Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,4,Mod(449,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.449");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.c (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: | \(47.2015280046\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.449 |
Dual form | 800.4.c.e.449.1 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.00000i | 0.384900i | 0.981307 | + | 0.192450i | \(0.0616434\pi\) | ||||
−0.981307 | + | 0.192450i | \(0.938357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.00000i | 0.323970i | 0.986793 | + | 0.161985i | \(0.0517895\pi\) | ||||
−0.986793 | + | 0.161985i | \(0.948210\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 23.0000 | 0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −60.0000 | −1.64461 | −0.822304 | − | 0.569049i | \(-0.807311\pi\) | ||||
−0.822304 | + | 0.569049i | \(0.807311\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 50.0000i | 1.06673i | 0.845885 | + | 0.533366i | \(0.179073\pi\) | ||||
−0.845885 | + | 0.533366i | \(0.820927\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 30.0000i | 0.428004i | 0.976833 | + | 0.214002i | \(0.0686499\pi\) | ||||
−0.976833 | + | 0.214002i | \(0.931350\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 40.0000 | 0.482980 | 0.241490 | − | 0.970403i | \(-0.422364\pi\) | ||||
0.241490 | + | 0.970403i | \(0.422364\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.0000 | −0.124696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 178.000i | − 1.61372i | −0.590743 | − | 0.806860i | \(-0.701165\pi\) | ||||
0.590743 | − | 0.806860i | \(-0.298835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 100.000i | 0.712778i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −166.000 | −1.06295 | −0.531473 | − | 0.847075i | \(-0.678361\pi\) | ||||
−0.531473 | + | 0.847075i | \(0.678361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.0000 | −0.115874 | −0.0579372 | − | 0.998320i | \(-0.518452\pi\) | ||||
−0.0579372 | + | 0.998320i | \(0.518452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 120.000i | − 0.633010i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 10.0000i | − 0.0444322i | −0.999753 | − | 0.0222161i | \(-0.992928\pi\) | ||||
0.999753 | − | 0.0222161i | \(-0.00707218\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −100.000 | −0.410585 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −250.000 | −0.952279 | −0.476140 | − | 0.879370i | \(-0.657964\pi\) | ||||
−0.476140 | + | 0.879370i | \(0.657964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 142.000i | − 0.503600i | −0.967779 | − | 0.251800i | \(-0.918977\pi\) | ||||
0.967779 | − | 0.251800i | \(-0.0810225\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 214.000i | 0.664151i | 0.943253 | + | 0.332076i | \(0.107749\pi\) | ||||
−0.943253 | + | 0.332076i | \(0.892251\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 307.000 | 0.895044 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −60.0000 | −0.164739 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 490.000i | 1.26994i | 0.772538 | + | 0.634969i | \(0.218987\pi\) | ||||
−0.772538 | + | 0.634969i | \(0.781013\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 80.0000i | 0.185899i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −800.000 | −1.76527 | −0.882637 | − | 0.470056i | \(-0.844234\pi\) | ||||
−0.882637 | + | 0.470056i | \(0.844234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 250.000 | 0.524741 | 0.262371 | − | 0.964967i | \(-0.415496\pi\) | ||||
0.262371 | + | 0.964967i | \(0.415496\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 138.000i | 0.275974i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 774.000i | − 1.41133i | −0.708545 | − | 0.705665i | \(-0.750648\pi\) | ||||
0.708545 | − | 0.705665i | \(-0.249352\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 356.000 | 0.621121 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −100.000 | −0.167152 | −0.0835762 | − | 0.996501i | \(-0.526634\pi\) | ||||
−0.0835762 | + | 0.996501i | \(0.526634\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 230.000i | − 0.368760i | −0.982855 | − | 0.184380i | \(-0.940972\pi\) | ||||
0.982855 | − | 0.184380i | \(-0.0590277\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 360.000i | − 0.532803i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1320.00 | −1.87989 | −0.939947 | − | 0.341321i | \(-0.889126\pi\) | ||||
−0.939947 | + | 0.341321i | \(0.889126\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 982.000i | − 1.29866i | −0.760508 | − | 0.649328i | \(-0.775050\pi\) | ||||
0.760508 | − | 0.649328i | \(-0.224950\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 332.000i | − 0.409128i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −874.000 | −1.04094 | −0.520471 | − | 0.853879i | \(-0.674244\pi\) | ||||
−0.520471 | + | 0.853879i | \(0.674244\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −300.000 | −0.345588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 40.0000i | − 0.0446001i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 310.000i | 0.324492i | 0.986750 | + | 0.162246i | \(0.0518738\pi\) | ||||
−0.986750 | + | 0.162246i | \(0.948126\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1380.00 | −1.40096 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1498.00 | −1.47581 | −0.737904 | − | 0.674906i | \(-0.764184\pi\) | ||||
−0.737904 | + | 0.674906i | \(0.764184\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1402.00i | − 1.34120i | −0.741821 | − | 0.670598i | \(-0.766038\pi\) | ||||
0.741821 | − | 0.670598i | \(-0.233962\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1194.00i | 1.07877i | 0.842059 | + | 0.539385i | \(0.181343\pi\) | ||||
