Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(1025,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 576) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.2 | ||
Root | \(-0.517638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1025 |
Dual form | 2304.3.e.h.1025.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | − 2.44949i | − 0.489898i | −0.969536 | − | 0.244949i | \(-0.921229\pi\) | ||||
0.969536 | − | 0.244949i | \(-0.0787712\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410 | 0.494872 | 0.247436 | − | 0.968904i | \(-0.420412\pi\) | ||||
0.247436 | + | 0.968904i | \(0.420412\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.48528i | 0.771389i | 0.922627 | + | 0.385695i | \(0.126038\pi\) | ||||
−0.922627 | + | 0.385695i | \(0.873962\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.3923 | 0.799408 | 0.399704 | − | 0.916644i | \(-0.369113\pi\) | ||||
0.399704 | + | 0.916644i | \(0.369113\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 12.7279i | − 0.748701i | −0.927287 | − | 0.374351i | \(-0.877866\pi\) | ||||
0.927287 | − | 0.374351i | \(-0.122134\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.210526 | −0.105263 | − | 0.994444i | \(-0.533568\pi\) | ||||
−0.105263 | + | 0.994444i | \(0.533568\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 34.2929i | 1.49099i | 0.666509 | + | 0.745497i | \(0.267788\pi\) | ||||
−0.666509 | + | 0.745497i | \(0.732212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.760000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 46.5403i | 1.60484i | 0.596761 | + | 0.802419i | \(0.296454\pi\) | ||||
−0.596761 | + | 0.802419i | \(0.703546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −38.1051 | −1.22920 | −0.614599 | − | 0.788840i | \(-0.710682\pi\) | ||||
−0.614599 | + | 0.788840i | \(0.710682\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 8.48528i | − 0.242437i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27.7128 | −0.748995 | −0.374497 | − | 0.927228i | \(-0.622185\pi\) | ||||
−0.374497 | + | 0.927228i | \(0.622185\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 29.6985i | 0.724353i | 0.932109 | + | 0.362177i | \(0.117966\pi\) | ||||
−0.932109 | + | 0.362177i | \(0.882034\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 56.0000 | 1.30233 | 0.651163 | − | 0.758938i | \(-0.274282\pi\) | ||||
0.651163 | + | 0.758938i | \(0.274282\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 63.6867i | − 1.35504i | −0.735506 | − | 0.677518i | \(-0.763055\pi\) | ||||
0.735506 | − | 0.677518i | \(-0.236945\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −37.0000 | −0.755102 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 71.0352i | − 1.34029i | −0.742232 | − | 0.670143i | \(-0.766233\pi\) | ||||
0.742232 | − | 0.670143i | \(-0.233767\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.7846 | 0.377902 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 101.823i | 1.72582i | 0.505358 | + | 0.862910i | \(0.331361\pi\) | ||||
−0.505358 | + | 0.862910i | \(0.668639\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 69.2820 | 1.13577 | 0.567886 | − | 0.823108i | \(-0.307762\pi\) | ||||
0.567886 | + | 0.823108i | \(0.307762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 25.4558i | − 0.391628i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 28.0000 | 0.417910 | 0.208955 | − | 0.977925i | \(-0.432994\pi\) | ||||
0.208955 | + | 0.977925i | \(0.432994\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 53.8888i | 0.758997i | 0.925192 | + | 0.379498i | \(0.123903\pi\) | ||||
−0.925192 | + | 0.379498i | \(0.876097\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −20.0000 | −0.273973 | −0.136986 | − | 0.990573i | \(-0.543742\pi\) | ||||
−0.136986 | + | 0.990573i | \(0.543742\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 29.3939i | 0.381739i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −72.7461 | −0.920837 | −0.460419 | − | 0.887702i | \(-0.652301\pi\) | ||||
−0.460419 | + | 0.887702i | \(0.652301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76.3675i | 0.920091i | 0.887895 | + | 0.460045i | \(0.152167\pi\) | ||||
−0.887895 | + | 0.460045i | \(0.847833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −31.1769 | −0.366787 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 55.1543i | 0.619712i | 0.950784 | + | 0.309856i | \(0.100281\pi\) | ||||
−0.950784 | + | 0.309856i | \(0.899719\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 36.0000 | 0.395604 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.79796i | 0.103136i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | −0.0824742 | −0.0412371 | − | 0.999149i | \(-0.513130\pi\) | ||||
−0.0412371 | + | 0.999149i | \(0.513130\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.44949i | 0.0242524i | 0.999926 | + | 0.0121262i | \(0.00385998\pi\) | ||||
−0.999926 | + | 0.0121262i | \(0.996140\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 24.2487 | 0.235424 | 0.117712 | − | 0.993048i | \(-0.462444\pi\) | ||||
0.117712 | + | 0.993048i | \(0.462444\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 101.823i | 0.951620i | 0.879548 | + | 0.475810i | \(0.157845\pi\) | ||||
