Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(1439,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.1439");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.m (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1439.6 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.1439 |
Dual form | 2880.2.m.a.1439.8 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421 | − | 1.73205i | 0.632456 | − | 0.774597i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949 | 0.925820 | 0.462910 | − | 0.886405i | \(-0.346805\pi\) | ||||
0.462910 | + | 0.886405i | \(0.346805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.41421i | − | 0.426401i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | −0.679366 | −0.339683 | − | 0.940540i | \(-0.610320\pi\) | ||||
−0.339683 | + | 0.940540i | \(0.610320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.92820i | − | 1.44463i | −0.691564 | − | 0.722315i | \(-0.743078\pi\) | ||
0.691564 | − | 0.722315i | \(-0.256922\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 4.89898i | −0.200000 | − | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.65685 | −1.05045 | −0.525226 | − | 0.850963i | \(-0.676019\pi\) | ||||
−0.525226 | + | 0.850963i | \(0.676019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000i | 0.359211i | 0.983739 | + | 0.179605i | \(0.0574821\pi\) | ||||
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.46410 | − | 4.24264i | 0.585540 | − | 0.717137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.34847 | −1.20808 | −0.604040 | − | 0.796954i | \(-0.706443\pi\) | ||||
−0.604040 | + | 0.796954i | \(0.706443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.24264i | − | 0.662589i | −0.943527 | − | 0.331295i | \(-0.892515\pi\) | ||
0.943527 | − | 0.331295i | \(-0.107485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.89898i | − | 0.747087i | −0.927613 | − | 0.373544i | \(-0.878143\pi\) | ||
0.927613 | − | 0.373544i | \(-0.121857\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.46410i | 0.505291i | 0.967559 | + | 0.252646i | \(0.0813007\pi\) | ||||
−0.967559 | + | 0.252646i | \(0.918699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.92820i | − | 0.951662i | −0.879537 | − | 0.475831i | \(-0.842147\pi\) | ||
0.879537 | − | 0.475831i | \(-0.157853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.44949 | − | 2.00000i | −0.330289 | − | 0.269680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.41421i | − | 0.184115i | −0.995754 | − | 0.0920575i | \(-0.970656\pi\) | ||
0.995754 | − | 0.0920575i | \(-0.0293443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0000i | 1.53644i | 0.640184 | + | 0.768221i | \(0.278858\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.46410 | + | 4.24264i | −0.429669 | + | 0.526235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 14.6969i | − | 1.79552i | −0.440488 | − | 0.897758i | \(-0.645195\pi\) | ||
0.440488 | − | 0.897758i | \(-0.354805\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48528 | 1.00702 | 0.503509 | − | 0.863990i | \(-0.332042\pi\) | ||||
0.503509 | + | 0.863990i | \(0.332042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.79796i | 1.14676i | 0.819288 | + | 0.573382i | \(0.194369\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.46410i | − | 0.394771i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.00000i | − | 0.225018i | −0.993651 | − | 0.112509i | \(-0.964111\pi\) | ||
0.993651 | − | 0.112509i | \(-0.0358886\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.8564 | 1.52094 | 0.760469 | − | 0.649374i | \(-0.224969\pi\) | ||||
0.760469 | + | 0.649374i | \(0.224969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.89898 | + | 6.00000i | −0.531369 | + | 0.650791i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.24264i | 0.449719i | 0.974391 | + | 0.224860i | \(0.0721923\pi\) | ||||
−0.974391 | + | 0.224860i | \(0.927808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | −0.628971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.48528 | + | 10.3923i | −0.870572 | + | 1.06623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.89898i | − | 0.497416i | −0.968579 | − | 0.248708i | \(-0.919994\pi\) | ||
0.968579 | − | 0.248708i | \(-0.0800060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.1421 | −1.40720 | −0.703598 | − | 0.710599i | \(-0.748424\pi\) | ||||
−0.703598 | + | 0.710599i | \(0.748424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.34847 | 0.724066 | 0.362033 | − | 0.932165i | \(-0.382083\pi\) | ||||
0.362033 | + | 0.932165i | \(0.382083\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92820 | 0.669775 | 0.334887 | − | 0.942258i | \(-0.391302\pi\) | ||||
0.334887 | + | 0.942258i | \(0.391302\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0000i | 1.14939i | 0.818367 | + | 0.574696i | \(0.194880\pi\) | ||||
−0.818367 | + | 0.574696i | \(0.805120\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3205 | 1.62938 | 0.814688 | − | 0.579899i | \(-0.196908\pi\) | ||||
