Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,4,Mod(289,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.289");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.d (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: | \(33.9851001633\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 64) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.289 |
Dual form | 576.4.d.e.289.3 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 13.8564i | − 1.23935i | −0.784857 | − | 0.619677i | \(-0.787263\pi\) | ||||
0.784857 | − | 0.619677i | \(-0.212737\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −27.7128 | −1.49635 | −0.748176 | − | 0.663501i | \(-0.769070\pi\) | ||||
−0.748176 | + | 0.663501i | \(0.769070\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 42.0000i | − 1.15123i | −0.817723 | − | 0.575613i | \(-0.804764\pi\) | ||||
0.817723 | − | 0.575613i | \(-0.195236\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 41.5692i | 0.886864i | 0.896308 | + | 0.443432i | \(0.146239\pi\) | ||||
−0.896308 | + | 0.443432i | \(0.853761\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 0.0856008 | 0.0428004 | − | 0.999084i | \(-0.486372\pi\) | ||||
0.0428004 | + | 0.999084i | \(0.486372\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 94.0000i | − 1.13500i | −0.823372 | − | 0.567502i | \(-0.807910\pi\) | ||||
0.823372 | − | 0.567502i | \(-0.192090\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −138.564 | −1.25620 | −0.628100 | − | 0.778133i | \(-0.716167\pi\) | ||||
−0.628100 | + | 0.778133i | \(0.716167\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −67.0000 | −0.536000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 235.559i | 1.50835i | 0.656673 | + | 0.754176i | \(0.271963\pi\) | ||||
−0.656673 | + | 0.754176i | \(0.728037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 110.851 | 0.642241 | 0.321121 | − | 0.947038i | \(-0.395941\pi\) | ||||
0.321121 | + | 0.947038i | \(0.395941\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 384.000i | 1.85451i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.8564i | 0.0615670i | 0.999526 | + | 0.0307835i | \(0.00980024\pi\) | ||||
−0.999526 | + | 0.0307835i | \(0.990200\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 54.0000 | 0.205692 | 0.102846 | − | 0.994697i | \(-0.467205\pi\) | ||||
0.102846 | + | 0.994697i | \(0.467205\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 442.000i | 1.56754i | 0.621049 | + | 0.783772i | \(0.286707\pi\) | ||||
−0.621049 | + | 0.783772i | \(0.713293\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −55.4256 | −0.172014 | −0.0860070 | − | 0.996295i | \(-0.527411\pi\) | ||||
−0.0860070 | + | 0.996295i | \(0.527411\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 425.000 | 1.23907 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 69.2820i | − 0.179559i | −0.995962 | − | 0.0897794i | \(-0.971384\pi\) | ||||
0.995962 | − | 0.0897794i | \(-0.0286162\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −581.969 | −1.42678 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 138.000i | − 0.304510i | −0.988341 | − | 0.152255i | \(-0.951347\pi\) | ||||
0.988341 | − | 0.152255i | \(-0.0486534\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 429.549i | 0.901608i | 0.892623 | + | 0.450804i | \(0.148863\pi\) | ||||
−0.892623 | + | 0.450804i | \(0.851137\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 576.000 | 1.09914 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 178.000i | 0.324570i | 0.986744 | + | 0.162285i | \(0.0518863\pi\) | ||||
−0.986744 | + | 0.162285i | \(0.948114\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −859.097 | −1.43600 | −0.718001 | − | 0.696043i | \(-0.754942\pi\) | ||||
−0.718001 | + | 0.696043i | \(0.754942\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 434.000 | 0.695834 | 0.347917 | − | 0.937525i | \(-0.386889\pi\) | ||||
0.347917 | + | 0.937525i | \(0.386889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1163.94i | 1.72264i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 166.277 | 0.236805 | 0.118403 | − | 0.992966i | \(-0.462223\pi\) | ||||
0.118403 | + | 0.992966i | \(0.462223\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 270.000i | 0.357064i | 0.983934 | + | 0.178532i | \(0.0571349\pi\) | ||||
−0.983934 | + | 0.178532i | \(0.942865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 83.1384i | − 0.106090i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1182.00 | 1.40777 | 0.703886 | − | 0.710313i | \(-0.251446\pi\) | ||||
0.703886 | + | 0.710313i | \(0.251446\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1152.00i | − 1.32706i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1302.50 | −1.40667 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1238.00 | −1.29587 | −0.647937 | − | 0.761694i | \(-0.724368\pi\) | ||||
−0.647937 | + | 0.761694i | \(0.724368\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1759.76i | 1.73369i | 0.498575 | + | 0.866847i | \(0.333857\pi\) | ||||
−0.498575 | + | 0.866847i | \(0.666143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1025.37 | −0.980904 | −0.490452 | − | 0.871468i | \(-0.663168\pi\) | ||||
