Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,4,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.a (trivial) |
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: | yes |
Analytic conductor: | \(23.6007640023\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 200) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −9.00000 | −1.73205 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −26.0000 | −1.40387 | −0.701934 | − | 0.712242i | \(-0.747680\pi\) | ||||
−0.701934 | + | 0.712242i | \(0.747680\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 54.0000 | 2.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 59.0000 | 1.61720 | 0.808599 | − | 0.588361i | \(-0.200226\pi\) | ||||
0.808599 | + | 0.588361i | \(0.200226\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28.0000 | 0.597369 | 0.298685 | − | 0.954352i | \(-0.403452\pi\) | ||||
0.298685 | + | 0.954352i | \(0.403452\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00000 | 0.0713340 | 0.0356670 | − | 0.999364i | \(-0.488644\pi\) | ||||
0.0356670 | + | 0.999364i | \(0.488644\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −109.000 | −1.31612 | −0.658061 | − | 0.752965i | \(-0.728623\pi\) | ||||
−0.658061 | + | 0.752965i | \(0.728623\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 234.000 | 2.43157 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 194.000 | 1.75877 | 0.879387 | − | 0.476108i | \(-0.157953\pi\) | ||||
0.879387 | + | 0.476108i | \(0.157953\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −243.000 | −1.73205 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −32.0000 | −0.204905 | −0.102453 | − | 0.994738i | \(-0.532669\pi\) | ||||
−0.102453 | + | 0.994738i | \(0.532669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.0000 | −0.0579372 | −0.0289686 | − | 0.999580i | \(-0.509222\pi\) | ||||
−0.0289686 | + | 0.999580i | \(0.509222\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −531.000 | −2.80107 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −198.000 | −0.879757 | −0.439878 | − | 0.898057i | \(-0.644978\pi\) | ||||
−0.439878 | + | 0.898057i | \(0.644978\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −252.000 | −1.03467 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 117.000 | 0.445667 | 0.222833 | − | 0.974857i | \(-0.428469\pi\) | ||||
0.222833 | + | 0.974857i | \(0.428469\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −388.000 | −1.37603 | −0.688017 | − | 0.725695i | \(-0.741518\pi\) | ||||
−0.688017 | + | 0.725695i | \(0.741518\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 68.0000 | 0.211039 | 0.105519 | − | 0.994417i | \(-0.466350\pi\) | ||||
0.105519 | + | 0.994417i | \(0.466350\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 333.000 | 0.970845 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −45.0000 | −0.123554 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −18.0000 | −0.0466508 | −0.0233254 | − | 0.999728i | \(-0.507425\pi\) | ||||
−0.0233254 | + | 0.999728i | \(0.507425\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 981.000 | 2.27959 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −392.000 | −0.864984 | −0.432492 | − | 0.901638i | \(-0.642366\pi\) | ||||
−0.432492 | + | 0.901638i | \(0.642366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −710.000 | −1.49027 | −0.745133 | − | 0.666916i | \(-0.767614\pi\) | ||||
−0.745133 | + | 0.666916i | \(0.767614\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1404.00 | −2.80774 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 253.000 | 0.461326 | 0.230663 | − | 0.973034i | \(-0.425910\pi\) | ||||
0.230663 | + | 0.973034i | \(0.425910\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1746.00 | −3.04629 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 612.000 | 1.02297 | 0.511486 | − | 0.859292i | \(-0.329095\pi\) | ||||
0.511486 | + | 0.859292i | \(0.329095\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −549.000 | −0.880214 | −0.440107 | − | 0.897945i | \(-0.645059\pi\) | ||||
−0.440107 | + | 0.897945i | \(0.645059\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1534.00 | −2.27033 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −414.000 | −0.589603 | −0.294802 | − | 0.955559i | \(-0.595254\pi\) | ||||
−0.294802 | + | 0.955559i | \(0.595254\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 121.000 | 0.160018 | 0.0800089 | − | 0.996794i | \(-0.474505\pi\) | ||||
0.0800089 | + | 0.996794i | \(0.474505\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 288.000 | 0.354906 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −81.0000 | −0.0964717 | −0.0482359 | − | 0.998836i | \(-0.515360\pi\) | ||||
−0.0482359 | + | 0.998836i | \(0.515360\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −728.000 | −0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 90.0000 | 0.100350 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1502.00 | −1.57222 | −0.786108 | − | 0.618089i | \(-0.787907\pi\) | ||||
−0.786108 | + | 0.618089i | \(0.787907\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3186.00 | 3.23439 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −234.000 | −0.230533 | −0.115267 | − | 0.993335i | \(-0.536772\pi\) | ||||
−0.115267 | + | 0.993335i | \(0.536772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1172.00 | 1.12117 | 0.560585 | − | 0.828097i | \(-0.310576\pi\) | ||||
0.560585 | + | 0.828097i | \(0.310576\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1125.00 | −1.01643 | −0.508214 | − | 0.861231i | \(-0.669694\pi\) | ||||
−0.508214 | + | 0.861231i | \(0.669694\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1234.00 | −1.08436 | −0.542182 | − | 0.840261i | \(-0.682402\pi\) | ||||