−0.879548 | + | 0.475810i | \(0.842155\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −107.387 | −0.985203 | −0.492602 | − | 0.870255i | \(-0.663954\pi\) | ||||
−0.492602 | + | 0.870255i | \(0.663954\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.24264i | 0.0375455i | 0.999824 | + | 0.0187727i | \(0.00597590\pi\) | ||||
−0.999824 | + | 0.0187727i | \(0.994024\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 84.0000 | 0.730435 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 44.0908i | − 0.370511i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 49.0000 | 0.404959 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 107.778i | − 0.862220i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 225.167 | 1.77297 | 0.886483 | − | 0.462762i | \(-0.153141\pi\) | ||||
0.886483 | + | 0.462762i | \(0.153141\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 220.617i | 1.68410i | 0.539398 | + | 0.842051i | \(0.318652\pi\) | ||||
−0.539398 | + | 0.842051i | \(0.681348\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.8564 | −0.104184 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 199.404i | − 1.45550i | −0.685840 | − | 0.727752i | \(-0.740565\pi\) | ||||
0.685840 | − | 0.727752i | \(-0.259435\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 148.000 | 1.06475 | 0.532374 | − | 0.846509i | \(-0.321300\pi\) | ||||
0.532374 | + | 0.846509i | \(0.321300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 88.1816i | 0.616655i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 114.000 | 0.786207 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 80.8332i | 0.542504i | 0.962508 | + | 0.271252i | \(0.0874377\pi\) | ||||
−0.962508 | + | 0.271252i | \(0.912562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.46410 | 0.0229411 | 0.0114705 | − | 0.999934i | \(-0.496349\pi\) | ||||
0.0114705 | + | 0.999934i | \(0.496349\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 93.3381i | 0.602181i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −69.2820 | −0.441287 | −0.220643 | − | 0.975355i | \(-0.570816\pi\) | ||||
−0.220643 | + | 0.975355i | \(0.570816\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 118.794i | 0.737851i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 272.000 | 1.66871 | 0.834356 | − | 0.551226i | \(-0.185840\pi\) | ||||
0.834356 | + | 0.551226i | \(0.185840\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 254.747i | − 1.52543i | −0.646734 | − | 0.762715i | \(-0.723866\pi\) | ||||
0.646734 | − | 0.762715i | \(-0.276134\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −61.0000 | −0.360947 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 129.823i | − 0.750422i | −0.926939 | − | 0.375211i | \(-0.877570\pi\) | ||||
0.926939 | − | 0.375211i | \(-0.122430\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 65.8179 | 0.376102 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 288.500i | 1.61173i | 0.592100 | + | 0.805865i | \(0.298299\pi\) | ||||
−0.592100 | + | 0.805865i | \(0.701701\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 349.874 | 1.93301 | 0.966503 | − | 0.256653i | \(-0.0826199\pi\) | ||||
0.966503 | + | 0.256653i | \(0.0826199\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 67.8823i | 0.366931i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 108.000 | 0.577540 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 137.171i | 0.718175i | 0.933304 | + | 0.359088i | \(0.116912\pi\) | ||||
−0.933304 | + | 0.359088i | \(0.883088\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 86.0000 | 0.445596 | 0.222798 | − | 0.974865i | \(-0.428481\pi\) | ||||
0.222798 | + | 0.974865i | \(0.428481\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 286.590i | 1.45477i | 0.686228 | + | 0.727387i | \(0.259265\pi\) | ||||
−0.686228 | + | 0.727387i | \(0.740735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −239.023 | −1.20112 | −0.600560 | − | 0.799579i | \(-0.705056\pi\) | ||||
−0.600560 | + | 0.799579i | \(0.705056\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 161.220i | 0.794189i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 72.7461 | 0.354859 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 33.9411i | − 0.162398i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 244.000 | 1.15640 | 0.578199 | − | 0.815896i | \(-0.303756\pi\) | ||||
0.578199 | + | 0.815896i | \(0.303756\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 137.171i | − 0.638007i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −132.000 | −0.608295 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 132.272i | − 0.598518i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −107.387 | −0.481557 | −0.240778 | − | 0.970580i | \(-0.577403\pi\) | ||||
−0.240778 | + | 0.970580i | \(0.577403\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 296.985i | 1.30830i | 0.756363 | + | 0.654152i | \(0.226974\pi\) | ||||
−0.756363 | + | 0.654152i | \(0.773026\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −128.172 | −0.559702 | −0.279851 | − | 0.960043i | \(-0.590285\pi\) | ||||
−0.279851 | + | 0.960043i | \(0.590285\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 173.948i | − 0.746559i | −0.927719 | − | 0.373280i | \(-0.878233\pi\) | ||||