0.814688 | + | 0.579899i | \(0.196908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.0000 | − | 9.79796i | −1.11901 | − | 0.913664i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.48528 | −0.777844 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.89949 | − | 5.19615i | −0.885438 | − | 0.464758i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1464 | −1.52150 | −0.760750 | − | 0.649045i | \(-0.775169\pi\) | ||||
−0.760750 | + | 0.649045i | \(0.775169\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.07107i | − | 0.617802i | −0.951094 | − | 0.308901i | \(-0.900039\pi\) | ||
0.951094 | − | 0.308901i | \(-0.0999612\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.6969 | −1.27439 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923 | 0.887875 | 0.443937 | − | 0.896058i | \(-0.353581\pi\) | ||||
0.443937 | + | 0.896058i | \(0.353581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.46410i | 0.289683i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | + | 9.79796i | −0.664364 | + | 0.813676i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.65685 | 0.463428 | 0.231714 | − | 0.972784i | \(-0.425567\pi\) | ||||
0.231714 | + | 0.972784i | \(0.425567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0000i | 1.13930i | 0.821886 | + | 0.569652i | \(0.192922\pi\) | ||||
−0.821886 | + | 0.569652i | \(0.807078\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.46410 | + | 2.82843i | 0.278243 | + | 0.227185i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2474 | −0.977453 | −0.488726 | − | 0.872437i | \(-0.662538\pi\) | ||||
−0.488726 | + | 0.872437i | \(0.662538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 16.9706i | − | 1.33747i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.5959i | − | 1.53487i | −0.641126 | − | 0.767435i | \(-0.721533\pi\) | ||
0.641126 | − | 0.767435i | \(-0.278467\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.92820i | − | 0.526742i | −0.964695 | − | 0.263371i | \(-0.915166\pi\) | ||
0.964695 | − | 0.263371i | \(-0.0848343\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.44949 | − | 12.0000i | −0.185164 | − | 0.907115i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 24.0416i | − | 1.79696i | −0.439019 | − | 0.898478i | \(-0.644674\pi\) | ||
0.439019 | − | 0.898478i | \(-0.355326\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.3923 | + | 12.7279i | −0.764057 | + | 0.935775i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.89898i | 0.358249i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9706 | 1.22795 | 0.613973 | − | 0.789327i | \(-0.289570\pi\) | ||||
0.613973 | + | 0.789327i | \(0.289570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.89898i | − | 0.352636i | −0.984333 | − | 0.176318i | \(-0.943581\pi\) | ||
0.984333 | − | 0.176318i | \(-0.0564187\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.3205i | − | 1.23404i | −0.786949 | − | 0.617018i | \(-0.788341\pi\) | ||
0.786949 | − | 0.617018i | \(-0.211659\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.0000i | − | 0.708881i | −0.935079 | − | 0.354441i | \(-0.884671\pi\) | ||
0.935079 | − | 0.354441i | \(-0.115329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.8564 | −0.972529 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.34847 | − | 6.00000i | −0.513239 | − | 0.419058i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.48528i | 0.586939i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.0000 | −1.65223 | −0.826114 | − | 0.563503i | \(-0.809453\pi\) | ||||
−0.826114 | + | 0.563503i | \(0.809453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.48528 | − | 6.92820i | −0.578691 | − | 0.472500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.89898i | 0.332564i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.48528 | 0.570782 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.34847 | 0.492090 | 0.246045 | − | 0.969258i | \(-0.420869\pi\) | ||||
0.246045 | + | 0.969258i | \(0.420869\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.7846 | 1.37952 | 0.689761 | − | 0.724037i | \(-0.257715\pi\) | ||||
0.689761 | + | 0.724037i | \(0.257715\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0000i | 0.792982i | 0.918039 | + | 0.396491i | \(0.129772\pi\) | ||||
−0.918039 | + | 0.396491i | \(0.870228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.3923 | −0.680823 | −0.340411 | − | 0.940277i | \(-0.610566\pi\) | ||||
−0.340411 | + | 0.940277i | \(0.610566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | + | 4.89898i | 0.391397 | + | 0.319574i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0000 | 1.28831 | 0.644157 | − | 0.764894i | \(-0.277208\pi\) | ||||
0.644157 | + | 0.764894i | \(0.277208\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.41421 | + | 1.73205i | −0.0903508 | + | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.6969 | 0.935144 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.41421i | 0.0892644i | 0.999003 | + | 0.0446322i | \(0.0142116\pi\) | ||||