−0.542182 | + | 0.840261i | \(0.682402\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1782.00 | 1.52378 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 567.000 | 0.472025 | 0.236013 | − | 0.971750i | \(-0.424159\pi\) | ||||
0.236013 | + | 0.971750i | \(0.424159\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1512.00 | 1.19474 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −130.000 | −0.100144 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2150.00 | 1.61533 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1053.00 | −0.771917 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2358.00 | 1.64755 | 0.823774 | − | 0.566918i | \(-0.191864\pi\) | ||||
0.823774 | + | 0.566918i | \(0.191864\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3492.00 | 2.38336 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1692.00 | 1.12848 | 0.564239 | − | 0.825611i | \(-0.309169\pi\) | ||||
0.564239 | + | 0.825611i | \(0.309169\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2834.00 | 1.84766 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 229.000 | 0.142809 | 0.0714043 | − | 0.997447i | \(-0.477252\pi\) | ||||
0.0714043 | + | 0.997447i | \(0.477252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2781.00 | −1.69699 | −0.848494 | − | 0.529205i | \(-0.822490\pi\) | ||||
−0.848494 | + | 0.529205i | \(0.822490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −612.000 | −0.365530 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1652.00 | 0.966064 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2997.00 | −1.68155 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1472.00 | 0.809335 | 0.404668 | − | 0.914464i | \(-0.367387\pi\) | ||||
0.404668 | + | 0.914464i | \(0.367387\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1322.00 | −0.712469 | −0.356235 | − | 0.934397i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934397i | \(0.615940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 270.000 | 0.142668 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 298.000 | 0.151484 | 0.0757420 | − | 0.997127i | \(-0.475867\pi\) | ||||
0.0757420 | + | 0.997127i | \(0.475867\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 162.000 | 0.0808015 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5044.00 | −2.46909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 341.000 | 0.163860 | 0.0819300 | − | 0.996638i | \(-0.473892\pi\) | ||||
0.0819300 | + | 0.996638i | \(0.473892\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −684.000 | −0.316943 | −0.158472 | − | 0.987364i | \(-0.550657\pi\) | ||||
−0.158472 | + | 0.987364i | \(0.550657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1413.00 | −0.643150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5886.00 | −2.63224 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2344.00 | −1.03012 | −0.515061 | − | 0.857154i | \(-0.672231\pi\) | ||||
−0.515061 | + | 0.857154i | \(0.672231\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3528.00 | 1.49820 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1111.00 | 0.463911 | 0.231955 | − | 0.972726i | \(-0.425488\pi\) | ||||
0.231955 | + | 0.972726i | \(0.425488\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2042.00 | 0.838567 | 0.419284 | − | 0.907855i | \(-0.362281\pi\) | ||||
0.419284 | + | 0.907855i | \(0.362281\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6390.00 | 2.58122 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 295.000 | 0.115361 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6318.00 | 2.43157 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5270.00 | −1.99646 | −0.998230 | − | 0.0594735i | \(-0.981058\pi\) | ||||
−0.998230 | + | 0.0594735i | \(0.981058\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 613.000 | 0.228625 | 0.114313 | − | 0.993445i | \(-0.463533\pi\) | ||||
0.114313 | + | 0.993445i | \(0.463533\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1174.00 | 0.424589 | 0.212295 | − | 0.977206i | \(-0.431906\pi\) | ||||
0.212295 | + | 0.977206i | \(0.431906\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3428.00 | −1.22113 | −0.610564 | − | 0.791967i | \(-0.709057\pi\) | ||||
−0.610564 | + | 0.791967i | \(0.709057\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2277.00 | −0.799041 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 832.000 | 0.287660 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10476.0 | 3.51755 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6431.00 | −2.12843 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2339.00 | −0.763144 | −0.381572 | − | 0.924339i | \(-0.624617\pi\) | ||||
−0.381572 | + | 0.924339i | \(0.624617\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5508.00 | −1.77184 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 260.000 | 0.0813362 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4941.00 | 1.52457 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 140.000 | 0.0426128 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3932.00 | −1.18075 | −0.590373 | − | 0.807131i | \(-0.701019\pi\) | ||||
−0.590373 | + | 0.807131i | \(0.701019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6084.00 | −1.77890 | −0.889448 | − | 0.457037i | \(-0.848911\pi\) | ||||
−0.889448 | + | 0.457037i | \(0.848911\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4996.00 | 1.44168 | 0.720841 | − | 0.693101i | \(-0.243756\pi\) | ||||
0.720841 | + | 0.693101i | \(0.243756\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13806.0 | 3.93233 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3222.00 | 0.905924 | 0.452962 | − | 0.891530i | \(-0.350367\pi\) | ||||
