Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,4,Mod(1,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, 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("1600.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.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: | \(94.4030560092\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.5685.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 11x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 800) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.12873\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1 |
$q$-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 | ||||||||
\(3\) | −5.25747 | −1.01180 | −0.505900 | − | 0.862592i | \(-0.668840\pi\) | ||||
−0.505900 | + | 0.862592i | \(0.668840\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.15590 | 0.494372 | 0.247186 | − | 0.968968i | \(-0.420494\pi\) | ||||
0.247186 | + | 0.968968i | \(0.420494\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.640965 | 0.0237394 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.8984 | 0.326137 | 0.163069 | − | 0.986615i | \(-0.447861\pi\) | ||||
0.163069 | + | 0.986615i | \(0.447861\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 41.9826 | 0.895684 | 0.447842 | − | 0.894113i | \(-0.352193\pi\) | ||||
0.447842 | + | 0.894113i | \(0.352193\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −75.7604 | −1.08086 | −0.540430 | − | 0.841389i | \(-0.681738\pi\) | ||||
−0.540430 | + | 0.841389i | \(0.681738\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.49047 | −0.0300712 | −0.0150356 | − | 0.999887i | \(-0.504786\pi\) | ||||
−0.0150356 | + | 0.999887i | \(0.504786\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −48.1368 | −0.500206 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −17.8566 | −0.161885 | −0.0809426 | − | 0.996719i | \(-0.525793\pi\) | ||||
−0.0809426 | + | 0.996719i | \(0.525793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 138.582 | 0.987781 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 143.538 | 0.919117 | 0.459558 | − | 0.888148i | \(-0.348008\pi\) | ||||
0.459558 | + | 0.888148i | \(0.348008\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −88.6094 | −0.513378 | −0.256689 | − | 0.966494i | \(-0.582632\pi\) | ||||
−0.256689 | + | 0.966494i | \(0.582632\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −62.5556 | −0.329986 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 351.059 | 1.55983 | 0.779916 | − | 0.625884i | \(-0.215262\pi\) | ||||
0.779916 | + | 0.625884i | \(0.215262\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −220.722 | −0.906253 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 195.922 | 0.746291 | 0.373145 | − | 0.927773i | \(-0.378279\pi\) | ||||
0.373145 | + | 0.927773i | \(0.378279\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −366.067 | −1.29825 | −0.649125 | − | 0.760682i | \(-0.724865\pi\) | ||||
−0.649125 | + | 0.760682i | \(0.724865\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 58.5931 | 0.181844 | 0.0909222 | − | 0.995858i | \(-0.471019\pi\) | ||||
0.0909222 | + | 0.995858i | \(0.471019\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −259.169 | −0.755596 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 398.308 | 1.09361 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.374917 | −0.000971675 0 | −0.000485837 | − | 1.00000i | \(-0.500155\pi\) | ||||
−0.000485837 | 1.00000i | \(0.500155\pi\) | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.0936 | 0.0304261 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −318.952 | −0.703796 | −0.351898 | − | 0.936038i | \(-0.614464\pi\) | ||||
−0.351898 | + | 0.936038i | \(0.614464\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −446.597 | −0.937391 | −0.468695 | − | 0.883360i | \(-0.655276\pi\) | ||||
−0.468695 | + | 0.883360i | \(0.655276\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.86861 | 0.0117361 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 709.343 | 1.29343 | 0.646717 | − | 0.762730i | \(-0.276142\pi\) | ||||
0.646717 | + | 0.762730i | \(0.276142\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 93.8805 | 0.163795 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1137.43 | −1.90124 | −0.950621 | − | 0.310354i | \(-0.899552\pi\) | ||||
−0.950621 | + | 0.310354i | \(0.899552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 85.3855 | 0.136899 | 0.0684495 | − | 0.997655i | \(-0.478195\pi\) | ||||
0.0684495 | + | 0.997655i | \(0.478195\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 108.941 | 0.161233 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1249.83 | −1.77996 | −0.889981 | − | 0.455997i | \(-0.849283\pi\) | ||||
−0.889981 | + | 0.455997i | \(0.849283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −745.895 | −1.02318 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −926.261 | −1.22494 | −0.612472 | − | 0.790492i | \(-0.709825\pi\) | ||||
−0.612472 | + | 0.790492i | \(0.709825\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −754.648 | −0.929962 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 973.552 | 1.15951 | 0.579755 | − | 0.814791i | \(-0.303148\pi\) | ||||
0.579755 | + | 0.814791i | \(0.303148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 384.389 | 0.442801 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 465.861 | 0.519436 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1158.55 | 1.21271 | 0.606355 | − | 0.795194i | \(-0.292631\pi\) | ||||
0.606355 | + | 0.795194i | \(0.292631\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.62648 | 0.00774232 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 466.816 | 0.459900 | 0.229950 | − | 0.973202i | \(-0.426144\pi\) | ||||