−0.999003 | + | 0.0446322i | \(0.985788\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.79796 | −0.615992 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.2487 | −1.51259 | −0.756297 | − | 0.654229i | \(-0.772993\pi\) | ||||
−0.756297 | + | 0.654229i | \(0.772993\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.0000 | −1.11847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | − | 9.79796i | −0.737154 | − | 0.601884i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.3137 | −0.689809 | −0.344904 | − | 0.938638i | \(-0.612089\pi\) | ||||
−0.344904 | + | 0.938638i | \(0.612089\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0000i | 0.850439i | 0.905090 | + | 0.425220i | \(0.139803\pi\) | ||||
−0.905090 | + | 0.425220i | \(0.860197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.92820 | + | 1.41421i | −0.417786 | + | 0.0852803i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.34847 | 0.441527 | 0.220763 | − | 0.975327i | \(-0.429145\pi\) | ||||
0.220763 | + | 0.975327i | \(0.429145\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 29.6985i | − | 1.77166i | −0.464007 | − | 0.885832i | \(-0.653589\pi\) | ||
0.464007 | − | 0.885832i | \(-0.346411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6969i | 0.873642i | 0.899548 | + | 0.436821i | \(0.143896\pi\) | ||||
−0.899548 | + | 0.436821i | \(0.856104\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 10.3923i | − | 0.613438i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3923i | 0.607125i | 0.952812 | + | 0.303562i | \(0.0981761\pi\) | ||||
−0.952812 | + | 0.303562i | \(0.901824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.44949 | − | 2.00000i | −0.142615 | − | 0.116445i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.9706i | 0.981433i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 12.0000i | − | 0.691669i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.7846 | + | 16.9706i | 1.19012 | + | 0.971732i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.79796i | − | 0.559199i | −0.960117 | − | 0.279600i | \(-0.909798\pi\) | ||
0.960117 | − | 0.279600i | \(-0.0902017\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.9411 | 1.92462 | 0.962312 | − | 0.271947i | \(-0.0876674\pi\) | ||||
0.962312 | + | 0.271947i | \(0.0876674\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 24.4949i | − | 1.38453i | −0.721642 | − | 0.692267i | \(-0.756612\pi\) | ||
0.721642 | − | 0.692267i | \(-0.243388\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.46410i | − | 0.194563i | −0.995257 | − | 0.0972817i | \(-0.968985\pi\) | ||
0.995257 | − | 0.0972817i | \(-0.0310148\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000i | 0.447914i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.7846 | 1.15649 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.44949 | + | 12.0000i | 0.135873 | + | 0.665640i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.48528i | 0.467809i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.0000 | 1.64895 | 0.824475 | − | 0.565899i | \(-0.191471\pi\) | ||||
0.824475 | + | 0.565899i | \(0.191471\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.4558 | − | 20.7846i | −1.39080 | − | 1.13558i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.82843 | 0.153168 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5959 | −1.05808 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.7128 | −1.48770 | −0.743851 | − | 0.668346i | \(-0.767003\pi\) | ||||
−0.743851 | + | 0.668346i | \(0.767003\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.0000i | − | 0.642345i | −0.947021 | − | 0.321173i | \(-0.895923\pi\) | ||
0.947021 | − | 0.321173i | \(-0.104077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.2487 | −1.29063 | −0.645314 | − | 0.763917i | \(-0.723274\pi\) | ||||
−0.645314 | + | 0.763917i | \(0.723274\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000 | − | 14.6969i | 0.636894 | − | 0.780033i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.4558 | −1.34351 | −0.671754 | − | 0.740774i | \(-0.734459\pi\) | ||||
−0.671754 | + | 0.740774i | \(0.734459\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.9706 | + | 13.8564i | 0.888280 | + | 0.725277i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.8434 | 1.66221 | 0.831105 | − | 0.556115i | \(-0.187709\pi\) | ||||
0.831105 | + | 0.556115i | \(0.187709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 16.9706i | − | 0.881068i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.9444 | 1.39513 | 0.697564 | − | 0.716523i | \(-0.254267\pi\) | ||||
0.697564 | + | 0.716523i | \(0.254267\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.8564 | 0.713641 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000 | 1.23280 | 0.616399 | − | 0.787434i | \(-0.288591\pi\) | ||||
0.616399 | + | 0.787434i | \(0.288591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.46410i | − | 0.177007i | −0.996076 | − | 0.0885037i | \(-0.971792\pi\) | ||
