Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(1,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, 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("588.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{193}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.44622\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.4462 | −1.11322 | −0.556612 | − | 0.830773i | \(-0.687899\pi\) | ||||
−0.556612 | + | 0.830773i | \(0.687899\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −51.1236 | −1.40130 | −0.700651 | − | 0.713504i | \(-0.747107\pi\) | ||||
−0.700651 | + | 0.713504i | \(0.747107\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37.2311 | −0.794312 | −0.397156 | − | 0.917751i | \(-0.630003\pi\) | ||||
−0.397156 | + | 0.917751i | \(0.630003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 37.3387 | 0.642720 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.2151 | −0.316939 | −0.158469 | − | 0.987364i | \(-0.550656\pi\) | ||||
−0.158469 | + | 0.987364i | \(0.550656\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −54.3387 | −0.656113 | −0.328056 | − | 0.944658i | \(-0.606394\pi\) | ||||
−0.328056 | + | 0.944658i | \(0.606394\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 176.924 | 1.60397 | 0.801985 | − | 0.597345i | \(-0.203778\pi\) | ||||
0.801985 | + | 0.597345i | \(0.203778\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.9084 | 0.239268 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 61.0916 | 0.391187 | 0.195593 | − | 0.980685i | \(-0.437337\pi\) | ||||
0.195593 | + | 0.980685i | \(0.437337\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −319.924 | −1.85355 | −0.926776 | − | 0.375614i | \(-0.877432\pi\) | ||||
−0.926776 | + | 0.375614i | \(0.877432\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 153.371 | 0.809043 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −315.080 | −1.39997 | −0.699984 | − | 0.714158i | \(-0.746810\pi\) | ||||
−0.699984 | + | 0.714158i | \(0.746810\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 111.693 | 0.458596 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 206.032 | 0.784800 | 0.392400 | − | 0.919795i | \(-0.371645\pi\) | ||||
0.392400 | + | 0.919795i | \(0.371645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 339.661 | 1.20460 | 0.602301 | − | 0.798269i | \(-0.294251\pi\) | ||||
0.602301 | + | 0.798269i | \(0.294251\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −112.016 | −0.371075 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −142.064 | −0.440897 | −0.220449 | − | 0.975399i | \(-0.570752\pi\) | ||||
−0.220449 | + | 0.975399i | \(0.570752\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 66.6453 | 0.182985 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 310.016 | 0.803471 | 0.401736 | − | 0.915756i | \(-0.368407\pi\) | ||||
0.401736 | + | 0.915756i | \(0.368407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 636.295 | 1.55996 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 163.016 | 0.378807 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 281.650 | 0.621486 | 0.310743 | − | 0.950494i | \(-0.399422\pi\) | ||||
0.310743 | + | 0.950494i | \(0.399422\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 543.849 | 1.14152 | 0.570760 | − | 0.821117i | \(-0.306649\pi\) | ||||
0.570760 | + | 0.821117i | \(0.306649\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 463.387 | 0.884247 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −479.359 | −0.874075 | −0.437038 | − | 0.899443i | \(-0.643972\pi\) | ||||
−0.437038 | + | 0.899443i | \(0.643972\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −530.773 | −0.926052 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1105.63 | 1.84809 | 0.924046 | − | 0.382280i | \(-0.124861\pi\) | ||||
0.924046 | + | 0.382280i | \(0.124861\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −239.350 | −0.383751 | −0.191876 | − | 0.981419i | \(-0.561457\pi\) | ||||
−0.191876 | + | 0.981419i | \(0.561457\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −89.7253 | −0.138141 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1160.67 | 1.65298 | 0.826488 | − | 0.562954i | \(-0.190335\pi\) | ||||
0.826488 | + | 0.562954i | \(0.190335\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.93158 | 0.00387690 | 0.00193845 | − | 0.999998i | \(-0.499383\pi\) | ||||
0.00193845 | + | 0.999998i | \(0.499383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 276.494 | 0.352824 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −183.275 | −0.225852 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1278.74 | 1.52299 | 0.761496 | − | 0.648169i | \(-0.224465\pi\) | ||||
0.761496 | + | 0.648169i | \(0.224465\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 959.773 | 1.07015 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 676.311 | 0.730401 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −79.0596 | −0.0827555 | −0.0413777 | − | 0.999144i | \(-0.513175\pi\) | ||||
−0.0413777 | + | 0.999144i | \(0.513175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −460.112 | −0.467101 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1372.10 | −1.35178 | −0.675889 | − | 0.737004i | \(-0.736240\pi\) | ||||
−0.675889 | + | 0.737004i | \(0.736240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −258.531 | −0.247318 | −0.123659 | − | 0.992325i | \(-0.539463\pi\) | ||||
−0.123659 | + | 0.992325i | \(0.539463\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1262.37 | −1.14054 | −0.570270 | − | 0.821458i | \(-0.693161\pi\) | ||||
−0.570270 | + | 0.821458i | \(0.693161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 276.833 | 0.243264 | 0.121632 | − | 0.992575i | \(-0.461187\pi\) | ||||
0.121632 | + | 0.992575i | \(0.461187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 945.240 | 0.808272 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 52.9156 | 0.0440520 | 0.0220260 | − | 0.999757i | \(-0.492988\pi\) | ||||