−0.490452 | + | 0.871468i | \(0.663168\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1302.00i | 1.17635i | 0.808735 | + | 0.588173i | \(0.200153\pi\) | ||||
−0.808735 | + | 0.588173i | \(0.799847\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 263.272i | 0.231347i | 0.993287 | + | 0.115674i | \(0.0369027\pi\) | ||||
−0.993287 | + | 0.115674i | \(0.963097\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1650.00 | −1.37362 | −0.686809 | − | 0.726837i | \(-0.740989\pi\) | ||||
−0.686809 | + | 0.726837i | \(0.740989\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1920.00i | 1.55688i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −166.277 | −0.128089 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −433.000 | −0.325319 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 803.672i | − 0.575061i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1108.51 | −0.774524 | −0.387262 | − | 0.921970i | \(-0.626579\pi\) | ||||
−0.387262 | + | 0.921970i | \(0.626579\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 210.000i | − 0.140059i | −0.997545 | − | 0.0700297i | \(-0.977691\pi\) | ||||
0.997545 | − | 0.0700297i | \(-0.0223094\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2605.00i | 1.69836i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −522.000 | −0.325529 | −0.162764 | − | 0.986665i | \(-0.552041\pi\) | ||||
−0.162764 | + | 0.986665i | \(0.552041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 550.000i | − 0.335614i | −0.985820 | − | 0.167807i | \(-0.946331\pi\) | ||||
0.985820 | − | 0.167807i | \(-0.0536686\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1745.91 | 1.02098 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3264.00 | 1.86938 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 374.123i | 0.205700i | 0.994697 | + | 0.102850i | \(0.0327962\pi\) | ||||
−0.994697 | + | 0.102850i | \(0.967204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1468.78 | 0.791573 | 0.395787 | − | 0.918343i | \(-0.370472\pi\) | ||||
0.395787 | + | 0.918343i | \(0.370472\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1536.00i | − 0.795964i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1676.63i | − 0.852288i | −0.904655 | − | 0.426144i | \(-0.859872\pi\) | ||||
0.904655 | − | 0.426144i | \(-0.140128\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3840.00 | 1.87972 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 578.000i | 0.277745i | 0.990310 | + | 0.138873i | \(0.0443478\pi\) | ||||
−0.990310 | + | 0.138873i | \(0.955652\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1191.65 | −0.552172 | −0.276086 | − | 0.961133i | \(-0.589037\pi\) | ||||
−0.276086 | + | 0.961133i | \(0.589037\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 469.000 | 0.213473 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2591.15i | − 1.13874i | −0.822083 | − | 0.569368i | \(-0.807188\pi\) | ||||
0.822083 | − | 0.569368i | \(-0.192812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1856.76 | 0.802044 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3918.00i | 1.63601i | 0.575214 | + | 0.818003i | \(0.304919\pi\) | ||||
−0.575214 | + | 0.818003i | \(0.695081\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3588.81i | − 1.47378i | −0.676013 | − | 0.736890i | \(-0.736294\pi\) | ||||
0.676013 | − | 0.736890i | \(-0.263706\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 192.000 | 0.0763034 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 252.000i | − 0.0985458i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3103.84 | −1.17584 | −0.587920 | − | 0.808919i | \(-0.700053\pi\) | ||||
−0.587920 | + | 0.808919i | \(0.700053\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1846.00 | −0.688487 | −0.344243 | − | 0.938880i | \(-0.611865\pi\) | ||||
−0.344243 | + | 0.938880i | \(0.611865\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 457.261i | − 0.165373i | −0.996576 | − | 0.0826866i | \(-0.973650\pi\) | ||||
0.996576 | − | 0.0826866i | \(-0.0263501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2411.01 | 0.858856 | 0.429428 | − | 0.903101i | \(-0.358715\pi\) | ||||
0.429428 | + | 0.903101i | \(0.358715\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 6528.00i | − 2.25702i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 748.246i | − 0.254926i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3948.00 | −1.30665 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2990.00i | − 0.975545i | −0.872971 | − | 0.487773i | \(-0.837809\pi\) | ||||
0.872971 | − | 0.487773i | \(-0.162191\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6124.53 | 1.94274 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3072.00 | −0.961018 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 249.415i | 0.0759162i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5431.71 | −1.63110 | −0.815548 | − | 0.578690i | \(-0.803564\pi\) | ||||
−0.815548 | + | 0.578690i | \(0.803564\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3294.00i | 0.963130i | 0.876410 | + | 0.481565i | \(0.159931\pi\) | ||||
−0.876410 | + | 0.481565i | \(0.840069\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1898.33i | 0.547795i | 0.961759 | + | 0.273897i | \(0.0883129\pi\) | ||||
