 | −1.61243 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.5885 | 1.08349 | 0.541747 | − | 0.840542i | \(-0.317763\pi\) | ||||
0.541747 | + | 0.840542i | \(0.317763\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.2820 | − | 9.40044i | 0.813086 | − | 0.469436i | −0.0349403 | − | 0.999389i | \(-0.511124\pi\) |
0.848026 | + | 0.529954i | \(0.177791\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.8564 | + | 16.6603i | 1.43744 | + | 0.829906i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.4046 | − | 35.3417i | 1.01142 | − | 1.75182i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.40192 | − | 12.8205i | −0.366002 | − | 0.633933i | 0.622935 | − | 0.782274i | \(-0.285940\pi\) |
−0.988936 | + | 0.148340i | \(0.952607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.93048i | 0.390233i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.3923i | 1.00102i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.795040 | − | 1.37705i | −0.0388402 | − | 0.0672732i | 0.845952 | − | 0.533259i | \(-0.179033\pi\) |
−0.884792 | + | 0.465986i | \(0.845700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.42820 | + | 7.66987i | −0.215817 | + | 0.373807i | −0.953525 | − | 0.301313i | \(-0.902575\pi\) |
0.737708 | + | 0.675120i | \(0.235908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.984508 | + | 0.568406i | 0.0477557 | + | 0.0275717i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.758330 | + | 0.437822i | −0.0366982 | + | 0.0211877i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.48528 | 0.408722 | 0.204361 | − | 0.978896i | \(-0.434488\pi\) | ||||
0.204361 | + | 0.978896i | \(0.434488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.1769 | −1.64244 | −0.821219 | − | 0.570613i | \(-0.806706\pi\) | ||||
−0.821219 | + | 0.570613i | \(0.806706\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.55291 | − | 0.896575i | 0.0742860 | − | 0.0428890i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.46410 | − | 3.73205i | −0.308515 | − | 0.178121i | 0.337747 | − | 0.941237i | \(-0.390335\pi\) |
−0.646262 | + | 0.763116i | \(0.723669\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.52245 | − | 14.7613i | 0.404914 | − | 0.701331i | −0.589398 | − | 0.807843i | \(-0.700635\pi\) |
0.994311 | + | 0.106512i | \(0.0339682\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.4282 | + | 24.9904i | 0.683962 | + | 1.18466i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 23.0064i | − | 1.08574i | −0.839818 | − | 0.542868i | \(-0.817338\pi\) | ||
0.839818 | − | 0.542868i | \(-0.182662\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.00000i | − | 0.0941763i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.15660 | + | 5.46739i | 0.147984 | + | 0.256315i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.40192 | − | 2.42820i | 0.0655792 | − | 0.113587i | −0.831372 | − | 0.555717i | \(-0.812444\pi\) |
0.896951 | + | 0.442130i | \(0.145777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.8589 | + | 17.8164i | 1.43724 | + | 0.829791i | 0.997657 | − | 0.0684108i | \(-0.0217929\pi\) |
0.439583 | + | 0.898202i | \(0.355126\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.9282 | − | 9.19615i | 0.740246 | − | 0.427381i | −0.0819125 | − | 0.996640i | \(-0.526103\pi\) |
0.822159 | + | 0.569258i | \(0.192769\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0716 | 0.558606 | 0.279303 | − | 0.960203i | \(-0.409897\pi\) | ||||
0.279303 | + | 0.960203i | \(0.409897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.60770 | 0.443642 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −39.9125 | + | 23.0435i | −1.83518 | + | 1.05954i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.39230 | − | 0.803848i | −0.0638833 | − | 0.0368831i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.6443 | − | 27.0967i | 0.714805 | − | 1.23808i | −0.248229 | − | 0.968701i | \(-0.579849\pi\) |