0.0220260 | + | 0.999757i | \(0.492988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2202.04 | −1.78558 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −335.080 | −0.264771 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1282.62 | 0.963650 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −618.096 | −0.453104 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1183.53 | 0.846866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 443.700 | 0.310016 | 0.155008 | − | 0.987913i | \(-0.450460\pi\) | ||||
0.155008 | + | 0.987913i | \(0.450460\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1018.98 | −0.695477 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2153.48 | 1.43627 | 0.718133 | − | 0.695906i | \(-0.244997\pi\) | ||||
0.718133 | + | 0.695906i | \(0.244997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 336.048 | 0.214240 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 263.108 | 0.164079 | 0.0820394 | − | 0.996629i | \(-0.473857\pi\) | ||||
0.0820394 | + | 0.996629i | \(0.473857\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1165.77 | −0.711360 | −0.355680 | − | 0.934608i | \(-0.615751\pi\) | ||||
−0.355680 | + | 0.934608i | \(0.615751\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 426.192 | 0.254552 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1903.39 | 1.11307 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −760.359 | −0.435479 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1765.19 | −0.970539 | −0.485270 | − | 0.874364i | \(-0.661279\pi\) | ||||
−0.485270 | + | 0.874364i | \(0.661279\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2692.31 | 1.45098 | 0.725488 | − | 0.688235i | \(-0.241614\pi\) | ||||
0.725488 | + | 0.688235i | \(0.241614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −199.936 | −0.105646 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3981.85 | 2.06342 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1941.38 | 0.986873 | 0.493437 | − | 0.869782i | \(-0.335740\pi\) | ||||
0.493437 | + | 0.869782i | \(0.335740\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −930.048 | −0.463884 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2102.84 | 1.01047 | 0.505236 | − | 0.862981i | \(-0.331405\pi\) | ||||
0.505236 | + | 0.862981i | \(0.331405\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1908.89 | −0.900646 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2344.22 | 1.08623 | 0.543116 | − | 0.839658i | \(-0.317244\pi\) | ||||
0.543116 | + | 0.839658i | \(0.317244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −810.844 | −0.369069 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −489.048 | −0.218704 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3470.65 | −1.52525 | −0.762626 | − | 0.646840i | \(-0.776090\pi\) | ||||
−0.762626 | + | 0.646840i | \(0.776090\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −844.949 | −0.358815 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −955.771 | −0.399093 | −0.199547 | − | 0.979888i | \(-0.563947\pi\) | ||||
−0.199547 | + | 0.979888i | \(0.563947\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4220.26 | −1.73309 | −0.866546 | − | 0.499098i | \(-0.833665\pi\) | ||||
−0.866546 | + | 0.499098i | \(0.833665\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1631.55 | −0.659057 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3921.56 | 1.55848 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1135.72 | 0.444127 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3518.03 | −1.33275 | −0.666377 | − | 0.745615i | \(-0.732156\pi\) | ||||
−0.666377 | + | 0.745615i | \(0.732156\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5017.67 | −1.87140 | −0.935699 | − | 0.352799i | \(-0.885230\pi\) | ||||
−0.935699 | + | 0.352799i | \(0.885230\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1390.16 | −0.510520 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2838.14 | −1.02644 | −0.513221 | − | 0.858257i | \(-0.671548\pi\) | ||||
−0.513221 | + | 0.858257i | \(0.671548\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −354.901 | −0.126424 | −0.0632118 | − | 0.998000i | \(-0.520134\pi\) | ||||
−0.0632118 | + | 0.998000i | \(0.520134\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1438.08 | 0.504648 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2564.32 | −0.873658 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1592.32 | 0.534656 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2777.99 | 0.919413 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 752.672 | 0.245574 | 0.122787 | − | 0.992433i | \(-0.460817\pi\) | ||||
0.122787 | + | 0.992433i | \(0.460817\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3316.90 | −1.06700 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4227.50 | −1.34099 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 718.051 | 0.221559 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 827.093 | 0.251748 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3077.75 | 0.924221 | 0.462111 | − | 0.886822i | \(-0.347092\pi\) | ||||
0.462111 | + | 0.886822i | \(0.347092\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 269.176 | 0.0797558 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6217.43 | 1.81791 | 0.908955 | − | 0.416894i | \(-0.136881\pi\) | ||||
0.908955 | + | 0.416894i | \(0.136881\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −503.254 | −0.145223 | −0.0726113 | − | 0.997360i | \(-0.523133\pi\) | ||||
−0.0726113 | + | 0.997360i | \(0.523133\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −268.340 | −0.0754486 | −0.0377243 | − | 0.999288i | \(-0.512011\pi\) | ||||
−0.0377243 | + | 0.999288i | \(0.512011\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1768.16 | 0.490817 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3482.00 | −0.954346 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5189.77 | −1.40459 | −0.702297 | − | 0.711884i | \(-0.747842\pi\) | ||||