−0.961759 | + | 0.273897i | \(0.911687\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4818.00 | −1.35467 | −0.677334 | − | 0.735676i | \(-0.736865\pi\) | ||||
−0.677334 | + | 0.735676i | \(0.736865\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 768.000i | 0.213186i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5708.84 | 1.54508 | 0.772540 | − | 0.634966i | \(-0.218986\pi\) | ||||
0.772540 | + | 0.634966i | \(0.218986\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −550.000 | −0.147007 | −0.0735033 | − | 0.997295i | \(-0.523418\pi\) | ||||
−0.0735033 | + | 0.997295i | \(0.523418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 5888.97i | − 1.53564i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3907.51 | 1.00659 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 6666.00i | − 1.67631i | −0.545431 | − | 0.838156i | \(-0.683634\pi\) | ||||
0.545431 | − | 0.838156i | \(-0.316366\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5819.69i | 1.44617i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4962.00 | −1.20436 | −0.602181 | − | 0.798360i | \(-0.705701\pi\) | ||||
−0.602181 | + | 0.798360i | \(0.705701\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 384.000i | − 0.0921259i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5570.28 | 1.30600 | 0.653000 | − | 0.757358i | \(-0.273510\pi\) | ||||
0.653000 | + | 0.757358i | \(0.273510\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −960.000 | −0.222537 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1039.23i | − 0.235550i | −0.993040 | − | 0.117775i | \(-0.962424\pi\) | ||||
0.993040 | − | 0.117775i | \(-0.0375762\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1053.09 | 0.236053 | 0.118027 | − | 0.993010i | \(-0.462343\pi\) | ||||
0.118027 | + | 0.993010i | \(0.462343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2814.00i | 0.617057i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4919.02i | − 1.06699i | −0.845804 | − | 0.533494i | \(-0.820879\pi\) | ||||
0.845804 | − | 0.533494i | \(-0.179121\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3102.00 | 0.658540 | 0.329270 | − | 0.944236i | \(-0.393197\pi\) | ||||
0.329270 | + | 0.944236i | \(0.393197\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4102.00i | − 0.861620i | −0.902443 | − | 0.430810i | \(-0.858228\pi\) | ||||
0.902443 | − | 0.430810i | \(-0.141772\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1496.49 | −0.307788 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4877.00 | −0.992673 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3893.65i | − 0.776346i | −0.921586 | − | 0.388173i | \(-0.873106\pi\) | ||||
0.921586 | − | 0.388173i | \(-0.126894\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1912.18 | −0.377395 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5760.00i | − 1.11408i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 12249.1i | − 2.34560i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5952.00 | 1.11741 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4738.00i | 0.880821i | 0.897797 | + | 0.440410i | \(0.145167\pi\) | ||||
−0.897797 | + | 0.440410i | \(0.854833\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4683.47 | −0.853939 | −0.426969 | − | 0.904266i | \(-0.640419\pi\) | ||||
−0.426969 | + | 0.904266i | \(0.640419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9466.00 | 1.70942 | 0.854712 | − | 0.519102i | \(-0.173733\pi\) | ||||
0.854712 | + | 0.519102i | \(0.173733\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4115.35i | 0.729152i | 0.931174 | + | 0.364576i | \(0.118786\pi\) | ||||
−0.931174 | + | 0.364576i | \(0.881214\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9893.47 | 1.73645 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 564.000i | − 0.0971573i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2785.14i | − 0.475359i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1536.00 | 0.257393 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 8374.00i | − 1.39056i | −0.718737 | − | 0.695282i | \(-0.755279\pi\) | ||||
0.718737 | − | 0.695282i | \(-0.244721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2466.44 | 0.402257 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3566.00 | −0.576417 | −0.288208 | − | 0.957568i | \(-0.593060\pi\) | ||||
−0.288208 | + | 0.957568i | \(0.593060\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4655.75i | − 0.739364i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2272.45 | −0.357728 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3894.00i | 0.602423i | 0.953557 | + | 0.301212i | \(0.0973911\pi\) | ||||
−0.953557 | + | 0.301212i | \(0.902609\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5085.30i | 0.779971i | 0.920821 | + | 0.389986i | \(0.127520\pi\) | ||||
−0.920821 | + | 0.389986i | \(0.872480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1698.00 | −0.256021 | −0.128011 | − | 0.991773i | \(-0.540859\pi\) | ||||
−0.128011 | + | 0.991773i | \(0.540859\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11904.0i | 1.77971i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2521.87 | −0.370749 | −0.185375 | − | 0.982668i | \(-0.559350\pi\) | ||||