0.927719 | − | 0.373280i | \(-0.121767\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −156.000 | −0.663830 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 9.79796i | − 0.0409956i | −0.999790 | − | 0.0204978i | \(-0.993475\pi\) | ||||
0.999790 | − | 0.0204978i | \(-0.00652512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −196.000 | −0.813278 | −0.406639 | − | 0.913589i | \(-0.633299\pi\) | ||||
−0.406639 | + | 0.913589i | \(0.633299\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 90.6311i | 0.369923i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −41.5692 | −0.168296 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 161.220i | 0.642312i | 0.947026 | + | 0.321156i | \(0.104071\pi\) | ||||
−0.947026 | + | 0.321156i | \(0.895929\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −290.985 | −1.15014 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 250.316i | 0.973991i | 0.873404 | + | 0.486996i | \(0.161907\pi\) | ||||
−0.873404 | + | 0.486996i | \(0.838093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −96.0000 | −0.370656 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.3939i | 0.111764i | 0.998437 | + | 0.0558819i | \(0.0177970\pi\) | ||||
−0.998437 | + | 0.0558819i | \(0.982203\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −174.000 | −0.656604 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 257.196i | 0.956121i | 0.878327 | + | 0.478060i | \(0.158660\pi\) | ||||
−0.878327 | + | 0.478060i | \(0.841340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 266.736 | 0.984265 | 0.492133 | − | 0.870520i | \(-0.336218\pi\) | ||||
0.492133 | + | 0.870520i | \(0.336218\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 161.220i | 0.586256i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −65.8179 | −0.237610 | −0.118805 | − | 0.992918i | \(-0.537906\pi\) | ||||
−0.118805 | + | 0.992918i | \(0.537906\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 275.772i | 0.981394i | 0.871330 | + | 0.490697i | \(0.163258\pi\) | ||||
−0.871330 | + | 0.490697i | \(0.836742\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 496.000 | 1.75265 | 0.876325 | − | 0.481720i | \(-0.159988\pi\) | ||||
0.876325 | + | 0.481720i | \(0.159988\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 102.879i | 0.358462i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 127.000 | 0.439446 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 188.611i | − 0.643723i | −0.946787 | − | 0.321861i | \(-0.895692\pi\) | ||||
0.946787 | − | 0.321861i | \(-0.104308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 249.415 | 0.845476 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 356.382i | 1.19191i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 193.990 | 0.644484 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 169.706i | − 0.556412i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 220.000 | 0.716612 | 0.358306 | − | 0.933604i | \(-0.383354\pi\) | ||||
0.358306 | + | 0.933604i | \(0.383354\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 362.524i | 1.16567i | 0.812589 | + | 0.582837i | \(0.198057\pi\) | ||||
−0.812589 | + | 0.582837i | \(0.801943\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 554.000 | 1.76997 | 0.884984 | − | 0.465621i | \(-0.154169\pi\) | ||||
0.884984 | + | 0.465621i | \(0.154169\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.0454i | 0.0695439i | 0.999395 | + | 0.0347719i | \(0.0110705\pi\) | ||||
−0.999395 | + | 0.0347719i | \(0.988930\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −394.908 | −1.23795 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 50.9117i | 0.157621i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 197.454 | 0.607550 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 220.617i | − 0.670569i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 244.000 | 0.737160 | 0.368580 | − | 0.929596i | \(-0.379844\pi\) | ||||
0.368580 | + | 0.929596i | \(0.379844\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 68.5857i | − 0.204733i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −188.000 | −0.557864 | −0.278932 | − | 0.960311i | \(-0.589980\pi\) | ||||
−0.278932 | + | 0.960311i | \(0.589980\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 323.333i | − 0.948190i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −297.913 | −0.868550 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.4558i | 0.0733598i | 0.999327 | + | 0.0366799i | \(0.0116782\pi\) | ||||
−0.999327 | + | 0.0366799i | \(0.988322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 609.682 | 1.74694 | 0.873470 | − | 0.486878i | \(-0.161865\pi\) | ||||
0.873470 | + | 0.486878i | \(0.161865\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 267.286i | − 0.757185i | −0.925563 | − | 0.378593i | \(-0.876408\pi\) | ||||
0.925563 | − | 0.378593i | \(-0.123592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 132.000 | 0.371831 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 612.372i | 1.70577i | 0.522097 | + | 0.852886i | \(0.325150\pi\) | ||||
−0.522097 | + | 0.852886i | \(0.674850\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −345.000 | −0.955679 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 48.9898i | 0.134219i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −481.510 | −1.31202 | −0.656008 | − | 0.754754i | \(-0.727756\pi\) | ||||