0.996076 | − | 0.0885037i | \(-0.0282085\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | − | 4.89898i | −0.305788 | − | 0.249675i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.1421 | −0.717035 | −0.358517 | − | 0.933523i | \(-0.616718\pi\) | ||||
−0.358517 | + | 0.933523i | \(0.616718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000i | 1.21373i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.46410 | − | 2.82843i | −0.174298 | − | 0.142314i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.1464 | 0.860555 | 0.430277 | − | 0.902697i | \(-0.358416\pi\) | ||||
0.430277 | + | 0.902697i | \(0.358416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 29.6985i | − | 1.48307i | −0.670913 | − | 0.741536i | \(-0.734098\pi\) | ||
0.670913 | − | 0.741536i | \(-0.265902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.89898i | − | 0.244036i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.3923i | 0.515127i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.00000 | −0.0988936 | −0.0494468 | − | 0.998777i | \(-0.515746\pi\) | ||||
−0.0494468 | + | 0.998777i | \(0.515746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.46410i | − | 0.170457i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.5959 | − | 24.0000i | 0.961926 | − | 1.17811i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.3553i | 1.72722i | 0.504159 | + | 0.863611i | \(0.331802\pi\) | ||||
−0.504159 | + | 0.863611i | \(0.668198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0000i | 0.584844i | 0.956289 | + | 0.292422i | \(0.0944612\pi\) | ||||
−0.956289 | + | 0.292422i | \(0.905539\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.46410 | + | 16.9706i | 0.168034 | + | 0.823193i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.3939i | 1.42247i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.4558 | 1.22616 | 0.613082 | − | 0.790019i | \(-0.289929\pi\) | ||||
0.613082 | + | 0.790019i | \(0.289929\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.5959i | 0.941720i | 0.882208 | + | 0.470860i | \(0.156056\pi\) | ||||
−0.882208 | + | 0.470860i | \(0.843944\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 41.5692i | 1.98853i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 34.0000i | − | 1.62273i | −0.584539 | − | 0.811366i | \(-0.698725\pi\) | ||
0.584539 | − | 0.811366i | \(-0.301275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.7846 | −0.987507 | −0.493753 | − | 0.869602i | \(-0.664375\pi\) | ||||
−0.493753 | + | 0.869602i | \(0.664375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.34847 | + | 6.00000i | 0.348351 | + | 0.284427i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7279i | 0.600668i | 0.953834 | + | 0.300334i | \(0.0970981\pi\) | ||||
−0.953834 | + | 0.300334i | \(0.902902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.48528 | + | 10.3923i | −0.397796 | + | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.4949i | 1.14582i | 0.819617 | + | 0.572911i | \(0.194186\pi\) | ||||
−0.819617 | + | 0.572911i | \(0.805814\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.65685 | 0.263466 | 0.131733 | − | 0.991285i | \(-0.457946\pi\) | ||||
0.131733 | + | 0.991285i | \(0.457946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.9444 | −1.25221 | −0.626106 | − | 0.779738i | \(-0.715352\pi\) | ||||
−0.626106 | + | 0.779738i | \(0.715352\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.92820 | 0.320599 | 0.160300 | − | 0.987068i | \(-0.448754\pi\) | ||||
0.160300 | + | 0.987068i | \(0.448754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 36.0000i | − | 1.66233i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.92820 | −0.318559 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000 | + | 29.3939i | 0.275299 | + | 1.34868i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.48528 | 0.387702 | 0.193851 | − | 0.981031i | \(-0.437902\pi\) | ||||
0.193851 | + | 0.981031i | \(0.437902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.48528 | − | 6.92820i | −0.385297 | − | 0.314594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.7423 | −1.66495 | −0.832477 | − | 0.554059i | \(-0.813078\pi\) | ||||
−0.832477 | + | 0.554059i | \(0.813078\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.0122i | 1.85085i | 0.378925 | + | 0.925427i | \(0.376294\pi\) | ||||
−0.378925 | + | 0.925427i | \(0.623706\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.5959 | 0.882556 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.7846 | 0.932317 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.00000 | 0.268597 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.1051i | 1.69902i | 0.527570 | + | 0.849512i | \(0.323103\pi\) | ||||
−0.527570 | + | 0.849512i | \(0.676897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.0000 | + | 24.4949i | −0.889988 | + | 1.09001i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.1127 | 1.37905 | 0.689523 | − | 0.724264i | \(-0.257820\pi\) | ||||
