Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,3,Mod(4049,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.4049");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.c (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: | \(112.806829445\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.17 | ||
Character | \(\chi\) | \(=\) | 4140.4049 |
Dual form | 4140.3.c.a.4049.18 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.90943 | − | 3.11711i | −0.781886 | − | 0.623421i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.62373i | 1.08910i | 0.838727 | + | 0.544552i | \(0.183300\pi\) | ||||
−0.838727 | + | 0.544552i | \(0.816700\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.21524i | 0.292294i | 0.989263 | + | 0.146147i | \(0.0466873\pi\) | ||||
−0.989263 | + | 0.146147i | \(0.953313\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 21.1842i | − | 1.62955i | −0.579775 | − | 0.814776i | \(-0.696860\pi\) | ||
0.579775 | − | 0.814776i | \(-0.303140\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.40382 | 0.141401 | 0.0707005 | − | 0.997498i | \(-0.477477\pi\) | ||||
0.0707005 | + | 0.997498i | \(0.477477\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.95402 | 0.313370 | 0.156685 | − | 0.987649i | \(-0.449919\pi\) | ||||
0.156685 | + | 0.987649i | \(0.449919\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.79583 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.56729 | + | 24.3722i | 0.222691 | + | 0.974889i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 22.0845i | − | 0.761535i | −0.924671 | − | 0.380767i | \(-0.875660\pi\) | ||
0.924671 | − | 0.380767i | \(-0.124340\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.8439 | −0.349802 | −0.174901 | − | 0.984586i | \(-0.555961\pi\) | ||||
−0.174901 | + | 0.984586i | \(0.555961\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 23.7640 | − | 29.8044i | 0.678971 | − | 0.851556i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.39190i | − | 0.199781i | −0.994998 | − | 0.0998905i | \(-0.968151\pi\) | ||
0.994998 | − | 0.0998905i | \(-0.0318493\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.9081i | 0.461173i | 0.973052 | + | 0.230587i | \(0.0740645\pi\) | ||||
−0.973052 | + | 0.230587i | \(0.925936\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 58.6048i | 1.36290i | 0.731864 | + | 0.681451i | \(0.238651\pi\) | ||||
−0.731864 | + | 0.681451i | \(0.761349\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 33.2863 | 0.708219 | 0.354110 | − | 0.935204i | \(-0.384784\pi\) | ||||
0.354110 | + | 0.935204i | \(0.384784\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.12130 | −0.186149 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −34.2495 | −0.646216 | −0.323108 | − | 0.946362i | \(-0.604728\pi\) | ||||
−0.323108 | + | 0.946362i | \(0.604728\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.0222 | − | 12.5698i | 0.182223 | − | 0.228541i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 63.6692i | − | 1.07914i | −0.841941 | − | 0.539569i | \(-0.818587\pi\) | ||
0.841941 | − | 0.539569i | \(-0.181413\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 78.7741 | 1.29138 | 0.645690 | − | 0.763600i | \(-0.276570\pi\) | ||||
0.645690 | + | 0.763600i | \(0.276570\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −66.0334 | + | 82.8181i | −1.01590 | + | 1.27412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 79.0164i | − | 1.17935i | −0.807641 | − | 0.589675i | \(-0.799256\pi\) | ||
0.807641 | − | 0.589675i | \(-0.200744\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 46.2778i | − | 0.651800i | −0.945404 | − | 0.325900i | \(-0.894333\pi\) | ||
0.945404 | − | 0.325900i | \(-0.105667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 125.253i | 1.71580i | 0.513819 | + | 0.857899i | \(0.328230\pi\) | ||||
−0.513819 | + | 0.857899i | \(0.671770\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −24.5121 | −0.318339 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.15717 | 0.0779389 | 0.0389694 | − | 0.999240i | \(-0.487593\pi\) | ||||
0.0389694 | + | 0.999240i | \(0.487593\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −70.5276 | −0.849731 | −0.424865 | − | 0.905257i | \(-0.639679\pi\) | ||||
−0.424865 | + | 0.905257i | \(0.639679\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.39755 | − | 7.49295i | −0.110559 | − | 0.0881524i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 139.383i | 1.56610i | 0.621960 | + | 0.783049i | \(0.286337\pi\) | ||||
−0.621960 | + | 0.783049i | \(0.713663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 161.503 | 1.77475 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −23.2768 | − | 18.5593i | −0.245019 | − | 0.195361i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 145.917i | 1.50429i | 0.658995 | + | 0.752147i | \(0.270982\pi\) | ||||
−0.658995 | + | 0.752147i | \(0.729018\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 175.345i | − | 1.73609i | −0.496486 | − | 0.868045i | \(-0.665377\pi\) | ||
0.496486 | − | 0.868045i | \(-0.334623\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 58.8536i | − | 0.571394i | −0.958320 | − | 0.285697i | \(-0.907775\pi\) | ||
0.958320 | − | 0.285697i | \(-0.0922251\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −88.2174 | −0.824462 | −0.412231 | − | 0.911079i | \(-0.635250\pi\) | ||||