−0.842059 | + | 0.539385i | \(0.818657\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −650.000 | −0.571181 | −0.285590 | − | 0.958352i | \(-0.592190\pi\) | ||||
−0.285590 | + | 0.958352i | \(0.592190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20.0000 | 0.0171019 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1510.00i | − 1.25707i | −0.777782 | − | 0.628535i | \(-0.783655\pi\) | ||||
0.777782 | − | 0.628535i | \(-0.216345\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1150.00i | 0.908697i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −180.000 | −0.138660 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2269.00 | 1.70473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 500.000i | − 0.366532i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1246.00i | 0.870588i | 0.900288 | + | 0.435294i | \(0.143355\pi\) | ||||
−0.900288 | + | 0.435294i | \(0.856645\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 284.000 | 0.193836 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2660.00 | −1.77409 | −0.887043 | − | 0.461687i | \(-0.847244\pi\) | ||||
−0.887043 | + | 0.461687i | \(0.847244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 240.000i | 0.156471i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2770.00i | − 1.72742i | −0.503986 | − | 0.863712i | \(-0.668134\pi\) | ||||
0.503986 | − | 0.863712i | \(-0.331866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −560.000 | −0.341716 | −0.170858 | − | 0.985296i | \(-0.554654\pi\) | ||||
−0.170858 | + | 0.985296i | \(0.554654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −428.000 | −0.255632 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 3000.00i | − 1.75435i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 614.000i | 0.344502i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2350.00 | 1.29208 | 0.646039 | − | 0.763305i | \(-0.276424\pi\) | ||||
0.646039 | + | 0.763305i | \(0.276424\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −580.000 | −0.312581 | −0.156290 | − | 0.987711i | \(-0.549954\pi\) | ||||
−0.156290 | + | 0.987711i | \(0.549954\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 690.000i | 0.364596i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1310.00i | 0.665920i | 0.942941 | + | 0.332960i | \(0.108047\pi\) | ||||
−0.942941 | + | 0.332960i | \(0.891953\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −980.000 | −0.488799 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1068.00 | 0.522796 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1862.00i | − 0.894743i | −0.894348 | − | 0.447371i | \(-0.852360\pi\) | ||||
0.894348 | − | 0.447371i | \(-0.147640\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 726.000i | 0.336405i | 0.985752 | + | 0.168202i | \(0.0537962\pi\) | ||||
−0.985752 | + | 0.168202i | \(0.946204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −303.000 | −0.137915 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 920.000 | 0.411428 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3250.00i | 1.42828i | 0.700001 | + | 0.714141i | \(0.253183\pi\) | ||||
−0.700001 | + | 0.714141i | \(0.746817\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1600.00i | − 0.679454i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1120.00 | −0.467669 | −0.233834 | − | 0.972276i | \(-0.575127\pi\) | ||||
−0.233834 | + | 0.972276i | \(0.575127\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2842.00 | −1.16710 | −0.583548 | − | 0.812079i | \(-0.698336\pi\) | ||||
−0.583548 | + | 0.812079i | \(0.698336\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 500.000i | 0.201973i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1800.00i | − 0.703899i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −600.000 | −0.230918 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3180.00 | −1.20469 | −0.602347 | − | 0.798234i | \(-0.705768\pi\) | ||||
−0.602347 | + | 0.798234i | \(0.705768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 4670.00i | − 1.74173i | −0.491522 | − | 0.870865i | \(-0.663559\pi\) | ||||
0.491522 | − | 0.870865i | \(-0.336441\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2990.00i | 1.08136i | 0.841227 | + | 0.540682i | \(0.181834\pi\) | ||||
−0.841227 | + | 0.540682i | \(0.818166\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4240.00 | −1.51038 | −0.755190 | − | 0.655506i | \(-0.772455\pi\) | ||||
−0.755190 | + | 0.655506i | \(0.772455\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1548.00 | 0.543221 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 996.000i | − 0.344362i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 4094.00i | − 1.37465i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2400.00 | −0.794313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4060.00 | 1.32465 | 0.662327 | − | 0.749215i | \(-0.269569\pi\) | ||||
0.662327 | + | 0.749215i | \(0.269569\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 200.000i | − 0.0643370i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 120.000i | − 0.0375398i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 460.000 | 0.141936 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1500.00 | −0.456565 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5622.00i | 1.68824i | 0.536156 | + | 0.844119i | \(0.319876\pi\) | ||||
−0.536156 | + | 0.844119i | \(0.680124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1554.00i | 0.454373i | 0.973851 | + | 0.227186i | \(0.0729526\pi\) | ||||
−0.973851 | + | 0.227186i | \(0.927047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1134.00 | −0.327235 | −0.163618 | − | 0.986524i | \(-0.552316\pi\) | ||||
−0.163618 | + | 0.986524i | \(0.552316\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 720.000 | 0.205076 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1710.00i | − 0.480798i | −0.970674 | − | 0.240399i | \(-0.922722\pi\) | ||||