0.229950 | + | 0.973202i | \(0.426144\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 963.139 | 0.921368 | 0.460684 | − | 0.887564i | \(-0.347604\pi\) | ||||
0.460684 | + | 0.887564i | \(0.347604\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1066.94 | 0.963971 | 0.481986 | − | 0.876179i | \(-0.339916\pi\) | ||||
0.481986 | + | 0.876179i | \(0.339916\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 217.521 | 0.191145 | 0.0955723 | − | 0.995422i | \(-0.469532\pi\) | ||||
0.0955723 | + | 0.995422i | \(0.469532\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1845.68 | −1.57824 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1160.71 | 0.966286 | 0.483143 | − | 0.875542i | \(-0.339495\pi\) | ||||
0.483143 | + | 0.875542i | \(0.339495\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 26.9094 | 0.0212630 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −693.655 | −0.534347 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1189.43 | −0.893634 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1030.06 | −0.755097 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 34.2804 | 0.0239519 | 0.0119759 | − | 0.999928i | \(-0.496188\pi\) | ||||
0.0119759 | + | 0.999928i | \(0.496188\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1924.59 | 1.31357 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2364.02 | 1.57669 | 0.788343 | − | 0.615236i | \(-0.210939\pi\) | ||||
0.788343 | + | 0.615236i | \(0.210939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.8025 | −0.0148664 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2991.88 | 1.86579 | 0.932897 | − | 0.360144i | \(-0.117272\pi\) | ||||
0.932897 | + | 0.360144i | \(0.117272\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 132.246 | 0.0806974 | 0.0403487 | − | 0.999186i | \(-0.487153\pi\) | ||||
0.0403487 | + | 0.999186i | \(0.487153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −308.052 | −0.183990 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 499.528 | 0.292116 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1362.58 | 0.764512 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 788.190 | 0.433363 | 0.216681 | − | 0.976242i | \(-0.430477\pi\) | ||||
0.216681 | + | 0.976242i | \(0.430477\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2200.74 | −1.18605 | −0.593025 | − | 0.805184i | \(-0.702066\pi\) | ||||
−0.593025 | + | 0.805184i | \(0.702066\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −48.5598 | −0.0256590 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1702.05 | 0.865212 | 0.432606 | − | 0.901583i | \(-0.357594\pi\) | ||||
0.432606 | + | 0.901583i | \(0.357594\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.97111 | 0.000983140 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −163.493 | −0.0800315 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −822.009 | −0.394998 | −0.197499 | − | 0.980303i | \(-0.563282\pi\) | ||||
−0.197499 | + | 0.980303i | \(0.563282\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2545.32 | −1.17942 | −0.589710 | − | 0.807615i | \(-0.700758\pi\) | ||||
−0.589710 | + | 0.807615i | \(0.700758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −434.458 | −0.197751 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.59631 | −0.000713874 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −868.181 | −0.381541 | −0.190770 | − | 0.981635i | \(-0.561099\pi\) | ||||
−0.190770 | + | 0.981635i | \(0.561099\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1676.88 | 0.712101 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3255.65 | 1.35944 | 0.679718 | − | 0.733474i | \(-0.262102\pi\) | ||||
0.679718 | + | 0.733474i | \(0.262102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3482.49 | −1.43012 | −0.715059 | − | 0.699065i | \(-0.753600\pi\) | ||||
−0.715059 | + | 0.699065i | \(0.753600\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2347.97 | 0.948452 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −901.431 | −0.352509 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1268.84 | 0.488331 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2981.37 | 1.12945 | 0.564724 | − | 0.825280i | \(-0.308983\pi\) | ||||
0.564724 | + | 0.825280i | \(0.308983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1666.53 | 0.621552 | 0.310776 | − | 0.950483i | \(-0.399411\pi\) | ||||
0.310776 | + | 0.950483i | \(0.399411\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4355.01 | 1.57503 | 0.787516 | − | 0.616294i | \(-0.211367\pi\) | ||||
0.787516 | + | 0.616294i | \(0.211367\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 820.282 | 0.292202 | 0.146101 | − | 0.989270i | \(-0.453328\pi\) | ||||
0.146101 | + | 0.989270i | \(0.453328\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3729.35 | −1.30870 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1314.22 | 0.454386 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.4455 | −0.00384306 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.6327 | −0.00980736 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4678.00 | 1.52629 | 0.763144 | − | 0.646229i | \(-0.223655\pi\) | ||||
0.763144 | + | 0.646229i | \(0.223655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5980.00 | 1.92368 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −811.299 | −0.253800 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −448.912 | −0.138514 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3180.62 | −0.968108 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2238.14 | −0.672094 | −0.336047 | − | 0.941845i | \(-0.609090\pi\) | ||||
−0.336047 | + | 0.941845i | \(0.609090\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1036.89 | −0.303175 | −0.151588 | − | 0.988444i | \(-0.548439\pi\) | ||||