−0.656008 | + | 0.754754i | \(0.727756\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 246.073i | − 0.663270i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −540.400 | −1.44879 | −0.724397 | − | 0.689383i | \(-0.757882\pi\) | ||||
−0.724397 | + | 0.689383i | \(0.757882\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 483.661i | 1.28292i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −268.000 | −0.707124 | −0.353562 | − | 0.935411i | \(-0.615030\pi\) | ||||
−0.353562 | + | 0.935411i | \(0.615030\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 480.100i | − 1.25352i | −0.779210 | − | 0.626762i | \(-0.784380\pi\) | ||||
0.779210 | − | 0.626762i | \(-0.215620\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 72.0000 | 0.187013 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 438.459i | − 1.12714i | −0.826067 | − | 0.563572i | \(-0.809427\pi\) | ||||
0.826067 | − | 0.563572i | \(-0.190573\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 436.477 | 1.11631 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 178.191i | 0.451116i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −526.543 | −1.32631 | −0.663153 | − | 0.748484i | \(-0.730782\pi\) | ||||
−0.663153 | + | 0.748484i | \(0.730782\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 420.021i | − 1.04743i | −0.851892 | − | 0.523717i | \(-0.824545\pi\) | ||||
0.851892 | − | 0.523717i | \(-0.175455\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −396.000 | −0.982630 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 235.151i | − 0.577767i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 640.000 | 1.56479 | 0.782396 | − | 0.622781i | \(-0.213997\pi\) | ||||
0.782396 | + | 0.622781i | \(0.213997\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 352.727i | 0.854059i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 187.061 | 0.450751 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 364.867i | − 0.870805i | −0.900236 | − | 0.435402i | \(-0.856606\pi\) | ||||
0.900236 | − | 0.435402i | \(-0.143394\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −495.367 | −1.17664 | −0.588321 | − | 0.808627i | \(-0.700211\pi\) | ||||
−0.588321 | + | 0.808627i | \(0.700211\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 241.831i | − 0.569013i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 240.000 | 0.562061 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 83.2827i | − 0.193231i | −0.995322 | − | 0.0966156i | \(-0.969198\pi\) | ||||
0.995322 | − | 0.0966156i | \(-0.0308017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 106.000 | 0.244804 | 0.122402 | − | 0.992481i | \(-0.460940\pi\) | ||||
0.122402 | + | 0.992481i | \(0.460940\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 137.171i | − 0.313893i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 613.146 | 1.39669 | 0.698344 | − | 0.715762i | \(-0.253921\pi\) | ||||
0.698344 | + | 0.715762i | \(0.253921\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 212.132i | 0.478853i | 0.970914 | + | 0.239427i | \(0.0769595\pi\) | ||||
−0.970914 | + | 0.239427i | \(0.923041\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 135.100 | 0.303595 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 182.434i | 0.406311i | 0.979147 | + | 0.203155i | \(0.0651197\pi\) | ||||
−0.979147 | + | 0.203155i | \(0.934880\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −252.000 | −0.558758 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 88.1816i | − 0.193806i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −344.000 | −0.752735 | −0.376368 | − | 0.926470i | \(-0.622827\pi\) | ||||
−0.376368 | + | 0.926470i | \(0.622827\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 110.227i | 0.239104i | 0.992828 | + | 0.119552i | \(0.0381459\pi\) | ||||
−0.992828 | + | 0.119552i | \(0.961854\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −114.315 | −0.246901 | −0.123451 | − | 0.992351i | \(-0.539396\pi\) | ||||
−0.123451 | + | 0.992351i | \(0.539396\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.48528i | − 0.0181698i | −0.999959 | − | 0.00908488i | \(-0.997108\pi\) | ||||
0.999959 | − | 0.00908488i | \(-0.00289185\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 96.9948 | 0.206812 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 475.176i | 1.00460i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −76.0000 | −0.160000 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 778.938i | − 1.62617i | −0.582142 | − | 0.813087i | \(-0.697785\pi\) | ||||
0.582142 | − | 0.813087i | \(-0.302215\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −288.000 | −0.598753 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.5959i | 0.0404040i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −820.992 | −1.68582 | −0.842908 | − | 0.538058i | \(-0.819158\pi\) | ||||
−0.842908 | + | 0.538058i | \(0.819158\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 390.323i | − 0.794955i | −0.917612 | − | 0.397478i | \(-0.869886\pi\) | ||||