−0.412231 | + | 0.911079i | \(0.635250\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −29.8711 | −0.274047 | −0.137023 | − | 0.990568i | \(-0.543754\pi\) | ||||
−0.137023 | + | 0.990568i | \(0.543754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −29.5966 | −0.261917 | −0.130959 | − | 0.991388i | \(-0.541805\pi\) | ||||
−0.130959 | + | 0.991388i | \(0.541805\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.7490 | + | 14.9491i | 0.163035 | + | 0.129992i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.3260i | 0.154000i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 110.662 | 0.914564 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 54.2059 | − | 112.635i | 0.433647 | − | 0.901083i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.9306i | 0.290793i | 0.989374 | + | 0.145396i | \(0.0464457\pi\) | ||||
−0.989374 | + | 0.145396i | \(0.953554\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 203.365i | − | 1.55241i | −0.630482 | − | 0.776204i | \(-0.717143\pi\) | ||
0.630482 | − | 0.776204i | \(-0.282857\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 45.3919i | 0.341292i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −177.216 | −1.29354 | −0.646772 | − | 0.762683i | \(-0.723881\pi\) | ||||
−0.646772 | + | 0.762683i | \(0.723881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −228.337 | −1.64271 | −0.821356 | − | 0.570415i | \(-0.806782\pi\) | ||||
−0.821356 | + | 0.570415i | \(0.806782\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 68.1122 | 0.476309 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −68.8398 | + | 86.3378i | −0.474757 | + | 0.595433i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 98.0909i | 0.658328i | 0.944273 | + | 0.329164i | \(0.106767\pi\) | ||||
−0.944273 | + | 0.329164i | \(0.893233\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 78.0414 | 0.516831 | 0.258415 | − | 0.966034i | \(-0.416800\pi\) | ||||
0.258415 | + | 0.966034i | \(0.416800\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42.3933 | + | 33.8015i | 0.273505 | + | 0.218074i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 15.4850i | − | 0.0986304i | −0.998783 | − | 0.0493152i | \(-0.984296\pi\) | ||
0.998783 | − | 0.0493152i | \(-0.0157039\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 36.5621i | − | 0.227094i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 29.5903i | − | 0.181536i | −0.995872 | − | 0.0907678i | \(-0.971068\pi\) | ||
0.995872 | − | 0.0907678i | \(-0.0289321\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 58.6076 | 0.350944 | 0.175472 | − | 0.984484i | \(-0.443855\pi\) | ||||
0.175472 | + | 0.984484i | \(0.443855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −279.770 | −1.65544 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −80.8229 | −0.467184 | −0.233592 | − | 0.972335i | \(-0.575048\pi\) | ||||
−0.233592 | + | 0.972335i | \(0.575048\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −185.807 | + | 42.4435i | −1.06176 | + | 0.242534i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 155.177i | − | 0.866910i | −0.901175 | − | 0.433455i | \(-0.857294\pi\) | ||
0.901175 | − | 0.433455i | \(-0.142706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.1896 | −0.122594 | −0.0612972 | − | 0.998120i | \(-0.519524\pi\) | ||||
−0.0612972 | + | 0.998120i | \(0.519524\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.0413 | + | 28.8981i | −0.124548 | + | 0.156206i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.72884i | 0.0413307i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 198.804i | − | 1.04086i | −0.853905 | − | 0.520429i | \(-0.825772\pi\) | ||
0.853905 | − | 0.520429i | \(-0.174228\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 303.541i | − | 1.57275i | −0.617748 | − | 0.786376i | \(-0.711955\pi\) | ||
0.617748 | − | 0.786376i | \(-0.288045\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 98.2896 | 0.498932 | 0.249466 | − | 0.968384i | \(-0.419745\pi\) | ||||
0.249466 | + | 0.968384i | \(0.419745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −39.3046 | −0.197511 | −0.0987553 | − | 0.995112i | \(-0.531486\pi\) | ||||
−0.0987553 | + | 0.995112i | \(0.531486\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 168.366 | 0.829391 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 58.9386 | − | 73.9199i | 0.287505 | − | 0.360585i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.1436i | 0.0915962i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −324.356 | −1.53723 | −0.768615 | − | 0.639712i | \(-0.779054\pi\) | ||||
−0.768615 | + | 0.639712i | \(0.779054\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 182.677 | − | 229.111i | 0.849662 | − | 1.06563i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 82.6707i | − | 0.380971i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 50.9229i | − | 0.230420i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 64.1839i | 0.287820i | 0.989591 | + | 0.143910i | \(0.0459676\pi\) | ||||
−0.989591 | + | 0.143910i | \(0.954032\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 66.2929 | 0.292039 | 0.146020 | − | 0.989282i | \(-0.453354\pi\) | ||||
0.146020 | + | 0.989282i | \(0.453354\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −445.764 | −1.94657 | −0.973284 | − | 0.229602i | \(-0.926257\pi\) | ||||