−0.185375 | + | 0.982668i | \(0.559350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1977.00 | −0.288234 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 6013.68i | − 0.862385i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3270.11 | −0.465118 | −0.232559 | − | 0.972582i | \(-0.574710\pi\) | ||||
−0.232559 | + | 0.972582i | \(0.574710\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1920.00i | 0.268683i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 374.123i | − 0.0519339i | −0.999663 | − | 0.0259670i | \(-0.991734\pi\) | ||||
0.999663 | − | 0.0259670i | \(-0.00826647\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9792.00 | −1.33770 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 106.000i | 0.0143664i | 0.999974 | + | 0.00718319i | \(0.00228650\pi\) | ||||
−0.999974 | + | 0.00718319i | \(0.997714\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12858.7 | 1.71554 | 0.857769 | − | 0.514035i | \(-0.171850\pi\) | ||||
0.857769 | + | 0.514035i | \(0.171850\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16128.0 | 2.13496 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5417.85i | 0.706160i | 0.935593 | + | 0.353080i | \(0.114866\pi\) | ||||
−0.935593 | + | 0.353080i | \(0.885134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −831.384 | −0.107532 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2304.00i | − 0.293486i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14119.7i | 1.78500i | 0.451044 | + | 0.892502i | \(0.351052\pi\) | ||||
−0.451044 | + | 0.892502i | \(0.648948\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6918.00 | 0.861517 | 0.430759 | − | 0.902467i | \(-0.358246\pi\) | ||||
0.430759 | + | 0.902467i | \(0.358246\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4608.00i | 0.569580i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 581.969 | 0.0708775 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7270.00 | −0.878920 | −0.439460 | − | 0.898262i | \(-0.644830\pi\) | ||||
−0.439460 | + | 0.898262i | \(0.644830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3824.37i | 0.455653i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3741.23 | 0.442530 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10734.0i | 1.25153i | 0.780012 | + | 0.625764i | \(0.215213\pi\) | ||||
−0.780012 | + | 0.625764i | \(0.784787\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15643.9i | 1.81101i | 0.424333 | + | 0.905506i | \(0.360509\pi\) | ||||
−0.424333 | + | 0.905506i | \(0.639491\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −402.000 | −0.0458820 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 11904.0i | − 1.34912i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16239.7 | −1.81494 | −0.907470 | − | 0.420117i | \(-0.861989\pi\) | ||||
−0.907470 | + | 0.420117i | \(0.861989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10982.0 | −1.21885 | −0.609424 | − | 0.792844i | \(-0.708599\pi\) | ||||
−0.609424 | + | 0.792844i | \(0.708599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13025.0i | 1.42579i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17043.4 | −1.85293 | −0.926465 | − | 0.376381i | \(-0.877168\pi\) | ||||
−0.926465 | + | 0.376381i | \(0.877168\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2682.00i | − 0.287643i | −0.989604 | − | 0.143821i | \(-0.954061\pi\) | ||||
0.989604 | − | 0.143821i | \(-0.0459390\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 16378.3i | − 1.74473i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14346.0 | −1.50786 | −0.753931 | − | 0.656954i | \(-0.771844\pi\) | ||||
−0.753931 | + | 0.656954i | \(0.771844\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2268.00i | − 0.236798i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15962.6 | −1.64470 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7894.00 | −0.808021 | −0.404011 | − | 0.914754i | \(-0.632384\pi\) | ||||
−0.404011 | + | 0.914754i | \(0.632384\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3616.52i | 0.365376i | 0.983171 | + | 0.182688i | \(0.0584798\pi\) | ||||
−0.983171 | + | 0.182688i | \(0.941520\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6817.35 | 0.684296 | 0.342148 | − | 0.939646i | \(-0.388846\pi\) | ||||
0.342148 | + | 0.939646i | \(0.388846\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4734.00i | 0.469086i | 0.972106 | + | 0.234543i | \(0.0753594\pi\) | ||||
−0.972106 | + | 0.234543i | \(0.924641\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 4932.88i | − 0.485670i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18564.0 | 1.80460 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6298.00i | 0.608362i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12304.5 | −1.17371 | −0.586854 | − | 0.809693i | \(-0.699634\pi\) | ||||
−0.586854 | + | 0.809693i | \(0.699634\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −576.000 | −0.0546015 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17154.2i | 1.60605i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3907.51 | −0.363585 | −0.181793 | − | 0.983337i | \(-0.558190\pi\) | ||||
−0.181793 | + | 0.983337i | \(0.558190\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 6618.00i | − 0.608281i | −0.952627 | − | 0.304141i | \(-0.901631\pi\) | ||||