−0.702297 | + | 0.711884i | \(0.747842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6170.94 | −1.64940 | −0.824699 | − | 0.565571i | \(-0.808656\pi\) | ||||
−0.824699 | + | 0.565571i | \(0.808656\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2023.09 | 0.521158 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.79474 | −0.00223833 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1891.91 | −0.475763 | −0.237882 | − | 0.971294i | \(-0.576453\pi\) | ||||
−0.237882 | + | 0.971294i | \(0.576453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9045.01 | −2.24765 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −829.483 | −0.203703 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6539.93 | 1.58735 | 0.793676 | − | 0.608340i | \(-0.208164\pi\) | ||||
0.793676 | + | 0.608340i | \(0.208164\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 549.824 | 0.130396 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5375.90 | 1.26043 | 0.630214 | − | 0.776422i | \(-0.282967\pi\) | ||||
0.630214 | + | 0.776422i | \(0.282967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3858.53 | −0.894443 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3836.22 | −0.879300 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3238.88 | 0.734119 | 0.367060 | − | 0.930197i | \(-0.380364\pi\) | ||||
0.367060 | + | 0.930197i | \(0.380364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1357.46 | −0.304279 | −0.152140 | − | 0.988359i | \(-0.548616\pi\) | ||||
−0.152140 | + | 0.988359i | \(0.548616\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1529.03 | −0.335286 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2561.63 | −0.555645 | −0.277823 | − | 0.960632i | \(-0.589613\pi\) | ||||
−0.277823 | + | 0.960632i | \(0.589613\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2879.32 | −0.617851 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1786.17 | 0.379196 | 0.189598 | − | 0.981862i | \(-0.439282\pi\) | ||||
0.189598 | + | 0.981862i | \(0.439282\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7388.28 | 1.55190 | 0.775950 | − | 0.630794i | \(-0.217271\pi\) | ||||
0.775950 | + | 0.630794i | \(0.217271\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2028.93 | −0.421697 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4419.49 | −0.899550 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 237.179 | 0.0477789 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −492.981 | −0.0982945 | −0.0491472 | − | 0.998792i | \(-0.515650\pi\) | ||||
−0.0491472 | + | 0.998792i | \(0.515650\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3505.48 | −0.691853 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1380.34 | 0.269681 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6587.09 | −1.27405 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4116.31 | 0.780449 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6768.86 | −1.27077 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 988.810 | 0.183825 | 0.0919126 | − | 0.995767i | \(-0.470702\pi\) | ||||
0.0919126 | + | 0.995767i | \(0.470702\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 775.592 | 0.142789 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9596.57 | 1.74975 | 0.874874 | − | 0.484351i | \(-0.160944\pi\) | ||||
0.874874 | + | 0.484351i | \(0.160944\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −965.713 | −0.174394 | −0.0871970 | − | 0.996191i | \(-0.527791\pi\) | ||||
−0.0871970 | + | 0.996191i | \(0.527791\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8985.97 | −1.59212 | −0.796061 | − | 0.605217i | \(-0.793086\pi\) | ||||
−0.796061 | + | 0.605217i | \(0.793086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3123.22 | −0.548171 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3787.10 | 0.658491 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1207.14 | 0.207947 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1113.52 | −0.190053 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −830.499 | −0.140449 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3807.30 | −0.632230 | −0.316115 | − | 0.948721i | \(-0.602379\pi\) | ||||
−0.316115 | + | 0.948721i | \(0.602379\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2835.72 | −0.466656 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5966.21 | 0.973041 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1649.82 | −0.266681 | −0.133340 | − | 0.991070i | \(-0.542570\pi\) | ||||
−0.133340 | + | 0.991070i | \(0.542570\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −158.747 | −0.0254334 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16355.7 | 2.59739 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6606.12 | 1.03090 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5709.99 | 0.883368 | 0.441684 | − | 0.897171i | \(-0.354381\pi\) | ||||
0.441684 | + | 0.897171i | \(0.354381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 447.244 | 0.0685973 | 0.0342986 | − | 0.999412i | \(-0.489080\pi\) | ||||
0.0342986 | + | 0.999412i | \(0.489080\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1005.24 | 0.152865 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10645.7 | 1.60514 | 0.802569 | − | 0.596560i | \(-0.203466\pi\) | ||||
0.802569 | + | 0.596560i | \(0.203466\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13761.0 | −2.05734 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9097.47 | −1.33745 | −0.668727 | − | 0.743508i | \(-0.733161\pi\) | ||||
−0.668727 | + | 0.743508i | \(0.733161\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3906.31 | −0.569516 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3847.85 | −0.556363 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2979.01 | 0.427201 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5287.83 | −0.752104 | −0.376052 | − | 0.926598i | \(-0.622719\pi\) | ||||
