Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,3,Mod(209,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.209");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.l (of order \(4\), 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: | \(12.2071158433\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 433.17 | ||
Character | \(\chi\) | \(=\) | 448.433 |
Dual form | 448.3.l.b.209.17 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 1.00109 | + | 1.00109i | 0.333695 | + | 0.333695i | 0.853988 | − | 0.520293i | \(-0.174177\pi\) |
−0.520293 | + | 0.853988i | \(0.674177\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.03888 | + | 4.03888i | −0.807777 | + | 0.807777i | −0.984297 | − | 0.176520i | \(-0.943516\pi\) |
0.176520 | + | 0.984297i | \(0.443516\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.50171 | − | 2.59380i | 0.928815 | − | 0.370543i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 6.99566i | − | 0.777295i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.25649 | + | 6.25649i | 0.568772 | + | 0.568772i | 0.931784 | − | 0.363012i | \(-0.118252\pi\) |
−0.363012 | + | 0.931784i | \(0.618252\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.97013 | + | 4.97013i | 0.382318 | + | 0.382318i | 0.871936 | − | 0.489619i | \(-0.162864\pi\) |
−0.489619 | + | 0.871936i | \(0.662864\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.08654 | −0.539102 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.44402i | − | 0.320237i | −0.987098 | − | 0.160118i | \(-0.948812\pi\) | ||
0.987098 | − | 0.160118i | \(-0.0511876\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.3201 | + | 17.3201i | 0.911585 | + | 0.911585i | 0.996397 | − | 0.0848120i | \(-0.0270290\pi\) |
−0.0848120 | + | 0.996397i | \(0.527029\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.10538 | + | 3.91215i | 0.433590 | + | 0.186293i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.07936i | 0.351276i | 0.984455 | + | 0.175638i | \(0.0561989\pi\) | ||||
−0.984455 | + | 0.175638i | \(0.943801\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 7.62516i | − | 0.305006i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.0130 | − | 16.0130i | 0.593075 | − | 0.593075i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −27.3552 | + | 27.3552i | −0.943284 | + | 0.943284i | −0.998476 | − | 0.0551914i | \(-0.982423\pi\) |
0.0551914 | + | 0.998476i | \(0.482423\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 53.1316i | 1.71392i | 0.515382 | + | 0.856961i | \(0.327650\pi\) | ||||
−0.515382 | + | 0.856961i | \(0.672350\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.5266i | 0.379593i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −15.7836 | + | 36.7357i | −0.450959 | + | 1.04959i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.0922 | + | 13.0922i | 0.353842 | + | 0.353842i | 0.861537 | − | 0.507695i | \(-0.169502\pi\) |
−0.507695 | + | 0.861537i | \(0.669502\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.95105i | 0.255155i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.54538 | −0.0864728 | −0.0432364 | − | 0.999065i | \(-0.513767\pi\) | ||||
−0.0432364 | + | 0.999065i | \(0.513767\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −13.9574 | − | 13.9574i | −0.324590 | − | 0.324590i | 0.525935 | − | 0.850525i | \(-0.323715\pi\) |
−0.850525 | + | 0.525935i | \(0.823715\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 28.2546 | + | 28.2546i | 0.627881 | + | 0.627881i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 38.9511i | 0.828747i | 0.910107 | + | 0.414374i | \(0.135999\pi\) | ||||
−0.910107 | + | 0.414374i | \(0.864001\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 35.5444 | − | 33.7283i | 0.725396 | − | 0.688332i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.44993 | − | 5.44993i | 0.106861 | − | 0.106861i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −51.8947 | − | 51.8947i | −0.979144 | − | 0.979144i | 0.0206426 | − | 0.999787i | \(-0.493429\pi\) |
−0.999787 | + | 0.0206426i | \(0.993429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −50.5385 | −0.918882 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 34.6778i | 0.608383i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 56.4368 | − | 56.4368i | 0.956556 | − | 0.956556i | −0.0425390 | − | 0.999095i | \(-0.513545\pi\) |
0.999095 | + | 0.0425390i | \(0.0135447\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 84.3789 | + | 84.3789i | 1.38326 | + | 1.38326i | 0.838762 | + | 0.544499i | \(0.183280\pi\) |
0.544499 | + | 0.838762i | \(0.316720\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −18.1453 | − | 45.4837i | −0.288021 | − | 0.721964i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −40.1475 | −0.617654 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.603225 | + | 0.603225i | −0.00900335 | + | 0.00900335i | −0.711594 | − | 0.702591i | \(-0.752026\pi\) |
0.702591 | + | 0.711594i | \(0.252026\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.08813 | + | 8.08813i | −0.117219 | + | 0.117219i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 78.2455i | − | 1.10205i | −0.834489 | − | 0.551024i | \(-0.814237\pi\) | ||
0.834489 | − | 0.551024i | \(-0.185763\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 79.7314 | 1.09221 | 0.546106 | − | 0.837716i | \(-0.316110\pi\) | ||||
0.546106 | + | 0.837716i | \(0.316110\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.63344 | − | 7.63344i | 0.101779 | − | 0.101779i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 56.9060 | + | 24.4498i | 0.739039 | + | 0.317530i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 85.2911 | 1.07963 | 0.539817 | − | 0.841782i | \(-0.318493\pi\) | ||||
0.539817 | + | 0.841782i | \(0.318493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −30.9001 | −0.381483 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.96262 | − | 5.96262i | −0.0718387 | − | 0.0718387i | 0.670275 | − | 0.742113i | \(-0.266176\pi\) |
−0.742113 | + | 0.670275i | \(0.766176\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.9878 | + | 21.9878i | 0.258680 | + | 0.258680i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −54.7699 | −0.629539 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −163.829 | −1.84077 | −0.920385 | − | 0.391014i | \(-0.872125\pi\) | ||||
−0.920385 | + | 0.391014i | \(0.872125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 45.2058 | + | 19.4228i | 0.496767 | + | 0.213437i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −53.1892 | + | 53.1892i | −0.571927 | + | 0.571927i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −139.908 | −1.47271 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 89.6393i | − | 0.924117i | −0.886850 | − | 0.462058i | \(-0.847111\pi\) | ||
0.886850 | − | 0.462058i | \(-0.152889\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43.7683 | − | 43.7683i | 0.442104 | − | 0.442104i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −50.7141 | + | 50.7141i | −0.502120 | + | 0.502120i | −0.912096 | − | 0.409976i | \(-0.865537\pi\) |
0.409976 | + | 0.912096i | \(0.365537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −77.0434 | −0.747994 | −0.373997 | − | 0.927430i | \(-0.622013\pi\) | ||||
−0.373997 | + | 0.927430i | \(0.622013\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −52.5763 | + | 20.9749i | −0.500727 | + | 0.199761i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 140.533 | + | 140.533i | 1.31339 | + | 1.31339i | 0.918899 | + | 0.394494i | \(0.129080\pi\) |
0.394494 | + | 0.918899i | \(0.370920\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 46.2295 | − | 46.2295i | 0.424124 | − | 0.424124i | −0.462497 | − | 0.886621i | \(-0.653046\pi\) |