0.963035 | − | 0.269378i | \(-0.0868181\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.2583 | + | 29.8923i | 0.786912 | + | 1.36297i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 12.3490i | − | 0.560739i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 36.9282i | − | 1.67338i | −0.547679 | − | 0.836688i | \(-0.684489\pi\) | ||
0.547679 | − | 0.836688i | \(-0.315511\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.12184 | − | 12.3354i | −0.321404 | − | 0.556688i | 0.659374 | − | 0.751815i | \(-0.270821\pi\) |
−0.980778 | + | 0.195127i | \(0.937488\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.42820 | + | 4.20577i | −0.109361 | + | 0.189418i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.42091 | − | 4.86181i | −0.377729 | − | 0.218082i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.5622 | − | 18.2224i | 1.41292 | − | 0.815748i | 0.417255 | − | 0.908790i | \(-0.362992\pi\) |
0.995662 | + | 0.0930414i | \(0.0296589\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.1165 | −1.29824 | −0.649120 | − | 0.760686i | \(-0.724863\pi\) | ||||
−0.649120 | + | 0.760686i | \(0.724863\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1962 | 0.542722 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.9957 | + | 18.4727i | −1.41818 | + | 0.818788i | −0.996139 | − | 0.0877870i | \(-0.972021\pi\) |
−0.422044 | + | 0.906575i | \(0.638687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.70577 | + | 5.02628i | 0.385121 | + | 0.222350i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.86370 | − | 6.69213i | 0.170255 | − | 0.294891i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.1962 | + | 21.1244i | 0.536386 | + | 0.929048i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.2789i | 0.669383i | 0.942328 | + | 0.334691i | \(0.108632\pi\) | ||||
−0.942328 | + | 0.334691i | \(0.891368\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.1962i | − | 0.708208i | −0.935206 | − | 0.354104i | \(-0.884786\pi\) | ||
0.935206 | − | 0.354104i | \(-0.115214\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.34607 | + | 5.79555i | 0.145757 | + | 0.252458i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.5000 | − | 18.1865i | 0.456522 | − | 0.790719i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.46498 | + | 0.845807i | 0.0634554 | + | 0.0366360i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00000 | − | 1.73205i | 0.129701 | − | 0.0748831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.1170 | 1.46952 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.00000 | 0.300954 | 0.150477 | − | 0.988614i | \(-0.451919\pi\) | ||||
0.150477 | + | 0.988614i | \(0.451919\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.57201 | − | 3.79435i | 0.281514 | − | 0.162532i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.14359 | + | 0.660254i | 0.0488965 | + | 0.0282304i | 0.524249 | − | 0.851565i | \(-0.324346\pi\) |
−0.475352 | + | 0.879795i | \(0.657679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.43400 | − | 5.94786i | 0.146293 | − | 0.253387i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.07180 | + | 10.5167i | 0.258199 | + | 0.447214i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 2.03339i | − | 0.0861574i | −0.999072 | − | 0.0430787i | \(-0.986283\pi\) | ||
0.999072 | − | 0.0430787i | \(-0.0137166\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 38.9808i | − | 1.64871i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.27981 | + | 7.41284i | 0.180372 | + | 0.312414i | 0.942007 | − | 0.335592i | \(-0.108936\pi\) |
−0.761635 | + | 0.648006i | \(0.775603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.5263 | − | 33.8205i | 0.821477 | − | 1.42284i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.09154 | + | 3.51695i | 0.255371 | + | 0.147438i | 0.622221 | − | 0.782842i | \(-0.286231\pi\) |
−0.366850 | + | 0.930280i | \(0.619564\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.5167 | − | 19.9282i | 1.44448 | − | 0.833969i | 0.446333 | − | 0.894867i | \(-0.352730\pi\) |
0.998144 | + | 0.0608975i | \(0.0193963\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.79315 | 0.0747796 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4641 | 0.768671 | 0.384335 | − | 0.923194i | \(-0.374431\pi\) | ||||