−0.376052 | + | 0.926598i | \(0.622719\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1854.29 | 0.261600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5895.01 | 0.818317 | 0.409159 | − | 0.912463i | \(-0.365822\pi\) | ||||
0.409159 | + | 0.912463i | \(0.365822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3550.59 | −0.488938 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2274.51 | −0.310724 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3842.41 | 0.520769 | 0.260384 | − | 0.965505i | \(-0.416151\pi\) | ||||
0.260384 | + | 0.965505i | \(0.416151\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1331.10 | −0.178988 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5013.74 | −0.668903 | −0.334452 | − | 0.942413i | \(-0.608551\pi\) | ||||
−0.334452 | + | 0.942413i | \(0.608551\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3056.95 | 0.401534 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11182.5 | 1.45752 | 0.728758 | − | 0.684771i | \(-0.240098\pi\) | ||||
0.728758 | + | 0.684771i | \(0.240098\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3930.40 | −0.508360 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6460.45 | −0.829228 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14445.9 | −1.84013 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3406.80 | 0.430686 | 0.215343 | − | 0.976539i | \(-0.430913\pi\) | ||||
0.215343 | + | 0.976539i | \(0.430913\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 83.0401 | 0.0103412 | 0.00517061 | − | 0.999987i | \(-0.498354\pi\) | ||||
0.00517061 | + | 0.999987i | \(0.498354\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11911.1 | 1.47230 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1008.14 | −0.123692 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16108.0 | 1.96178 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2456.20 | −0.296947 | −0.148473 | − | 0.988916i | \(-0.547436\pi\) | ||||
−0.148473 | + | 0.988916i | \(0.547436\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −789.323 | −0.0947309 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.4871 | −0.00431586 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3497.30 | 0.410704 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3437.96 | 0.400848 | 0.200424 | − | 0.979709i | \(-0.435768\pi\) | ||||
0.200424 | + | 0.979709i | \(0.435768\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5347.62 | −0.619067 | −0.309533 | − | 0.950889i | \(-0.600173\pi\) | ||||
−0.309533 | + | 0.950889i | \(0.600173\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1278.58 | −0.146966 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −664.419 | −0.0758331 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5710.16 | −0.642632 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 851.643 | 0.0951791 | 0.0475895 | − | 0.998867i | \(-0.484846\pi\) | ||||
0.0475895 | + | 0.998867i | \(0.484846\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3433.42 | 0.381061 | 0.190531 | − | 0.981681i | \(-0.438979\pi\) | ||||
0.190531 | + | 0.981681i | \(0.438979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2281.08 | 0.251424 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9613.84 | −1.05238 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9738.39 | 1.05874 | 0.529371 | − | 0.848390i | \(-0.322428\pi\) | ||||
0.529371 | + | 0.848390i | \(0.322428\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9934.96 | 1.06552 | 0.532759 | − | 0.846267i | \(-0.321155\pi\) | ||||
0.532759 | + | 0.846267i | \(0.321155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15915.5 | −1.69543 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5295.58 | 0.560341 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7557.33 | −0.794327 | −0.397163 | − | 0.917748i | \(-0.630005\pi\) | ||||
−0.397163 | + | 0.917748i | \(0.630005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10533.1 | −1.09974 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8076.94 | −0.837721 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14011.8 | 1.43424 | 0.717118 | − | 0.696951i | \(-0.245461\pi\) | ||||
0.717118 | + | 0.696951i | \(0.245461\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 599.808 | 0.0609949 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1669.61 | 0.168680 | 0.0843399 | − | 0.996437i | \(-0.473122\pi\) | ||||
0.0843399 | + | 0.996437i | \(0.473122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14785.4 | 1.48409 | 0.742046 | − | 0.670349i | \(-0.233856\pi\) | ||||
0.742046 | + | 0.670349i | \(0.233856\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11945.6 | −1.19132 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4603.17 | −0.456122 | −0.228061 | − | 0.973647i | \(-0.573239\pi\) | ||||
−0.228061 | + | 0.973647i | \(0.573239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5824.14 | −0.569772 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17364.7 | −1.68801 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1625.18 | −0.156987 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2790.14 | 0.267824 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3477.35 | −0.331700 | −0.165850 | − | 0.986151i | \(-0.553037\pi\) | ||||
−0.165850 | + | 0.986151i | \(0.553037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11730.8 | 1.11201 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 983.993 | 0.0921254 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4344.17 | 0.404216 | 0.202108 | − | 0.979363i | \(-0.435221\pi\) | ||||
0.202108 | + | 0.979363i | \(0.435221\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6308.51 | −0.583396 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4982.89 | 0.457993 | 0.228997 | − | 0.973427i | \(-0.426456\pi\) | ||||
0.228997 | + | 0.973427i | \(0.426456\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1357.16 | −0.123982 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5726.66 | 0.519988 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15326.2 | 1.37494 | 0.687468 | − | 0.726215i | \(-0.258722\pi\) | ||||