−0.973284 | + | 0.229602i | \(0.926257\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −361.910 | −1.55326 | −0.776632 | − | 0.629955i | \(-0.783073\pi\) | ||||
−0.776632 | + | 0.629955i | \(0.783073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −130.130 | − | 103.757i | −0.553747 | − | 0.441519i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 442.262i | − | 1.85047i | −0.379397 | − | 0.925234i | \(-0.623868\pi\) | ||
0.379397 | − | 0.925234i | \(-0.376132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.24860 | −0.0176290 | −0.00881451 | − | 0.999961i | \(-0.502806\pi\) | ||||
−0.00881451 | + | 0.999961i | \(0.502806\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 35.6591 | + | 28.4321i | 0.145547 | + | 0.116049i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 126.131i | − | 0.510653i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 346.867i | − | 1.38194i | −0.722883 | − | 0.690970i | \(-0.757184\pi\) | ||
0.722883 | − | 0.690970i | \(-0.242816\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 15.4197i | − | 0.0609476i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 126.259 | 0.491280 | 0.245640 | − | 0.969361i | \(-0.421002\pi\) | ||||
0.245640 | + | 0.969361i | \(0.421002\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 56.3539 | 0.217582 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.29073 | −0.0277214 | −0.0138607 | − | 0.999904i | \(-0.504412\pi\) | ||||
−0.0138607 | + | 0.999904i | \(0.504412\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 133.896 | + | 106.759i | 0.505267 | + | 0.402865i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 257.321i | 0.956584i | 0.878201 | + | 0.478292i | \(0.158744\pi\) | ||||
−0.878201 | + | 0.478292i | \(0.841256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −108.965 | −0.402084 | −0.201042 | − | 0.979583i | \(-0.564433\pi\) | ||||
−0.201042 | + | 0.979583i | \(0.564433\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −78.3625 | + | 17.9002i | −0.284955 | + | 0.0650915i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 397.844i | 1.43626i | 0.695909 | + | 0.718130i | \(0.255002\pi\) | ||||
−0.695909 | + | 0.718130i | \(0.744998\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 325.194i | 1.15727i | 0.815585 | + | 0.578637i | \(0.196415\pi\) | ||||
−0.815585 | + | 0.578637i | \(0.803585\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 157.751i | − | 0.557423i | −0.960375 | − | 0.278712i | \(-0.910093\pi\) | ||
0.960375 | − | 0.278712i | \(-0.0899073\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −144.150 | −0.502266 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −283.222 | −0.980006 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −389.693 | −1.33001 | −0.665005 | − | 0.746839i | \(-0.731571\pi\) | ||||
−0.665005 | + | 0.746839i | \(0.731571\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −198.464 | + | 248.910i | −0.672758 | + | 0.843764i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 101.596i | 0.339785i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −446.787 | −1.48434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −307.962 | − | 245.547i | −1.00971 | − | 0.805074i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 81.0767i | 0.264094i | 0.991243 | + | 0.132047i | \(0.0421549\pi\) | ||||
−0.991243 | + | 0.132047i | \(0.957845\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 92.4751i | 0.297348i | 0.988886 | + | 0.148674i | \(0.0475004\pi\) | ||||
−0.988886 | + | 0.148674i | \(0.952500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 363.385i | 1.16097i | 0.814270 | + | 0.580487i | \(0.197138\pi\) | ||||
−0.814270 | + | 0.580487i | \(0.802862\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 51.1777 | 0.161444 | 0.0807219 | − | 0.996737i | \(-0.474277\pi\) | ||||
0.0807219 | + | 0.996737i | \(0.474277\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 71.0070 | 0.222592 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.3124 | 0.0443108 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 516.306 | − | 117.938i | 1.58863 | − | 0.362887i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 253.766i | 0.771325i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 441.929 | 1.33513 | 0.667567 | − | 0.744550i | \(-0.267336\pi\) | ||||
0.667567 | + | 0.744550i | \(0.267336\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −246.303 | + | 308.909i | −0.735231 | + | 0.922116i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 288.958i | 0.857441i | 0.903437 | + | 0.428720i | \(0.141035\pi\) | ||||
−0.903437 | + | 0.428720i | \(0.858965\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 34.8656i | − | 0.102245i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 304.025i | 0.886369i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −639.619 | −1.84328 | −0.921641 | − | 0.388044i | \(-0.873151\pi\) | ||||
−0.921641 | + | 0.388044i | \(0.873151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −452.401 | −1.29628 | −0.648139 | − | 0.761522i | \(-0.724452\pi\) | ||||
−0.648139 | + | 0.761522i | \(0.724452\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −297.051 | −0.841503 | −0.420751 | − | 0.907176i | \(-0.638234\pi\) | ||||