0.384335 | + | 0.923194i | \(0.374431\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.69213 | − | 3.86370i | 0.277636 | − | 0.160293i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.1962 | − | 6.46410i | −0.463697 | − | 0.267716i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.845807 | − | 1.46498i | 0.0349102 | − | 0.0604663i | −0.848042 | − | 0.529928i | \(-0.822219\pi\) |
0.882953 | + | 0.469462i | \(0.155552\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.73205 | − | 8.19615i | −0.194981 | − | 0.337717i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 21.1488i | − | 0.868478i | −0.900798 | − | 0.434239i | \(-0.857017\pi\) | ||
0.900798 | − | 0.434239i | \(-0.142983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.26795i | 0.0519808i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.20977 | − | 12.4877i | −0.294583 | − | 0.510233i | 0.680305 | − | 0.732929i | \(-0.261847\pi\) |
−0.974888 | + | 0.222696i | \(0.928514\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.89230 | + | 3.27757i | −0.0771887 | + | 0.133695i | −0.902036 | − | 0.431661i | \(-0.857928\pi\) |
0.824847 | + | 0.565356i | \(0.191261\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.2013 | − | 16.2820i | −1.14655 | − | 0.661959i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.83013 | + | 3.36603i | −0.236638 | + | 0.136623i | −0.613630 | − | 0.789593i | \(-0.710291\pi\) |
0.376993 | + | 0.926216i | \(0.376958\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.6312 | −0.834649 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.6077 | 0.549610 | 0.274805 | − | 0.961500i | \(-0.411387\pi\) | ||||
0.274805 | + | 0.961500i | \(0.411387\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.03699 | + | 4.64016i | −0.323557 | + | 0.186806i | −0.652977 | − | 0.757378i | \(-0.726480\pi\) |
0.329420 | + | 0.944184i | \(0.393147\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.26795 | − | 2.46410i | −0.171543 | − | 0.0990406i | 0.411770 | − | 0.911288i | \(-0.364911\pi\) |
−0.583313 | + | 0.812247i | \(0.698244\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.46739 | − | 9.46979i | 0.219046 | − | 0.379399i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.52628 | + | 14.7679i | 0.341051 | + | 0.590718i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.93237i | 0.276412i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.4046 | + | 35.3417i | 0.809730 | + | 1.40249i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.4282 | + | 24.9904i | −0.571666 | + | 0.990155i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.1158 | + | 18.5421i | 1.26850 | + | 0.732367i | 0.974704 | − | 0.223502i | \(-0.0717488\pi\) |
0.293794 | + | 0.955869i | \(0.405082\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.46410 | + | 2.00000i | −0.136611 | + | 0.0788723i | −0.566748 | − | 0.823891i | \(-0.691799\pi\) |
0.430137 | + | 0.902764i | \(0.358465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.6660 | −0.655206 | −0.327603 | − | 0.944815i | \(-0.606241\pi\) | ||||
−0.327603 | + | 0.944815i | \(0.606241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57.1769 | 2.24439 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.64566 | − | 5.56892i | 0.377464 | − | 0.217929i | −0.299251 | − | 0.954175i | \(-0.596737\pi\) |
0.676714 | + | 0.736246i | \(0.263403\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.169873 | + | 0.0980762i | 0.00663749 | + | 0.00383215i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.8840 | + | 18.8516i | −0.423981 | + | 0.734356i | −0.996325 | − | 0.0856577i | \(-0.972701\pi\) |
0.572344 | + | 0.820014i | \(0.306034\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.25833 | + | 7.37564i | 0.165630 | + | 0.286879i | 0.936879 | − | 0.349654i | \(-0.113701\pi\) |