0.917612 | − | 0.397478i | \(-0.130114\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 592.361 | 1.20154 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 186.676i | 0.375606i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −128.000 | −0.256513 | −0.128257 | − | 0.991741i | \(-0.540938\pi\) | ||||
−0.128257 | + | 0.991741i | \(0.540938\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 181.262i | 0.360362i | 0.983633 | + | 0.180181i | \(0.0576684\pi\) | ||||
−0.983633 | + | 0.180181i | \(0.942332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.0118812 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 438.459i | 0.861412i | 0.902492 | + | 0.430706i | \(0.141735\pi\) | ||||
−0.902492 | + | 0.430706i | \(0.858265\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −69.2820 | −0.135581 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 59.3970i | − 0.115334i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 540.400 | 1.04526 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 691.550i | − 1.32735i | −0.748020 | − | 0.663676i | \(-0.768995\pi\) | ||||
0.748020 | − | 0.663676i | \(-0.231005\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −484.000 | −0.925430 | −0.462715 | − | 0.886507i | \(-0.653125\pi\) | ||||
−0.462715 | + | 0.886507i | \(0.653125\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 484.999i | 0.920302i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −647.000 | −1.22306 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 308.636i | 0.579054i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 249.415 | 0.466197 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 313.955i | − 0.582478i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −523.079 | −0.966875 | −0.483437 | − | 0.875379i | \(-0.660612\pi\) | ||||
−0.483437 | + | 0.875379i | \(0.660612\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 263.044i | 0.482649i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −184.000 | −0.336380 | −0.168190 | − | 0.985755i | \(-0.553792\pi\) | ||||
−0.168190 | + | 0.985755i | \(0.553792\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 186.161i | − 0.337861i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −252.000 | −0.455696 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 918.559i | − 1.64912i | −0.565776 | − | 0.824559i | \(-0.691423\pi\) | ||||
0.565776 | − | 0.824559i | \(-0.308577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 581.969 | 1.04109 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 330.926i | − 0.587790i | −0.955838 | − | 0.293895i | \(-0.905048\pi\) | ||||
0.955838 | − | 0.293895i | \(-0.0949517\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3923 | 0.0183935 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1056.42i | 1.85662i | 0.371805 | + | 0.928311i | \(0.378739\pi\) | ||||
−0.371805 | + | 0.928311i | \(0.621261\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −152.000 | −0.266200 | −0.133100 | − | 0.991103i | \(-0.542493\pi\) | ||||
−0.133100 | + | 0.991103i | \(0.542493\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 651.564i | 1.13316i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 790.000 | 1.36915 | 0.684575 | − | 0.728942i | \(-0.259988\pi\) | ||||
0.684575 | + | 0.728942i | \(0.259988\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 264.545i | 0.455327i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 602.754 | 1.03388 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1154.00i | − 1.96593i | −0.183805 | − | 0.982963i | \(-0.558841\pi\) | ||||
0.183805 | − | 0.982963i | \(-0.441159\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 152.420 | 0.258778 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 377.595i | − 0.636754i | −0.947964 | − | 0.318377i | \(-0.896862\pi\) | ||||
0.947964 | − | 0.318377i | \(-0.103138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −108.000 | −0.181513 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 318.434i | − 0.531609i | −0.964027 | − | 0.265804i | \(-0.914362\pi\) | ||||
0.964027 | − | 0.265804i | \(-0.0856375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 202.000 | 0.336106 | 0.168053 | − | 0.985778i | \(-0.446252\pi\) | ||||
0.168053 | + | 0.985778i | \(0.446252\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 120.025i | − 0.198388i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 391.443 | 0.644882 | 0.322441 | − | 0.946590i | \(-0.395497\pi\) | ||||
0.322441 | + | 0.946590i | \(0.395497\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 661.852i | − 1.08323i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 803.672 | 1.31105 | 0.655523 | − | 0.755175i | \(-0.272448\pi\) | ||||
0.655523 | + | 0.755175i | \(0.272448\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1115.81i | − 1.80845i | −0.427055 | − | 0.904226i | \(-0.640449\pi\) | ||||
0.427055 | − | 0.904226i | \(-0.359551\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −200.000 | −0.323102 | −0.161551 | − | 0.986864i | \(-0.551650\pi\) | ||||
−0.161551 | + | 0.986864i | \(0.551650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 191.060i | 0.306678i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 211.000 | 0.337600 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 352.727i | 0.560773i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −668.572 | −1.05954 | −0.529771 | − | 0.848140i | \(-0.677722\pi\) | ||||