−0.151588 | + | 0.988444i | \(0.548439\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3888.44 | 1.12208 | 0.561038 | − | 0.827790i | \(-0.310402\pi\) | ||||
0.561038 | + | 0.827790i | \(0.310402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −572.753 | −0.163136 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 130.042 | 0.0365638 | 0.0182819 | − | 0.999833i | \(-0.494180\pi\) | ||||
0.0182819 | + | 0.999833i | \(0.494180\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6570.95 | 1.80097 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5724.03 | 1.54919 | 0.774595 | − | 0.632458i | \(-0.217954\pi\) | ||||
0.774595 | + | 0.632458i | \(0.217954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1818.75 | 0.486123 | 0.243062 | − | 0.970011i | \(-0.421848\pi\) | ||||
0.243062 | + | 0.970011i | \(0.421848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 179.812 | 0.0474689 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −104.557 | −0.0269343 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4869.79 | 1.23940 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3637.78 | −0.914800 | −0.457400 | − | 0.889261i | \(-0.651219\pi\) | ||||
−0.457400 | + | 0.889261i | \(0.651219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −212.466 | −0.0527968 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2969.73 | 0.720804 | 0.360402 | − | 0.932797i | \(-0.382640\pi\) | ||||
0.360402 | + | 0.932797i | \(0.382640\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3214.26 | 0.771137 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 92.0030 | 0.0218193 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3035.72 | 0.711752 | 0.355876 | − | 0.934533i | \(-0.384183\pi\) | ||||
0.355876 | + | 0.934533i | \(0.384183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5118.42 | −1.17319 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6888.55 | 1.56135 | 0.780673 | − | 0.624939i | \(-0.214876\pi\) | ||||
0.780673 | + | 0.624939i | \(0.214876\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6173.52 | 1.38382 | 0.691909 | − | 0.721985i | \(-0.256770\pi\) | ||||
0.691909 | + | 0.721985i | \(0.256770\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2020.91 | −0.448026 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3273.30 | 0.710013 | 0.355007 | − | 0.934864i | \(-0.384479\pi\) | ||||
0.355007 | + | 0.934864i | \(0.384479\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −56.7955 | −0.0121873 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 458.400 | 0.0973161 | 0.0486581 | − | 0.998815i | \(-0.484506\pi\) | ||||
0.0486581 | + | 0.998815i | \(0.484506\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8064.66 | 1.69397 | 0.846987 | − | 0.531614i | \(-0.178414\pi\) | ||||
0.846987 | + | 0.531614i | \(0.178414\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1793.84 | 0.368945 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 826.645 | 0.168257 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6091.03 | −1.22702 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 812.863 | 0.162075 | 0.0810375 | − | 0.996711i | \(-0.474177\pi\) | ||||
0.0810375 | + | 0.996711i | \(0.474177\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1648.91 | 0.322152 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −749.667 | −0.144998 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3351.68 | −0.641819 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2454.27 | −0.465327 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −383.469 | −0.0712891 | −0.0356445 | − | 0.999365i | \(-0.511348\pi\) | ||||
−0.0356445 | + | 0.999365i | \(0.511348\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5063.67 | −0.932240 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1665.18 | 0.303613 | 0.151807 | − | 0.988410i | \(-0.451491\pi\) | ||||
0.151807 | + | 0.988410i | \(0.451491\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3769.02 | 0.680632 | 0.340316 | − | 0.940311i | \(-0.389466\pi\) | ||||
0.340316 | + | 0.940311i | \(0.389466\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1859.70 | −0.329498 | −0.164749 | − | 0.986336i | \(-0.552681\pi\) | ||||
−0.164749 | + | 0.986336i | \(0.552681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1707.88 | 0.299758 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5609.40 | −0.975346 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 188.679 | 0.0325028 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1143.61 | −0.193400 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 536.473 | 0.0898988 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7235.06 | −1.20144 | −0.600718 | − | 0.799461i | \(-0.705118\pi\) | ||||
−0.600718 | + | 0.799461i | \(0.705118\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 225.017 | 0.0370295 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9890.08 | 1.59866 | 0.799328 | − | 0.600895i | \(-0.205189\pi\) | ||||
0.799328 | + | 0.600895i | \(0.205189\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6102.39 | −0.977688 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1054.31 | −0.167432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5513.40 | −0.867918 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6269.88 | −0.969984 | −0.484992 | − | 0.874519i | \(-0.661178\pi\) | ||||
−0.484992 | + | 0.874519i | \(0.661178\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2436.94 | 0.373772 | 0.186886 | − | 0.982382i | \(-0.440160\pi\) | ||||
0.186886 | + | 0.982382i | \(0.440160\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5818.03 | 0.884739 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10712.4 | 1.61519 | 0.807595 | − | 0.589738i | \(-0.200769\pi\) | ||||