0.952627 | − | 0.304141i | \(-0.0983693\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1413.35i | 0.129116i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23808.0 | 2.14876 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 17006.0i | − 1.52564i | −0.646612 | − | 0.762819i | \(-0.723815\pi\) | ||||
0.646612 | − | 0.762819i | \(-0.276185\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11777.9 | −1.04404 | −0.522021 | − | 0.852933i | \(-0.674822\pi\) | ||||
−0.522021 | + | 0.852933i | \(0.674822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24384.0 | 2.14866 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 9297.65i | − 0.809648i | −0.914395 | − | 0.404824i | \(-0.867333\pi\) | ||||
0.914395 | − | 0.404824i | \(-0.132667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12027.4 | −1.04121 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14208.0i | 1.21569i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2327.88i | 0.198027i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 246.000 | 0.0206861 | 0.0103430 | − | 0.999947i | \(-0.496708\pi\) | ||||
0.0103430 | + | 0.999947i | \(0.496708\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14218.0i | 1.18874i | 0.804193 | + | 0.594369i | \(0.202598\pi\) | ||||
−0.804193 | + | 0.594369i | \(0.797402\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 665.108 | 0.0549764 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7033.00 | 0.578039 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2244.74i | 0.182421i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18041.0 | 1.45791 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 17850.0i | − 1.42645i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10073.6i | 0.800551i | 0.916395 | + | 0.400276i | \(0.131086\pi\) | ||||
−0.916395 | + | 0.400276i | \(0.868914\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3648.00 | 0.286721 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21458.0i | 1.67729i | 0.544678 | + | 0.838645i | \(0.316652\pi\) | ||||
−0.544678 | + | 0.838645i | \(0.683348\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22142.5 | 1.71199 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4608.00 | −0.354344 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10932.7i | 0.831658i | 0.909443 | + | 0.415829i | \(0.136509\pi\) | ||||
−0.909443 | + | 0.415829i | \(0.863491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18373.6 | −1.39020 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22206.0i | 1.66229i | 0.556053 | + | 0.831147i | \(0.312315\pi\) | ||||
−0.556053 | + | 0.831147i | \(0.687685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22863.1i | 1.70240i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2202.00 | −0.162237 | −0.0811183 | − | 0.996704i | \(-0.525849\pi\) | ||||
−0.0811183 | + | 0.996704i | \(0.525849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5690.00i | 0.417021i | 0.978020 | + | 0.208511i | \(0.0668616\pi\) | ||||
−0.978020 | + | 0.208511i | \(0.933138\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9283.79 | 0.673323 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18466.0 | 1.33232 | 0.666161 | − | 0.745808i | \(-0.267936\pi\) | ||||
0.666161 | + | 0.745808i | \(0.267936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 7482.46i | − 0.534294i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2909.85 | −0.206713 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4950.00i | 0.348055i | 0.984741 | + | 0.174028i | \(0.0556782\pi\) | ||||
−0.984741 | + | 0.174028i | \(0.944322\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 10420.0i | − 0.728946i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6834.00 | −0.473253 | −0.236626 | − | 0.971601i | \(-0.576042\pi\) | ||||
−0.236626 | + | 0.971601i | \(0.576042\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2304.00i | 0.158748i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1468.78 | −0.100188 | −0.0500941 | − | 0.998745i | \(-0.515952\pi\) | ||||
−0.0500941 | + | 0.998745i | \(0.515952\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2014.00 | −0.136693 | −0.0683467 | − | 0.997662i | \(-0.521772\pi\) | ||||
−0.0683467 | + | 0.997662i | \(0.521772\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5999.82i | 0.403186i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4544.90 | 0.303908 | 0.151954 | − | 0.988388i | \(-0.451444\pi\) | ||||
0.151954 | + | 0.988388i | \(0.451444\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2304.00i | − 0.152553i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 28918.3i | − 1.90538i | −0.303939 | − | 0.952692i | \(-0.598302\pi\) | ||||
0.303939 | − | 0.952692i | \(-0.401698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11730.0 | −0.765368 | −0.382684 | − | 0.923879i | \(-0.625000\pi\) | ||||
−0.382684 | + | 0.923879i | \(0.625000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18314.0i | 1.18918i | 0.804029 | + | 0.594590i | \(0.202685\pi\) | ||||
−0.804029 | + | 0.594590i | \(0.797315\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32756.5 | −2.10652 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19511.0 | −1.24870 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 83.1384i | 0.00527019i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4628.04 | −0.291980 | −0.145990 | − | 0.989286i | \(-0.546637\pi\) | ||||