0.970674 | − | 0.240399i | \(-0.0772782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2640.00i | − 0.723571i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4440.00 | 1.20167 | 0.600836 | − | 0.799372i | \(-0.294834\pi\) | ||||
0.600836 | + | 0.799372i | \(0.294834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −850.000 | −0.227192 | −0.113596 | − | 0.993527i | \(-0.536237\pi\) | ||||
−0.113596 | + | 0.993527i | \(0.536237\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3542.00i | 0.935059i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2000.00i | 0.515210i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1964.00 | 0.499853 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 660.000 | 0.165971 | 0.0829857 | − | 0.996551i | \(-0.473554\pi\) | ||||
0.0829857 | + | 0.996551i | \(0.473554\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10680.0i | 2.65394i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7590.00i | 1.84222i | 0.389299 | + | 0.921111i | \(0.372717\pi\) | ||||
−0.389299 | + | 0.921111i | \(0.627283\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 60.0000 | 0.0143947 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3818.00 | −0.905472 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 762.000i | − 0.178658i | −0.996002 | − | 0.0893288i | \(-0.971528\pi\) | ||||
0.996002 | − | 0.0893288i | \(-0.0284722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1748.00i | − 0.400659i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 150.000 | 0.0339987 | 0.0169994 | − | 0.999856i | \(-0.494589\pi\) | ||||
0.0169994 | + | 0.999856i | \(0.494589\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6580.00 | 1.47493 | 0.737466 | − | 0.675384i | \(-0.236022\pi\) | ||||
0.737466 | + | 0.675384i | \(0.236022\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 600.000i | − 0.133017i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4530.00i | − 0.982604i | −0.870989 | − | 0.491302i | \(-0.836521\pi\) | ||||
0.870989 | − | 0.491302i | \(-0.163479\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −460.000 | −0.0987078 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6950.00 | 1.47545 | 0.737726 | − | 0.675100i | \(-0.235899\pi\) | ||||
0.737726 | + | 0.675100i | \(0.235899\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3882.00i | 0.815410i | 0.913114 | + | 0.407705i | \(0.133671\pi\) | ||||
−0.913114 | + | 0.407705i | \(0.866329\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1500.00i | − 0.308509i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4013.00 | 0.816813 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −620.000 | −0.124897 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1370.00i | 0.273161i | 0.990629 | + | 0.136581i | \(0.0436113\pi\) | ||||
−0.990629 | + | 0.136581i | \(0.956389\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 6000.00i | − 1.17224i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8900.00 | 1.72141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 852.000 | 0.163151 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2996.00i | − 0.568039i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4106.00i | 0.763328i | 0.924301 | + | 0.381664i | \(0.124649\pi\) | ||||
−0.924301 | + | 0.381664i | \(0.875351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2804.00 | 0.516226 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2220.00 | −0.404774 | −0.202387 | − | 0.979306i | \(-0.564870\pi\) | ||||
−0.202387 | + | 0.979306i | \(0.564870\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 9430.00i | − 1.70292i | −0.524417 | − | 0.851462i | \(-0.675717\pi\) | ||||
0.524417 | − | 0.851462i | \(-0.324283\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6470.00i | 1.14635i | 0.819435 | + | 0.573173i | \(0.194288\pi\) | ||||
−0.819435 | + | 0.573173i | \(0.805712\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9960.00 | 1.74813 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2388.00 | −0.415219 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1200.00i | 0.206718i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1300.00i | − 0.219848i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1284.00 | −0.215165 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −900.000 | −0.149452 | −0.0747258 | − | 0.997204i | \(-0.523808\pi\) | ||||
−0.0747258 | + | 0.997204i | \(0.523808\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 230.000i | − 0.0378496i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 530.000i | − 0.0856704i | −0.999082 | − | 0.0428352i | \(-0.986361\pi\) | ||||
0.999082 | − | 0.0428352i | \(-0.0136390\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3020.00 | 0.483846 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1200.00 | 0.190568 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3900.00i | 0.613936i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 414.000i | − 0.0640481i | −0.999487 | − | 0.0320240i | \(-0.989805\pi\) | ||||
0.999487 | − | 0.0320240i | \(-0.0101953\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8614.00 | −1.32119 | −0.660597 | − | 0.750741i | \(-0.729697\pi\) | ||||
−0.660597 | + | 0.750741i | \(0.729697\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5000.00 | −0.760343 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2270.00i | − 0.342266i | −0.985248 | − | 0.171133i | \(-0.945257\pi\) | ||||
0.985248 | − | 0.171133i | \(-0.0547428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 360.000i | − 0.0533704i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8080.00 | 1.18787 | 0.593936 | − | 0.804512i | \(-0.297573\pi\) | ||||
0.593936 | + | 0.804512i | \(0.297573\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5259.00 | −0.766730 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4538.00i | 0.656152i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2374.00i | 0.337662i | 0.985645 | + | 0.168831i | \(0.0539991\pi\) | ||||