0.886621 | + | 0.462497i | \(0.153046\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.2127i | 0.236151i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 163.269 | 1.44486 | 0.722431 | − | 0.691443i | \(-0.243025\pi\) | ||||
0.722431 | + | 0.691443i | \(0.243025\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −32.6316 | − | 32.6316i | −0.283753 | − | 0.283753i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 34.7693 | − | 34.7693i | 0.297173 | − | 0.297173i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.1207 | − | 35.3954i | −0.118661 | − | 0.297441i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 42.7126i | − | 0.352997i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.54923 | − | 3.54923i | −0.0288556 | − | 0.0288556i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −70.1750 | − | 70.1750i | −0.561400 | − | 0.561400i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −31.3100 | −0.246535 | −0.123268 | − | 0.992373i | \(-0.539337\pi\) | ||||
−0.123268 | + | 0.992373i | \(0.539337\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 27.9450i | − | 0.216628i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.8179 | − | 21.8179i | −0.166549 | − | 0.166549i | 0.618912 | − | 0.785461i | \(-0.287574\pi\) |
−0.785461 | + | 0.618912i | \(0.787574\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 157.535 | + | 67.6854i | 1.18448 | + | 0.508913i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 129.349i | 0.958144i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 125.561i | − | 0.916503i | −0.888823 | − | 0.458251i | \(-0.848476\pi\) | ||
0.888823 | − | 0.458251i | \(-0.151524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.99666 | + | 9.99666i | −0.0719184 | + | 0.0719184i | −0.742151 | − | 0.670233i | \(-0.766194\pi\) |
0.670233 | + | 0.742151i | \(0.266194\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −38.9934 | + | 38.9934i | −0.276549 | + | 0.276549i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 62.1911i | 0.434903i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 220.969i | − | 1.52393i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 69.3479 | + | 1.81808i | 0.471754 | + | 0.0123679i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −109.367 | − | 109.367i | −0.734004 | − | 0.734004i | 0.237406 | − | 0.971410i | \(-0.423703\pi\) |
−0.971410 | + | 0.237406i | \(0.923703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 212.815i | − | 1.40937i | −0.709519 | − | 0.704686i | \(-0.751088\pi\) | ||
0.709519 | − | 0.704686i | \(-0.248912\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −38.0845 | −0.248918 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −214.592 | − | 214.592i | −1.38447 | − | 1.38447i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −159.296 | − | 159.296i | −1.01463 | − | 1.01463i | −0.999891 | − | 0.0147347i | \(-0.995310\pi\) |
−0.0147347 | − | 0.999891i | \(-0.504690\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 103.902i | − | 0.653472i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.9562 | + | 52.5296i | 0.130163 | + | 0.326271i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.8052 | − | 12.8052i | 0.0785594 | − | 0.0785594i | −0.666735 | − | 0.745295i | \(-0.732309\pi\) |
0.745295 | + | 0.666735i | \(0.232309\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −50.5934 | − | 50.5934i | −0.306626 | − | 0.306626i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −29.3992 | −0.176043 | −0.0880214 | − | 0.996119i | \(-0.528054\pi\) | ||||
−0.0880214 | + | 0.996119i | \(0.528054\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 119.596i | − | 0.707667i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 121.166 | − | 121.166i | 0.708570 | − | 0.708570i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.6282 | − | 21.6282i | −0.125018 | − | 0.125018i | 0.641829 | − | 0.766848i | \(-0.278176\pi\) |
−0.766848 | + | 0.641829i | \(0.778176\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.7781 | − | 49.5765i | −0.113018 | − | 0.283295i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 112.996 | 0.638396 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −42.8249 | + | 42.8249i | −0.239245 | + | 0.239245i | −0.816538 | − | 0.577292i | \(-0.804109\pi\) |
0.577292 | + | 0.816538i | \(0.304109\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −148.030 | + | 148.030i | −0.817848 | + | 0.817848i | −0.985796 | − | 0.167948i | \(-0.946286\pi\) |
0.167948 | + | 0.985796i | \(0.446286\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 168.941i | 0.923175i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −105.755 | −0.571651 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.0605 | − | 34.0605i | 0.182142 | − | 0.182142i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 62.5774 | − | 145.647i | 0.331097 | − | 0.770617i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 266.000 | 1.39267 | 0.696336 | − | 0.717716i | \(-0.254813\pi\) | ||||
0.696336 | + | 0.717716i | \(0.254813\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −287.377 | −1.48900 | −0.744499 | − | 0.667624i | \(-0.767312\pi\) | ||||
−0.744499 | + | 0.667624i | \(0.767312\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −40.1911 | − | 40.1911i | −0.206108 | − | 0.206108i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.88931 | − | 7.88931i | −0.0400473 | − | 0.0400473i | 0.686800 | − | 0.726847i | \(-0.259015\pi\) |
−0.726847 | + | 0.686800i | \(0.759015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 55.3752 | 0.278267 | 0.139134 | − | 0.990274i | \(-0.455568\pi\) | ||||
0.139134 | + | 0.990274i | \(0.455568\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.20776 | −0.00600875 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −106.902 | + | 248.810i | −0.526609 | + | 1.22566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.3194 | − | 14.3194i | 0.0698507 | − | 0.0698507i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 56.5204 | 0.273045 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 216.726i | 1.03697i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −120.578 | + | 120.578i | −0.571461 | + | 0.571461i | −0.932537 | − | 0.361075i | \(-0.882410\pi\) |
0.361075 | + | 0.932537i | \(0.382410\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 78.3304 | − | 78.3304i | 0.367748 | − | 0.367748i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 112.744 | 0.524392 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 137.813 | + | 345.446i | 0.635082 | + | 1.59192i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 79.8180 | + | 79.8180i | 0.364466 | + | 0.364466i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.0575 | − | 27.0575i | 0.122432 | − | 0.122432i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 120.836i | − | 0.541865i | −0.962598 | − | 0.270933i | \(-0.912668\pi\) | ||
0.962598 | − | 0.270933i | \(-0.0873321\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −53.3430 | −0.237080 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −57.4724 | − | 57.4724i | −0.253183 | − | 0.253183i | 0.569092 | − | 0.822274i | \(-0.307295\pi\) |
−0.822274 | + | 0.569092i | \(0.807295\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 175.590 | − | 175.590i | 0.766771 | − | 0.766771i | −0.210766 | − | 0.977537i | \(-0.567596\pi\) |
0.977537 | + | 0.210766i | \(0.0675958\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 32.4914 | + | 81.4441i | 0.140656 | + | 0.352572i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 184.061i | 0.789959i | 0.918690 | + | 0.394980i | \(0.129248\pi\) | ||||