0.452962 | + | 0.891530i | \(0.350367\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3726.00 | 1.02122 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2736.00 | −0.740490 | −0.370245 | − | 0.928934i | \(-0.620726\pi\) | ||||
−0.370245 | + | 0.928934i | \(0.620726\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1673.00 | 0.447168 | 0.223584 | − | 0.974685i | \(-0.428224\pi\) | ||||
0.223584 | + | 0.974685i | \(0.428224\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3052.00 | −0.786211 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1089.00 | −0.277159 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5355.00 | −1.34663 | −0.673316 | − | 0.739355i | \(-0.735131\pi\) | ||||
−0.673316 | + | 0.739355i | \(0.735131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11446.0 | 2.84428 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5490.00 | −1.33252 | −0.666258 | − | 0.745721i | \(-0.732105\pi\) | ||||
−0.666258 | + | 0.745721i | \(0.732105\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5148.00 | 1.23506 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1728.00 | −0.409810 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3150.00 | −0.738545 | −0.369272 | − | 0.929321i | \(-0.620393\pi\) | ||||
−0.369272 | + | 0.929321i | \(0.620393\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 729.000 | 0.167094 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 176.000 | 0.0398919 | 0.0199459 | − | 0.999801i | \(-0.493651\pi\) | ||||
0.0199459 | + | 0.999801i | \(0.493651\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2394.00 | −0.536624 | −0.268312 | − | 0.963332i | \(-0.586466\pi\) | ||||
−0.268312 | + | 0.963332i | \(0.586466\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6552.00 | 1.45255 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6256.00 | −1.35699 | −0.678496 | − | 0.734604i | \(-0.737368\pi\) | ||||
−0.678496 | + | 0.734604i | \(0.737368\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −540.000 | −0.115874 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4802.00 | −1.01944 | −0.509721 | − | 0.860340i | \(-0.670251\pi\) | ||||
−0.509721 | + | 0.860340i | \(0.670251\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2123.00 | −0.445934 | −0.222967 | − | 0.974826i | \(-0.571574\pi\) | ||||
−0.222967 | + | 0.974826i | \(0.571574\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3042.00 | −0.625657 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4888.00 | −0.994911 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13518.0 | 2.72316 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8834.00 | −1.76139 | −0.880696 | − | 0.473682i | \(-0.842925\pi\) | ||||
−0.880696 | + | 0.473682i | \(0.842925\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14337.0 | −2.80107 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5432.00 | 1.05064 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10088.0 | 1.93177 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2106.00 | 0.399296 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1369.00 | −0.254505 | −0.127252 | − | 0.991870i | \(-0.540616\pi\) | ||||
−0.127252 | + | 0.991870i | \(0.540616\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10548.0 | −1.94192 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10426.0 | 1.90098 | 0.950489 | − | 0.310758i | \(-0.100583\pi\) | ||||
0.950489 | + | 0.310758i | \(0.100583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3574.00 | −0.645413 | −0.322707 | − | 0.946499i | \(-0.604593\pi\) | ||||
−0.322707 | + | 0.946499i | \(0.604593\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9036.00 | 1.60099 | 0.800493 | − | 0.599343i | \(-0.204571\pi\) | ||||
0.800493 | + | 0.599343i | \(0.204571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1888.00 | −0.331372 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10125.0 | 1.76051 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −545.000 | −0.0938842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11106.0 | 1.87817 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1768.00 | −0.296271 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10233.0 | −1.69926 | −0.849632 | − | 0.527376i | \(-0.823176\pi\) | ||||
−0.849632 | + | 0.527376i | \(0.823176\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10692.0 | −1.75951 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4627.00 | 0.747919 | 0.373960 | − | 0.927445i | \(-0.378000\pi\) | ||||
0.373960 | + | 0.927445i | \(0.378000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5103.00 | −0.817572 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −590.000 | −0.0936959 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 260.000 | 0.0409291 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4901.00 | −0.758212 | −0.379106 | − | 0.925353i | \(-0.623768\pi\) | ||||
−0.379106 | + | 0.925353i | \(0.623768\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4482.00 | −0.687438 | −0.343719 | − | 0.939072i | \(-0.611687\pi\) | ||||
−0.343719 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6804.00 | −1.03467 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1210.00 | −0.182441 | −0.0912207 | − | 0.995831i | \(-0.529077\pi\) | ||||
−0.0912207 | + | 0.995831i | \(0.529077\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1170.00 | 0.173454 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9882.00 | 1.45279 | 0.726396 | − | 0.687277i | \(-0.241194\pi\) | ||||
0.726396 | + | 0.687277i | \(0.241194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5022.00 | 0.732177 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19350.0 | −2.79783 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11260.0 | 1.60155 | 0.800773 | − | 0.598968i | \(-0.204422\pi\) | ||||