0.807595 | + | 0.589738i | \(0.200769\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3646.87 | 0.540652 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3540.39 | 0.520487 | 0.260243 | − | 0.965543i | \(-0.416197\pi\) | ||||
0.260243 | + | 0.965543i | \(0.416197\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6852.80 | −0.999096 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6253.38 | 0.904179 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12208.3 | 1.73642 | 0.868212 | − | 0.496193i | \(-0.165269\pi\) | ||||
0.868212 | + | 0.496193i | \(0.165269\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 125.579 | 0.0177165 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.43270 | −0.000480369 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3056.65 | −0.424309 | −0.212154 | − | 0.977236i | \(-0.568048\pi\) | ||||
−0.212154 | + | 0.977236i | \(0.568048\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6026.11 | 0.823238 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1476.91 | −0.200168 | −0.100084 | − | 0.994979i | \(-0.531911\pi\) | ||||
−0.100084 | + | 0.994979i | \(0.531911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −180.228 | −0.0242345 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5567.95 | −0.742843 | −0.371422 | − | 0.928464i | \(-0.621130\pi\) | ||||
−0.371422 | + | 0.928464i | \(0.621130\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −234.636 | −0.0308197 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5401.03 | −0.703966 | −0.351983 | − | 0.936006i | \(-0.614493\pi\) | ||||
−0.351983 | + | 0.936006i | \(0.614493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1352.82 | 0.174975 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12428.8 | −1.59529 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8592.52 | −1.08626 | −0.543131 | − | 0.839648i | \(-0.682761\pi\) | ||||
−0.543131 | + | 0.839648i | \(0.682761\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 119.884 | 0.0150418 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1794.62 | −0.223489 | −0.111745 | − | 0.993737i | \(-0.535644\pi\) | ||||
−0.111745 | + | 0.993737i | \(0.535644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3720.06 | −0.459824 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4177.05 | 0.508720 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11342.3 | 1.37125 | 0.685623 | − | 0.727957i | \(-0.259530\pi\) | ||||
0.685623 | + | 0.727957i | \(0.259530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15729.7 | −1.88781 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2920.29 | −0.347937 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −695.278 | −0.0816496 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8568.54 | −0.999047 | −0.499524 | − | 0.866300i | \(-0.666492\pi\) | ||||
−0.499524 | + | 0.866300i | \(0.666492\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7705.53 | 0.892030 | 0.446015 | − | 0.895026i | \(-0.352843\pi\) | ||||
0.446015 | + | 0.895026i | \(0.352843\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 37.5561 | 0.00431688 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4088.99 | −0.463420 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2626.25 | −0.295563 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12316.2 | 1.37645 | 0.688226 | − | 0.725496i | \(-0.258390\pi\) | ||||
0.688226 | + | 0.725496i | \(0.258390\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7105.69 | 0.788632 | 0.394316 | − | 0.918975i | \(-0.370981\pi\) | ||||
0.394316 | + | 0.918975i | \(0.370981\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 44.4714 | 0.00486809 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17585.8 | −1.91190 | −0.955951 | − | 0.293527i | \(-0.905171\pi\) | ||||
−0.955951 | + | 0.293527i | \(0.905171\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −166.119 | −0.0179374 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2154.24 | −0.231041 | −0.115520 | − | 0.993305i | \(-0.536854\pi\) | ||||
−0.115520 | + | 0.993305i | \(0.536854\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4143.88 | −0.438476 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6853.94 | −0.720395 | −0.360197 | − | 0.932876i | \(-0.617291\pi\) | ||||
−0.360197 | + | 0.932876i | \(0.617291\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2331.17 | 0.243393 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11570.3 | 1.20005 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1822.27 | −0.186526 | −0.0932629 | − | 0.995642i | \(-0.529730\pi\) | ||||
−0.0932629 | + | 0.995642i | \(0.529730\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10499.0 | −1.06765 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3510.72 | −0.354687 | −0.177343 | − | 0.984149i | \(-0.556750\pi\) | ||||
−0.177343 | + | 0.984149i | \(0.556750\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13454.1 | −1.35047 | −0.675235 | − | 0.737603i | \(-0.735958\pi\) | ||||
−0.675235 | + | 0.737603i | \(0.735958\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12549.1 | 1.24347 | 0.621736 | − | 0.783227i | \(-0.286428\pi\) | ||||
0.621736 | + | 0.783227i | \(0.286428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6494.67 | 0.639438 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8948.46 | −0.875421 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4355.63 | −0.423408 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.240308 | −2.30670e−5 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6582.21 | 0.627868 | 0.313934 | − | 0.949445i | \(-0.398353\pi\) | ||||
0.313934 | + | 0.949445i | \(0.398353\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14738.4 | 1.39712 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 859.561 | 0.0809759 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10288.5 | 0.957326 | 0.478663 | − | 0.877999i | \(-0.341122\pi\) | ||||