−0.529771 | + | 0.848140i | \(0.677722\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 551.543i | − 0.868572i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −384.515 | −0.603635 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1090.36i | 1.70103i | 0.525953 | + | 0.850514i | \(0.323709\pi\) | ||||
−0.525953 | + | 0.850514i | \(0.676291\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 416.000 | 0.646967 | 0.323484 | − | 0.946234i | \(-0.395146\pi\) | ||||
0.323484 | + | 0.946234i | \(0.395146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 680.958i | − 1.05249i | −0.850334 | − | 0.526243i | \(-0.823600\pi\) | ||||
0.850334 | − | 0.526243i | \(-0.176400\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −864.000 | −1.33128 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 110.227i | − 0.168801i | −0.996432 | − | 0.0844005i | \(-0.973102\pi\) | ||||
0.996432 | − | 0.0844005i | \(-0.0268975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 540.400 | 0.825038 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 441.235i | − 0.669552i | −0.942298 | − | 0.334776i | \(-0.891339\pi\) | ||||
0.942298 | − | 0.334776i | \(-0.108661\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −484.974 | −0.733698 | −0.366849 | − | 0.930281i | \(-0.619563\pi\) | ||||
−0.366849 | + | 0.930281i | \(0.619563\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.9411i | 0.0510393i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1596.00 | −2.39280 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 587.878i | 0.876122i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 334.000 | 0.496285 | 0.248143 | − | 0.968724i | \(-0.420180\pi\) | ||||
0.248143 | + | 0.968724i | \(0.420180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 879.367i | 1.29892i | 0.760397 | + | 0.649459i | \(0.225004\pi\) | ||||
−0.760397 | + | 0.649459i | \(0.774996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.7128 | −0.0408142 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 568.514i | − 0.832378i | −0.909278 | − | 0.416189i | \(-0.863366\pi\) | ||||
0.909278 | − | 0.416189i | \(-0.136634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −488.438 | −0.713049 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 738.219i | − 1.07144i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −832.000 | −1.20405 | −0.602026 | − | 0.798476i | \(-0.705640\pi\) | ||||
−0.602026 | + | 0.798476i | \(0.705640\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 362.524i | − 0.521618i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 378.000 | 0.542324 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 433.560i | − 0.618487i | −0.950983 | − | 0.309244i | \(-0.899924\pi\) | ||||
0.950983 | − | 0.309244i | \(-0.100076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 110.851 | 0.157683 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.48528i | 0.0120018i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −197.454 | −0.278496 | −0.139248 | − | 0.990258i | \(-0.544469\pi\) | ||||
−0.139248 | + | 0.990258i | \(0.544469\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1306.73i | − 1.83273i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 216.000 | 0.302098 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 220.454i | − 0.306612i | −0.988179 | − | 0.153306i | \(-0.951008\pi\) | ||||
0.988179 | − | 0.153306i | \(-0.0489920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 84.0000 | 0.116505 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 884.266i | 1.21968i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −862.561 | −1.18647 | −0.593233 | − | 0.805031i | \(-0.702149\pi\) | ||||
−0.593233 | + | 0.805031i | \(0.702149\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 712.764i | − 0.975053i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −169.741 | −0.231570 | −0.115785 | − | 0.993274i | \(-0.536938\pi\) | ||||
−0.115785 | + | 0.993274i | \(0.536938\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 237.588i | 0.322372i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −872.000 | −1.17997 | −0.589986 | − | 0.807413i | \(-0.700867\pi\) | ||||
−0.589986 | + | 0.807413i | \(0.700867\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 195.959i | − 0.263740i | −0.991267 | − | 0.131870i | \(-0.957902\pi\) | ||||
0.991267 | − | 0.131870i | \(-0.0420982\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 198.000 | 0.265772 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 352.727i | 0.470930i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −481.510 | −0.641159 | −0.320579 | − | 0.947222i | \(-0.603878\pi\) | ||||
−0.320579 | + | 0.947222i | \(0.603878\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 8.48528i | − 0.0112388i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1202.04 | 1.58790 | 0.793952 | − | 0.607981i | \(-0.208020\pi\) | ||||
0.793952 | + | 0.607981i | \(0.208020\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 929.138i | 1.22094i | 0.792038 | + | 0.610472i | \(0.209020\pi\) | ||||