−0.420751 | + | 0.907176i | \(0.638234\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −144.253 | + | 180.920i | −0.406346 | + | 0.509633i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 40.7532i | 0.113519i | 0.998388 | + | 0.0567593i | \(0.0180768\pi\) | ||||
−0.998388 | + | 0.0567593i | \(0.981923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −325.550 | −0.901799 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 390.428 | − | 489.669i | 1.06967 | − | 1.34156i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 450.788i | 1.22830i | 0.789188 | + | 0.614152i | \(0.210502\pi\) | ||||
−0.789188 | + | 0.614152i | \(0.789498\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 261.109i | − | 0.703797i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 75.9119i | − | 0.203517i | −0.994809 | − | 0.101759i | \(-0.967553\pi\) | ||
0.994809 | − | 0.101759i | \(-0.0324469\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −467.842 | −1.24096 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −550.199 | −1.45171 | −0.725856 | − | 0.687847i | \(-0.758556\pi\) | ||||
−0.725856 | + | 0.687847i | \(0.758556\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −751.680 | −1.96261 | −0.981306 | − | 0.192456i | \(-0.938355\pi\) | ||||
−0.981306 | + | 0.192456i | \(0.938355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 95.8284 | + | 76.4069i | 0.248905 | + | 0.198460i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 27.8168i | − | 0.0715084i | −0.999361 | − | 0.0357542i | \(-0.988617\pi\) | ||
0.999361 | − | 0.0357542i | \(-0.0113833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.5283 | −0.0294841 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.0710 | − | 19.1926i | −0.0609393 | − | 0.0485888i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 507.708i | − | 1.27886i | −0.768849 | − | 0.639431i | \(-0.779170\pi\) | ||
0.768849 | − | 0.639431i | \(-0.220830\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 270.184i | − | 0.673774i | −0.941545 | − | 0.336887i | \(-0.890626\pi\) | ||
0.941545 | − | 0.336887i | \(-0.109374\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 229.718i | 0.570021i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.7667 | 0.0583949 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −95.9356 | −0.234561 | −0.117281 | − | 0.993099i | \(-0.537418\pi\) | ||||
−0.117281 | + | 0.993099i | \(0.537418\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 485.397 | 1.17530 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 275.723 | + | 219.842i | 0.664392 | + | 0.529740i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 485.607i | − | 1.15897i | −0.814984 | − | 0.579483i | \(-0.803254\pi\) | ||
0.814984 | − | 0.579483i | \(-0.196746\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.0169 | −0.0879261 | −0.0439631 | − | 0.999033i | \(-0.513998\pi\) | ||||
−0.0439631 | + | 0.999033i | \(0.513998\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.3827 | + | 58.5863i | 0.0314888 | + | 0.137850i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 600.553i | 1.40645i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 264.228i | 0.613057i | 0.951861 | + | 0.306529i | \(0.0991675\pi\) | ||||
−0.951861 | + | 0.306529i | \(0.900832\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 223.032i | − | 0.515087i | −0.966267 | − | 0.257543i | \(-0.917087\pi\) | ||
0.966267 | − | 0.257543i | \(-0.0829130\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.5545 | −0.0653421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 856.080 | 1.95007 | 0.975034 | − | 0.222056i | \(-0.0712766\pi\) | ||||
0.975034 | + | 0.222056i | \(0.0712766\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −327.558 | −0.739408 | −0.369704 | − | 0.929150i | \(-0.620541\pi\) | ||||
−0.369704 | + | 0.929150i | \(0.620541\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 434.471 | − | 544.907i | 0.976339 | − | 1.22451i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 220.079i | 0.490154i | 0.969504 | + | 0.245077i | \(0.0788133\pi\) | ||||
−0.969504 | + | 0.245077i | \(0.921187\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −60.7940 | −0.134798 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −631.383 | − | 503.421i | −1.38766 | − | 1.10642i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 184.792i | − | 0.404358i | −0.979349 | − | 0.202179i | \(-0.935198\pi\) | ||
0.979349 | − | 0.202179i | \(-0.0648023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 526.656i | 1.14242i | 0.820804 | + | 0.571210i | \(0.193526\pi\) | ||||
−0.820804 | + | 0.571210i | \(0.806474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 622.938i | − | 1.34544i | −0.739898 | − | 0.672719i | \(-0.765126\pi\) | ||
0.739898 | − | 0.672719i | \(-0.234874\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −282.557 | −0.605048 | −0.302524 | − | 0.953142i | \(-0.597829\pi\) | ||||
−0.302524 | + | 0.953142i | \(0.597829\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 602.400 | 1.28443 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −188.428 | −0.398369 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.1478 | + | 145.113i | 0.0697848 | + | 0.305501i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 24.5133i | − | 0.0511761i | −0.999673 | − | 0.0255880i | \(-0.991854\pi\) | ||