−0.918690 | + | 0.394980i | \(0.870752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −157.319 | − | 157.319i | −0.669443 | − | 0.669443i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 85.3837 | + | 85.3837i | 0.360269 | + | 0.360269i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 33.1847 | 0.138848 | 0.0694240 | − | 0.997587i | \(-0.477884\pi\) | ||||
0.0694240 | + | 0.997587i | \(0.477884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 55.7768i | 0.231439i | 0.993282 | + | 0.115719i | \(0.0369173\pi\) | ||||
−0.993282 | + | 0.115719i | \(0.963083\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −175.051 | − | 175.051i | −0.720374 | − | 0.720374i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.33506 | + | 279.784i | −0.0299390 | + | 1.14198i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 172.166i | 0.697030i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 11.9382i | − | 0.0479445i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −181.168 | + | 181.168i | −0.721785 | + | 0.721785i | −0.968969 | − | 0.247184i | \(-0.920495\pi\) |
0.247184 | + | 0.968969i | \(0.420495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −50.5484 | + | 50.5484i | −0.199796 | + | 0.199796i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 44.0233i | 0.172640i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 363.112i | 1.41289i | 0.707770 | + | 0.706443i | \(0.249701\pi\) | ||||
−0.707770 | + | 0.706443i | \(0.750299\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 119.080 | + | 51.1629i | 0.459768 | + | 0.197540i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 191.368 | + | 191.368i | 0.733210 | + | 0.733210i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 421.236i | − | 1.60166i | −0.598892 | − | 0.800829i | \(-0.704392\pi\) | ||
0.598892 | − | 0.800829i | \(-0.295608\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 419.193 | 1.58186 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −164.006 | − | 164.006i | −0.614256 | − | 0.614256i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 171.203 | + | 171.203i | 0.636441 | + | 0.636441i | 0.949676 | − | 0.313235i | \(-0.101413\pi\) |
−0.313235 | + | 0.949676i | \(0.601413\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.9792i | 0.0589637i | 0.999565 | + | 0.0294819i | \(0.00938573\pi\) | ||||
−0.999565 | + | 0.0294819i | \(0.990614\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.8110 | + | 64.6988i | 0.0945459 | + | 0.236992i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 47.7068 | − | 47.7068i | 0.173479 | − | 0.173479i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −201.173 | − | 201.173i | −0.726256 | − | 0.726256i | 0.243615 | − | 0.969872i | \(-0.421667\pi\) |
−0.969872 | + | 0.243615i | \(0.921667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 371.690 | 1.33222 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 364.700i | − | 1.29786i | −0.760846 | − | 0.648932i | \(-0.775216\pi\) | ||
0.760846 | − | 0.648932i | \(-0.224784\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −311.354 | + | 311.354i | −1.10019 | + | 1.10019i | −0.105806 | + | 0.994387i | \(0.533742\pi\) |
−0.994387 | + | 0.105806i | \(0.966258\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −140.060 | − | 140.060i | −0.491438 | − | 0.491438i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.0511 | + | 9.19602i | −0.0803173 | + | 0.0320419i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 259.363 | 0.897449 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 89.7366 | − | 89.7366i | 0.308373 | − | 0.308373i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 249.211 | − | 249.211i | 0.850550 | − | 0.850550i | −0.139651 | − | 0.990201i | \(-0.544598\pi\) |
0.990201 | + | 0.139651i | \(0.0445980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 455.883i | 1.54537i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 200.371 | 0.674649 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −40.1554 | + | 40.1554i | −0.134299 | + | 0.134299i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −126.949 | − | 54.5440i | −0.421758 | − | 0.181209i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −101.538 | −0.335110 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −681.593 | −2.23473 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 265.892 | + | 265.892i | 0.866098 | + | 0.866098i | 0.992038 | − | 0.125940i | \(-0.0401947\pi\) |
−0.125940 | + | 0.992038i | \(0.540195\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −77.1270 | − | 77.1270i | −0.249602 | − | 0.249602i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 115.392 | 0.371035 | 0.185518 | − | 0.982641i | \(-0.440604\pi\) | ||||
0.185518 | + | 0.982641i | \(0.440604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 334.318 | 1.06811 | 0.534054 | − | 0.845450i | \(-0.320668\pi\) | ||||
0.534054 | + | 0.845450i | \(0.320668\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 256.990 | + | 110.416i | 0.815842 | + | 0.350528i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.5251 | − | 26.5251i | 0.0836755 | − | 0.0836755i | −0.664030 | − | 0.747706i | \(-0.731155\pi\) |
0.747706 | + | 0.664030i | \(0.231155\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −342.296 | −1.07303 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 281.371i | 0.876545i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 94.2911 | − | 94.2911i | 0.291923 | − | 0.291923i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 37.8980 | − | 37.8980i | 0.116609 | − | 0.116609i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 92.5593 | 0.283056 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 101.031 | + | 253.249i | 0.307087 | + | 0.769753i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.5611 | − | 33.5611i | −0.101393 | − | 0.101393i | 0.654591 | − | 0.755984i | \(-0.272841\pi\) |
−0.755984 | + | 0.654591i | \(0.772841\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 91.5882 | − | 91.5882i | 0.275040 | − | 0.275040i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.87271i | − | 0.0145454i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 402.236 | 1.19358 | 0.596789 | − | 0.802398i | \(-0.296443\pi\) | ||||
0.596789 | + | 0.802398i | \(0.296443\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 163.447 | + | 163.447i | 0.482144 | + | 0.482144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −332.417 | + | 332.417i | −0.974830 | + | 0.974830i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 143.615 | − | 311.486i | 0.418702 | − | 0.908124i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 65.3340i | − | 0.189374i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 66.0997 | + | 66.0997i | 0.190489 | + | 0.190489i | 0.795907 | − | 0.605418i | \(-0.206994\pi\) |
−0.605418 | + | 0.795907i | \(0.706994\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −224.860 | − | 224.860i | −0.644299 | − | 0.644299i | 0.307310 | − | 0.951609i | \(-0.400571\pi\) |
−0.951609 | + | 0.307310i | \(0.900571\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 159.174 | 0.453486 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 278.155i | 0.787974i | 0.919116 | + | 0.393987i | \(0.128905\pi\) | ||||
−0.919116 | + | 0.393987i | \(0.871095\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 316.024 | + | 316.024i | 0.890209 | + | 0.890209i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.2978 | − | 49.5699i | 0.0596578 | − | 0.138851i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 473.744i | 1.31962i | 0.751432 | + | 0.659810i | \(0.229363\pi\) | ||||