−0.985645 | + | 0.168831i | \(0.946001\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5750.00 | −0.811201 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2940.00 | −0.411421 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1810.00i | 0.251255i | 0.992077 | + | 0.125628i | \(0.0400945\pi\) | ||||
−0.992077 | + | 0.125628i | \(0.959906\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 8300.00i | − 1.13388i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8120.00 | 1.10052 | 0.550259 | − | 0.834994i | \(-0.314529\pi\) | ||||
0.550259 | + | 0.834994i | \(0.314529\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2492.00 | −0.335089 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11782.0i | 1.57189i | 0.618299 | + | 0.785943i | \(0.287822\pi\) | ||||
−0.618299 | + | 0.785943i | \(0.712178\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3266.00i | − 0.428993i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4350.00 | 0.566976 | 0.283488 | − | 0.958976i | \(-0.408508\pi\) | ||||
0.283488 | + | 0.958976i | \(0.408508\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5340.00 | 0.690679 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 5320.00i | − 0.682846i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7470.00i | 0.944354i | 0.881504 | + | 0.472177i | \(0.156532\pi\) | ||||
−0.881504 | + | 0.472177i | \(0.843468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −480.000 | −0.0602257 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11698.0 | 1.45678 | 0.728392 | − | 0.685161i | \(-0.240268\pi\) | ||||
0.728392 | + | 0.685161i | \(0.240268\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1000.00i | − 0.123607i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 600.000i | 0.0730735i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3650.00 | 0.441274 | 0.220637 | − | 0.975356i | \(-0.429186\pi\) | ||||
0.220637 | + | 0.975356i | \(0.429186\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5540.00 | 0.664886 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4800.00i | − 0.571895i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 1120.00i | − 0.131527i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1120.00 | −0.130586 | −0.0652931 | − | 0.997866i | \(-0.520798\pi\) | ||||
−0.0652931 | + | 0.997866i | \(0.520798\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4850.00 | 0.561460 | 0.280730 | − | 0.959787i | \(-0.409424\pi\) | ||||
0.280730 | + | 0.959787i | \(0.409424\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4922.00i | 0.565758i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1500.00i | 0.170000i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6000.00 | 0.675251 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12580.0 | 1.40593 | 0.702967 | − | 0.711223i | \(-0.251858\pi\) | ||||
0.702967 | + | 0.711223i | \(0.251858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13130.0i | 1.45725i | 0.684915 | + | 0.728623i | \(0.259839\pi\) | ||||
−0.684915 | + | 0.728623i | \(0.740161\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7120.00i | − 0.779395i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8560.00 | 0.930630 | 0.465315 | − | 0.885145i | \(-0.345941\pi\) | ||||
0.465315 | + | 0.885145i | \(0.345941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7061.00 | 0.762445 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4258.00i | 0.456667i | 0.973583 | + | 0.228334i | \(0.0733277\pi\) | ||||
−0.973583 | + | 0.228334i | \(0.926672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4700.00i | 0.497321i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2550.00 | −0.268022 | −0.134011 | − | 0.990980i | \(-0.542786\pi\) | ||||
−0.134011 | + | 0.990980i | \(0.542786\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15000.0 | 1.56613 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1160.00i | − 0.120312i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6710.00i | 0.686828i | 0.939184 | + | 0.343414i | \(0.111583\pi\) | ||||
−0.939184 | + | 0.343414i | \(0.888417\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3000.00 | −0.305072 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14482.0 | −1.46311 | −0.731555 | − | 0.681782i | \(-0.761205\pi\) | ||||
−0.731555 | + | 0.681782i | \(0.761205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 162.000i | − 0.0162609i | −0.999967 | − | 0.00813043i | \(-0.997412\pi\) | ||||
0.999967 | − | 0.00813043i | \(-0.00258802\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 15974.0i | − 1.58284i | −0.611270 | − | 0.791422i | \(-0.709341\pi\) | ||||
0.611270 | − | 0.791422i | \(-0.290659\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4644.00 | 0.457228 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2620.00 | −0.256313 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8520.00i | 0.828224i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11270.0i | 1.08180i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10760.0 | −1.02638 | −0.513191 | − | 0.858274i | \(-0.671537\pi\) | ||||
−0.513191 | + | 0.858274i | \(0.671537\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 500.000 | 0.0473972 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2136.00i | 0.201224i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 9266.00i | − 0.862182i | −0.902309 | − | 0.431091i | \(-0.858129\pi\) | ||||
0.902309 | − | 0.431091i | \(-0.141871\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3724.00 | 0.344387 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2860.00 | −0.262872 | −0.131436 | − | 0.991325i | \(-0.541959\pi\) | ||||