−0.145990 | + | 0.989286i | \(0.546637\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15360.0i | 0.959910i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17666.9i | 1.09888i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18570.0 | −1.14426 | −0.572130 | − | 0.820163i | \(-0.693883\pi\) | ||||
−0.572130 | + | 0.820163i | \(0.693883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 27022.0i | − 1.65730i | −0.559767 | − | 0.828650i | \(-0.689110\pi\) | ||||
0.559767 | − | 0.828650i | \(-0.310890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2854.42 | −0.173445 | −0.0867224 | − | 0.996233i | \(-0.527639\pi\) | ||||
−0.0867224 | + | 0.996233i | \(0.527639\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5796.00 | −0.350559 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28225.5i | 1.69150i | 0.533580 | + | 0.845750i | \(0.320846\pi\) | ||||
−0.533580 | + | 0.845750i | \(0.679154\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2909.85 | −0.173583 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 8562.00i | − 0.506113i | −0.967452 | − | 0.253056i | \(-0.918564\pi\) | ||||
0.967452 | − | 0.253056i | \(-0.0814358\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 16115.0i | − 0.948262i | −0.880454 | − | 0.474131i | \(-0.842762\pi\) | ||||
0.880454 | − | 0.474131i | \(-0.157238\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36096.0 | 2.10488 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 32640.0i | − 1.89479i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18041.0 | 1.03795 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25430.0 | −1.45654 | −0.728272 | − | 0.685288i | \(-0.759676\pi\) | ||||
−0.728272 | + | 0.685288i | \(0.759676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 15976.4i | − 0.906978i | −0.891262 | − | 0.453489i | \(-0.850179\pi\) | ||||
0.891262 | − | 0.453489i | \(-0.149821\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34308.5 | 1.93908 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8358.00i | 0.468243i | 0.972207 | + | 0.234122i | \(0.0752214\pi\) | ||||
−0.972207 | + | 0.234122i | \(0.924779\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7233.04i | 0.403446i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2880.00 | 0.159244 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22898.0i | 1.26061i | 0.776348 | + | 0.630305i | \(0.217070\pi\) | ||||
−0.776348 | + | 0.630305i | \(0.782930\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7621.02 | −0.415945 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 324.000 | 0.0176074 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 8854.24i | − 0.477062i | −0.971135 | − | 0.238531i | \(-0.923334\pi\) | ||||
0.971135 | − | 0.238531i | \(-0.0766658\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1302.50 | 0.0698788 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 48768.0i | − 2.59421i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14757.1i | 0.781683i | 0.920458 | + | 0.390842i | \(0.127816\pi\) | ||||
−0.920458 | + | 0.390842i | \(0.872184\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15360.0 | −0.806783 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 24192.0i | − 1.26536i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13135.9 | 0.681343 | 0.340671 | − | 0.940182i | \(-0.389346\pi\) | ||||
0.340671 | + | 0.940182i | \(0.389346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28416.0 | 1.46778 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 15782.4i | − 0.808476i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16710.8 | −0.852504 | −0.426252 | − | 0.904605i | \(-0.640166\pi\) | ||||
−0.426252 | + | 0.904605i | \(0.640166\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2652.00i | 0.134183i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 31495.6i | − 1.58706i | −0.608529 | − | 0.793531i | \(-0.708240\pi\) | ||||
0.608529 | − | 0.793531i | \(-0.291760\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7476.00 | 0.373653 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 14750.0i | − 0.734219i | −0.930178 | − | 0.367109i | \(-0.880348\pi\) | ||||
0.930178 | − | 0.367109i | \(-0.119652\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2133.89 | 0.105363 | 0.0526815 | − | 0.998611i | \(-0.483223\pi\) | ||||
0.0526815 | + | 0.998611i | \(0.483223\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5184.00 | 0.254936 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 36082.1i | − 1.76023i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5265.43 | −0.255843 | −0.127922 | − | 0.991784i | \(-0.540831\pi\) | ||||
−0.127922 | + | 0.991784i | \(0.540831\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 20352.0i | − 0.981040i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27006.1i | 1.29664i | 0.761369 | + | 0.648319i | \(0.224528\pi\) | ||||
−0.761369 | + | 0.648319i | \(0.775472\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20538.0 | −0.978321 | −0.489160 | − | 0.872194i | \(-0.662697\pi\) | ||||