−0.751432 | + | 0.659810i | \(0.770637\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 238.973i | 0.661974i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 42.7590 | − | 42.7590i | 0.117793 | − | 0.117793i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −322.026 | + | 322.026i | −0.882263 | + | 0.882263i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 717.099i | − | 1.95395i | −0.213360 | − | 0.976974i | \(-0.568441\pi\) | ||
0.213360 | − | 0.976974i | \(-0.431559\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.8023i | 0.0672149i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −472.008 | − | 202.799i | −1.27226 | − | 0.546629i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 226.840 | + | 226.840i | 0.608150 | + | 0.608150i | 0.942462 | − | 0.334312i | \(-0.108504\pi\) |
−0.334312 | + | 0.942462i | \(0.608504\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 140.502i | − | 0.374673i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −271.918 | −0.721268 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −181.444 | − | 181.444i | −0.478744 | − | 0.478744i | 0.425986 | − | 0.904730i | \(-0.359927\pi\) |
−0.904730 | + | 0.425986i | \(0.859927\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −31.3440 | − | 31.3440i | −0.0822677 | − | 0.0822677i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 453.443i | 1.18393i | 0.805965 | + | 0.591963i | \(0.201647\pi\) | ||||
−0.805965 | + | 0.591963i | \(0.798353\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −328.586 | + | 131.087i | −0.853471 | + | 0.340485i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −97.6408 | + | 97.6408i | −0.252302 | + | 0.252302i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.485255 | − | 0.485255i | −0.00124744 | − | 0.00124744i | 0.706483 | − | 0.707730i | \(-0.250281\pi\) |
−0.707730 | + | 0.706483i | \(0.750281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.9842 | 0.112492 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 43.6832i | − | 0.111153i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −344.481 | + | 344.481i | −0.872103 | + | 0.872103i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 113.596 | + | 113.596i | 0.286135 | + | 0.286135i | 0.835550 | − | 0.549415i | \(-0.185149\pi\) |
−0.549415 | + | 0.835550i | \(0.685149\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 89.9474 | + | 225.465i | 0.225432 | + | 0.565075i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −115.312 | −0.287561 | −0.143781 | − | 0.989610i | \(-0.545926\pi\) | ||||
−0.143781 | + | 0.989610i | \(0.545926\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −264.071 | + | 264.071i | −0.655262 | + | 0.655262i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 124.802 | − | 124.802i | 0.308153 | − | 0.308153i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 163.822i | 0.402511i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −498.247 | −1.21821 | −0.609104 | − | 0.793091i | \(-0.708471\pi\) | ||||
−0.609104 | + | 0.793091i | \(0.708471\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 125.697 | − | 125.697i | 0.305832 | − | 0.305832i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 220.550 | − | 513.321i | 0.534019 | − | 1.24291i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 48.1646 | 0.116059 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.0150 | −0.0479977 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −63.7497 | − | 63.7497i | −0.152147 | − | 0.152147i | 0.626929 | − | 0.779076i | \(-0.284312\pi\) |
−0.779076 | + | 0.626929i | \(0.784312\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −454.190 | − | 454.190i | −1.07884 | − | 1.07884i | −0.996614 | − | 0.0822213i | \(-0.973799\pi\) |
−0.0822213 | − | 0.996614i | \(-0.526201\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 272.489 | 0.644181 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −41.5115 | −0.0976742 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 767.469 | + | 329.745i | 1.79735 | + | 0.772236i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −62.2586 | + | 62.2586i | −0.145125 | + | 0.145125i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −726.777 | −1.68626 | −0.843128 | − | 0.537712i | \(-0.819289\pi\) | ||||
−0.843128 | + | 0.537712i | \(0.819289\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 797.491i | − | 1.84178i | −0.389822 | − | 0.920890i | \(-0.627464\pi\) | ||
0.389822 | − | 0.920890i | \(-0.372536\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 221.209 | − | 221.209i | 0.508527 | − | 0.508527i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −139.935 | + | 139.935i | −0.320218 | + | 0.320218i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 238.672 | 0.543671 | 0.271835 | − | 0.962344i | \(-0.412369\pi\) | ||||
0.271835 | + | 0.962344i | \(0.412369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −235.951 | − | 248.656i | −0.535037 | − | 0.563846i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −340.379 | − | 340.379i | −0.768351 | − | 0.768351i | 0.209466 | − | 0.977816i | \(-0.432828\pi\) |
−0.977816 | + | 0.209466i | \(0.932828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 661.684 | − | 661.684i | 1.48693 | − | 1.48693i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 218.971i | − | 0.489867i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 260.491 | 0.580159 | 0.290079 | − | 0.957003i | \(-0.406318\pi\) | ||||
0.290079 | + | 0.957003i | \(0.406318\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.1817 | − | 22.1817i | −0.0491833 | − | 0.0491833i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 213.046 | − | 213.046i | 0.470301 | − | 0.470301i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −261.027 | + | 104.135i | −0.573687 | + | 0.228868i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 599.916i | 1.31273i | 0.754445 | + | 0.656363i | \(0.227906\pi\) | ||||
−0.754445 | + | 0.656363i | \(0.772094\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −87.1752 | − | 87.1752i | −0.189924 | − | 0.189924i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 140.443 | + | 140.443i | 0.304648 | + | 0.304648i | 0.842829 | − | 0.538181i | \(-0.180888\pi\) |
−0.538181 | + | 0.842829i | \(0.680888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 830.793 | 1.79437 | 0.897185 | − | 0.441655i | \(-0.145608\pi\) | ||||
0.897185 | + | 0.441655i | \(0.145608\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 429.650i | − | 0.923979i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −198.168 | − | 198.168i | −0.424343 | − | 0.424343i | 0.462353 | − | 0.886696i | \(-0.347005\pi\) |
−0.886696 | + | 0.462353i | \(0.847005\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.35735 | + | 5.48664i | −0.00502632 | + | 0.0116986i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 318.938i | − | 0.677152i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 174.648i | − | 0.369235i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 132.069 | − | 132.069i | 0.278039 | − | 0.278039i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −363.037 | + | 363.037i | −0.761084 | + | 0.761084i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 309.380i | 0.645887i | 0.946418 | + | 0.322944i | \(0.104672\pi\) | ||||
−0.946418 | + | 0.322944i | \(0.895328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 130.139i | 0.270560i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −31.6076 | + | 73.5656i | −0.0654402 | + | 0.152310i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 362.043 | + | 362.043i | 0.746480 | + | 0.746480i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 376.712i | − | 0.773537i | −0.922177 | − | 0.386768i | \(-0.873591\pi\) | ||
0.922177 | − | 0.386768i | \(-0.126409\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.6382 | 0.0524298 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −404.340 | − | 404.340i | −0.823502 | − | 0.823502i | 0.163106 | − | 0.986608i | \(-0.447849\pi\) |