0.478663 | + | 0.877999i | \(0.341122\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4321.68 | 0.399659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3423.20 | 0.314637 | 0.157319 | − | 0.987548i | \(-0.449715\pi\) | ||||
0.157319 | + | 0.987548i | \(0.449715\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10874.5 | −0.993436 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10414.2 | −0.939921 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8210.85 | 0.736609 | 0.368305 | − | 0.929705i | \(-0.379938\pi\) | ||||
0.368305 | + | 0.929705i | \(0.379938\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13382.0 | 1.19334 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7377.71 | −0.653988 | −0.326994 | − | 0.945026i | \(-0.606036\pi\) | ||||
−0.326994 | + | 0.945026i | \(0.606036\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2284.15 | 0.200084 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 456.652 | 0.0397657 | 0.0198829 | − | 0.999802i | \(-0.493671\pi\) | ||||
0.0198829 | + | 0.999802i | \(0.493671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 781.781 | 0.0676790 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −345.134 | −0.0297038 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 697.166 | 0.0593063 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4564.43 | 0.386043 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3000.32 | 0.252297 | 0.126148 | − | 0.992011i | \(-0.459738\pi\) | ||||
0.126148 | + | 0.992011i | \(0.459738\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7731.71 | −0.646433 | −0.323216 | − | 0.946325i | \(-0.604764\pi\) | ||||
−0.323216 | + | 0.946325i | \(0.604764\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6713.09 | 0.554889 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11848.1 | −0.973793 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −204.437 | −0.0167077 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8225.33 | 0.668440 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17116.5 | −1.37548 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3083.71 | −0.246428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13614.4 | −1.08194 | −0.540971 | − | 0.841041i | \(-0.681943\pi\) | ||||
−0.540971 | + | 0.841041i | \(0.681943\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18309.1 | 1.44699 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3198.43 | −0.250009 | −0.125005 | − | 0.992156i | \(-0.539895\pi\) | ||||
−0.125005 | + | 0.992156i | \(0.539895\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −286.253 | −0.0222531 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −357.478 | −0.0276390 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11443.3 | −0.879964 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 178.506 | 0.0135790 | 0.00678952 | − | 0.999977i | \(-0.497839\pi\) | ||||
0.00678952 | + | 0.999977i | \(0.497839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15368.5 | −1.16282 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4739.24 | 0.356668 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10610.5 | −0.794280 | −0.397140 | − | 0.917758i | \(-0.629997\pi\) | ||||
−0.397140 | + | 0.917758i | \(0.629997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6829.34 | −0.505830 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21286.8 | −1.56834 | −0.784171 | − | 0.620544i | \(-0.786912\pi\) | ||||
−0.784171 | + | 0.620544i | \(0.786912\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12064.5 | 0.884209 | 0.442104 | − | 0.896964i | \(-0.354232\pi\) | ||||
0.442104 | + | 0.896964i | \(0.354232\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15674.5 | −1.14278 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8292.57 | −0.598309 | −0.299155 | − | 0.954205i | \(-0.596705\pi\) | ||||
−0.299155 | + | 0.954205i | \(0.596705\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8761.74 | −0.628887 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8480.75 | −0.605578 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.46092 | −0.000316900 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15928.8 | 1.12002 | 0.560011 | − | 0.828485i | \(-0.310797\pi\) | ||||
0.560011 | + | 0.828485i | \(0.310797\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 220.679 | 0.0154379 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22896.3 | −1.59362 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13330.3 | 0.923116 | 0.461558 | − | 0.887110i | \(-0.347291\pi\) | ||||
0.461558 | + | 0.887110i | \(0.347291\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4312.61 | −0.295650 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3311.48 | −0.225882 | −0.112941 | − | 0.993602i | \(-0.536027\pi\) | ||||
−0.112941 | + | 0.993602i | \(0.536027\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6082.46 | −0.412826 | −0.206413 | − | 0.978465i | \(-0.566179\pi\) | ||||
−0.206413 | + | 0.978465i | \(0.566179\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 454.664 | 0.0307054 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6162.45 | −0.412069 | −0.206035 | − | 0.978545i | \(-0.566056\pi\) | ||||
−0.206035 | + | 0.978545i | \(0.566056\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6909.48 | −0.459747 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2459.89 | 0.162875 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8628.65 | 0.568529 | 0.284264 | − | 0.958746i | \(-0.408251\pi\) | ||||
0.284264 | + | 0.958746i | \(0.408251\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16309.0 | −1.06414 | −0.532070 | − | 0.846700i | \(-0.678586\pi\) | ||||
−0.532070 | + | 0.846700i | \(0.678586\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25185.0 | 1.63533 | 0.817665 | − | 0.575694i | \(-0.195268\pi\) | ||||