0.999673 | − | 0.0255880i | \(-0.00814581\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −156.591 | −0.325554 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 454.837 | − | 570.450i | 0.937809 | − | 1.17619i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 502.670i | 1.03218i | 0.856536 | + | 0.516088i | \(0.172612\pi\) | ||||
−0.856536 | + | 0.516088i | \(0.827388\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 358.223i | − | 0.729578i | −0.931090 | − | 0.364789i | \(-0.881141\pi\) | ||
0.931090 | − | 0.364789i | \(-0.118859\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 53.0871i | − | 0.107682i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 352.809 | 0.709878 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −352.130 | −0.705672 | −0.352836 | − | 0.935685i | \(-0.614783\pi\) | ||||
−0.352836 | + | 0.935685i | \(0.614783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −668.684 | −1.32939 | −0.664695 | − | 0.747114i | \(-0.731439\pi\) | ||||
−0.664695 | + | 0.747114i | \(0.731439\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −546.569 | + | 685.499i | −1.08232 | + | 1.35742i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 743.009i | − | 1.45974i | −0.683585 | − | 0.729871i | \(-0.739580\pi\) | ||
0.683585 | − | 0.729871i | \(-0.260420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −954.897 | −1.86868 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −183.453 | + | 230.084i | −0.356219 | + | 0.446765i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 107.023i | 0.207009i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 26.9328i | − | 0.0516944i | −0.999666 | − | 0.0258472i | \(-0.991772\pi\) | ||
0.999666 | − | 0.0258472i | \(-0.00822833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 645.889i | 1.23497i | 0.786583 | + | 0.617484i | \(0.211848\pi\) | ||||
−0.786583 | + | 0.617484i | \(0.788152\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.0666 | −0.0494623 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 400.553 | 0.751506 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 344.880 | + | 274.983i | 0.644635 | + | 0.513987i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 29.3272i | − | 0.0544103i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −668.559 | −1.23578 | −0.617892 | − | 0.786263i | \(-0.712013\pi\) | ||||
−0.617892 | + | 0.786263i | \(0.712013\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 116.779 | + | 93.1113i | 0.214273 | + | 0.170846i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 432.280i | − | 0.790274i | −0.918622 | − | 0.395137i | \(-0.870697\pi\) | ||
0.918622 | − | 0.395137i | \(-0.129303\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 131.492i | − | 0.238642i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.9406i | 0.0848836i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 289.965 | 0.520583 | 0.260291 | − | 0.965530i | \(-0.416181\pi\) | ||||
0.260291 | + | 0.965530i | \(0.416181\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1241.49 | 2.22092 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 993.271 | 1.76425 | 0.882123 | − | 0.471018i | \(-0.156113\pi\) | ||||
0.882123 | + | 0.471018i | \(0.156113\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 115.706 | + | 92.2559i | 0.204789 | + | 0.163285i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 591.750i | − | 1.03998i | −0.854171 | − | 0.519991i | \(-0.825935\pi\) | ||
0.854171 | − | 0.519991i | \(-0.174065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.49753 | −0.0148818 | −0.00744092 | − | 0.999972i | \(-0.502369\pi\) | ||||
−0.00744092 | + | 0.999972i | \(0.502369\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.6998 | − | 116.885i | −0.0464344 | − | 0.203278i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 98.2139i | 0.170215i | 0.996372 | + | 0.0851074i | \(0.0271233\pi\) | ||||
−0.996372 | + | 0.0851074i | \(0.972877\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 537.684i | − | 0.925446i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 110.120i | − | 0.188885i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 462.810 | 0.788432 | 0.394216 | − | 0.919018i | \(-0.371016\pi\) | ||||
0.394216 | + | 0.919018i | \(0.371016\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −64.5646 | −0.109617 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −385.900 | −0.650759 | −0.325380 | − | 0.945583i | \(-0.605492\pi\) | ||||
−0.325380 | + | 0.945583i | \(0.605492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 57.1243 | − | 71.6444i | 0.0960072 | − | 0.120411i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 300.516i | − | 0.501695i | −0.968027 | − | 0.250848i | \(-0.919291\pi\) | ||
0.968027 | − | 0.250848i | \(-0.0807093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 735.625 | 1.22400 | 0.612000 | − | 0.790857i | \(-0.290365\pi\) | ||||
0.612000 | + | 0.790857i | \(0.290365\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −432.626 | − | 344.946i | −0.715085 | − | 0.570159i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 520.875i | − | 0.858113i | −0.903278 | − | 0.429057i | \(-0.858846\pi\) | ||
0.903278 | − | 0.429057i | \(-0.141154\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 705.143i | − | 1.15408i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 720.853i | − | 1.17594i | −0.808882 | − | 0.587971i | \(-0.799927\pi\) | ||