−0.771249 | + | 0.636534i | \(0.780368\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.79315i | − | 0.0695354i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.66025i | 0.296606i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.15660 | + | 5.46739i | 0.121859 | + | 0.211066i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.1603 | + | 26.2583i | −0.584385 | + | 1.01218i | 0.410567 | + | 0.911830i | \(0.365331\pi\) |
−0.994952 | + | 0.100354i | \(0.968003\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.6130 | + | 19.4064i | 1.29185 | + | 0.745850i | 0.978982 | − | 0.203946i | \(-0.0653767\pi\) |
0.312869 | + | 0.949796i | \(0.398710\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.05256 | + | 2.33975i | −0.155523 | + | 0.0897912i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.37945 | −0.205839 | −0.102920 | − | 0.994690i | \(-0.532818\pi\) | ||||
−0.102920 | + | 0.994690i | \(0.532818\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.39230 | 0.358862 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.46979 | − | 5.46739i | 0.360770 | − | 0.208291i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.24167 | − | 1.29423i | −0.0852771 | − | 0.0492348i | 0.456755 | − | 0.889593i | \(-0.349012\pi\) |
−0.542032 | + | 0.840358i | \(0.682345\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.9700 | + | 20.7327i | −0.454050 | + | 0.786437i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.169873 | + | 0.294229i | 0.00643440 | + | 0.0111447i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.06918i | 0.304769i | 0.988321 | + | 0.152384i | \(0.0486952\pi\) | ||||
−0.988321 | + | 0.152384i | \(0.951305\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.80385i | − | 0.369759i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.31079 | − | 4.00240i | −0.0869062 | − | 0.150526i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.50000 | − | 11.2583i | 0.244113 | − | 0.422815i | −0.717769 | − | 0.696281i | \(-0.754837\pi\) |
0.961882 | + | 0.273466i | \(0.0881700\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.14162 | + | 5.27792i | 0.342356 | + | 0.197660i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39.4186 | − | 22.7583i | 1.47417 | − | 0.851113i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.3906 | −1.35714 | −0.678570 | − | 0.734535i | \(-0.737400\pi\) | ||||
−0.678570 | + | 0.734535i | \(0.737400\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.92820 | −0.109052 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.94786 | − | 3.43400i | 0.220898 | − | 0.127535i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.4378 | + | 12.9545i | 0.832173 | + | 0.480455i | 0.854596 | − | 0.519293i | \(-0.173805\pi\) |
−0.0224233 | + | 0.999749i | \(0.507138\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.91447 | − | 6.78006i | 0.144782 | − | 0.250770i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.6603 | − | 34.0526i | −0.726168 | − | 1.25776i | −0.958491 | − | 0.285121i | \(-0.907966\pi\) |
0.232323 | − | 0.972639i | \(-0.425367\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 69.2693i | − | 2.55157i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 32.0000i | − | 1.17714i | −0.808447 | − | 0.588570i | \(-0.799691\pi\) | ||
0.808447 | − | 0.588570i | \(-0.200309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.9000 | + | 25.8076i | 0.546628 | + | 0.946788i | 0.998502 | + | 0.0547064i | \(0.0174223\pi\) |
−0.451874 | + | 0.892082i | \(0.649244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.76795 | − | 3.06218i | 0.0647726 | − | 0.112190i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.13681 | − | 0.656339i | −0.0415382 | − | 0.0239821i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.15064 | − | 4.70577i | 0.297421 | − | 0.171716i | −0.343863 | − | 0.939020i | \(-0.611736\pi\) |
0.641284 | + | 0.767304i | \(0.278402\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.07055 | 0.0753551 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.7846 | −0.900812 | −0.450406 | − | 0.892824i | \(-0.648721\pi\) | ||||