0.817665 | + | 0.575694i | \(0.195268\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2474.60 | −0.159907 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8913.75 | 0.573229 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 155.793 | 0.00992309 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26596.4 | −1.68596 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13579.0 | −0.856689 | −0.428344 | − | 0.903616i | \(-0.640903\pi\) | ||||
−0.428344 | + | 0.903616i | \(0.640903\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24594.4 | −1.54430 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10880.6 | −0.676775 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −729.053 | −0.0451344 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26562.1 | 1.63672 | 0.818362 | − | 0.574703i | \(-0.194883\pi\) | ||||
0.818362 | + | 0.574703i | \(0.194883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10349.9 | 0.634773 | 0.317387 | − | 0.948296i | \(-0.397195\pi\) | ||||
0.317387 | + | 0.948296i | \(0.397195\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30738.0 | −1.86775 | −0.933875 | − | 0.357598i | \(-0.883596\pi\) | ||||
−0.933875 | + | 0.357598i | \(0.883596\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3795.02 | −0.229534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4265.38 | 0.256795 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6912.35 | −0.414244 | −0.207122 | − | 0.978315i | \(-0.566410\pi\) | ||||
−0.207122 | + | 0.978315i | \(0.566410\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 54.7291 | 0.00324990 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3793.27 | 0.224226 | 0.112113 | − | 0.993695i | \(-0.464238\pi\) | ||||
0.112113 | + | 0.993695i | \(0.464238\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30232.2 | 1.77897 | 0.889483 | − | 0.456968i | \(-0.151065\pi\) | ||||
0.889483 | + | 0.456968i | \(0.151065\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16722.0 | 0.979532 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2563.11 | −0.148791 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11767.0 | 0.680025 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5313.80 | −0.305718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8389.60 | −0.480528 | −0.240264 | − | 0.970708i | \(-0.577234\pi\) | ||||
−0.240264 | + | 0.970708i | \(0.577234\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8879.70 | −0.504099 | −0.252049 | − | 0.967714i | \(-0.581105\pi\) | ||||
−0.252049 | + | 0.967714i | \(0.581105\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10607.6 | 0.599530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5451.42 | 0.306753 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12555.2 | −0.703384 | −0.351692 | − | 0.936116i | \(-0.614394\pi\) | ||||
−0.351692 | + | 0.936116i | \(0.614394\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20443.3 | −1.13532 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.7400 | −0.000870313 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30372.7 | 1.67211 | 0.836057 | − | 0.548642i | \(-0.184855\pi\) | ||||
0.836057 | + | 0.548642i | \(0.184855\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 69.8272 | 0.00382759 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14843.2 | −0.806635 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −683.694 | −0.0369953 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33508.8 | 1.80543 | 0.902716 | − | 0.430237i | \(-0.141570\pi\) | ||||
0.902716 | + | 0.430237i | \(0.141570\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −874.303 | −0.0469061 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4274.12 | 0.227362 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29743.4 | −1.57551 | −0.787756 | − | 0.615987i | \(-0.788757\pi\) | ||||
−0.787756 | + | 0.615987i | \(0.788757\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −801.098 | −0.0422553 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1582.26 | 0.0831083 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30093.9 | −1.56747 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −404.733 | −0.0209930 | −0.0104965 | − | 0.999945i | \(-0.503341\pi\) | ||||
−0.0104965 | + | 0.999945i | \(0.503341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8818.40 | 0.455499 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9561.99 | −0.491859 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19096.9 | 0.974230 | 0.487115 | − | 0.873338i | \(-0.338049\pi\) | ||||
0.487115 | + | 0.873338i | \(0.338049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19193.8 | 0.975147 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27733.4 | 1.40323 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28856.0 | −1.45405 | −0.727026 | − | 0.686610i | \(-0.759098\pi\) | ||||
−0.727026 | + | 0.686610i | \(0.759098\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8440.07 | 0.421837 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36005.6 | 1.79227 | 0.896134 | − | 0.443784i | \(-0.146364\pi\) | ||||
0.896134 | + | 0.443784i | \(0.146364\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 549.703 | 0.0272522 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36423.7 | 1.79846 | 0.899230 | − | 0.437475i | \(-0.144127\pi\) | ||||
0.899230 | + | 0.437475i | \(0.144127\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −593.701 | −0.0290795 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9768.79 | 0.476560 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25845.4 | −1.25581 | −0.627905 | − | 0.778290i | \(-0.716088\pi\) | ||||