0.689523 | + | 0.724264i | \(0.257820\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0000i | 1.06170i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.3923 | − | 12.7279i | 0.457940 | − | 0.560859i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.89898 | 0.215457 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.2132i | − | 0.929367i | −0.885477 | − | 0.464684i | \(-0.846168\pi\) | ||
0.885477 | − | 0.464684i | \(-0.153832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.1918i | 1.71374i | 0.515533 | + | 0.856870i | \(0.327594\pi\) | ||||
−0.515533 | + | 0.856870i | \(0.672406\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 6.92820i | − | 0.301797i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −25.0000 | −1.08696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3923i | 0.450141i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.79796 | − | 12.0000i | 0.423603 | − | 0.518805i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.41421i | 0.0609145i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 24.0000i | − | 1.03184i | −0.856637 | − | 0.515920i | \(-0.827450\pi\) | ||
0.856637 | − | 0.515920i | \(-0.172550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.7846 | + | 16.9706i | 0.890315 | + | 0.726939i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.89898i | − | 0.209465i | −0.994500 | − | 0.104733i | \(-0.966601\pi\) | ||
0.994500 | − | 0.104733i | \(-0.0333987\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.9411 | 1.44594 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.89898i | − | 0.208326i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.92820i | 0.293557i | 0.989169 | + | 0.146779i | \(0.0468905\pi\) | ||||
−0.989169 | + | 0.146779i | \(0.953109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0000i | 0.507546i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.7128 | −1.16796 | −0.583978 | − | 0.811770i | \(-0.698505\pi\) | ||||
−0.583978 | + | 0.811770i | \(0.698505\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.4949 | − | 30.0000i | 1.03051 | − | 1.26211i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.7279i | 0.533582i | 0.963754 | + | 0.266791i | \(0.0859634\pi\) | ||||
−0.963754 | + | 0.266791i | \(0.914037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.0000 | 1.25546 | 0.627730 | − | 0.778431i | \(-0.283984\pi\) | ||||
0.627730 | + | 0.778431i | \(0.283984\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.9411 | + | 6.92820i | −1.41544 | + | 0.288926i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 44.0908i | − | 1.83552i | −0.397130 | − | 0.917762i | \(-0.629994\pi\) | ||
0.397130 | − | 0.917762i | \(-0.370006\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.9411 | 1.40812 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.79796 | −0.405790 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.6410 | −1.42979 | −0.714894 | − | 0.699233i | \(-0.753525\pi\) | ||||
−0.714894 | + | 0.699233i | \(0.753525\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 12.0000i | − | 0.494451i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.46410 | −0.142254 | −0.0711268 | − | 0.997467i | \(-0.522659\pi\) | ||||
−0.0711268 | + | 0.997467i | \(0.522659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | + | 14.6969i | −0.491952 | + | 0.602516i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.4264 | −1.73350 | −0.866748 | − | 0.498746i | \(-0.833794\pi\) | ||||
−0.866748 | + | 0.498746i | \(0.833794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.0000 | 1.30531 | 0.652654 | − | 0.757656i | \(-0.273656\pi\) | ||||
0.652654 | + | 0.757656i | \(0.273656\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.7279 | − | 15.5885i | 0.517464 | − | 0.633761i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.34847 | −0.298265 | −0.149133 | − | 0.988817i | \(-0.547648\pi\) | ||||
−0.149133 | + | 0.988817i | \(0.547648\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 8.48528i | − | 0.343278i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.44949 | −0.0989340 | −0.0494670 | − | 0.998776i | \(-0.515752\pi\) | ||||
−0.0494670 | + | 0.998776i | \(0.515752\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.2487 | 0.976216 | 0.488108 | − | 0.872783i | \(-0.337687\pi\) | ||||
0.488108 | + | 0.872783i | \(0.337687\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0000 | 0.964641 | 0.482321 | − | 0.875995i | \(-0.339794\pi\) | ||||
0.482321 | + | 0.875995i | \(0.339794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.3923i | 0.416359i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | + | 9.79796i | −0.920000 | + | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.4558 | 1.01499 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0000i | 0.875806i | 0.899022 | + | 0.437903i | \(0.144279\pi\) | ||||
−0.899022 | + | 0.437903i | \(0.855721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.2487 | + | 29.6985i | −0.962281 | + | 1.17855i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.44949 | 0.0970523 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 29.6985i | − | 1.17302i | −0.809942 | − | 0.586510i | \(-0.800502\pi\) | ||