0.800773 | + | 0.598968i | \(0.204422\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6318.00 | 0.891333 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 468.000 | 0.0654915 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3230.00 | −0.448373 | −0.224186 | − | 0.974546i | \(-0.571972\pi\) | ||||
−0.224186 | + | 0.974546i | \(0.571972\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −896.000 | −0.122404 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11575.0 | −1.56878 | −0.784390 | − | 0.620268i | \(-0.787024\pi\) | ||||
−0.784390 | + | 0.620268i | \(0.787024\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21222.0 | −2.85364 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.0000 | 0.00240145 | 0.00120073 | − | 0.999999i | \(-0.499618\pi\) | ||||
0.00120073 | + | 0.999999i | \(0.499618\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20952.0 | −2.75207 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10710.0 | 1.39593 | 0.697967 | − | 0.716130i | \(-0.254088\pi\) | ||||
0.697967 | + | 0.716130i | \(0.254088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 970.000 | 0.125460 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15228.0 | −1.95458 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3788.00 | −0.478877 | −0.239439 | − | 0.970912i | \(-0.576963\pi\) | ||||
−0.239439 | + | 0.970912i | \(0.576963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25506.0 | −3.20024 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10539.0 | −1.31245 | −0.656225 | − | 0.754565i | \(-0.727848\pi\) | ||||
−0.656225 | + | 0.754565i | \(0.727848\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −280.000 | −0.0346099 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11682.0 | −1.42274 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5581.00 | 0.674725 | 0.337363 | − | 0.941375i | \(-0.390465\pi\) | ||||
0.337363 | + | 0.941375i | \(0.390465\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2061.00 | −0.247352 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10192.0 | 1.21432 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25029.0 | 2.93927 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5193.00 | −0.605476 | −0.302738 | − | 0.953074i | \(-0.597901\pi\) | ||||
−0.302738 | + | 0.953074i | \(0.597901\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4788.00 | 0.554282 | 0.277141 | − | 0.960829i | \(-0.410613\pi\) | ||||
0.277141 | + | 0.960829i | \(0.410613\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3672.00 | 0.422077 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18460.0 | 2.09214 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14868.0 | −1.67327 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8006.00 | −0.894746 | −0.447373 | − | 0.894348i | \(-0.647640\pi\) | ||||
−0.447373 | + | 0.894348i | \(0.647640\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2395.00 | −0.265811 | −0.132906 | − | 0.991129i | \(-0.542431\pi\) | ||||
−0.132906 | + | 0.991129i | \(0.542431\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21146.0 | −2.31476 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1864.00 | −0.202651 | −0.101326 | − | 0.994853i | \(-0.532308\pi\) | ||||
−0.101326 | + | 0.994853i | \(0.532308\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17982.0 | 1.94169 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5463.00 | −0.585903 | −0.292951 | − | 0.956127i | \(-0.594637\pi\) | ||||
−0.292951 | + | 0.956127i | \(0.594637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13248.0 | −1.40181 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12969.0 | 1.36313 | 0.681565 | − | 0.731758i | \(-0.261300\pi\) | ||||
0.681565 | + | 0.731758i | \(0.261300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6903.00 | 0.720731 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11898.0 | 1.23403 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18313.0 | 1.87450 | 0.937249 | − | 0.348659i | \(-0.113363\pi\) | ||||
0.937249 | + | 0.348659i | \(0.113363\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1215.00 | −0.123554 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12492.0 | 1.26206 | 0.631031 | − | 0.775758i | \(-0.282632\pi\) | ||||
0.631031 | + | 0.775758i | \(0.282632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4428.00 | −0.444464 | −0.222232 | − | 0.974994i | \(-0.571334\pi\) | ||||
−0.222232 | + | 0.974994i | \(0.571334\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1084.00 | 0.107412 | 0.0537061 | − | 0.998557i | \(-0.482897\pi\) | ||||
0.0537061 | + | 0.998557i | \(0.482897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6578.00 | −0.647641 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2682.00 | −0.262378 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22892.0 | −2.22532 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −972.000 | −0.0933015 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13082.0 | 1.24787 | 0.623937 | − | 0.781474i | \(-0.285532\pi\) | ||||
0.623937 | + | 0.781474i | \(0.285532\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5544.00 | −0.525540 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 45396.0 | 4.27658 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3014.00 | 0.280446 | 0.140223 | − | 0.990120i | \(-0.455218\pi\) | ||||
0.140223 | + | 0.990120i | \(0.455218\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3069.00 | −0.283814 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3564.00 | 0.327579 | 0.163789 | − | 0.986495i | \(-0.447628\pi\) | ||||