−0.450406 | + | 0.892824i | \(0.648721\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.82534 | + | 1.05386i | −0.0661684 | + | 0.0382023i | −0.532719 | − | 0.846292i | \(-0.678830\pi\) |
0.466551 | + | 0.884494i | \(0.345496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.49038 | − | 1.43782i | −0.0901578 | − | 0.0520527i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.1803 | + | 41.8816i | −0.873101 | + | 1.51226i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0167 | + | 34.6699i | 0.721819 | + | 1.25023i | 0.960270 | + | 0.279073i | \(0.0900271\pi\) |
−0.238451 | + | 0.971155i | \(0.576640\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 35.9745i | − | 1.29391i | −0.762527 | − | 0.646957i | \(-0.776041\pi\) | ||
0.762527 | − | 0.646957i | \(-0.223959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 9.46410i | − | 0.339961i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.240237 | − | 0.416102i | −0.00860737 | − | 0.0149084i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.0526 | + | 60.7128i | −1.25428 | + | 2.17248i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.8350 | − | 10.2970i | −0.636557 | − | 0.367516i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.4186 | + | 12.3660i | −0.763490 | + | 0.440801i | −0.830547 | − | 0.556948i | \(-0.811972\pi\) |
0.0670573 | + | 0.997749i | \(0.478639\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.7985 | −0.526173 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.33975 | −0.189620 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.3632 | + | 25.6131i | −1.57143 | + | 0.907264i | −0.575432 | + | 0.817850i | \(0.695166\pi\) |
−0.995995 | + | 0.0894138i | \(0.971501\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.58846 | − | 2.07180i | −0.126950 | − | 0.0732949i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.2383 | − | 62.7666i | 1.27882 | − | 2.21499i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.00000 | + | 1.73205i | 0.0352454 | + | 0.0610468i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.3930i | 1.42014i | 0.704130 | + | 0.710071i | \(0.251337\pi\) | ||||
−0.704130 | + | 0.710071i | \(0.748663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.6410i | 1.63779i | 0.573945 | + | 0.818894i | \(0.305412\pi\) | ||||
−0.573945 | + | 0.818894i | \(0.694588\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.55291 | + | 2.68973i | 0.0543962 | + | 0.0942170i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.53590 | + | 9.58846i | −0.193677 | + | 0.335458i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.8649 | − | 23.5933i | −1.42619 | − | 0.823413i | −0.429376 | − | 0.903126i | \(-0.641266\pi\) |
−0.996818 | + | 0.0797126i | \(0.974600\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.12436 | − | 1.80385i | 0.108908 | − | 0.0628782i | −0.444557 | − | 0.895751i | \(-0.646639\pi\) |
0.553465 | + | 0.832873i | \(0.313305\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.92996 | −0.101885 | −0.0509424 | − | 0.998702i | \(-0.516222\pi\) | ||||
−0.0509424 | + | 0.998702i | \(0.516222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.7128 | 0.545729 | 0.272864 | − | 0.962053i | \(-0.412029\pi\) | ||||
0.272864 | + | 0.962053i | \(0.412029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.01910 | + | 2.89778i | −0.173901 | + | 0.100402i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.8301 | − | 10.2942i | −0.617037 | − | 0.356246i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.5075 | + | 25.1277i | −0.500853 | + | 0.867504i | 0.499146 | + | 0.866518i | \(0.333647\pi\) |
−1.00000 | 0.000985792i | \(0.999686\pi\) | ||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.169873 | + | 0.294229i | 0.00585769 | + | 0.0101458i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.3843i | 0.460433i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.3397i | 0.423999i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.46739 | + | 9.46979i | 0.187420 | + | 0.324620i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.7846 | − | 37.7321i | 0.745891 | − | 1.29192i | −0.203887 | − | 0.978995i | \(-0.565357\pi\) |