0.809942 | − | 0.586510i | \(-0.199498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.79796i | 0.386394i | 0.981160 | + | 0.193197i | \(0.0618856\pi\) | ||||
−0.981160 | + | 0.193197i | \(0.938114\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 10.3923i | − | 0.408564i | −0.978912 | − | 0.204282i | \(-0.934514\pi\) | ||
0.978912 | − | 0.204282i | \(-0.0654859\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.00000 | −0.0785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45.0333i | 1.76229i | 0.472846 | + | 0.881145i | \(0.343227\pi\) | ||||
−0.472846 | + | 0.881145i | \(0.656773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.2474 | − | 10.0000i | −0.478547 | − | 0.390732i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 43.8406i | − | 1.70779i | −0.520447 | − | 0.853894i | \(-0.674235\pi\) | ||
0.520447 | − | 0.853894i | \(-0.325765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24.0000i | − | 0.933492i | −0.884391 | − | 0.466746i | \(-0.845426\pi\) | ||
0.884391 | − | 0.466746i | \(-0.154574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.7846 | + | 25.4558i | −0.805993 | + | 0.987135i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.1918i | 1.51751i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.9706 | 0.655141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.79796i | 0.377684i | 0.982008 | + | 0.188842i | \(0.0604733\pi\) | ||||
−0.982008 | + | 0.188842i | \(0.939527\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 10.3923i | − | 0.399409i | −0.979856 | − | 0.199704i | \(-0.936002\pi\) | ||
0.979856 | − | 0.199704i | \(-0.0639982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 12.0000i | − | 0.460518i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6969 | − | 18.0000i | 0.561541 | − | 0.687745i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.9706i | 0.646527i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.00000 | 0.228251 | 0.114125 | − | 0.993466i | \(-0.463593\pi\) | ||||
0.114125 | + | 0.993466i | \(0.463593\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.6969i | 0.556686i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.0833 | −1.81608 | −0.908040 | − | 0.418884i | \(-0.862421\pi\) | ||||
−0.908040 | + | 0.418884i | \(0.862421\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.0908 | 1.66292 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −34.6410 | −1.30281 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0000i | 0.450669i | 0.974281 | + | 0.225335i | \(0.0723476\pi\) | ||||
−0.974281 | + | 0.225335i | \(0.927652\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.8564 | 0.518927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | + | 4.89898i | 0.224387 | + | 0.183211i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.4558 | 0.949343 | 0.474671 | − | 0.880163i | \(-0.342567\pi\) | ||||
0.474671 | + | 0.880163i | \(0.342567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0000 | 0.670355 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.65685 | + | 27.7128i | 0.210090 | + | 1.02923i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.44949 | −0.0908465 | −0.0454233 | − | 0.998968i | \(-0.514464\pi\) | ||||
−0.0454233 | + | 0.998968i | \(0.514464\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.9706i | 0.627679i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0454 | 0.814266 | 0.407133 | − | 0.913369i | \(-0.366529\pi\) | ||||
0.407133 | + | 0.913369i | \(0.366529\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.7846 | −0.765611 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.00000 | −0.220714 | −0.110357 | − | 0.993892i | \(-0.535199\pi\) | ||||
−0.110357 | + | 0.993892i | \(0.535199\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.46410i | − | 0.127086i | −0.997979 | − | 0.0635428i | \(-0.979760\pi\) | ||
0.997979 | − | 0.0635428i | \(-0.0202399\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.00000 | − | 9.79796i | 0.293097 | − | 0.358969i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.9706 | 0.620091 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000i | 0.0729810i | 0.999334 | + | 0.0364905i | \(0.0116179\pi\) | ||||
−0.999334 | + | 0.0364905i | \(0.988382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.2487 | + | 19.7990i | 0.882501 | + | 0.720559i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.9444 | 0.979310 | 0.489655 | − | 0.871916i | \(-0.337123\pi\) | ||||
0.489655 | + | 0.871916i | \(0.337123\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 46.6690i | − | 1.69175i | −0.533380 | − | 0.845876i | \(-0.679078\pi\) | ||
0.533380 | − | 0.845876i | \(-0.320922\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.3939i | 1.06413i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.46410i | 0.125081i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0000 | 0.576975 | 0.288487 | − | 0.957484i | \(-0.406848\pi\) | ||||
0.288487 | + | 0.957484i | \(0.406848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 31.1769i | − | 1.12136i | −0.828034 | − | 0.560678i | \(-0.810541\pi\) | ||