0.163789 | + | 0.986495i | \(0.447628\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −160.000 | −0.0146167 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15912.0 | −1.43612 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15796.0 | 1.41709 | 0.708543 | − | 0.705667i | \(-0.249353\pi\) | ||||
0.708543 | + | 0.705667i | \(0.249353\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6156.00 | 0.548962 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10908.0 | 0.966926 | 0.483463 | − | 0.875365i | \(-0.339379\pi\) | ||||
0.483463 | + | 0.875365i | \(0.339379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12717.0 | 1.11397 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21946.0 | 1.91108 | 0.955540 | − | 0.294863i | \(-0.0952739\pi\) | ||||
0.955540 | + | 0.294863i | \(0.0952739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14274.0 | 1.23570 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 26487.0 | 2.27959 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4012.00 | 0.341291 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21096.0 | 1.78422 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6395.00 | −0.537754 | −0.268877 | − | 0.963174i | \(-0.586653\pi\) | ||||
−0.268877 | + | 0.963174i | \(0.586653\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5615.00 | 0.469459 | 0.234729 | − | 0.972061i | \(-0.424580\pi\) | ||||
0.234729 | + | 0.972061i | \(0.424580\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −50.0000 | −0.00413289 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25469.0 | 2.09329 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21168.0 | −1.72997 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3276.00 | 0.266228 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9999.00 | −0.803517 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19647.0 | 1.57005 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4112.00 | −0.326781 | −0.163391 | − | 0.986561i | \(-0.552243\pi\) | ||||
−0.163391 | + | 0.986561i | \(0.552243\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18378.0 | −1.45244 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2167.00 | 0.169386 | 0.0846931 | − | 0.996407i | \(-0.473009\pi\) | ||||
0.0846931 | + | 0.996407i | \(0.473009\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −38340.0 | −2.98053 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3488.00 | 0.269680 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10764.0 | 0.827725 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19444.0 | −1.47912 | −0.739559 | − | 0.673092i | \(-0.764966\pi\) | ||||
−0.739559 | + | 0.673092i | \(0.764966\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10864.0 | −0.822000 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2655.00 | −0.199811 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20416.0 | −1.52830 | −0.764149 | − | 0.645040i | \(-0.776841\pi\) | ||||
−0.764149 | + | 0.645040i | \(0.776841\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18954.0 | −1.40387 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3127.00 | −0.230388 | −0.115194 | − | 0.993343i | \(-0.536749\pi\) | ||||
−0.115194 | + | 0.993343i | \(0.536749\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22580.0 | 1.65489 | 0.827446 | − | 0.561545i | \(-0.189793\pi\) | ||||
0.827446 | + | 0.561545i | \(0.189793\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 47430.0 | 3.45797 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −829.000 | −0.0598123 | −0.0299062 | − | 0.999553i | \(-0.509521\pi\) | ||||
−0.0299062 | + | 0.999553i | \(0.509521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5517.00 | −0.395991 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3146.00 | −0.224644 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1062.00 | −0.0754435 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7119.00 | −0.500567 | −0.250283 | − | 0.968173i | \(-0.580524\pi\) | ||||
−0.250283 | + | 0.968173i | \(0.580524\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1090.00 | 0.0762524 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10566.0 | −0.735410 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8217.00 | −0.569025 | −0.284512 | − | 0.958672i | \(-0.591832\pi\) | ||||
−0.284512 | + | 0.958672i | \(0.591832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30852.0 | 2.11506 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 90.0000 | 0.00613907 | 0.00306953 | − | 0.999995i | \(-0.499023\pi\) | ||||
0.00306953 | + | 0.999995i | \(0.499023\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17117.0 | −1.16176 | −0.580879 | − | 0.813990i | \(-0.697291\pi\) | ||||
−0.580879 | + | 0.813990i | \(0.697291\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13662.0 | 0.922653 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15120.0 | 1.01104 | 0.505520 | − | 0.862815i | \(-0.331301\pi\) | ||||
0.505520 | + | 0.862815i | \(0.331301\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7488.00 | −0.498241 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1904.00 | 0.126068 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6570.00 | −0.432887 | −0.216444 | − | 0.976295i | \(-0.569446\pi\) | ||||
−0.216444 | + | 0.976295i | \(0.569446\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18846.0 | 1.22968 | 0.614839 | − | 0.788653i | \(-0.289221\pi\) | ||||
0.614839 | + | 0.788653i | \(0.289221\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16316.0 | −1.05944 | −0.529722 | − | 0.848172i | \(-0.677704\pi\) | ||||
−0.529722 | + | 0.848172i | \(0.677704\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −47142.0 | −3.04629 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2106.00 | 0.135434 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 57879.0 | 3.68655 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −990.000 | −0.0627566 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20170.0 | −1.27251 | −0.636256 | − | 0.771478i | \(-0.719518\pi\) | ||||