0.687468 | + | 0.726215i | \(0.258722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7032.65 | −0.627137 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1516.04 | 0.134387 | 0.0671936 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671936 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17077.5 | 1.50483 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2432.53 | 0.213082 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2653.64 | −0.231081 | −0.115541 | − | 0.993303i | \(-0.536860\pi\) | ||||
−0.115541 | + | 0.993303i | \(0.536860\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1467.14 | 0.126269 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3217.73 | 0.275321 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7262.82 | 0.617830 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10411.9 | 0.880604 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13132.1 | 1.10428 | 0.552139 | − | 0.833752i | \(-0.313812\pi\) | ||||
0.552139 | + | 0.833752i | \(0.313812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3086.34 | 0.258042 | 0.129021 | − | 0.991642i | \(-0.458816\pi\) | ||||
0.129021 | + | 0.991642i | \(0.458816\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7107.16 | 0.587462 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19135.3 | 1.57272 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2534.85 | 0.207162 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7670.80 | −0.623376 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15711.7 | 1.26968 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2867.31 | 0.230416 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 926.095 | 0.0735969 | 0.0367985 | − | 0.999323i | \(-0.488284\pi\) | ||||
0.0367985 | + | 0.999323i | \(0.488284\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12660.8 | 1.00060 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3445.52 | −0.270807 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 592.871 | 0.0463425 | 0.0231712 | − | 0.999732i | \(-0.492624\pi\) | ||||
0.0231712 | + | 0.999732i | \(0.492624\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4894.64 | 0.380507 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3319.63 | −0.256663 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11764.7 | −0.899788 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12245.3 | −0.931512 | −0.465756 | − | 0.884913i | \(-0.654217\pi\) | ||||
−0.465756 | + | 0.884913i | \(0.654217\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12646.0 | −0.956829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3407.15 | −0.256417 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14594.6 | −1.09252 | −0.546261 | − | 0.837615i | \(-0.683949\pi\) | ||||
−0.546261 | + | 0.837615i | \(0.683949\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −658.599 | −0.0490398 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22911.2 | 1.68803 | 0.844015 | − | 0.536320i | \(-0.180186\pi\) | ||||
0.844015 | + | 0.536320i | \(0.180186\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5904.64 | 0.432752 | 0.216376 | − | 0.976310i | \(-0.430576\pi\) | ||||
0.216376 | + | 0.976310i | \(0.430576\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10554.1 | 0.769465 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5291.53 | 0.383778 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9513.21 | −0.686378 | −0.343189 | − | 0.939266i | \(-0.611507\pi\) | ||||
−0.343189 | + | 0.939266i | \(0.611507\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15053.0 | 1.08045 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15849.1 | −1.12591 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4170.48 | 0.294749 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22790.6 | 1.60250 | 0.801252 | − | 0.598327i | \(-0.204167\pi\) | ||||
0.801252 | + | 0.598327i | \(0.204167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17384.3 | 1.21614 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8514.41 | 0.592616 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18262.8 | 1.26469 | 0.632346 | − | 0.774686i | \(-0.282092\pi\) | ||||
0.632346 | + | 0.774686i | \(0.282092\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1064.70 | 0.0729907 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6958.09 | 0.474624 | 0.237312 | − | 0.971433i | \(-0.423734\pi\) | ||||
0.237312 | + | 0.971433i | \(0.423734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2305.39 | −0.156471 | −0.0782353 | − | 0.996935i | \(-0.524929\pi\) | ||||
−0.0782353 | + | 0.996935i | \(0.524929\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4314.23 | −0.291358 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15963.7 | −1.07276 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16179.2 | 1.08187 | 0.540935 | − | 0.841064i | \(-0.318071\pi\) | ||||
0.540935 | + | 0.841064i | \(0.318071\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5289.20 | 0.350210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20540.7 | 1.35340 | 0.676699 | − | 0.736260i | \(-0.263410\pi\) | ||||
0.676699 | + | 0.736260i | \(0.263410\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7692.96 | 0.504407 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6918.19 | 0.451403 | 0.225702 | − | 0.974196i | \(-0.427533\pi\) | ||||
0.225702 | + | 0.974196i | \(0.427533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8081.62 | 0.524762 | 0.262381 | − | 0.964964i | \(-0.415492\pi\) | ||||
0.262381 | + | 0.964964i | \(0.415492\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4776.96 | −0.308684 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18469.0 | −1.18202 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8333.96 | −0.530823 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6999.54 | 0.443704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27293.3 | −1.72191 | −0.860957 | − | 0.508677i | \(-0.830135\pi\) | ||||