−0.627905 | + | 0.778290i | \(0.716088\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19125.5 | 0.925594 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17862.6 | −0.857634 | −0.428817 | − | 0.903391i | \(-0.641069\pi\) | ||||
−0.428817 | + | 0.903391i | \(0.641069\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1117.03 | 0.0534198 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22733.0 | −1.08288 | −0.541439 | − | 0.840740i | \(-0.682120\pi\) | ||||
−0.541439 | + | 0.840740i | \(0.682120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1991.60 | 0.0944965 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13390.4 | −0.630379 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23153.6 | −1.08575 | −0.542873 | − | 0.839815i | \(-0.682664\pi\) | ||||
−0.542873 | + | 0.839815i | \(0.682664\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15613.3 | −0.729309 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26456.0 | 1.23099 | 0.615494 | − | 0.788141i | \(-0.288956\pi\) | ||||
0.615494 | + | 0.788141i | \(0.288956\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16898.9 | −0.780237 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −487.939 | −0.0224419 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13533.6 | −0.620066 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19891.8 | 0.907886 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13415.1 | −0.607619 | −0.303809 | − | 0.952733i | \(-0.598259\pi\) | ||||
−0.303809 | + | 0.952733i | \(0.598259\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15960.2 | −0.720151 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10627.3 | 0.477705 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18749.3 | −0.839605 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31375.6 | −1.39445 | −0.697227 | − | 0.716850i | \(-0.745583\pi\) | ||||
−0.697227 | + | 0.716850i | \(0.745583\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4439.04 | −0.196548 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 624.013 | 0.0275261 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1015.95 | 0.0446479 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36216.3 | −1.57977 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28335.1 | 1.23141 | 0.615705 | − | 0.787977i | \(-0.288871\pi\) | ||||
0.615705 | + | 0.787977i | \(0.288871\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34538.1 | 1.49543 | 0.747717 | − | 0.664018i | \(-0.231150\pi\) | ||||
0.747717 | + | 0.664018i | \(0.231150\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −32457.1 | −1.40015 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 911.681 | 0.0390400 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 246.380 | 0.0105118 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29834.1 | 1.26823 | 0.634115 | − | 0.773239i | \(-0.281365\pi\) | ||||
0.634115 | + | 0.773239i | \(0.281365\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36246.8 | −1.53522 | −0.767608 | − | 0.640919i | \(-0.778553\pi\) | ||||
−0.767608 | + | 0.640919i | \(0.778553\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21831.3 | 0.917955 | 0.458978 | − | 0.888448i | \(-0.348216\pi\) | ||||
0.458978 | + | 0.888448i | \(0.348216\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12273.0 | −0.514186 | −0.257093 | − | 0.966387i | \(-0.582765\pi\) | ||||
−0.257093 | + | 0.966387i | \(0.582765\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17209.3 | −0.718391 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19634.8 | 0.816693 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12279.6 | −0.507105 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37441.0 | 1.54065 | 0.770326 | − | 0.637650i | \(-0.220094\pi\) | ||||
0.770326 | + | 0.637650i | \(0.220094\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3785.77 | −0.155224 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2410.02 | −0.0984644 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10890.3 | −0.441788 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −42399.7 | −1.71396 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6268.72 | −0.252514 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1247.81 | 0.0500871 | 0.0250436 | − | 0.999686i | \(-0.492028\pi\) | ||||
0.0250436 | + | 0.999686i | \(0.492028\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2927.40 | 0.116684 | 0.0583419 | − | 0.998297i | \(-0.481419\pi\) | ||||
0.0583419 | + | 0.998297i | \(0.481419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30892.1 | 1.22704 | 0.613518 | − | 0.789681i | \(-0.289754\pi\) | ||||
0.613518 | + | 0.789681i | \(0.289754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9431.08 | −0.373299 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5815.96 | 0.229406 | 0.114703 | − | 0.993400i | \(-0.463408\pi\) | ||||
0.114703 | + | 0.993400i | \(0.463408\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4346.06 | −0.170242 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14871.0 | −0.580513 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29780.1 | 1.15851 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 742.589 | 0.0287890 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4732.26 | −0.182209 | −0.0911044 | − | 0.995841i | \(-0.529040\pi\) | ||||
−0.0911044 | + | 0.995841i | \(0.529040\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4273.60 | −0.163988 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43833.1 | 1.67625 | 0.838124 | − | 0.545480i | \(-0.183653\pi\) | ||||
0.838124 | + | 0.545480i | \(0.183653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37311.7 | 1.42201 | 0.711007 | − | 0.703185i | \(-0.248239\pi\) | ||||
0.711007 | + | 0.703185i | \(0.248239\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44940.5 | 1.70119 | 0.850595 | − | 0.525822i | \(-0.176242\pi\) | ||||