0.808882 | − | 0.587971i | \(-0.200073\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 159.490 | 0.258493 | 0.129246 | − | 0.991613i | \(-0.458744\pi\) | ||||
0.129246 | + | 0.991613i | \(0.458744\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −681.600 | −1.10113 | −0.550565 | − | 0.834792i | \(-0.685588\pi\) | ||||
−0.550565 | + | 0.834792i | \(0.685588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1062.62 | −1.70565 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −563.011 | + | 271.374i | −0.900817 | + | 0.434199i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 17.7688i | − | 0.0282492i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 849.204 | 1.34581 | 0.672903 | − | 0.739730i | \(-0.265047\pi\) | ||||
0.672903 | + | 0.739730i | \(0.265047\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 115.117 | − | 144.378i | 0.181286 | − | 0.227367i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 193.227i | 0.303340i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 395.174i | 0.616496i | 0.951306 | + | 0.308248i | \(0.0997427\pi\) | ||||
−0.951306 | + | 0.308248i | \(0.900257\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 545.806i | − | 0.848843i | −0.905465 | − | 0.424422i | \(-0.860477\pi\) | ||
0.905465 | − | 0.424422i | \(-0.139523\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 445.714 | 0.688893 | 0.344446 | − | 0.938806i | \(-0.388067\pi\) | ||||
0.344446 | + | 0.938806i | \(0.388067\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 204.712 | 0.315426 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 857.780 | 1.31360 | 0.656800 | − | 0.754065i | \(-0.271910\pi\) | ||||
0.656800 | + | 0.754065i | \(0.271910\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −633.912 | + | 795.043i | −0.967804 | + | 1.21381i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 850.528i | − | 1.29063i | −0.763915 | − | 0.645317i | \(-0.776725\pi\) | ||
0.763915 | − | 0.645317i | \(-0.223275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −331.769 | −0.501919 | −0.250960 | − | 0.967998i | \(-0.580746\pi\) | ||||
−0.250960 | + | 0.967998i | \(0.580746\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 141.491 | − | 177.456i | 0.212769 | − | 0.266852i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 105.914i | 0.158791i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 253.278i | 0.377463i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 987.624i | − | 1.46750i | −0.679422 | − | 0.733748i | \(-0.737770\pi\) | ||
0.679422 | − | 0.733748i | \(-0.262230\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −396.595 | −0.585812 | −0.292906 | − | 0.956141i | \(-0.594622\pi\) | ||||
−0.292906 | + | 0.956141i | \(0.594622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1112.43 | −1.63833 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.9937 | 0.0497711 | 0.0248855 | − | 0.999690i | \(-0.492078\pi\) | ||||
0.0248855 | + | 0.999690i | \(0.492078\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 692.812 | + | 552.400i | 1.01140 | + | 0.806423i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 725.547i | 1.05304i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −995.845 | −1.44117 | −0.720583 | − | 0.693369i | \(-0.756126\pi\) | ||||
−0.720583 | + | 0.693369i | \(0.756126\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 892.668 | + | 711.751i | 1.28441 | + | 1.02410i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.4516i | 0.0652103i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 400.145i | − | 0.570820i | −0.958406 | − | 0.285410i | \(-0.907870\pi\) | ||
0.958406 | − | 0.285410i | \(-0.0921297\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 44.0116i | − | 0.0626053i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1336.78 | 1.89078 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 376.581 | 0.531144 | 0.265572 | − | 0.964091i | \(-0.414439\pi\) | ||||
0.265572 | + | 0.964091i | \(0.414439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.0053 | 0.0729387 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −266.280 | − | 212.313i | −0.372420 | − | 0.296941i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 560.265i | − | 0.779229i | −0.920978 | − | 0.389614i | \(-0.872608\pi\) | ||
0.920978 | − | 0.389614i | \(-0.127392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 448.684 | 0.622308 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 538.249 | − | 122.951i | 0.742412 | − | 0.169587i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 407.313i | − | 0.560266i | −0.959961 | − | 0.280133i | \(-0.909621\pi\) | ||
0.959961 | − | 0.280133i | \(-0.0903785\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 140.875i | 0.192716i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 66.8245i | 0.0911658i | 0.998961 | + | 0.0455829i | \(0.0145145\pi\) | ||||
−0.998961 | + | 0.0455829i | \(0.985485\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 254.057 | 0.344717 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.2775 | −0.0490900 | −0.0245450 | − | 0.999699i | \(-0.507814\pi\) | ||||
−0.0245450 | + | 0.999699i | \(0.507814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −390.878 | −0.526081 | −0.263040 | − | 0.964785i | \(-0.584725\pi\) | ||||