−0.986608 | + | 0.163106i | \(0.947849\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 148.923 | + | 148.923i | 0.302074 | + | 0.302074i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 353.550i | 0.714242i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −202.953 | − | 508.729i | −0.408357 | − | 1.02360i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 134.474 | − | 134.474i | 0.269487 | − | 0.269487i | −0.559406 | − | 0.828893i | \(-0.688971\pi\) |
0.828893 | + | 0.559406i | \(0.188971\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.4311 | − | 29.4311i | −0.0587446 | − | 0.0587446i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −550.735 | −1.09490 | −0.547451 | − | 0.836838i | \(-0.684402\pi\) | ||||
−0.547451 | + | 0.836838i | \(0.684402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 409.657i | − | 0.811202i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 119.725 | − | 119.725i | 0.236145 | − | 0.236145i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −244.631 | − | 244.631i | −0.480610 | − | 0.480610i | 0.424716 | − | 0.905327i | \(-0.360374\pi\) |
−0.905327 | + | 0.424716i | \(0.860374\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 518.390 | − | 206.807i | 1.01446 | − | 0.404711i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 554.695 | 1.08128 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 311.169 | − | 311.169i | 0.604212 | − | 0.604212i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −243.697 | + | 243.697i | −0.471368 | + | 0.471368i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 43.3034i | − | 0.0834361i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −244.953 | −0.470160 | −0.235080 | − | 0.971976i | \(-0.575535\pi\) | ||||
−0.235080 | + | 0.971976i | \(0.575535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −113.030 | + | 113.030i | −0.216118 | + | 0.216118i | −0.806860 | − | 0.590742i | \(-0.798835\pi\) |
0.590742 | + | 0.806860i | \(0.298835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 29.8307 | − | 69.4300i | 0.0568205 | − | 0.132248i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 289.249 | 0.548860 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 463.724 | 0.876605 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −394.812 | − | 394.812i | −0.743526 | − | 0.743526i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.6210 | − | 17.6210i | −0.0330601 | − | 0.0330601i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1135.19 | −2.12186 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −85.7428 | −0.159670 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 433.404 | + | 11.3625i | 0.804089 | + | 0.0210807i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −282.140 | + | 282.140i | −0.521515 | + | 0.521515i | −0.918029 | − | 0.396514i | \(-0.870220\pi\) |
0.396514 | + | 0.918029i | \(0.370220\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −296.382 | −0.545824 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 373.431i | 0.685195i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −152.625 | + | 152.625i | −0.279023 | + | 0.279023i | −0.832719 | − | 0.553696i | \(-0.813217\pi\) |
0.553696 | + | 0.832719i | \(0.313217\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 590.286 | − | 590.286i | 1.07520 | − | 1.07520i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −947.592 | −1.71977 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 554.538 | − | 221.228i | 1.00278 | − | 0.400051i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −105.870 | − | 105.870i | −0.190757 | − | 0.190757i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −55.7663 | + | 55.7663i | −0.100119 | + | 0.100119i | −0.755392 | − | 0.655273i | \(-0.772554\pi\) |
0.655273 | + | 0.755392i | \(0.272554\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 138.740i | − | 0.248193i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 68.1949 | 0.121560 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 101.194 | + | 101.194i | 0.179741 | + | 0.179741i | 0.791243 | − | 0.611502i | \(-0.209434\pi\) |
−0.611502 | + | 0.791243i | \(0.709434\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −659.426 | + | 659.426i | −1.16713 | + | 1.16713i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −200.903 | + | 80.1487i | −0.354327 | + | 0.141356i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 754.689i | − | 1.32634i | −0.748468 | − | 0.663171i | \(-0.769210\pi\) | ||
0.748468 | − | 0.663171i | \(-0.230790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 595.857 | + | 595.857i | 1.04353 | + | 1.04353i | 0.999008 | + | 0.0445235i | \(0.0141770\pi\) |
0.0445235 | + | 0.999008i | \(0.485823\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 266.289 | + | 266.289i | 0.464728 | + | 0.464728i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 61.6064 | 0.107142 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 118.627i | − | 0.205593i | −0.994702 | − | 0.102796i | \(-0.967221\pi\) | ||
0.994702 | − | 0.102796i | \(-0.0327790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −287.689 | − | 287.689i | −0.496872 | − | 0.496872i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −54.2330 | − | 23.3013i | −0.0933443 | − | 0.0401056i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 649.357i | − | 1.11382i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 280.858i | 0.480100i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 386.365 | − | 386.365i | 0.658203 | − | 0.658203i | −0.296751 | − | 0.954955i | \(-0.595903\pi\) |
0.954955 | + | 0.296751i | \(0.0959032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −920.245 | + | 920.245i | −1.56238 | + | 1.56238i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 15.7958i | − | 0.0267272i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 475.843i | − | 0.802433i | −0.915983 | − | 0.401216i | \(-0.868588\pi\) | ||
0.915983 | − | 0.401216i | \(-0.131412\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 199.990 | + | 85.9261i | 0.336118 | + | 0.144414i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 55.4353 | + | 55.4353i | 0.0928564 | + | 0.0928564i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 38.9554i | − | 0.0650341i | −0.999471 | − | 0.0325171i | \(-0.989648\pi\) | ||
0.999471 | − | 0.0325171i | \(-0.0103523\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −646.318 | −1.07540 | −0.537702 | − | 0.843135i | \(-0.680708\pi\) | ||||
−0.537702 | + | 0.843135i | \(0.680708\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.21995 | + | 4.21995i | 0.00699826 | + | 0.00699826i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 172.511 | + | 172.511i | 0.285143 | + | 0.285143i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1192.00i | − | 1.96376i | −0.189505 | − | 0.981880i | \(-0.560688\pi\) | ||
0.189505 | − | 0.981880i | \(-0.439312\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −356.098 | + | 142.062i | −0.584725 | + | 0.233271i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −193.592 | + | 193.592i | −0.316845 | + | 0.316845i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 48.8446 | + | 48.8446i | 0.0796812 | + | 0.0796812i | 0.745824 | − | 0.666143i | \(-0.232056\pi\) |
−0.666143 | + | 0.745824i | \(0.732056\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.6699 | 0.0466177 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 225.471i | − | 0.365432i | −0.983166 | − | 0.182716i | \(-0.941511\pi\) | ||
0.983166 | − | 0.182716i | \(-0.0584888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 801.515 | − | 801.515i | 1.29485 | − | 1.29485i | 0.363108 | − | 0.931747i | \(-0.381716\pi\) |