−0.131436 | + | 0.991325i | \(0.541959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4980.00i | − 0.454945i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 600.000i | − 0.0541523i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7160.00 | 0.642336 | 0.321168 | − | 0.947022i | \(-0.395925\pi\) | ||||
0.321168 | + | 0.947022i | \(0.395925\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1452.00 | −0.129482 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1398.00i | 0.123924i | 0.998079 | + | 0.0619620i | \(0.0197357\pi\) | ||||
−0.998079 | + | 0.0619620i | \(0.980264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 606.000i | − 0.0530836i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7446.00 | −0.648405 | −0.324203 | − | 0.945988i | \(-0.605096\pi\) | ||||
−0.324203 | + | 0.945988i | \(0.605096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1380.00 | 0.119467 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4000.00i | 0.344258i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 12840.0i | − 1.09227i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6500.00 | −0.549746 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16438.0 | −1.38227 | −0.691134 | − | 0.722726i | \(-0.742889\pi\) | ||||
−0.691134 | + | 0.722726i | \(0.742889\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7322.00i | 0.612177i | 0.952003 | + | 0.306089i | \(0.0990204\pi\) | ||||
−0.952003 | + | 0.306089i | \(0.900980\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 600.000i | − 0.0495947i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19517.0 | −1.60409 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18400.0 | −1.50375 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 12500.0i | − 1.01583i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 2240.00i | − 0.180006i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18420.0 | −1.47200 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10878.0 | 0.864476 | 0.432238 | − | 0.901759i | \(-0.357724\pi\) | ||||
0.432238 | + | 0.901759i | \(0.357724\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 5684.00i | − 0.449215i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16114.0i | 1.25957i | 0.776769 | + | 0.629785i | \(0.216857\pi\) | ||||
−0.776769 | + | 0.629785i | \(0.783143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5750.00 | 0.447002 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6640.00 | −0.513382 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 7920.00i | − 0.609028i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 3690.00i | − 0.280701i | −0.990102 | − | 0.140350i | \(-0.955177\pi\) | ||||
0.990102 | − | 0.140350i | \(-0.0448229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7100.00 | 0.537206 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3600.00 | 0.270931 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2562.00i | 0.191786i | 0.995392 | + | 0.0958929i | \(0.0305706\pi\) | ||||
−0.995392 | + | 0.0958929i | \(0.969429\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2526.00i | 0.187094i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6050.00 | 0.445746 | 0.222873 | − | 0.974848i | \(-0.428457\pi\) | ||||
0.222873 | + | 0.974848i | \(0.428457\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8260.00 | −0.605377 | −0.302688 | − | 0.953090i | \(-0.597884\pi\) | ||||
−0.302688 | + | 0.953090i | \(0.597884\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 6360.00i | − 0.463687i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16870.0i | 1.21717i | 0.793489 | + | 0.608585i | \(0.208263\pi\) | ||||
−0.793489 | + | 0.608585i | \(0.791737\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9340.00 | 0.670392 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5892.00 | 0.420725 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 29400.0i | − 2.08855i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 966.000i | − 0.0679235i | −0.999423 | − | 0.0339617i | \(-0.989188\pi\) | ||||
0.999423 | − | 0.0339617i | \(-0.0108124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −800.000 | −0.0559651 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5980.00 | −0.416217 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26290.0i | 1.82057i | 0.413977 | + | 0.910287i | \(0.364139\pi\) | ||||
−0.413977 | + | 0.910287i | \(0.635861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 8480.00i | − 0.581346i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11640.0 | −0.793986 | −0.396993 | − | 0.917822i | \(-0.629946\pi\) | ||||
−0.396993 | + | 0.917822i | \(0.629946\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25450.0 | −1.72733 | −0.863667 | − | 0.504064i | \(-0.831838\pi\) | ||||
−0.863667 | + | 0.504064i | \(0.831838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 17802.0i | − 1.20224i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16694.0i | 1.11629i | 0.829743 | + | 0.558145i | \(0.188487\pi\) | ||||
−0.829743 | + | 0.558145i | \(0.811513\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1992.00 | 0.132545 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10700.0 | −0.708471 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15890.0i | 1.04697i | 0.852036 | + | 0.523484i | \(0.175368\pi\) | ||||
−0.852036 | + | 0.523484i | \(0.824632\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1230.00i | 0.0802560i | 0.999195 | + | 0.0401280i | \(0.0127766\pi\) | ||||
−0.999195 | + | 0.0401280i | \(0.987223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10840.0 | −0.703871 | −0.351936 | − | 0.936024i | \(-0.614476\pi\) | ||||
−0.351936 | + | 0.936024i | \(0.614476\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17800.0 | 1.15022 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 5244.00i | − 0.337233i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4800.00i | − 0.305731i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 300.000 | 0.0190171 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14060.0 | 0.887036 | 0.443518 | − | 0.896265i | \(-0.353730\pi\) | ||||