−0.263040 | + | 0.964785i | \(0.584725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 305.760 | − | 383.479i | 0.410416 | − | 0.514738i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 672.546i | − | 0.897925i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.2884 | −0.0176943 | −0.00884717 | − | 0.999961i | \(-0.502816\pi\) | ||||
−0.00884717 | + | 0.999961i | \(0.502816\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −305.097 | − | 243.263i | −0.404103 | − | 0.322203i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 975.953i | 1.28924i | 0.764504 | + | 0.644619i | \(0.222984\pi\) | ||||
−0.764504 | + | 0.644619i | \(0.777016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 616.620i | 0.810277i | 0.914255 | + | 0.405138i | \(0.132777\pi\) | ||||
−0.914255 | + | 0.405138i | \(0.867223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 227.729i | − | 0.298465i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1348.78 | −1.75851 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 288.659 | 0.375369 | 0.187685 | − | 0.982229i | \(-0.439902\pi\) | ||||
0.187685 | + | 0.982229i | \(0.439902\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −826.552 | −1.06928 | −0.534639 | − | 0.845081i | \(-0.679552\pi\) | ||||
−0.534639 | + | 0.845081i | \(0.679552\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −60.3709 | − | 264.289i | −0.0778979 | − | 0.341018i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 112.579i | 0.144518i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 148.794 | 0.190517 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.2683 | + | 60.5374i | −0.0614883 | + | 0.0771177i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 739.060i | 0.939085i | 0.882910 | + | 0.469543i | \(0.155581\pi\) | ||||
−0.882910 | + | 0.469543i | \(0.844419\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 225.637i | − | 0.285255i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1668.77i | − | 2.10437i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1030.90 | −1.29348 | −0.646739 | − | 0.762711i | \(-0.723868\pi\) | ||||
−0.646739 | + | 0.762711i | \(0.723868\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 80.0141 | 0.100143 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −402.719 | −0.501518 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −113.968 | + | 142.937i | −0.141575 | + | 0.177562i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 741.519i | 0.916587i | 0.888801 | + | 0.458294i | \(0.151539\pi\) | ||||
−0.888801 | + | 0.458294i | \(0.848461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 723.965 | 0.892682 | 0.446341 | − | 0.894863i | \(-0.352727\pi\) | ||||
0.446341 | + | 0.894863i | \(0.352727\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −92.2362 | + | 115.681i | −0.113173 | + | 0.141940i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 348.934i | 0.427092i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1522.59i | 1.85456i | 0.374370 | + | 0.927279i | \(0.377859\pi\) | ||||
−0.374370 | + | 0.927279i | \(0.622141\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1134.31i | 1.37826i | 0.724637 | + | 0.689131i | \(0.242007\pi\) | ||||
−0.724637 | + | 0.689131i | \(0.757993\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −545.247 | −0.659308 | −0.329654 | − | 0.944102i | \(-0.606932\pi\) | ||||
−0.329654 | + | 0.944102i | \(0.606932\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −117.564 | −0.141814 | −0.0709071 | − | 0.997483i | \(-0.522589\pi\) | ||||
−0.0709071 | + | 0.997483i | \(0.522589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.9259 | −0.0263216 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −229.122 | − | 182.686i | −0.274398 | − | 0.218786i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 719.479i | 0.857543i | 0.903413 | + | 0.428772i | \(0.141054\pi\) | ||||
−0.903413 | + | 0.428772i | \(0.858946\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 353.274 | 0.420065 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1093.74 | + | 872.072i | 1.29437 | + | 1.03204i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 843.659i | 0.996056i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.4503i | 0.0416572i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 780.772i | 0.915325i | 0.889126 | + | 0.457663i | \(0.151313\pi\) | ||||
−0.889126 | + | 0.457663i | \(0.848687\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −183.816 | −0.214488 | −0.107244 | − | 0.994233i | \(-0.534203\pi\) | ||||
−0.107244 | + | 0.994233i | \(0.534203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1051.01 | 1.22352 | 0.611761 | − | 0.791042i | \(-0.290461\pi\) | ||||
0.611761 | + | 0.791042i | \(0.290461\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 357.434 | 0.414177 | 0.207088 | − | 0.978322i | \(-0.433601\pi\) | ||||
0.207088 | + | 0.978322i | \(0.433601\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 315.971 | + | 251.933i | 0.365285 | + | 0.291253i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.7968i | 0.0227811i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1673.90 | −1.92181 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 858.702 | + | 413.251i | 0.981373 | + | 0.472287i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 968.591i | − | 1.10444i | −0.833700 | − | 0.552218i | \(-0.813782\pi\) | ||