0.850595 | + | 0.525822i | \(0.176242\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 313.867 | 0.0118411 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8874.98 | −0.333696 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −145.925 | −0.00546829 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3941.35 | 0.146709 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12718.8 | −0.471854 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.4038 | 0.00105024 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17621.3 | 0.649392 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16241.6 | 0.594591 | 0.297295 | − | 0.954786i | \(-0.403915\pi\) | ||||
0.297295 | + | 0.954786i | \(0.403915\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 299.213 | 0.0109178 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2088.21 | 0.0759444 | 0.0379722 | − | 0.999279i | \(-0.487910\pi\) | ||||
0.0379722 | + | 0.999279i | \(0.487910\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11021.1 | −0.399500 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21644.8 | 0.779469 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40755.3 | −1.46289 | −0.731443 | − | 0.681903i | \(-0.761153\pi\) | ||||
−0.731443 | + | 0.681903i | \(0.761153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2016.08 | 0.0721303 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −47752.3 | −1.70291 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 617.338 | 0.0218728 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24239.7 | −0.856058 | −0.428029 | − | 0.903765i | \(-0.640792\pi\) | ||||
−0.428029 | + | 0.903765i | \(0.640792\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 645.455 | 0.0227217 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8754.64 | −0.307196 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37308.1 | −1.30075 | −0.650374 | − | 0.759614i | \(-0.725388\pi\) | ||||
−0.650374 | + | 0.759614i | \(0.725388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19815.5 | −0.688663 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −109.276 | −0.00378566 | −0.00189283 | − | 0.999998i | \(-0.500603\pi\) | ||||
−0.00189283 | + | 0.999998i | \(0.500603\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3498.51 | −0.120813 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13256.9 | −0.454902 | −0.227451 | − | 0.973790i | \(-0.573039\pi\) | ||||
−0.227451 | + | 0.973790i | \(0.573039\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3584.71 | 0.122618 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9777.29 | 0.333386 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56535.2 | −1.92167 | −0.960837 | − | 0.277112i | \(-0.910623\pi\) | ||||
−0.960837 | + | 0.277112i | \(0.910623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8979.12 | −0.303296 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27393.4 | 0.922396 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21939.4 | −0.736443 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 683.870 | 0.0228841 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32548.6 | 1.08241 | 0.541206 | − | 0.840890i | \(-0.317968\pi\) | ||||
0.541206 | + | 0.840890i | \(0.317968\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −991.976 | −0.0328863 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1604.29 | −0.0530216 | −0.0265108 | − | 0.999649i | \(-0.508440\pi\) | ||||
−0.0265108 | + | 0.999649i | \(0.508440\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1210.83 | 0.0398945 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11269.0 | −0.369014 | −0.184507 | − | 0.982831i | \(-0.559069\pi\) | ||||
−0.184507 | + | 0.982831i | \(0.559069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11583.7 | 0.378159 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 139.423 | 0.00453766 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48373.3 | −1.56955 | −0.784775 | − | 0.619781i | \(-0.787221\pi\) | ||||
−0.784775 | + | 0.619781i | \(0.787221\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2820.49 | −0.0909596 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6536.72 | 0.210167 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 792.959 | 0.0254179 | 0.0127090 | − | 0.999919i | \(-0.495954\pi\) | ||||
0.0127090 | + | 0.999919i | \(0.495954\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38038.1 | 1.21561 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52187.1 | 1.65775 | 0.828877 | − | 0.559430i | \(-0.188980\pi\) | ||||
0.828877 | + | 0.559430i | \(0.188980\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 48650.4 | 1.54077 |
(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 | 1600.4.a.ct.1.1 | 3 | ||
4.3 | odd | 2 | 1600.4.a.cq.1.3 | 3 | |||
5.4 | even | 2 | 1600.4.a.cr.1.3 | 3 | |||
8.3 | odd | 2 | 800.4.a.x.1.1 | yes | 3 | ||
8.5 | even | 2 | 800.4.a.u.1.3 | ✓ | 3 | ||
20.19 | odd | 2 | 1600.4.a.cs.1.1 | 3 | |||
40.3 | even | 4 | 800.4.c.n.449.2 | 6 | |||
40.13 | odd | 4 | 800.4.c.m.449.5 | 6 | |||
40.19 | odd | 2 | 800.4.a.v.1.3 | yes | 3 | ||
40.27 | even | 4 | 800.4.c.n.449.5 | 6 | |||
40.29 | even | 2 | 800.4.a.w.1.1 | yes | 3 | ||
40.37 | odd | 4 | 800.4.c.m.449.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
800.4.a.u.1.3 | ✓ | 3 | 8.5 | even | 2 | ||
800.4.a.v.1.3 | yes | 3 | 40.19 | odd | 2 | ||
800.4.a.w.1.1 | yes | 3 | 40.29 | even | 2 | ||
800.4.a.x.1.1 | yes | 3 | 8.3 | odd | 2 | ||
800.4.c.m.449.2 | 6 | 40.37 | odd | 4 | |||
800.4.c.m.449.5 | 6 | 40.13 | odd | 4 | |||
800.4.c.n.449.2 | 6 | 40.3 | even | 4 | |||
800.4.c.n.449.5 | 6 | 40.27 | even | 4 | |||
1600.4.a.cq.1.3 | 3 | 4.3 | odd | 2 | |||
1600.4.a.cr.1.3 | 3 | 5.4 | even | 2 | |||
1600.4.a.cs.1.1 | 3 | 20.19 | odd | 2 | |||
1600.4.a.ct.1.1 | 3 | 1.1 | even | 1 | trivial |