−0.636256 | + | 0.771478i | \(0.719518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21051.0 | 1.32180 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9324.00 | 0.579953 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33048.0 | 2.04594 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12726.0 | −0.784160 | −0.392080 | − | 0.919931i | \(-0.628244\pi\) | ||||
−0.392080 | + | 0.919931i | \(0.628244\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2196.00 | −0.134684 | −0.0673420 | − | 0.997730i | \(-0.521452\pi\) | ||||
−0.0673420 | + | 0.997730i | \(0.521452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16884.0 | 1.02593 | 0.512966 | − | 0.858409i | \(-0.328547\pi\) | ||||
0.512966 | + | 0.858409i | \(0.328547\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23128.0 | −1.39885 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2340.00 | −0.140878 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4018.00 | −0.240791 | −0.120395 | − | 0.992726i | \(-0.538416\pi\) | ||||
−0.120395 | + | 0.992726i | \(0.538416\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −29646.0 | −1.76043 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19071.0 | −1.12732 | −0.563658 | − | 0.826009i | \(-0.690606\pi\) | ||||
−0.563658 | + | 0.826009i | \(0.690606\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17424.0 | 1.02529 | 0.512644 | − | 0.858601i | \(-0.328666\pi\) | ||||
0.512644 | + | 0.858601i | \(0.328666\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1260.00 | −0.0738075 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6208.00 | −0.360382 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 35388.0 | 2.04511 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41890.0 | −2.41005 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5382.00 | −0.308263 | −0.154131 | − | 0.988050i | \(-0.549258\pi\) | ||||
−0.154131 | + | 0.988050i | \(0.549258\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4496.00 | −0.255237 | −0.127618 | − | 0.991823i | \(-0.540733\pi\) | ||||
−0.127618 | + | 0.991823i | \(0.540733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39052.0 | 2.20718 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 54756.0 | 3.08114 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3249.00 | −0.182020 | −0.0910099 | − | 0.995850i | \(-0.529009\pi\) | ||||
−0.0910099 | + | 0.995850i | \(0.529009\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −44964.0 | −2.49706 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −504.000 | −0.0278677 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13399.0 | 0.737658 | 0.368829 | − | 0.929497i | \(-0.379759\pi\) | ||||
0.368829 | + | 0.929497i | \(0.379759\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −82836.0 | −4.54066 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 585.000 | 0.0317912 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28998.0 | −1.56911 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18148.0 | −0.977804 | −0.488902 | − | 0.872339i | \(-0.662602\pi\) | ||||
−0.488902 | + | 0.872339i | \(0.662602\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21582.0 | 1.15787 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6084.00 | 0.323638 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4868.00 | 0.257858 | 0.128929 | − | 0.991654i | \(-0.458846\pi\) | ||||
0.128929 | + | 0.991654i | \(0.458846\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22356.0 | −1.17921 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1940.00 | −0.101898 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24624.0 | 1.28257 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17366.0 | 0.900755 | 0.450377 | − | 0.892838i | \(-0.351289\pi\) | ||||
0.450377 | + | 0.892838i | \(0.351289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30472.0 | −1.57398 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15057.0 | −0.774517 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21824.0 | −1.11335 | −0.556676 | − | 0.830729i | \(-0.687924\pi\) | ||||
−0.556676 | + | 0.830729i | \(0.687924\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1940.00 | −0.0981580 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31428.0 | −1.58366 | −0.791828 | − | 0.610744i | \(-0.790870\pi\) | ||||
−0.791828 | + | 0.610744i | \(0.790870\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14927.0 | 0.746056 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14292.0 | 0.711420 | 0.355710 | − | 0.934596i | \(-0.384239\pi\) | ||||
0.355710 | + | 0.934596i | \(0.384239\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27468.0 | 1.36176 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13950.0 | −0.688797 | −0.344398 | − | 0.938824i | \(-0.611917\pi\) | ||||
−0.344398 | + | 0.938824i | \(0.611917\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6534.00 | 0.320036 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29250.0 | 1.42693 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38736.0 | 1.88215 | 0.941076 | − | 0.338194i | \(-0.109816\pi\) | ||||
0.941076 | + | 0.338194i | \(0.109816\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 48195.0 | 2.33243 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3664.00 | −0.175919 | −0.0879593 | − | 0.996124i | \(-0.528035\pi\) | ||||
−0.0879593 | + | 0.996124i | \(0.528035\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −103014. | −4.92644 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19557.0 | 0.931591 | 0.465795 | − | 0.884892i | \(-0.345768\pi\) | ||||