0.949777 | − | 0.312926i | \(-0.101309\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.0321856 | − | 0.0185824i | −0.00109944 | − | 0.000634762i | 0.499450 | − | 0.866343i | \(-0.333535\pi\) |
−0.500550 | + | 0.865708i | \(0.666869\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.6410 | + | 18.2679i | −1.07958 | + | 0.623294i | −0.930782 | − | 0.365574i | \(-0.880873\pi\) |
−0.148795 | + | 0.988868i | \(0.547539\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.5355 | −1.31176 | −0.655882 | − | 0.754864i | \(-0.727703\pi\) | ||||
−0.655882 | + | 0.754864i | \(0.727703\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.3923 | −0.727360 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 75.8227 | − | 43.7762i | 2.57211 | − | 1.48501i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.7391 | + | 29.2942i | 1.71923 | + | 0.992597i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.43211 | − | 7.67664i | 0.149833 | − | 0.259518i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.06218 | − | 3.57180i | −0.0696348 | − | 0.120611i | 0.829106 | − | 0.559092i | \(-0.188850\pi\) |
−0.898741 | + | 0.438481i | \(0.855517\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.2084i | − | 0.445002i | −0.974932 | − | 0.222501i | \(-0.928578\pi\) | ||
0.974932 | − | 0.222501i | \(-0.0714221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 0.679492i | − | 0.0228667i | −0.999935 | − | 0.0114334i | \(-0.996361\pi\) | ||
0.999935 | − | 0.0114334i | \(-0.00363943\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.2982 | − | 21.3011i | −0.412934 | − | 0.715222i | 0.582275 | − | 0.812992i | \(-0.302163\pi\) |
−0.995209 | + | 0.0977695i | \(0.968829\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.73205 | − | 13.3923i | 0.259325 | − | 0.449163i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.07484 | + | 2.92996i | 0.169823 | + | 0.0980475i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.5885 | + | 21.1244i | −1.22302 | + | 0.706109i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.4302 | 1.34842 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.19615 | 0.0731644 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39.0160 | + | 22.5259i | −1.29693 | + | 0.748786i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.8564 | + | 6.26795i | 0.360481 | + | 0.208124i | 0.669292 | − | 0.743000i | \(-0.266598\pi\) |
−0.308811 | + | 0.951124i | \(0.599931\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.36585 | − | 9.29392i | 0.177779 | − | 0.307921i | −0.763341 | − | 0.645996i | \(-0.776442\pi\) |
0.941119 | + | 0.338075i | \(0.109776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.8564 | − | 48.2487i | −0.921912 | − | 1.59680i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.0743295i | − | 0.00245458i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 38.4449i | − | 1.26818i | −0.773260 | − | 0.634090i | \(-0.781375\pi\) | ||
0.773260 | − | 0.634090i | \(-0.218625\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.6477 | − | 51.3514i | −0.975866 | − | 1.69025i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.90192 | − | 8.49038i | 0.161174 | − | 0.279162i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.6532 | − | 20.0070i | −1.13693 | − | 0.656410i | −0.191265 | − | 0.981538i | \(-0.561259\pi\) |
−0.945670 | + | 0.325129i | \(0.894592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.09808 | − | 4.09808i | 0.232630 | − | 0.134309i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.14162 | 0.298963 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.39230 | 0.241496 | 0.120748 | − | 0.992683i | \(-0.461471\pi\) | ||||
0.120748 | + | 0.992683i | \(0.461471\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.7379 | + | 24.0974i | −1.36062 | + | 0.785552i | −0.989706 | − | 0.143117i | \(-0.954288\pi\) |