−0.860957 | + | 0.508677i | \(0.830135\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2258.02 | −0.141782 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5522.39 | −0.345117 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9950.70 | 0.616031 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19255.6 | 1.18651 | 0.593254 | − | 0.805015i | \(-0.297843\pi\) | ||||
0.593254 | + | 0.805015i | \(0.297843\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19996.4 | 1.22641 | 0.613204 | − | 0.789925i | \(-0.289880\pi\) | ||||
0.613204 | + | 0.789925i | \(0.289880\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12682.5 | 0.774222 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7064.20 | −0.429246 | −0.214623 | − | 0.976697i | \(-0.568852\pi\) | ||||
−0.214623 | + | 0.976697i | \(0.568852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14398.9 | −0.870890 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13821.1 | −0.828269 | −0.414134 | − | 0.910216i | \(-0.635916\pi\) | ||||
−0.414134 | + | 0.910216i | \(0.635916\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26802.7 | −1.59889 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2154.15 | −0.127917 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7802.80 | −0.461235 | −0.230617 | − | 0.973044i | \(-0.574075\pi\) | ||||
−0.230617 | + | 0.973044i | \(0.574075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15817.3 | −0.930744 | −0.465372 | − | 0.885115i | \(-0.654079\pi\) | ||||
−0.465372 | + | 0.885115i | \(0.654079\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2481.28 | −0.145347 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10808.6 | 0.627452 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9233.25 | −0.533599 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27803.5 | −1.59962 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2943.30 | 0.168582 | 0.0842911 | − | 0.996441i | \(-0.473137\pi\) | ||||
0.0842911 | + | 0.996441i | \(0.473137\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −807.528 | −0.0460471 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3171.48 | 0.180044 | 0.0900220 | − | 0.995940i | \(-0.471306\pi\) | ||||
0.0900220 | + | 0.995940i | \(0.471306\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18652.3 | −1.04957 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24453.2 | −1.36995 | −0.684975 | − | 0.728567i | \(-0.740187\pi\) | ||||
−0.684975 | + | 0.728567i | \(0.740187\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3274.70 | −0.182656 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1509.76 | 0.0838443 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11542.2 | −0.638207 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8595.89 | −0.473232 | −0.236616 | − | 0.971603i | \(-0.576038\pi\) | ||||
−0.236616 | + | 0.971603i | \(0.576038\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14509.4 | 0.791903 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4577.02 | −0.248733 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 805.019 | 0.0435602 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21476.1 | −1.15712 | −0.578561 | − | 0.815639i | \(-0.696385\pi\) | ||||
−0.578561 | + | 0.815639i | \(0.696385\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17121.0 | 0.918537 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5304.48 | −0.283373 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13538.9 | −0.717158 | −0.358579 | − | 0.933499i | \(-0.616739\pi\) | ||||
−0.358579 | + | 0.933499i | \(0.616739\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10446.0 | 0.550992 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −56602.5 | −2.97304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23690.0 | −1.23910 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15569.3 | 0.810943 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13883.7 | −0.720131 | −0.360065 | − | 0.932927i | \(-0.617246\pi\) | ||||
−0.360065 | + | 0.932927i | \(0.617246\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18512.8 | 0.952281 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1827.15 | 0.0935983 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18292.9 | 0.933215 | 0.466607 | − | 0.884465i | \(-0.345476\pi\) | ||||
0.466607 | + | 0.884465i | \(0.345476\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7545.61 | −0.381785 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14245.8 | −0.717848 | −0.358924 | − | 0.933367i | \(-0.616856\pi\) | ||||
−0.358924 | + | 0.933367i | \(0.616856\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24506.5 | 1.22484 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1363.89 | −0.0678913 | −0.0339456 | − | 0.999424i | \(-0.510807\pi\) | ||||
−0.0339456 | + | 0.999424i | \(0.510807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6069.27 | −0.300891 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21789.4 | 1.07588 | 0.537938 | − | 0.842984i | \(-0.319203\pi\) | ||||
0.537938 | + | 0.842984i | \(0.319203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21970.0 | 1.08043 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.3842 | 0.00129230 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2119.55 | −0.102987 | −0.0514937 | − | 0.998673i | \(-0.516398\pi\) | ||||
−0.0514937 | + | 0.998673i | \(0.516398\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5675.74 | 0.274682 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33509.1 | −1.61526 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28202.4 | 1.35408 | 0.677038 | − | 0.735948i | \(-0.263263\pi\) | ||||
0.677038 | + | 0.735948i | \(0.263263\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27135.0 | 1.29768 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11147.0 | −0.530985 | −0.265493 | − | 0.964113i | \(-0.585535\pi\) | ||||