0.931747 | − | 0.363108i | \(-0.118284\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 129.375 | + | 129.375i | 0.208333 | + | 0.208333i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1065.16 | + | 424.939i | −1.70974 | + | 0.682084i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 757.486 | 1.21198 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −216.962 | + | 216.962i | −0.346031 | + | 0.346031i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 71.2740 | − | 71.2740i | 0.113313 | − | 0.113313i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 826.708i | 1.31016i | 0.755561 | + | 0.655078i | \(0.227364\pi\) | ||||
−0.755561 | + | 0.655078i | \(0.772636\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −241.419 | −0.381388 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 126.457 | − | 126.457i | 0.199146 | − | 0.199146i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 344.294 | + | 9.02631i | 0.540493 | + | 0.0141700i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −547.378 | −0.856617 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −616.538 | −0.961838 | −0.480919 | − | 0.876765i | \(-0.659697\pi\) | ||||
−0.480919 | + | 0.876765i | \(0.659697\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −266.078 | − | 266.078i | −0.413807 | − | 0.413807i | 0.469256 | − | 0.883062i | \(-0.344522\pi\) |
−0.883062 | + | 0.469256i | \(0.844522\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 112.867 | + | 112.867i | 0.174987 | + | 0.174987i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 856.520 | 1.32383 | 0.661917 | − | 0.749577i | \(-0.269743\pi\) | ||||
0.661917 | + | 0.749577i | \(0.269743\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 706.193 | 1.08812 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −207.858 | + | 483.783i | −0.319291 | + | 0.743138i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.2597 | + | 36.2597i | −0.0555279 | + | 0.0555279i | −0.734325 | − | 0.678798i | \(-0.762501\pi\) |
0.678798 | + | 0.734325i | \(0.262501\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 176.240 | 0.269069 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 557.773i | − | 0.848970i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 875.515 | − | 875.515i | 1.32855 | − | 1.32855i | 0.421917 | − | 0.906634i | \(-0.361357\pi\) |
0.906634 | − | 0.421917i | \(-0.138643\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −837.005 | + | 837.005i | −1.26627 | + | 1.26627i | −0.318271 | + | 0.948000i | \(0.603102\pi\) |
−0.948000 | + | 0.318271i | \(0.896898\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 54.1737 | 0.0817100 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −909.640 | + | 362.893i | −1.36788 | + | 0.545704i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −221.013 | − | 221.013i | −0.331354 | − | 0.331354i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 120.967 | − | 120.967i | 0.180818 | − | 0.180818i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1055.83i | 1.57352i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 104.129 | 0.154723 | 0.0773615 | − | 0.997003i | \(-0.475350\pi\) | ||||
0.0773615 | + | 0.997003i | \(0.475350\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −122.102 | − | 122.102i | −0.180892 | − | 0.180892i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 465.462 | − | 465.462i | 0.687536 | − | 0.687536i | −0.274151 | − | 0.961687i | \(-0.588397\pi\) |
0.961687 | + | 0.274151i | \(0.0883968\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −232.507 | − | 582.809i | −0.342425 | − | 0.858334i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 115.070i | − | 0.168972i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 616.133 | + | 616.133i | 0.902098 | + | 0.902098i | 0.995617 | − | 0.0935198i | \(-0.0298118\pi\) |
−0.0935198 | + | 0.995617i | \(0.529812\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 507.126 | + | 507.126i | 0.740329 | + | 0.740329i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 351.562 | 0.511735 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 515.846i | − | 0.748688i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 512.637 | + | 512.637i | 0.741878 | + | 0.741878i | 0.972939 | − | 0.231061i | \(-0.0742198\pi\) |
−0.231061 | + | 0.972939i | \(0.574220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 171.042 | − | 398.095i | 0.246814 | − | 0.574451i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 80.7507i | − | 0.116188i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.3012i | 0.0276918i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −184.260 | + | 184.260i | −0.263606 | + | 0.263606i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.7578 | + | 11.7578i | −0.0167729 | + | 0.0167729i | −0.715443 | − | 0.698671i | \(-0.753775\pi\) |
0.698671 | + | 0.715443i | \(0.253775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 453.515i | 0.645114i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 314.980i | − | 0.446780i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −198.186 | + | 461.271i | −0.280320 | + | 0.652434i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −400.746 | − | 400.746i | −0.565228 | − | 0.565228i | 0.365560 | − | 0.930788i | \(-0.380877\pi\) |
−0.930788 | + | 0.365560i | \(0.880877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 596.667i | − | 0.839194i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −429.269 | −0.602060 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −251.183 | − | 251.183i | −0.351305 | − | 0.351305i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.2207 | + | 33.2207i | 0.0463329 | + | 0.0463329i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 125.701i | 0.174827i | 0.996172 | + | 0.0874135i | \(0.0278601\pi\) | ||||
−0.996172 | + | 0.0874135i | \(0.972140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −500.914 | + | 199.835i | −0.694748 | + | 0.277164i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −55.8373 | + | 55.8373i | −0.0772300 | + | 0.0772300i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 208.588 | + | 208.588i | 0.287708 | + | 0.287708i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −216.647 | −0.298001 | −0.149001 | − | 0.988837i | \(-0.547606\pi\) | ||||
−0.149001 | + | 0.988837i | \(0.547606\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 72.3809i | − | 0.0992879i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −75.9842 | + | 75.9842i | −0.103945 | + | 0.103945i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −71.7298 | − | 71.7298i | −0.0978579 | − | 0.0978579i | 0.656483 | − | 0.754341i | \(-0.272043\pi\) |
−0.754341 | + | 0.656483i | \(0.772043\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −287.431 | + | 272.745i | −0.391063 | + | 0.371082i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.54814 | −0.0102417 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −532.903 | + | 532.903i | −0.721113 | + | 0.721113i | −0.968832 | − | 0.247719i | \(-0.920319\pi\) |
0.247719 | + | 0.968832i | \(0.420319\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −172.353 | + | 172.353i | −0.232595 | + | 0.232595i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 579.975i | 0.780585i | 0.920691 | + | 0.390292i | \(0.127626\pi\) | ||||
−0.920691 | + | 0.390292i | \(0.872374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 883.438 | 1.18582 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −41.7124 | + | 41.7124i | −0.0558399 | + | 0.0558399i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1278.22 | + | 549.190i | 1.70657 | + | 0.733230i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −666.251 | −0.887151 | −0.443576 | − | 0.896237i | \(-0.646290\pi\) | ||||