0.833700 | − | 0.552218i | \(-0.186218\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 984.881i | − | 1.11791i | −0.829197 | − | 0.558956i | \(-0.811202\pi\) | ||
0.829197 | − | 0.558956i | \(-0.188798\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1399.06i | − | 1.58444i | −0.610238 | − | 0.792218i | \(-0.708926\pi\) | ||
0.610238 | − | 0.792218i | \(-0.291074\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1071.56 | −1.20807 | −0.604035 | − | 0.796958i | \(-0.706441\pi\) | ||||
−0.604035 | + | 0.796958i | \(0.706441\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −281.549 | −0.316703 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 198.187 | 0.221934 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −483.703 | + | 606.654i | −0.540451 | + | 0.677825i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 239.481i | 0.266386i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −82.3294 | −0.0913756 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 86.7486 | + | 69.1673i | 0.0958548 | + | 0.0764280i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 62.2104i | − | 0.0685892i | −0.999412 | − | 0.0342946i | \(-0.989082\pi\) | ||
0.999412 | − | 0.0342946i | \(-0.0109185\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 38.4024i | − | 0.0421541i | −0.999778 | − | 0.0210771i | \(-0.993290\pi\) | ||
0.999778 | − | 0.0210771i | \(-0.00670954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 226.763i | − | 0.248372i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1550.40 | 1.69073 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −612.247 | −0.666210 | −0.333105 | − | 0.942890i | \(-0.608096\pi\) | ||||
−0.333105 | + | 0.942890i | \(0.608096\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −980.357 | −1.06214 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 180.157 | − | 41.1528i | 0.194764 | − | 0.0444895i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 110.243i | − | 0.118668i | −0.998238 | − | 0.0593340i | \(-0.981102\pi\) | ||
0.998238 | − | 0.0593340i | \(-0.0188977\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −54.3084 | −0.0583335 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.0916 | − | 30.2154i | 0.0257664 | − | 0.0323159i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 327.959i | − | 0.350010i | −0.984568 | − | 0.175005i | \(-0.944006\pi\) | ||
0.984568 | − | 0.175005i | \(-0.0559942\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1671.55i | 1.77636i | 0.459497 | + | 0.888179i | \(0.348030\pi\) | ||||
−0.459497 | + | 0.888179i | \(0.651970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 90.6800i | − | 0.0961612i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 982.416 | 1.03740 | 0.518699 | − | 0.854957i | \(-0.326417\pi\) | ||||
0.518699 | + | 0.854957i | \(0.326417\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2653.39 | 2.79598 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 957.587 | 1.00481 | 0.502406 | − | 0.864632i | \(-0.332448\pi\) | ||||
0.502406 | + | 0.864632i | \(0.332448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −619.693 | + | 777.210i | −0.648893 | + | 0.813832i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1351.04i | − | 1.40880i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −843.411 | −0.877639 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −946.170 | + | 1186.67i | −0.980487 | + | 1.22971i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 298.269i | − | 0.308448i | −0.988036 | − | 0.154224i | \(-0.950712\pi\) | ||
0.988036 | − | 0.154224i | \(-0.0492877\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1568.44i | 1.61529i | 0.589670 | + | 0.807644i | \(0.299258\pi\) | ||||
−0.589670 | + | 0.807644i | \(0.700742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1740.78i | − | 1.78909i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 671.177 | 0.686977 | 0.343489 | − | 0.939157i | \(-0.388391\pi\) | ||||
0.343489 | + | 0.939157i | \(0.388391\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −448.149 | −0.457762 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1102.45 | −1.12152 | −0.560759 | − | 0.827979i | \(-0.689491\pi\) | ||||
−0.560759 | + | 0.827979i | \(0.689491\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −384.256 | − | 306.379i | −0.390108 | − | 0.311045i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 281.059i | − | 0.284185i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 126.154 | 0.127300 | 0.0636498 | − | 0.997972i | \(-0.479726\pi\) | ||||
0.0636498 | + | 0.997972i | \(0.479726\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 153.659 | + | 122.517i | 0.154431 | + | 0.123132i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 133.802i | − | 0.134204i | −0.997746 | − | 0.0671021i | \(-0.978625\pi\) | ||
0.997746 | − | 0.0671021i | \(-0.0213753\pi\) | |||||||
\(998\) | 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 | 4140.3.c.a.4049.17 | ✓ | 88 | |
3.2 | odd | 2 | inner | 4140.3.c.a.4049.72 | yes | 88 | |
5.4 | even | 2 | inner | 4140.3.c.a.4049.71 | yes | 88 | |
15.14 | odd | 2 | inner | 4140.3.c.a.4049.18 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.3.c.a.4049.17 | ✓ | 88 | 1.1 | even | 1 | trivial | |
4140.3.c.a.4049.18 | yes | 88 | 15.14 | odd | 2 | inner | |
4140.3.c.a.4049.71 | yes | 88 | 5.4 | even | 2 | inner | |
4140.3.c.a.4049.72 | yes | 88 | 3.2 | odd | 2 | inner |