−0.792038 | + | 0.610472i | \(0.790980\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −372.000 | −0.487549 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1058.18i | 1.37963i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 218.000 | 0.283485 | 0.141743 | − | 0.989904i | \(-0.454729\pi\) | ||||
0.141743 | + | 0.989904i | \(0.454729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1041.03i | − 1.34674i | −0.739304 | − | 0.673372i | \(-0.764845\pi\) | ||||
0.739304 | − | 0.673372i | \(-0.235155\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −723.997 | −0.934190 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 118.794i | − 0.152495i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −457.261 | −0.585482 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 169.706i | 0.216186i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 404.000 | 0.513342 | 0.256671 | − | 0.966499i | \(-0.417374\pi\) | ||||
0.256671 | + | 0.966499i | \(0.417374\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.6969i | 0.0185802i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 720.000 | 0.907945 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1511.34i | − 1.89628i | −0.317853 | − | 0.948140i | \(-0.602962\pi\) | ||||
0.317853 | − | 0.948140i | \(-0.397038\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −810.600 | −1.01452 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 169.706i | − 0.211340i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 290.985 | 0.361471 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 106.066i | − 0.131108i | −0.997849 | − | 0.0655538i | \(-0.979119\pi\) | ||||
0.997849 | − | 0.0655538i | \(-0.0208814\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1132.00 | −1.39581 | −0.697904 | − | 0.716191i | \(-0.745884\pi\) | ||||
−0.697904 | + | 0.716191i | \(0.745884\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 666.261i | − 0.817498i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −224.000 | −0.274174 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 722.599i | − 0.880146i | −0.897962 | − | 0.440073i | \(-0.854953\pi\) | ||||
0.897962 | − | 0.440073i | \(-0.145047\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3923 | −0.0126273 | −0.00631367 | − | 0.999980i | \(-0.502010\pi\) | ||||
−0.00631367 | + | 0.999980i | \(0.502010\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1306.73i | − 1.58009i | −0.613050 | − | 0.790044i | \(-0.710057\pi\) | ||||
0.613050 | − | 0.790044i | \(-0.289943\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 530.008 | 0.639334 | 0.319667 | − | 0.947530i | \(-0.396429\pi\) | ||||
0.319667 | + | 0.947530i | \(0.396429\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 470.933i | 0.565346i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −624.000 | −0.747305 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 827.928i | 0.986803i | 0.869802 | + | 0.493401i | \(0.164247\pi\) | ||||
−0.869802 | + | 0.493401i | \(0.835753\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1325.00 | −1.57551 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 149.419i | 0.176827i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 169.741 | 0.200403 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 950.352i | − 1.11675i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1011.52 | −1.18584 | −0.592918 | − | 0.805263i | \(-0.702024\pi\) | ||||
−0.592918 | + | 0.805263i | \(0.702024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 538.815i | 0.628723i | 0.949303 | + | 0.314361i | \(0.101790\pi\) | ||||
−0.949303 | + | 0.314361i | \(0.898210\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1160.00 | 1.35041 | 0.675204 | − | 0.737631i | \(-0.264056\pi\) | ||||
0.675204 | + | 0.737631i | \(0.264056\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 391.918i | − 0.454135i | −0.973879 | − | 0.227067i | \(-0.927086\pi\) | ||||
0.973879 | − | 0.227067i | \(-0.0729138\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −318.000 | −0.367630 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 617.271i | − 0.710324i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 290.985 | 0.334081 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 373.352i | − 0.426688i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 526.543 | 0.600392 | 0.300196 | − | 0.953878i | \(-0.402948\pi\) | ||||
0.300196 | + | 0.953878i | \(0.402948\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 258.801i | − 0.293758i | −0.989154 | − | 0.146879i | \(-0.953077\pi\) | ||||
0.989154 | − | 0.146879i | \(-0.0469228\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −520.000 | −0.588901 | −0.294451 | − | 0.955667i | \(-0.595137\pi\) | ||||
−0.294451 | + | 0.955667i | \(0.595137\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 29.3939i | − 0.0331385i | −0.999863 | − | 0.0165693i | \(-0.994726\pi\) | ||||
0.999863 | − | 0.0165693i | \(-0.00527440\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 780.000 | 0.877390 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 254.747i | 0.285271i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 706.677 | 0.789583 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1773.42i | − 1.97266i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −904.131 | −1.00347 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 857.013i | − 0.946976i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1288.00 | −1.42007 | −0.710033 | − | 0.704168i | \(-0.751320\pi\) | ||||