0.828034 | − | 0.560678i | \(-0.189459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.79796 | − | 2.00000i | 0.351953 | − | 0.0718421i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.4558i | 0.912050i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 12.0000i | − | 0.429394i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.3205 | + | 21.2132i | −0.618195 | + | 0.757132i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 9.79796i | − | 0.349260i | −0.984634 | − | 0.174630i | \(-0.944127\pi\) | ||
0.984634 | − | 0.174630i | \(-0.0558729\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.4264 | 1.50851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 29.3939i | − | 1.04381i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.4974i | 1.71787i | 0.512087 | + | 0.858933i | \(0.328872\pi\) | ||||
−0.512087 | + | 0.858933i | \(0.671128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.0000i | − | 0.424529i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.8564 | 0.488982 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.3939 | − | 24.0000i | −1.03600 | − | 0.845889i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.24264i | 0.149163i | 0.997215 | + | 0.0745817i | \(0.0237621\pi\) | ||||
−0.997215 | + | 0.0745817i | \(0.976238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.0000 | 0.842754 | 0.421377 | − | 0.906886i | \(-0.361547\pi\) | ||||
0.421377 | + | 0.906886i | \(0.361547\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.9411 | − | 27.7128i | −1.18891 | − | 0.970737i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.3939i | 1.02836i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2843 | 0.987128 | 0.493564 | − | 0.869710i | \(-0.335694\pi\) | ||||
0.493564 | + | 0.869710i | \(0.335694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.9444 | 0.939222 | 0.469611 | − | 0.882873i | \(-0.344394\pi\) | ||||
0.469611 | + | 0.882873i | \(0.344394\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7846 | 0.722752 | 0.361376 | − | 0.932420i | \(-0.382307\pi\) | ||||
0.361376 | + | 0.932420i | \(0.382307\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.0000i | 0.833554i | 0.909009 | + | 0.416777i | \(0.136840\pi\) | ||||
−0.909009 | + | 0.416777i | \(0.863160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.46410 | 0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.4264 | −1.46472 | −0.732361 | − | 0.680916i | \(-0.761582\pi\) | ||||
−0.732361 | + | 0.680916i | \(0.761582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.89949 | + | 12.1244i | −0.340553 | + | 0.417091i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.0454 | 0.757489 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50.9117i | 1.74523i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.9444 | 0.922558 | 0.461279 | − | 0.887255i | \(-0.347391\pi\) | ||||
0.461279 | + | 0.887255i | \(0.347391\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −51.9615 | −1.77497 | −0.887486 | − | 0.460835i | \(-0.847550\pi\) | ||||
−0.887486 | + | 0.460835i | \(0.847550\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0000 | 0.818869 | 0.409435 | − | 0.912339i | \(-0.365726\pi\) | ||||
0.409435 | + | 0.912339i | \(0.365726\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 55.4256i | − | 1.88671i | −0.331785 | − | 0.943355i | \(-0.607651\pi\) | ||
0.331785 | − | 0.943355i | \(-0.392349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0000 | − | 9.79796i | −0.408012 | − | 0.333141i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.82843 | −0.0959478 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.0000i | 1.21981i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.2487 | − | 12.7279i | −0.819756 | − | 0.430282i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.8434 | 1.07527 | 0.537637 | − | 0.843176i | \(-0.319317\pi\) | ||||
0.537637 | + | 0.843176i | \(0.319317\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29.6985i | − | 1.00057i | −0.865862 | − | 0.500284i | \(-0.833229\pi\) | ||
0.865862 | − | 0.500284i | \(-0.166771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.3939i | − | 0.989183i | −0.869126 | − | 0.494591i | \(-0.835318\pi\) | ||
0.869126 | − | 0.494591i | \(-0.164682\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 13.8564i | − | 0.465253i | −0.972566 | − | 0.232626i | \(-0.925268\pi\) | ||
0.972566 | − | 0.232626i | \(-0.0747319\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42.0000 | −1.40863 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 20.7846i | − | 0.695530i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.6413 | − | 34.0000i | −1.39192 | − | 1.13649i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 11.3137i | − | 0.377333i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0000i | 0.799556i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.89898i | 0.162668i | 0.996687 | + | 0.0813340i | \(0.0259180\pi\) | ||||
−0.996687 | + | 0.0813340i | \(0.974082\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9706 | 0.562260 | 0.281130 | − | 0.959670i | \(-0.409291\pi\) | ||||