−0.265493 | + | 0.964113i | \(0.585535\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2488.45 | 0.117608 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10486.1 | −0.493654 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4109.29 | 0.192698 | 0.0963491 | − | 0.995348i | \(-0.469283\pi\) | ||||
0.0963491 | + | 0.995348i | \(0.469283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19619.8 | −0.916459 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13891.4 | −0.646362 | −0.323181 | − | 0.946337i | \(-0.604752\pi\) | ||||
−0.323181 | + | 0.946337i | \(0.604752\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9568.44 | −0.443495 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11195.5 | −0.514917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −56523.9 | −2.58974 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1649.47 | −0.0752839 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24162.9 | −1.09861 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9342.35 | 0.423150 | 0.211575 | − | 0.977362i | \(-0.432141\pi\) | ||||
0.211575 | + | 0.977362i | \(0.432141\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16127.7 | −0.727708 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20248.1 | −0.906723 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11575.6 | 0.516407 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24324.3 | 1.08107 | 0.540534 | − | 0.841322i | \(-0.318222\pi\) | ||||
0.540534 | + | 0.841322i | \(0.318222\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3155.97 | 0.139737 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11508.7 | 0.507664 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12236.4 | 0.537751 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9716.65 | −0.423844 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34454.9 | 1.49737 | 0.748684 | − | 0.662927i | \(-0.230686\pi\) | ||||
0.748684 | + | 0.662927i | \(0.230686\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8350.13 | 0.361545 | 0.180772 | − | 0.983525i | \(-0.442140\pi\) | ||||
0.180772 | + | 0.983525i | \(0.442140\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4072.37 | 0.175676 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26172.4 | −1.12488 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18456.7 | −0.790355 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18834.8 | −0.800655 | −0.400327 | − | 0.916372i | \(-0.631104\pi\) | ||||
−0.400327 | + | 0.916372i | \(0.631104\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9656.76 | 0.409008 | 0.204504 | − | 0.978866i | \(-0.434442\pi\) | ||||
0.204504 | + | 0.978866i | \(0.434442\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4587.08 | 0.193578 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20759.6 | −0.872892 | −0.436446 | − | 0.899731i | \(-0.643763\pi\) | ||||
−0.436446 | + | 0.899731i | \(0.643763\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15616.1 | 0.654245 | 0.327123 | − | 0.944982i | \(-0.393921\pi\) | ||||
0.327123 | + | 0.944982i | \(0.393921\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7684.90 | 0.320802 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29176.6 | −1.20922 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8637.96 | 0.356716 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 417.027 | 0.0171601 | 0.00858007 | − | 0.999963i | \(-0.497269\pi\) | ||||
0.00858007 | + | 0.999963i | \(0.497269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20656.8 | −0.846973 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5358.52 | −0.218929 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10092.0 | 0.410856 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22164.8 | −0.895990 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55745.4 | −2.24551 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24917.4 | 1.00018 | 0.500092 | − | 0.865972i | \(-0.333300\pi\) | ||||
0.500092 | + | 0.865972i | \(0.333300\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6086.80 | 0.243467 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44523.8 | 1.77468 | 0.887342 | − | 0.461112i | \(-0.152549\pi\) | ||||
0.887342 | + | 0.461112i | \(0.152549\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24146.4 | 0.959097 | 0.479548 | − | 0.877515i | \(-0.340800\pi\) | ||||
0.479548 | + | 0.877515i | \(0.340800\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26442.6 | −1.04301 | −0.521505 | − | 0.853248i | \(-0.674629\pi\) | ||||
−0.521505 | + | 0.853248i | \(0.674629\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43196.5 | 1.69795 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13258.5 | 0.519355 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −59337.4 | −2.31632 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17847.1 | 0.694288 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −711.536 | −0.0275852 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22516.1 | −0.866950 | −0.433475 | − | 0.901166i | \(-0.642713\pi\) | ||||
−0.433475 | + | 0.901166i | \(0.642713\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1478.94 | 0.0567503 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10120.6 | −0.387027 | −0.193514 | − | 0.981098i | \(-0.561988\pi\) | ||||
−0.193514 | + | 0.981098i | \(0.561988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20748.5 | −0.790761 | −0.395380 | − | 0.918517i | \(-0.629387\pi\) | ||||
−0.395380 | + | 0.918517i | \(0.629387\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10516.4 | 0.399442 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25499.4 | −0.965259 | −0.482630 | − | 0.875825i | \(-0.660318\pi\) | ||||