−0.710033 | + | 0.704168i | \(0.751320\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.1918i | 0.0430207i | 0.999769 | + | 0.0215103i | \(0.00684748\pi\) | ||||
−0.999769 | + | 0.0215103i | \(0.993153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −648.000 | −0.709748 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 764.241i | 0.833414i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1569.24 | 1.70755 | 0.853775 | − | 0.520643i | \(-0.174308\pi\) | ||||
0.853775 | + | 0.520643i | \(0.174308\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 560.029i | 0.606748i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −526.543 | −0.569236 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 997.021i | − 1.07322i | −0.843831 | − | 0.536610i | \(-0.819705\pi\) | ||||
0.843831 | − | 0.536610i | \(-0.180295\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 148.000 | 0.158969 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 264.545i | − 0.282936i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −874.000 | −0.932764 | −0.466382 | − | 0.884583i | \(-0.654443\pi\) | ||||
−0.466382 | + | 0.884583i | \(0.654443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1383.96i | 1.47074i | 0.677668 | + | 0.735368i | \(0.262990\pi\) | ||||
−0.677668 | + | 0.735368i | \(0.737010\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1018.45 | −1.08001 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 678.823i | − 0.716814i | −0.933566 | − | 0.358407i | \(-0.883320\pi\) | ||||
0.933566 | − | 0.358407i | \(-0.116680\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −207.846 | −0.219016 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1650.39i | 1.73178i | 0.500234 | + | 0.865890i | \(0.333247\pi\) | ||||
−0.500234 | + | 0.865890i | \(0.666753\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 336.000 | 0.351832 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 690.756i | − 0.720288i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 491.000 | 0.510926 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 210.656i | − 0.218296i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −543.864 | −0.562424 | −0.281212 | − | 0.959646i | \(-0.590736\pi\) | ||||
−0.281212 | + | 0.959646i | \(0.590736\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 449.720i | 0.463151i | 0.972817 | + | 0.231576i | \(0.0743881\pi\) | ||||
−0.972817 | + | 0.231576i | \(0.925612\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 512.687 | 0.526914 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 80.6102i | 0.0825079i | 0.999149 | + | 0.0412539i | \(0.0131353\pi\) | ||||
−0.999149 | + | 0.0412539i | \(0.986865\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −468.000 | −0.478039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1734.24i | 1.76423i | 0.471033 | + | 0.882115i | \(0.343881\pi\) | ||||
−0.471033 | + | 0.882115i | \(0.656119\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 702.000 | 0.712690 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1920.40i | 1.94176i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −232.095 | −0.234203 | −0.117101 | − | 0.993120i | \(-0.537360\pi\) | ||||
−0.117101 | + | 0.993120i | \(0.537360\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 585.484i | 0.588427i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −290.985 | −0.291860 | −0.145930 | − | 0.989295i | \(-0.546617\pi\) | ||||
−0.145930 | + | 0.989295i | \(0.546617\pi\) | |||||||
\(998\) | 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 | 2304.3.e.h.1025.2 | 4 | ||
3.2 | odd | 2 | inner | 2304.3.e.h.1025.4 | 4 | ||
4.3 | odd | 2 | 2304.3.e.i.1025.1 | 4 | |||
8.3 | odd | 2 | inner | 2304.3.e.h.1025.3 | 4 | ||
8.5 | even | 2 | 2304.3.e.i.1025.4 | 4 | |||
12.11 | even | 2 | 2304.3.e.i.1025.3 | 4 | |||
16.3 | odd | 4 | 576.3.h.a.161.4 | yes | 8 | ||
16.5 | even | 4 | 576.3.h.a.161.5 | yes | 8 | ||
16.11 | odd | 4 | 576.3.h.a.161.7 | yes | 8 | ||
16.13 | even | 4 | 576.3.h.a.161.2 | yes | 8 | ||
24.5 | odd | 2 | 2304.3.e.i.1025.2 | 4 | |||
24.11 | even | 2 | inner | 2304.3.e.h.1025.1 | 4 | ||
48.5 | odd | 4 | 576.3.h.a.161.1 | ✓ | 8 | ||
48.11 | even | 4 | 576.3.h.a.161.3 | yes | 8 | ||
48.29 | odd | 4 | 576.3.h.a.161.6 | yes | 8 | ||
48.35 | even | 4 | 576.3.h.a.161.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.3.h.a.161.1 | ✓ | 8 | 48.5 | odd | 4 | ||
576.3.h.a.161.2 | yes | 8 | 16.13 | even | 4 | ||
576.3.h.a.161.3 | yes | 8 | 48.11 | even | 4 | ||
576.3.h.a.161.4 | yes | 8 | 16.3 | odd | 4 | ||
576.3.h.a.161.5 | yes | 8 | 16.5 | even | 4 | ||
576.3.h.a.161.6 | yes | 8 | 48.29 | odd | 4 | ||
576.3.h.a.161.7 | yes | 8 | 16.11 | odd | 4 | ||
576.3.h.a.161.8 | yes | 8 | 48.35 | even | 4 | ||
2304.3.e.h.1025.1 | 4 | 24.11 | even | 2 | inner | ||
2304.3.e.h.1025.2 | 4 | 1.1 | even | 1 | trivial | ||
2304.3.e.h.1025.3 | 4 | 8.3 | odd | 2 | inner | ||
2304.3.e.h.1025.4 | 4 | 3.2 | odd | 2 | inner | ||
2304.3.e.i.1025.1 | 4 | 4.3 | odd | 2 | |||
2304.3.e.i.1025.2 | 4 | 24.5 | odd | 2 | |||
2304.3.e.i.1025.3 | 4 | 12.11 | even | 2 | |||
2304.3.e.i.1025.4 | 4 | 8.5 | even | 2 |