0.465795 | + | 0.884892i | \(0.345768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32084.0 | 1.52231 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10976.0 | −0.516715 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13283.0 | −0.622883 | −0.311442 | − | 0.950265i | \(-0.600812\pi\) | ||||
−0.311442 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 49410.0 | 2.30799 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24840.0 | 1.15580 | 0.577900 | − | 0.816108i | \(-0.303873\pi\) | ||||
0.577900 | + | 0.816108i | \(0.303873\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −46332.0 | −2.13919 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12753.0 | −0.586552 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36108.0 | 1.65435 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7776.00 | 0.354906 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18044.0 | −0.817280 | −0.408640 | − | 0.912696i | \(-0.633997\pi\) | ||||
−0.408640 | + | 0.912696i | \(0.633997\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28350.0 | 1.27920 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14742.0 | −0.662661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19880.0 | −0.890239 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6174.00 | −0.274397 | −0.137198 | − | 0.990544i | \(-0.543810\pi\) | ||||
−0.137198 | + | 0.990544i | \(0.543810\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 340.000 | 0.0150542 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4374.00 | −0.192943 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32391.0 | −1.42348 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1584.00 | −0.0690947 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1998.00 | −0.0868306 | −0.0434153 | − | 0.999057i | \(-0.513824\pi\) | ||||
−0.0434153 | + | 0.999057i | \(0.513824\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7156.00 | 0.309841 | 0.154921 | − | 0.987927i | \(-0.450488\pi\) | ||||
0.154921 | + | 0.987927i | \(0.450488\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21546.0 | 0.929460 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42292.0 | 1.81103 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −39312.0 | −1.67726 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27922.0 | 1.18695 | 0.593474 | − | 0.804853i | \(-0.297756\pi\) | ||||
0.593474 | + | 0.804853i | \(0.297756\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22636.0 | −0.958738 | −0.479369 | − | 0.877613i | \(-0.659134\pi\) | ||||
−0.479369 | + | 0.877613i | \(0.659134\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26559.0 | −1.11674 | −0.558372 | − | 0.829591i | \(-0.688574\pi\) | ||||
−0.558372 | + | 0.829591i | \(0.688574\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12580.0 | 0.527046 | 0.263523 | − | 0.964653i | \(-0.415115\pi\) | ||||
0.263523 | + | 0.964653i | \(0.415115\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 56304.0 | 2.35038 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1665.00 | 0.0692543 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2430.00 | 0.100350 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11344.0 | 0.466792 | 0.233396 | − | 0.972382i | \(-0.425016\pi\) | ||||
0.233396 | + | 0.972382i | \(0.425016\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23365.0 | −0.958014 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 43218.0 | 1.76573 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −55900.0 | −2.26771 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19107.0 | 0.772380 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38412.0 | −1.54729 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14786.0 | 0.593509 | 0.296754 | − | 0.954954i | \(-0.404096\pi\) | ||||
0.296754 | + | 0.954954i | \(0.404096\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29259.0 | −1.16624 | −0.583120 | − | 0.812386i | \(-0.698168\pi\) | ||||
−0.583120 | + | 0.812386i | \(0.698168\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13651.0 | 0.542219 | 0.271109 | − | 0.962549i | \(-0.412609\pi\) | ||||
0.271109 | + | 0.962549i | \(0.412609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27378.0 | 1.08367 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29016.0 | −1.14451 | −0.572257 | − | 0.820074i | \(-0.693932\pi\) | ||||
−0.572257 | + | 0.820074i | \(0.693932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 43992.0 | 1.72324 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24426.0 | −0.953504 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7084.00 | 0.275582 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −81108.0 | −3.14443 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21412.0 | 0.824438 | 0.412219 | − | 0.911085i | \(-0.364754\pi\) | ||||
0.412219 | + | 0.911085i | \(0.364754\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 79506.0 | 3.05082 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1170.00 | −0.0447427 | −0.0223713 | − | 0.999750i | \(-0.507122\pi\) | ||||
−0.0223713 | + | 0.999750i | \(0.507122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12655.0 | 0.482304 | 0.241152 | − | 0.970487i | \(-0.422475\pi\) | ||||
0.241152 | + | 0.970487i | \(0.422475\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32764.0 | −1.24026 | −0.620128 | − | 0.784500i | \(-0.712919\pi\) | ||||