−0.489160 | + | 0.872194i | \(0.662697\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7296.00i | − 0.346177i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5736.55 | 0.270059 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10678.0 | −0.500726 | −0.250363 | − | 0.968152i | \(-0.580550\pi\) | ||||
−0.250363 | + | 0.968152i | \(0.580550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 27837.5i | − 1.29527i | −0.761949 | − | 0.647636i | \(-0.775758\pi\) | ||||
0.761949 | − | 0.647636i | \(-0.224242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7427.03 | −0.344241 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 5076.00i | − 0.233462i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36082.1i | 1.65316i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23232.0 | −1.05629 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12818.0i | 0.580575i | 0.956940 | + | 0.290287i | \(0.0937509\pi\) | ||||
−0.956940 | + | 0.290287i | \(0.906249\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45726.1 | 2.05542 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17856.0 | −0.799603 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 6748.07i | − 0.299911i | −0.988693 | − | 0.149955i | \(-0.952087\pi\) | ||||
0.988693 | − | 0.149955i | \(-0.0479130\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −332.554 | −0.0147245 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 18228.0i | − 0.801061i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 53208.6i | − 2.32964i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29130.0 | −1.26595 | −0.632977 | − | 0.774171i | \(-0.718167\pi\) | ||||
−0.632977 | + | 0.774171i | \(0.718167\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28618.0i | 1.23910i | 0.784955 | + | 0.619552i | \(0.212686\pi\) | ||||
−0.784955 | + | 0.619552i | \(0.787314\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8009.00 | 0.344225 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41548.0 | 1.77917 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12124.4i | 0.515399i | 0.966225 | + | 0.257700i | \(0.0829645\pi\) | ||||
−0.966225 | + | 0.257700i | \(0.917035\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42816.3 | 1.81347 | 0.906733 | − | 0.421706i | \(-0.138568\pi\) | ||||
0.906733 | + | 0.421706i | \(0.138568\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41574.0i | 1.74809i | 0.485846 | + | 0.874045i | \(0.338512\pi\) | ||||
−0.485846 | + | 0.874045i | \(0.661488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 22405.8i | − 0.938704i | −0.883011 | − | 0.469352i | \(-0.844487\pi\) | ||||
0.883011 | − | 0.469352i | \(-0.155513\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2550.00 | 0.106065 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16512.0i | 0.684337i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31287.8 | 1.28745 | 0.643727 | − | 0.765255i | \(-0.277387\pi\) | ||||
0.643727 | + | 0.765255i | \(0.277387\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31099.0 | −1.27512 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 6498.65i | − 0.264569i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11999.6 | 0.486792 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1920.00i | − 0.0773405i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 4253.92i | − 0.170752i | −0.996349 | − | 0.0853759i | \(-0.972791\pi\) | ||||
0.996349 | − | 0.0853759i | \(-0.0272091\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41862.0 | 1.66859 | 0.834293 | − | 0.551321i | \(-0.185876\pi\) | ||||
0.834293 | + | 0.551321i | \(0.185876\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10762.0i | 0.427468i | 0.976892 | + | 0.213734i | \(0.0685625\pi\) | ||||
−0.976892 | + | 0.213734i | \(0.931437\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1884.47 | 0.0743316 | 0.0371658 | − | 0.999309i | \(-0.488167\pi\) | ||||
0.0371658 | + | 0.999309i | \(0.488167\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35904.0 | −1.41130 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 6983.63i | − 0.272616i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7399.32 | −0.287849 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22272.0i | 0.860493i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 37647.9i | − 1.44958i | −0.688972 | − | 0.724788i | \(-0.741938\pi\) | ||||
0.688972 | − | 0.724788i | \(-0.258062\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4722.00 | −0.180577 | −0.0902884 | − | 0.995916i | \(-0.528779\pi\) | ||||
−0.0902884 | + | 0.995916i | \(0.528779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 31390.0i | − 1.19633i | −0.801374 | − | 0.598164i | \(-0.795897\pi\) | ||||
0.801374 | − | 0.598164i | \(-0.204103\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39490.8 | −1.49489 | −0.747446 | − | 0.664322i | \(-0.768720\pi\) | ||||
−0.747446 | + | 0.664322i | \(0.768720\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30720.0 | 1.15896 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5210.01i | 0.195237i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 54289.4 | 2.02759 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26112.0i | 0.968725i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 415.692i | − 0.0153704i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49728.0 | −1.82654 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5242.00i | 0.191905i | 0.995386 | + | 0.0959525i | \(0.0305897\pi\) | ||||