−0.443576 | + | 0.896237i | \(0.646290\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −362.729 | −0.481712 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 859.536 | + | 859.536i | 1.13846 | + | 1.13846i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −148.454 | − | 148.454i | −0.196108 | − | 0.196108i | 0.602221 | − | 0.798329i | \(-0.294282\pi\) |
−0.798329 | + | 0.602221i | \(0.794282\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −101.207 | −0.133342 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −714.400 | −0.938765 | −0.469382 | − | 0.882995i | \(-0.655523\pi\) | ||||
−0.469382 | + | 0.882995i | \(0.655523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 180.660 | − | 420.481i | 0.236776 | − | 0.551089i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 153.819 | − | 153.819i | 0.201070 | − | 0.201070i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 560.996 | 0.731416 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 175.219i | 0.227854i | 0.993489 | + | 0.113927i | \(0.0363429\pi\) | ||||
−0.993489 | + | 0.113927i | \(0.963657\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −363.506 | + | 363.506i | −0.471473 | + | 0.471473i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 385.461 | − | 385.461i | 0.498655 | − | 0.498655i | −0.412364 | − | 0.911019i | \(-0.635297\pi\) |
0.911019 | + | 0.412364i | \(0.135297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 405.137 | 0.522757 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 67.9906 | + | 170.428i | 0.0875040 | + | 0.219340i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −61.4065 | − | 61.4065i | −0.0788273 | − | 0.0788273i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 489.542 | − | 489.542i | 0.626814 | − | 0.626814i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 876.080i | 1.11888i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1286.76 | 1.63918 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 661.030 | + | 661.030i | 0.839937 | + | 0.839937i | 0.988850 | − | 0.148913i | \(-0.0475775\pi\) |
−0.148913 | + | 0.988850i | \(0.547578\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 421.694 | − | 421.694i | 0.534466 | − | 0.534466i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1061.53 | − | 423.489i | 1.34201 | − | 0.535384i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 838.748i | 1.05769i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 419.648 | + | 419.648i | 0.527859 | + | 0.527859i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −644.542 | − | 644.542i | −0.808711 | − | 0.808711i | 0.175728 | − | 0.984439i | \(-0.443772\pi\) |
−0.984439 | + | 0.175728i | \(0.943772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 212.051 | 0.265395 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1146.09i | 1.43082i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 498.839 | + | 498.839i | 0.621219 | + | 0.621219i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −296.801 | − | 127.521i | −0.368697 | − | 0.158411i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 342.777i | 0.424755i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1222.06i | 1.51058i | 0.655388 | + | 0.755292i | \(0.272505\pi\) | ||||
−0.655388 | + | 0.755292i | \(0.727495\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −236.769 | + | 236.769i | −0.291947 | + | 0.291947i | −0.837849 | − | 0.545902i | \(-0.816187\pi\) |
0.545902 | + | 0.837849i | \(0.316187\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.9965 | + | 15.9965i | −0.0196759 | + | 0.0196759i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 103.437i | 0.126917i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 483.486i | − | 0.591782i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 135.875 | − | 316.244i | 0.165904 | − | 0.386135i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −927.111 | − | 927.111i | −1.12925 | − | 1.12925i | −0.990300 | − | 0.138946i | \(-0.955629\pi\) |
−0.138946 | − | 0.990300i | \(-0.544371\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 386.940i | 0.470158i | 0.971976 | + | 0.235079i | \(0.0755348\pi\) | ||||
−0.971976 | + | 0.235079i | \(0.924465\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 95.5171 | 0.115778 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −431.979 | − | 431.979i | −0.522345 | − | 0.522345i | 0.395934 | − | 0.918279i | \(-0.370421\pi\) |
−0.918279 | + | 0.395934i | \(0.870421\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −546.644 | − | 546.644i | −0.659401 | − | 0.659401i | 0.295837 | − | 0.955238i | \(-0.404401\pi\) |
−0.955238 | + | 0.295837i | \(0.904401\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 402.783i | − | 0.484697i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −183.617 | − | 193.504i | −0.220429 | − | 0.232298i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 118.740 | − | 118.740i | 0.142203 | − | 0.142203i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 850.797 | + | 850.797i | 1.01648 | + | 1.01648i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −196.129 | −0.233765 | −0.116883 | − | 0.993146i | \(-0.537290\pi\) | ||||
−0.116883 | + | 0.993146i | \(0.537290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 655.619i | − | 0.779571i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 365.096 | − | 365.096i | 0.433091 | − | 0.433091i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 483.033 | + | 483.033i | 0.571637 | + | 0.571637i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −110.788 | − | 277.705i | −0.130800 | − | 0.327869i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −623.385 | −0.734258 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −105.776 | + | 105.776i | −0.124296 | + | 0.124296i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −463.772 | + | 463.772i | −0.543695 | + | 0.543695i | −0.924610 | − | 0.380915i | \(-0.875609\pi\) |
0.380915 | + | 0.924610i | \(0.375609\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 978.747i | 1.14473i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1536.03 | 1.79234 | 0.896168 | − | 0.443714i | \(-0.146339\pi\) | ||||
0.896168 | + | 0.443714i | \(0.146339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.4535 | − | 36.4535i | 0.0424371 | − | 0.0424371i | −0.685570 | − | 0.728007i | \(-0.740447\pi\) |
0.728007 | + | 0.685570i | \(0.240447\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.2821 | − | 13.8701i | −0.0374937 | − | 0.0161093i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 304.834 | 0.353226 | 0.176613 | − | 0.984280i | \(-0.443486\pi\) | ||||
0.176613 | + | 0.984280i | \(0.443486\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 174.708 | 0.201974 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 259.644 | + | 259.644i | 0.299474 | + | 0.299474i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 533.623 | + | 533.623i | 0.614066 | + | 0.614066i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.99621 | −0.00688428 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −627.086 | −0.718311 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −638.277 | − | 274.237i | −0.729459 | − | 0.313414i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −545.809 | + | 545.809i | −0.622359 | + | 0.622359i | −0.946134 | − | 0.323775i | \(-0.895048\pi\) |
0.323775 | + | 0.946134i | \(0.395048\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 498.963 | 0.567649 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1051.42i | 1.19344i | 0.802449 | + | 0.596721i | \(0.203530\pi\) | ||||