−0.620128 | + | 0.784500i | \(0.712919\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −61308.0 | −2.31294 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43011.0 | 1.61720 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7412.00 | −0.277753 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −48888.0 | −1.81976 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 320.000 | 0.0118716 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −90.0000 | −0.00332779 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −90792.0 | −3.34592 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29844.0 | 1.09256 | 0.546281 | − | 0.837602i | \(-0.316043\pi\) | ||||
0.546281 | + | 0.837602i | \(0.316043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12636.0 | −0.461067 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15628.0 | −0.568363 | −0.284182 | − | 0.958770i | \(-0.591722\pi\) | ||||
−0.284182 | + | 0.958770i | \(0.591722\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7139.00 | 0.258780 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43992.0 | −1.58424 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42974.0 | −1.54253 | −0.771263 | − | 0.636517i | \(-0.780375\pi\) | ||||
−0.771263 | + | 0.636517i | \(0.780375\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12321.0 | 0.440815 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17136.0 | 0.611092 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 63288.0 | 2.24234 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13342.0 | 0.471191 | 0.235596 | − | 0.971851i | \(-0.424296\pi\) | ||||
0.235596 | + | 0.971851i | \(0.424296\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36297.0 | −1.27775 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −93834.0 | −3.29259 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3005.00 | −0.104770 | −0.0523848 | − | 0.998627i | \(-0.516682\pi\) | ||||
−0.0523848 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32166.0 | 1.11789 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16204.0 | 0.561355 | 0.280678 | − | 0.959802i | \(-0.409441\pi\) | ||||
0.280678 | + | 0.959802i | \(0.409441\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22698.0 | 0.783827 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30200.0 | 1.03629 | 0.518146 | − | 0.855292i | \(-0.326622\pi\) | ||||
0.518146 | + | 0.855292i | \(0.326622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15372.0 | −0.525813 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −81324.0 | −2.77299 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29583.0 | −1.00555 | −0.502774 | − | 0.864418i | \(-0.667687\pi\) | ||||
−0.502774 | + | 0.864418i | \(0.667687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16992.0 | 0.573953 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5954.00 | −0.200485 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29691.0 | −0.996643 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −60750.0 | −2.03286 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6480.00 | 0.215494 | 0.107747 | − | 0.994178i | \(-0.465636\pi\) | ||||
0.107747 | + | 0.994178i | \(0.465636\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4905.00 | 0.162612 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40171.0 | 1.32765 | 0.663825 | − | 0.747888i | \(-0.268932\pi\) | ||||
0.663825 | + | 0.747888i | \(0.268932\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 72306.0 | 2.38235 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50801.0 | 1.66353 | 0.831765 | − | 0.555129i | \(-0.187331\pi\) | ||||
0.831765 | + | 0.555129i | \(0.187331\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4779.00 | −0.156014 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −66636.0 | −2.16873 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 58338.0 | 1.89287 | 0.946436 | − | 0.322891i | \(-0.104655\pi\) | ||||
0.946436 | + | 0.322891i | \(0.104655\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15912.0 | 0.513156 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −75272.0 | −2.42013 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51202.0 | 1.64126 | 0.820628 | − | 0.571462i | \(-0.193624\pi\) | ||||
0.820628 | + | 0.571462i | \(0.193624\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 92097.0 | 2.94321 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1764.00 | 0.0560345 | 0.0280173 | − | 0.999607i | \(-0.491081\pi\) | ||||
0.0280173 | + | 0.999607i | \(0.491081\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 48114.0 | 1.52378 |
(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 | 400.4.a.a.1.1 | 1 | ||
4.3 | odd | 2 | 200.4.a.j.1.1 | yes | 1 | ||
5.2 | odd | 4 | 400.4.c.b.49.2 | 2 | |||
5.3 | odd | 4 | 400.4.c.b.49.1 | 2 | |||
5.4 | even | 2 | 400.4.a.t.1.1 | 1 | |||
8.3 | odd | 2 | 1600.4.a.c.1.1 | 1 | |||
8.5 | even | 2 | 1600.4.a.by.1.1 | 1 | |||
12.11 | even | 2 | 1800.4.a.bh.1.1 | 1 | |||
20.3 | even | 4 | 200.4.c.b.49.2 | 2 | |||
20.7 | even | 4 | 200.4.c.b.49.1 | 2 | |||
20.19 | odd | 2 | 200.4.a.b.1.1 | ✓ | 1 | ||
40.19 | odd | 2 | 1600.4.a.bz.1.1 | 1 | |||
40.29 | even | 2 | 1600.4.a.b.1.1 | 1 | |||
60.23 | odd | 4 | 1800.4.f.w.649.1 | 2 | |||
60.47 | odd | 4 | 1800.4.f.w.649.2 | 2 | |||
60.59 | even | 2 | 1800.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.4.a.b.1.1 | ✓ | 1 | 20.19 | odd | 2 | ||
200.4.a.j.1.1 | yes | 1 | 4.3 | odd | 2 | ||
200.4.c.b.49.1 | 2 | 20.7 | even | 4 | |||
200.4.c.b.49.2 | 2 | 20.3 | even | 4 | |||
400.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
400.4.a.t.1.1 | 1 | 5.4 | even | 2 | |||
400.4.c.b.49.1 | 2 | 5.3 | odd | 4 | |||
400.4.c.b.49.2 | 2 | 5.2 | odd | 4 | |||
1600.4.a.b.1.1 | 1 | 40.29 | even | 2 | |||
1600.4.a.c.1.1 | 1 | 8.3 | odd | 2 | |||
1600.4.a.by.1.1 | 1 | 8.5 | even | 2 | |||
1600.4.a.bz.1.1 | 1 | 40.19 | odd | 2 | |||
1800.4.a.c.1.1 | 1 | 60.59 | even | 2 | |||
1800.4.a.bh.1.1 | 1 | 12.11 | even | 2 | |||
1800.4.f.w.649.1 | 2 | 60.23 | odd | 4 | |||
1800.4.f.w.649.2 | 2 | 60.47 | odd | 4 |