0.443518 | + | 0.896265i | \(0.353730\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8120.00i | 0.509859i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15350.0i | 0.954771i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2300.00 | −0.142389 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17650.0 | −1.08757 | −0.543786 | − | 0.839224i | \(-0.683010\pi\) | ||||
−0.543786 | + | 0.839224i | \(0.683010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 27358.0i | − 1.67791i | −0.544203 | − | 0.838953i | \(-0.683168\pi\) | ||||
0.544203 | − | 0.838953i | \(-0.316832\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 6786.00i | − 0.412342i | −0.978516 | − | 0.206171i | \(-0.933900\pi\) | ||||
0.978516 | − | 0.206171i | \(-0.0661003\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48000.0 | 2.90318 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 240.000 | 0.0144491 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 9030.00i | − 0.541150i | −0.962699 | − | 0.270575i | \(-0.912786\pi\) | ||||
0.962699 | − | 0.270575i | \(-0.0872139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 5290.00i | − 0.314129i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15600.0 | −0.922139 | −0.461070 | − | 0.887364i | \(-0.652534\pi\) | ||||
−0.461070 | + | 0.887364i | \(0.652534\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16850.0 | 0.991511 | 0.495756 | − | 0.868462i | \(-0.334891\pi\) | ||||
0.495756 | + | 0.868462i | \(0.334891\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3000.00i | − 0.175732i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29548.0i | 1.71530i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11244.0 | −0.649803 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15000.0 | −0.862993 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 7990.00i | − 0.457640i | −0.973469 | − | 0.228820i | \(-0.926513\pi\) | ||||
0.973469 | − | 0.228820i | \(-0.0734868\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 18690.0i | − 1.06103i | −0.847677 | − | 0.530513i | \(-0.821999\pi\) | ||||
0.847677 | − | 0.530513i | \(-0.178001\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1860.00 | −0.105126 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3108.00 | −0.174888 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 19182.0i | − 1.07464i | −0.843379 | − | 0.537320i | \(-0.819437\pi\) | ||||
0.843379 | − | 0.537320i | \(-0.180563\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 2268.00i | − 0.125953i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24500.0 | −1.35468 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23380.0 | 1.28714 | 0.643572 | − | 0.765385i | \(-0.277452\pi\) | ||||
0.643572 | + | 0.765385i | \(0.277452\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 8280.00i | − 0.453869i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 7500.00i | − 0.407579i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3420.00 | 0.185059 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11850.0 | 0.638471 | 0.319236 | − | 0.947675i | \(-0.396574\pi\) | ||||
0.319236 | + | 0.947675i | \(0.396574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 400.000i | − 0.0214599i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 8988.00i | − 0.478117i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25646.0 | −1.35847 | −0.679235 | − | 0.733921i | \(-0.737688\pi\) | ||||
−0.679235 | + | 0.733921i | \(0.737688\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30360.0 | −1.60139 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3560.00i | 0.186989i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8880.00i | 0.462524i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30280.0 | −1.57059 | −0.785294 | − | 0.619122i | \(-0.787488\pi\) | ||||
−0.785294 | + | 0.619122i | \(0.787488\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8412.00 | 0.434507 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1700.00i | − 0.0874463i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17446.0i | 0.890009i | 0.895528 | + | 0.445004i | \(0.146798\pi\) | ||||
−0.895528 | + | 0.445004i | \(0.853202\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4283.00 | 0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4260.00 | 0.215543 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 16750.0i | − 0.844032i | −0.906588 | − | 0.422016i | \(-0.861323\pi\) | ||||
0.906588 | − | 0.422016i | \(-0.138677\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 46440.0i | 2.32108i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36560.0 | −1.81987 | −0.909933 | − | 0.414755i | \(-0.863867\pi\) | ||||
−0.909933 | + | 0.414755i | \(0.863867\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4000.00 | −0.198305 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30142.0i | 1.48829i | 0.668016 | + | 0.744147i | \(0.267144\pi\) | ||||
−0.668016 | + | 0.744147i | \(0.732856\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 22586.0i | − 1.10626i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7164.00 | −0.349488 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11860.0 | −0.576268 | −0.288134 | − | 0.957590i | \(-0.593035\pi\) | ||||
−0.288134 | + | 0.957590i | \(0.593035\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1320.00i | 0.0638824i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 37010.0i | − 1.77695i | −0.458925 | − | 0.888475i | \(-0.651765\pi\) | ||||
0.458925 | − | 0.888475i | \(-0.348235\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21360.0 | −1.02150 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11718.0 | −0.558183 | −0.279091 | − | 0.960265i | \(-0.590033\pi\) | ||||