−0.370910 | + | 0.928669i | \(0.620954\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.464102 | + | 0.267949i | 0.0151132 | + | 0.00872563i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.9203 | − | 37.9671i | 0.712314 | − | 1.23376i | −0.251672 | − | 0.967813i | \(-0.580980\pi\) |
0.963986 | − | 0.265952i | \(-0.0856863\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.6506 | + | 53.0885i | 0.994962 | + | 1.72332i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.1862i | 1.36654i | 0.730164 | + | 0.683272i | \(0.239444\pi\) | ||||
−0.730164 | + | 0.683272i | \(0.760556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 39.5167i | − | 1.27873i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.77955 | − | 3.08227i | −0.0574646 | − | 0.0995316i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3564 | − | 21.4019i | 0.398594 | − | 0.690385i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.1607 | + | 8.17569i | 0.455850 | + | 0.263185i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.2032 | − | 19.1699i | 1.06774 | − | 0.616462i | 0.140179 | − | 0.990126i | \(-0.455232\pi\) |
0.927564 | + | 0.373665i | \(0.121899\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.0523 | 1.60625 | 0.803127 | − | 0.595808i | \(-0.203168\pi\) | ||||
0.803127 | + | 0.595808i | \(0.203168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.07180 | 0.290828 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.3751 | − | 21.5785i | 1.19574 | − | 0.690359i | 0.236134 | − | 0.971720i | \(-0.424119\pi\) |
0.959602 | + | 0.281362i | \(0.0907861\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −68.2750 | − | 39.4186i | −2.18208 | − | 1.25982i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.7308 | + | 37.6389i | −0.693106 | + | 1.20050i | 0.277709 | + | 0.960665i | \(0.410425\pi\) |
−0.970815 | + | 0.239830i | \(0.922908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.42820 | − | 16.3301i | −0.300408 | − | 0.520321i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 12.3490i | − | 0.392675i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 26.4449i | − | 0.840049i | −0.907513 | − | 0.420024i | \(-0.862022\pi\) | ||
0.907513 | − | 0.420024i | \(-0.137978\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.72741 | + | 13.3843i | 0.244975 | + | 0.424310i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.59808 | − | 2.76795i | 0.0506116 | − | 0.0876618i | −0.839610 | − | 0.543190i | \(-0.817216\pi\) |
0.890221 | + | 0.455528i | \(0.150550\pi\) | |||||||
\(998\) | 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 | 2592.2.s.b.1727.4 | 8 | ||
3.2 | odd | 2 | inner | 2592.2.s.b.1727.1 | 8 | ||
4.3 | odd | 2 | 2592.2.s.f.1727.4 | 8 | |||
9.2 | odd | 6 | 2592.2.c.a.2591.2 | yes | 8 | ||
9.4 | even | 3 | 2592.2.s.f.863.1 | 8 | |||
9.5 | odd | 6 | 2592.2.s.f.863.4 | 8 | |||
9.7 | even | 3 | 2592.2.c.a.2591.8 | yes | 8 | ||
12.11 | even | 2 | 2592.2.s.f.1727.1 | 8 | |||
36.7 | odd | 6 | 2592.2.c.a.2591.7 | yes | 8 | ||
36.11 | even | 6 | 2592.2.c.a.2591.1 | ✓ | 8 | ||
36.23 | even | 6 | inner | 2592.2.s.b.863.4 | 8 | ||
36.31 | odd | 6 | inner | 2592.2.s.b.863.1 | 8 | ||
72.11 | even | 6 | 5184.2.c.i.5183.7 | 8 | |||
72.29 | odd | 6 | 5184.2.c.i.5183.8 | 8 | |||
72.43 | odd | 6 | 5184.2.c.i.5183.1 | 8 | |||
72.61 | even | 6 | 5184.2.c.i.5183.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2592.2.c.a.2591.1 | ✓ | 8 | 36.11 | even | 6 | ||
2592.2.c.a.2591.2 | yes | 8 | 9.2 | odd | 6 | ||
2592.2.c.a.2591.7 | yes | 8 | 36.7 | odd | 6 | ||
2592.2.c.a.2591.8 | yes | 8 | 9.7 | even | 3 | ||
2592.2.s.b.863.1 | 8 | 36.31 | odd | 6 | inner | ||
2592.2.s.b.863.4 | 8 | 36.23 | even | 6 | inner | ||
2592.2.s.b.1727.1 | 8 | 3.2 | odd | 2 | inner | ||
2592.2.s.b.1727.4 | 8 | 1.1 | even | 1 | trivial | ||
2592.2.s.f.863.1 | 8 | 9.4 | even | 3 | |||
2592.2.s.f.863.4 | 8 | 9.5 | odd | 6 | |||
2592.2.s.f.1727.1 | 8 | 12.11 | even | 2 | |||
2592.2.s.f.1727.4 | 8 | 4.3 | odd | 2 | |||
5184.2.c.i.5183.1 | 8 | 72.43 | odd | 6 | |||
5184.2.c.i.5183.2 | 8 | 72.61 | even | 6 | |||
5184.2.c.i.5183.7 | 8 | 72.11 | even | 6 | |||
5184.2.c.i.5183.8 | 8 | 72.29 | odd | 6 |