0.281130 | + | 0.959670i | \(0.409291\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 19.5959i | − | 0.648530i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 17.3205i | − | 0.571974i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.0000i | − | 0.329870i | −0.986304 | − | 0.164935i | \(-0.947259\pi\) | ||
0.986304 | − | 0.164935i | \(-0.0527414\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.7846 | −0.684134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.34847 | + | 36.0000i | 0.241616 | + | 1.18367i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 4.24264i | − | 0.139197i | −0.997575 | − | 0.0695983i | \(-0.977828\pi\) | ||
0.997575 | − | 0.0695983i | \(-0.0221717\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.48528 | + | 6.92820i | 0.277498 | + | 0.226576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 39.1918i | − | 1.28034i | −0.768233 | − | 0.640171i | \(-0.778864\pi\) | ||
0.768233 | − | 0.640171i | \(-0.221136\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.7990 | 0.645429 | 0.322714 | − | 0.946496i | \(-0.395405\pi\) | ||||
0.322714 | + | 0.946496i | \(0.395405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.3939 | −0.957196 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.6410 | 1.12568 | 0.562841 | − | 0.826565i | \(-0.309708\pi\) | ||||
0.562841 | + | 0.826565i | \(0.309708\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 24.0000i | − | 0.779073i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.2487 | 0.785493 | 0.392746 | − | 0.919647i | \(-0.371525\pi\) | ||||
0.392746 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0000 | − | 29.3939i | 0.776622 | − | 0.951164i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.4558 | 0.822012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.48528 | − | 6.92820i | −0.273151 | − | 0.223027i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.9444 | 0.866473 | 0.433237 | − | 0.901280i | \(-0.357371\pi\) | ||||
0.433237 | + | 0.901280i | \(0.357371\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 41.0122i | − | 1.31614i | −0.752955 | − | 0.658072i | \(-0.771372\pi\) | ||
0.752955 | − | 0.658072i | \(-0.228628\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.3205 | −0.554132 | −0.277066 | − | 0.960851i | \(-0.589362\pi\) | ||||
−0.277066 | + | 0.960851i | \(0.589362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 38.1051i | − | 1.21536i | −0.794180 | − | 0.607682i | \(-0.792099\pi\) | ||
0.794180 | − | 0.607682i | \(-0.207901\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.0000 | − | 24.4949i | −0.955879 | − | 0.780472i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.9411 | −1.07927 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0000i | 0.317660i | 0.987306 | + | 0.158830i | \(0.0507723\pi\) | ||||
−0.987306 | + | 0.158830i | \(0.949228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.3205 | − | 14.1421i | −0.549097 | − | 0.448336i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.8434 | −1.00849 | −0.504245 | − | 0.863561i | \(-0.668229\pi\) | ||||
−0.504245 | + | 0.863561i | \(0.668229\pi\) | |||||||
\(998\) | 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 | 2880.2.m.a.1439.6 | yes | 8 | |
3.2 | odd | 2 | inner | 2880.2.m.a.1439.4 | yes | 8 | |
4.3 | odd | 2 | 2880.2.m.b.1439.5 | yes | 8 | ||
5.4 | even | 2 | inner | 2880.2.m.a.1439.7 | yes | 8 | |
8.3 | odd | 2 | inner | 2880.2.m.a.1439.3 | yes | 8 | |
8.5 | even | 2 | 2880.2.m.b.1439.4 | yes | 8 | ||
12.11 | even | 2 | 2880.2.m.b.1439.3 | yes | 8 | ||
15.14 | odd | 2 | inner | 2880.2.m.a.1439.1 | ✓ | 8 | |
20.19 | odd | 2 | 2880.2.m.b.1439.8 | yes | 8 | ||
24.5 | odd | 2 | 2880.2.m.b.1439.6 | yes | 8 | ||
24.11 | even | 2 | inner | 2880.2.m.a.1439.5 | yes | 8 | |
40.19 | odd | 2 | inner | 2880.2.m.a.1439.2 | yes | 8 | |
40.29 | even | 2 | 2880.2.m.b.1439.1 | yes | 8 | ||
60.59 | even | 2 | 2880.2.m.b.1439.2 | yes | 8 | ||
120.29 | odd | 2 | 2880.2.m.b.1439.7 | yes | 8 | ||
120.59 | even | 2 | inner | 2880.2.m.a.1439.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2880.2.m.a.1439.1 | ✓ | 8 | 15.14 | odd | 2 | inner | |
2880.2.m.a.1439.2 | yes | 8 | 40.19 | odd | 2 | inner | |
2880.2.m.a.1439.3 | yes | 8 | 8.3 | odd | 2 | inner | |
2880.2.m.a.1439.4 | yes | 8 | 3.2 | odd | 2 | inner | |
2880.2.m.a.1439.5 | yes | 8 | 24.11 | even | 2 | inner | |
2880.2.m.a.1439.6 | yes | 8 | 1.1 | even | 1 | trivial | |
2880.2.m.a.1439.7 | yes | 8 | 5.4 | even | 2 | inner | |
2880.2.m.a.1439.8 | yes | 8 | 120.59 | even | 2 | inner | |
2880.2.m.b.1439.1 | yes | 8 | 40.29 | even | 2 | ||
2880.2.m.b.1439.2 | yes | 8 | 60.59 | even | 2 | ||
2880.2.m.b.1439.3 | yes | 8 | 12.11 | even | 2 | ||
2880.2.m.b.1439.4 | yes | 8 | 8.5 | even | 2 | ||
2880.2.m.b.1439.5 | yes | 8 | 4.3 | odd | 2 | ||
2880.2.m.b.1439.6 | yes | 8 | 24.5 | odd | 2 | ||
2880.2.m.b.1439.7 | yes | 8 | 120.29 | odd | 2 | ||
2880.2.m.b.1439.8 | yes | 8 | 20.19 | odd | 2 |