−0.279091 | + | 0.960265i | \(0.590033\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3900.00i | − 0.185045i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 40000.0i | − 1.88307i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4706.00 | −0.220680 | −0.110340 | − | 0.993894i | \(-0.535194\pi\) | ||||
−0.110340 | + | 0.993894i | \(0.535194\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15180.0 | −0.709072 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 28670.0i | − 1.33401i | −0.745054 | − | 0.667004i | \(-0.767576\pi\) | ||||
0.745054 | − | 0.667004i | \(-0.232424\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 120.000i | 0.00554051i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10000.0 | −0.459932 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6000.00 | 0.274900 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 16600.0i | − 0.757644i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20434.0i | 0.925532i | 0.886481 | + | 0.462766i | \(0.153143\pi\) | ||||
−0.886481 | + | 0.462766i | \(0.846857\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1524.00 | 0.0687653 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9060.00 | 0.407252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12500.0i | 0.559758i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3930.00i | − 0.174665i | −0.996179 | − | 0.0873323i | \(-0.972166\pi\) | ||||
0.996179 | − | 0.0873323i | \(-0.0278342\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6420.00 | −0.284259 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20102.0 | −0.886728 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13800.0i | 0.606465i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 300.000i | 0.0130861i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4854.00 | 0.210949 | 0.105474 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13140.0 | 0.568937 | 0.284468 | − | 0.958685i | \(-0.408183\pi\) | ||||
0.284468 | + | 0.958685i | \(0.408183\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13160.0i | 0.567702i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 5680.00i | − 0.243229i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6900.00 | −0.294390 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22050.0 | 0.937333 | 0.468666 | − | 0.883375i | \(-0.344735\pi\) | ||||
0.468666 | + | 0.883375i | \(0.344735\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 14578.0i | − 0.617445i | −0.951152 | − | 0.308722i | \(-0.900099\pi\) | ||||
0.951152 | − | 0.308722i | \(-0.0999014\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 37054.0i | − 1.55803i | −0.627003 | − | 0.779017i | \(-0.715719\pi\) | ||||
0.627003 | − | 0.779017i | \(-0.284281\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6150.00 | 0.257658 | 0.128829 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128829 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9060.00 | 0.378204 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9210.00i | 0.383082i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2000.00i | − 0.0825927i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8200.00 | −0.337420 | −0.168710 | − | 0.985666i | \(-0.553960\pi\) | ||||
−0.168710 | + | 0.985666i | \(0.553960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3167.00 | 0.129854 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13900.0i | 0.567902i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13614.0i | 0.552282i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7764.00 | −0.313851 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1780.00 | −0.0717011 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 42990.0i | − 1.72561i | −0.505533 | − | 0.862807i | \(-0.668704\pi\) | ||||
0.505533 | − | 0.862807i | \(-0.331296\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 32130.0i | − 1.28068i | −0.768093 | − | 0.640338i | \(-0.778794\pi\) | ||||
0.768093 | − | 0.640338i | \(-0.221206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15440.0 | 0.613278 | 0.306639 | − | 0.951826i | \(-0.400796\pi\) | ||||
0.306639 | + | 0.951826i | \(0.400796\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3000.00 | 0.118745 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 46938.0i | − 1.85143i | −0.378216 | − | 0.925717i | \(-0.623462\pi\) | ||||
0.378216 | − | 0.925717i | \(-0.376538\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8026.00i | 0.314391i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 79200.0 | 3.09169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38700.0 | 1.50551 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7130.00i | 0.276419i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31230.0i | 1.20247i | 0.799074 | + | 0.601233i | \(0.205324\pi\) | ||||
−0.799074 | + | 0.601233i | \(0.794676\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2740.00 | −0.105140 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25550.0 | 0.977073 | 0.488537 | − | 0.872543i | \(-0.337531\pi\) | ||||
0.488537 | + | 0.872543i | \(0.337531\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 4318.00i | − 0.164567i | −0.996609 | − | 0.0822833i | \(-0.973779\pi\) | ||||
0.996609 | − | 0.0822833i | \(-0.0262212\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1766.00i | 0.0668506i | 0.999441 | + | 0.0334253i | \(0.0106416\pi\) | ||||
−0.999441 | + | 0.0334253i | \(0.989358\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7476.00 | −0.282044 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25260.0 | −0.949766 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8560.00i | 0.320772i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17800.0i | 0.662569i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3320.00 | 0.123168 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14700.0 | −0.543538 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1704.00i | 0.0627969i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41906.0i | 1.53414i | 0.641563 | + | 0.767071i | \(0.278286\pi\) | ||||