−0.802449 | + | 0.596721i | \(0.796470\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −693.577 | + | 693.577i | −0.785478 | + | 0.785478i | −0.980749 | − | 0.195271i | \(-0.937441\pi\) |
0.195271 | + | 0.980749i | \(0.437441\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −456.378 | + | 456.378i | −0.515682 | + | 0.515682i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 579.072 | 0.652843 | 0.326422 | − | 0.945224i | \(-0.394157\pi\) | ||||
0.326422 | + | 0.945224i | \(0.394157\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −203.568 | + | 81.2119i | −0.228986 | + | 0.0913520i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −193.326 | − | 193.326i | −0.216977 | − | 0.216977i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −674.638 | + | 674.638i | −0.755474 | + | 0.755474i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 345.929i | − | 0.386513i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −80.3981 | −0.0896299 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1453.43 | − | 1453.43i | −1.61672 | − | 1.61672i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −282.516 | + | 282.516i | −0.313558 | + | 0.313558i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −72.4838 | − | 181.690i | −0.0802700 | − | 0.201207i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1195.76i | − | 1.32128i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 134.035 | + | 134.035i | 0.147778 | + | 0.147778i | 0.777125 | − | 0.629347i | \(-0.216677\pi\) |
−0.629347 | + | 0.777125i | \(0.716677\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 354.779 | + | 354.779i | 0.390296 | + | 0.390296i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.6323 | −0.0456996 | −0.0228498 | − | 0.999739i | \(-0.507274\pi\) | ||||
−0.0228498 | + | 0.999739i | \(0.507274\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 74.6101i | − | 0.0817197i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −682.333 | − | 682.333i | −0.745719 | − | 0.745719i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −198.445 | − | 85.2623i | −0.216407 | − | 0.0929796i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 772.416i | 0.840496i | 0.907409 | + | 0.420248i | \(0.138057\pi\) | ||||
−0.907409 | + | 0.420248i | \(0.861943\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 532.361i | 0.578025i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 388.890 | − | 388.890i | 0.421333 | − | 0.421333i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 99.8298 | − | 99.8298i | 0.107924 | − | 0.107924i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 538.969i | 0.581412i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1353.43i | 1.45687i | 0.685114 | + | 0.728436i | \(0.259753\pi\) | ||||
−0.685114 | + | 0.728436i | \(0.740247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1199.81 | + | 31.4553i | 1.28873 | + | 0.0337865i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 115.517 | + | 115.517i | 0.123813 | + | 0.123813i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 275.133i | 0.294260i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1628.25 | 1.73772 | 0.868861 | − | 0.495056i | \(-0.164852\pi\) | ||||
0.868861 | + | 0.495056i | \(0.164852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 334.681 | + | 334.681i | 0.356423 | + | 0.356423i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −293.378 | − | 293.378i | −0.311772 | − | 0.311772i | 0.533824 | − | 0.845596i | \(-0.320755\pi\) |
−0.845596 | + | 0.533824i | \(0.820755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 28.6444i | − | 0.0303759i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 335.507 | + | 840.992i | 0.355034 | + | 0.889939i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 375.023 | − | 375.023i | 0.396012 | − | 0.396012i | −0.480812 | − | 0.876824i | \(-0.659658\pi\) |
0.876824 | + | 0.480812i | \(0.159658\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 396.275 | + | 396.275i | 0.417571 | + | 0.417571i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 53.1079 | 0.0558442 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 263.530i | − | 0.276527i | −0.990395 | − | 0.138264i | \(-0.955848\pi\) | ||
0.990395 | − | 0.138264i | \(-0.0441521\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1074.34 | + | 1074.34i | −1.12497 | + | 1.12497i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −342.667 | − | 342.667i | −0.358064 | − | 0.358064i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −325.680 | − | 816.360i | −0.339604 | − | 0.851262i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1861.96 | −1.93753 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 983.120 | − | 983.120i | 1.02089 | − | 1.02089i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1160.68 | − | 1160.68i | 1.20278 | − | 1.20278i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 791.495i | − | 0.818505i | −0.912421 | − | 0.409253i | \(-0.865789\pi\) | ||
0.912421 | − | 0.409253i | \(-0.134211\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 188.787 | 0.194827 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1184.27 | + | 1184.27i | −1.21964 | + | 1.21964i | −0.251883 | + | 0.967758i | \(0.581050\pi\) |
−0.967758 | + | 0.251883i | \(0.918950\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39.0660 | + | 90.9247i | −0.0401501 | + | 0.0934478i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 75.8783 | 0.0778239 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 615.856 | 0.630354 | 0.315177 | − | 0.949033i | \(-0.397936\pi\) | ||||
0.315177 | + | 0.949033i | \(0.397936\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1024.99 | − | 1024.99i | −1.04698 | − | 1.04698i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −323.406 | − | 323.406i | −0.329669 | − | 0.329669i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 534.869 | 0.544119 | 0.272059 | − | 0.962280i | \(-0.412295\pi\) | ||||
0.272059 | + | 0.962280i | \(0.412295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 63.7280 | 0.0646985 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −152.383 | + | 354.665i | −0.154390 | + | 0.359336i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 112.766 | − | 112.766i | 0.114021 | − | 0.114021i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 125.613 | 0.126754 | 0.0633768 | − | 0.997990i | \(-0.479813\pi\) | ||||
0.0633768 | + | 0.997990i | \(0.479813\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 67.1950i | − | 0.0676687i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −223.654 | + | 223.654i | −0.224778 | + | 0.224778i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −83.7554 | + | 83.7554i | −0.0840075 | + | 0.0840075i | −0.747862 | − | 0.663854i | \(-0.768919\pi\) |
0.663854 | + | 0.747862i | \(0.268919\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 419.290 | 0.419710 |
(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 | 448.3.l.b.433.17 | 56 | ||
4.3 | odd | 2 | 112.3.l.b.69.17 | yes | 56 | ||
7.6 | odd | 2 | inner | 448.3.l.b.433.12 | 56 | ||
16.3 | odd | 4 | 112.3.l.b.13.18 | yes | 56 | ||
16.13 | even | 4 | inner | 448.3.l.b.209.12 | 56 | ||
28.27 | even | 2 | 112.3.l.b.69.18 | yes | 56 | ||
112.13 | odd | 4 | inner | 448.3.l.b.209.17 | 56 | ||
112.83 | even | 4 | 112.3.l.b.13.17 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.3.l.b.13.17 | ✓ | 56 | 112.83 | even | 4 | ||
112.3.l.b.13.18 | yes | 56 | 16.3 | odd | 4 | ||
112.3.l.b.69.17 | yes | 56 | 4.3 | odd | 2 | ||
112.3.l.b.69.18 | yes | 56 | 28.27 | even | 2 | ||
448.3.l.b.209.12 | 56 | 16.13 | even | 4 | inner | ||
448.3.l.b.209.17 | 56 | 112.13 | odd | 4 | inner | ||
448.3.l.b.433.12 | 56 | 7.6 | odd | 2 | inner | ||
448.3.l.b.433.17 | 56 | 1.1 | even | 1 | trivial |