−0.482630 | + | 0.875825i | \(0.660318\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4141.01 | −0.155700 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7719.57 | 0.289278 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11895.7 | 0.444280 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19761.3 | 0.735574 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19544.7 | −0.725085 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6887.04 | −0.254651 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 52526.3 | 1.92932 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37807.0 | 1.38408 | 0.692040 | − | 0.721859i | \(-0.256712\pi\) | ||||
0.692040 | + | 0.721859i | \(0.256712\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12348.9 | −0.450593 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3230.08 | −0.117472 | −0.0587362 | − | 0.998274i | \(-0.518707\pi\) | ||||
−0.0587362 | + | 0.998274i | \(0.518707\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −149.873 | −0.00543271 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20306.6 | 0.733678 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35343.1 | −1.26862 | −0.634310 | − | 0.773079i | \(-0.718716\pi\) | ||||
−0.634310 | + | 0.773079i | \(0.718716\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2966.43 | −0.106132 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41164.0 | −1.46796 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9423.55 | −0.334967 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2326.78 | −0.0824394 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33030.2 | −1.16651 | −0.583254 | − | 0.812289i | \(-0.698221\pi\) | ||||
−0.583254 | + | 0.812289i | \(0.698221\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28789.7 | −1.01022 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14135.4 | −0.494413 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54695.9 | −1.90698 | −0.953488 | − | 0.301430i | \(-0.902536\pi\) | ||||
−0.953488 | + | 0.301430i | \(0.902536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2897.14 | 0.100686 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18255.3 | 0.632418 | 0.316209 | − | 0.948690i | \(-0.397590\pi\) | ||||
0.316209 | + | 0.948690i | \(0.397590\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36452.1 | 1.25879 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6215.75 | 0.213289 | 0.106645 | − | 0.994297i | \(-0.465989\pi\) | ||||
0.106645 | + | 0.994297i | \(0.465989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8911.27 | 0.304818 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26957.9 | 0.919212 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8594.53 | 0.292135 | 0.146067 | − | 0.989275i | \(-0.453338\pi\) | ||||
0.146067 | + | 0.989275i | \(0.453338\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43786.2 | 1.48365 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9369.65 | 0.316487 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 72560.6 | 2.43566 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11361.3 | −0.380180 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 62451.1 | 2.08329 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17168.1 | −0.570929 | −0.285464 | − | 0.958389i | \(-0.592148\pi\) | ||||
−0.285464 | + | 0.958389i | \(0.592148\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3621.42 | −0.120059 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11926.2 | −0.394162 | −0.197081 | − | 0.980387i | \(-0.563146\pi\) | ||||
−0.197081 | + | 0.980387i | \(0.563146\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3340.57 | 0.109727 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14038.2 | 0.459696 | 0.229848 | − | 0.973227i | \(-0.426177\pi\) | ||||
0.229848 | + | 0.973227i | \(0.426177\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −65373.8 | −2.13417 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2491.50 | 0.0810880 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20351.4 | −0.660334 | −0.330167 | − | 0.943923i | \(-0.607105\pi\) | ||||
−0.330167 | + | 0.943923i | \(0.607105\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35324.1 | 1.14266 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60094.4 | 1.93214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32505.7 | −1.04196 | −0.520978 | − | 0.853570i | \(-0.674433\pi\) | ||||
−0.520978 | + | 0.853570i | \(0.674433\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11421.9 | 0.365018 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4417.18 | 0.140738 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24847.1 | 0.789282 | 0.394641 | − | 0.918835i | \(-0.370869\pi\) | ||||
0.394641 | + | 0.918835i | \(0.370869\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8507.16 | 0.269424 |
(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 | 588.4.a.f.1.1 | 2 | ||
3.2 | odd | 2 | 1764.4.a.y.1.2 | 2 | |||
4.3 | odd | 2 | 2352.4.a.bx.1.1 | 2 | |||
7.2 | even | 3 | 588.4.i.j.361.2 | 4 | |||
7.3 | odd | 6 | 84.4.i.a.37.1 | yes | 4 | ||
7.4 | even | 3 | 588.4.i.j.373.2 | 4 | |||
7.5 | odd | 6 | 84.4.i.a.25.1 | ✓ | 4 | ||
7.6 | odd | 2 | 588.4.a.i.1.2 | 2 | |||
21.2 | odd | 6 | 1764.4.k.q.361.1 | 4 | |||
21.5 | even | 6 | 252.4.k.f.109.2 | 4 | |||
21.11 | odd | 6 | 1764.4.k.q.1549.1 | 4 | |||
21.17 | even | 6 | 252.4.k.f.37.2 | 4 | |||
21.20 | even | 2 | 1764.4.a.o.1.1 | 2 | |||
28.3 | even | 6 | 336.4.q.i.289.1 | 4 | |||
28.19 | even | 6 | 336.4.q.i.193.1 | 4 | |||
28.27 | even | 2 | 2352.4.a.bt.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.a.25.1 | ✓ | 4 | 7.5 | odd | 6 | ||
84.4.i.a.37.1 | yes | 4 | 7.3 | odd | 6 | ||
252.4.k.f.37.2 | 4 | 21.17 | even | 6 | |||
252.4.k.f.109.2 | 4 | 21.5 | even | 6 | |||
336.4.q.i.193.1 | 4 | 28.19 | even | 6 | |||
336.4.q.i.289.1 | 4 | 28.3 | even | 6 | |||
588.4.a.f.1.1 | 2 | 1.1 | even | 1 | trivial | ||
588.4.a.i.1.2 | 2 | 7.6 | odd | 2 | |||
588.4.i.j.361.2 | 4 | 7.2 | even | 3 | |||
588.4.i.j.373.2 | 4 | 7.4 | even | 3 | |||
1764.4.a.o.1.1 | 2 | 21.20 | even | 2 | |||
1764.4.a.y.1.2 | 2 | 3.2 | odd | 2 | |||
1764.4.k.q.361.1 | 4 | 21.2 | odd | 6 | |||
1764.4.k.q.1549.1 | 4 | 21.11 | odd | 6 | |||
2352.4.a.bt.1.2 | 2 | 28.27 | even | 2 | |||
2352.4.a.bx.1.1 | 2 | 4.3 | odd | 2 |