−0.641563 | + | 0.767071i | \(0.721714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34454.0 | −1.25717 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25140.0 | −0.914298 | −0.457149 | − | 0.889390i | \(-0.651129\pi\) | ||||
−0.457149 | + | 0.889390i | \(0.651129\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 58920.0i | 2.13578i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 15960.0i | − 0.574750i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32920.0 | 1.18164 | 0.590822 | − | 0.806802i | \(-0.298804\pi\) | ||||
0.590822 | + | 0.806802i | \(0.298804\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8212.00 | −0.293805 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5000.00i | − 0.178307i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 32246.0i | − 1.14250i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10150.0 | −0.358461 | −0.179231 | − | 0.983807i | \(-0.557361\pi\) | ||||
−0.179231 | + | 0.983807i | \(0.557361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12280.0 | 0.432289 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 4440.00i | − 0.155798i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 28530.0i | − 0.994701i | −0.867550 | − | 0.497350i | \(-0.834306\pi\) | ||||
0.867550 | − | 0.497350i | \(-0.165694\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18860.0 | 0.655456 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9678.00 | 0.335275 | 0.167638 | − | 0.985849i | \(-0.446386\pi\) | ||||
0.167638 | + | 0.985849i | \(0.446386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44500.0i | 1.53671i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36986.0i | 1.26915i | 0.772862 | + | 0.634574i | \(0.218824\pi\) | ||||
−0.772862 | + | 0.634574i | \(0.781176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11500.0 | 0.393368 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12940.0 | −0.441228 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 3350.00i | − 0.113869i | −0.998378 | − | 0.0569345i | \(-0.981867\pi\) | ||||
0.998378 | − | 0.0569345i | \(-0.0181326\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19920.0i | 0.672855i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16620.0 | 0.559633 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29391.0 | −0.986573 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27462.0i | 0.918952i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43774.0i | 1.45572i | 0.685728 | + | 0.727858i | \(0.259484\pi\) | ||||
−0.685728 | + | 0.727858i | \(0.740516\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2400.00 | −0.0795656 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8740.00 | −0.288857 | −0.144428 | − | 0.989515i | \(-0.546134\pi\) | ||||
−0.144428 | + | 0.989515i | \(0.546134\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3360.00i | − 0.110706i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48310.0i | 1.58196i | 0.611843 | + | 0.790979i | \(0.290429\pi\) | ||||
−0.611843 | + | 0.790979i | \(0.709571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 52440.0 | 1.71194 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14950.0 | −0.486561 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 2282.00i | − 0.0740432i | −0.999314 | − | 0.0370216i | \(-0.988213\pi\) | ||||
0.999314 | − | 0.0370216i | \(-0.0117870\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2568.00i | − 0.0828170i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25276.0 | −0.812669 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31580.0 | 1.01228 | 0.506141 | − | 0.862451i | \(-0.331071\pi\) | ||||
0.506141 | + | 0.862451i | \(0.331071\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 1800.00i | − 0.0575239i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2790.00i | 0.0886261i | 0.999018 | + | 0.0443130i | \(0.0141099\pi\) | ||||
−0.999018 | + | 0.0443130i | \(0.985890\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1000.00 | 0.0316703 |
(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 | 800.4.c.e.449.2 | 2 | ||
4.3 | odd | 2 | 800.4.c.f.449.1 | 2 | |||
5.2 | odd | 4 | 160.4.a.b.1.1 | yes | 1 | ||
5.3 | odd | 4 | 800.4.a.d.1.1 | 1 | |||
5.4 | even | 2 | inner | 800.4.c.e.449.1 | 2 | ||
15.2 | even | 4 | 1440.4.a.n.1.1 | 1 | |||
20.3 | even | 4 | 800.4.a.h.1.1 | 1 | |||
20.7 | even | 4 | 160.4.a.a.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 800.4.c.f.449.2 | 2 | |||
40.3 | even | 4 | 1600.4.a.r.1.1 | 1 | |||
40.13 | odd | 4 | 1600.4.a.bj.1.1 | 1 | |||
40.27 | even | 4 | 320.4.a.i.1.1 | 1 | |||
40.37 | odd | 4 | 320.4.a.f.1.1 | 1 | |||
60.47 | odd | 4 | 1440.4.a.o.1.1 | 1 | |||
80.27 | even | 4 | 1280.4.d.f.641.2 | 2 | |||
80.37 | odd | 4 | 1280.4.d.k.641.1 | 2 | |||
80.67 | even | 4 | 1280.4.d.f.641.1 | 2 | |||
80.77 | odd | 4 | 1280.4.d.k.641.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.4.a.a.1.1 | ✓ | 1 | 20.7 | even | 4 | ||
160.4.a.b.1.1 | yes | 1 | 5.2 | odd | 4 | ||
320.4.a.f.1.1 | 1 | 40.37 | odd | 4 | |||
320.4.a.i.1.1 | 1 | 40.27 | even | 4 | |||
800.4.a.d.1.1 | 1 | 5.3 | odd | 4 | |||
800.4.a.h.1.1 | 1 | 20.3 | even | 4 | |||
800.4.c.e.449.1 | 2 | 5.4 | even | 2 | inner | ||
800.4.c.e.449.2 | 2 | 1.1 | even | 1 | trivial | ||
800.4.c.f.449.1 | 2 | 4.3 | odd | 2 | |||
800.4.c.f.449.2 | 2 | 20.19 | odd | 2 | |||
1280.4.d.f.641.1 | 2 | 80.67 | even | 4 | |||
1280.4.d.f.641.2 | 2 | 80.27 | even | 4 | |||
1280.4.d.k.641.1 | 2 | 80.37 | odd | 4 | |||
1280.4.d.k.641.2 | 2 | 80.77 | odd | 4 | |||
1440.4.a.n.1.1 | 1 | 15.2 | even | 4 | |||
1440.4.a.o.1.1 | 1 | 60.47 | odd | 4 | |||
1600.4.a.r.1.1 | 1 | 40.3 | even | 4 | |||
1600.4.a.bj.1.1 | 1 | 40.13 | odd | 4 |