−0.995386 | + | 0.0959525i | \(0.969410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28211.6 | 1.02601 | 0.513004 | − | 0.858386i | \(-0.328533\pi\) | ||||
0.513004 | + | 0.858386i | \(0.328533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11340.0 | 0.411062 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5819.69i | 0.209578i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1912.18 | 0.0686367 | 0.0343184 | − | 0.999411i | \(-0.489074\pi\) | ||||
0.0343184 | + | 0.999411i | \(0.489074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 35712.0i | − 1.27354i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 928.379i | − 0.0329999i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20118.0 | 0.710495 | 0.355248 | − | 0.934772i | \(-0.384397\pi\) | ||||
0.355248 | + | 0.934772i | \(0.384397\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 39950.0i | − 1.40635i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3491.81 | −0.122133 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3950.00 | −0.137717 | −0.0688585 | − | 0.997626i | \(-0.521936\pi\) | ||||
−0.0688585 | + | 0.997626i | \(0.521936\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 11570.1i | − 0.400823i | −0.979712 | − | 0.200412i | \(-0.935772\pi\) | ||||
0.979712 | − | 0.200412i | \(-0.0642279\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7482.46 | −0.258391 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 46146.0i | − 1.58347i | −0.610866 | − | 0.791734i | \(-0.709179\pi\) | ||||
0.610866 | − | 0.791734i | \(-0.290821\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18041.0i | 0.617110i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47718.0 | 1.62197 | 0.810985 | − | 0.585067i | \(-0.198932\pi\) | ||||
0.810985 | + | 0.585067i | \(0.198932\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43008.0i | 1.45728i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14466.1 | 0.487106 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17503.0 | −0.587526 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25578.9i | 0.853280i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34391.6 | −1.14370 | −0.571851 | − | 0.820358i | \(-0.693774\pi\) | ||||
−0.571851 | + | 0.820358i | \(0.693774\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2118.00i | 0.0699999i | 0.999387 | + | 0.0349999i | \(0.0111431\pi\) | ||||
−0.999387 | + | 0.0349999i | \(0.988857\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15242.0i | 0.502197i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8826.00 | −0.289016 | −0.144508 | − | 0.989504i | \(-0.546160\pi\) | ||||
−0.144508 | + | 0.989504i | \(0.546160\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 49644.0i | − 1.62066i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23361.9 | 0.758015 | 0.379008 | − | 0.925394i | \(-0.376265\pi\) | ||||
0.379008 | + | 0.925394i | \(0.376265\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6336.00 | −0.204956 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 61245.3i | − 1.96915i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16738.5 | −0.536546 | −0.268273 | − | 0.963343i | \(-0.586453\pi\) | ||||
−0.268273 | + | 0.963343i | \(0.586453\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 33408.0i | − 1.06443i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13094.3i | 0.415949i | 0.978134 | + | 0.207974i | \(0.0666870\pi\) | ||||
−0.978134 | + | 0.207974i | \(0.933313\pi\) | |||||||
\(998\) | 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 | 576.4.d.e.289.1 | 4 | ||
3.2 | odd | 2 | 64.4.b.b.33.4 | yes | 4 | ||
4.3 | odd | 2 | inner | 576.4.d.e.289.2 | 4 | ||
8.3 | odd | 2 | inner | 576.4.d.e.289.4 | 4 | ||
8.5 | even | 2 | inner | 576.4.d.e.289.3 | 4 | ||
12.11 | even | 2 | 64.4.b.b.33.2 | yes | 4 | ||
16.3 | odd | 4 | 2304.4.a.bi.1.1 | 2 | |||
16.5 | even | 4 | 2304.4.a.bi.1.2 | 2 | |||
16.11 | odd | 4 | 2304.4.a.ba.1.2 | 2 | |||
16.13 | even | 4 | 2304.4.a.ba.1.1 | 2 | |||
24.5 | odd | 2 | 64.4.b.b.33.1 | ✓ | 4 | ||
24.11 | even | 2 | 64.4.b.b.33.3 | yes | 4 | ||
48.5 | odd | 4 | 256.4.a.m.1.1 | 2 | |||
48.11 | even | 4 | 256.4.a.i.1.1 | 2 | |||
48.29 | odd | 4 | 256.4.a.i.1.2 | 2 | |||
48.35 | even | 4 | 256.4.a.m.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
64.4.b.b.33.1 | ✓ | 4 | 24.5 | odd | 2 | ||
64.4.b.b.33.2 | yes | 4 | 12.11 | even | 2 | ||
64.4.b.b.33.3 | yes | 4 | 24.11 | even | 2 | ||
64.4.b.b.33.4 | yes | 4 | 3.2 | odd | 2 | ||
256.4.a.i.1.1 | 2 | 48.11 | even | 4 | |||
256.4.a.i.1.2 | 2 | 48.29 | odd | 4 | |||
256.4.a.m.1.1 | 2 | 48.5 | odd | 4 | |||
256.4.a.m.1.2 | 2 | 48.35 | even | 4 | |||
576.4.d.e.289.1 | 4 | 1.1 | even | 1 | trivial | ||
576.4.d.e.289.2 | 4 | 4.3 | odd | 2 | inner | ||
576.4.d.e.289.3 | 4 | 8.5 | even | 2 | inner | ||
576.4.d.e.289.4 | 4 | 8.3 | odd | 2 | inner | ||
2304.4.a.ba.1.1 | 2 | 16.13 | even | 4 | |||
2304.4.a.ba.1.2 | 2 | 16.11 | odd | 4 | |||
2304.4.a.bi.1.1 | 2 | 16.3 | odd | 4 | |||
2304.4.a.bi.1.2 | 2 | 16.5 | even | 4 |