Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.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: | \(69.3862461668\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.58461.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 65x - 126 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.20369\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-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 | ||||||||
\(5\) | −0.239289 | −0.0214026 | −0.0107013 | − | 0.999943i | \(-0.503406\pi\) | ||||
−0.0107013 | + | 0.999943i | \(0.503406\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.09691 | 0.221937 | 0.110969 | − | 0.993824i | \(-0.464605\pi\) | ||||
0.110969 | + | 0.993824i | \(0.464605\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −43.7693 | −0.933802 | −0.466901 | − | 0.884310i | \(-0.654630\pi\) | ||||
−0.466901 | + | 0.884310i | \(0.654630\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.717867 | 0.0123568 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 60.8148 | 0.867632 | 0.433816 | − | 0.901001i | \(-0.357167\pi\) | ||||
0.433816 | + | 0.901001i | \(0.357167\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 98.8861 | 1.19400 | 0.597000 | − | 0.802241i | \(-0.296359\pi\) | ||||
0.597000 | + | 0.802241i | \(0.296359\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −213.875 | −1.93896 | −0.969478 | − | 0.245179i | \(-0.921153\pi\) | ||||
−0.969478 | + | 0.245179i | \(0.921153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.943 | −0.999542 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 110.313 | 0.706367 | 0.353184 | − | 0.935554i | \(-0.385099\pi\) | ||||
0.353184 | + | 0.935554i | \(0.385099\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 80.0138 | 0.463578 | 0.231789 | − | 0.972766i | \(-0.425542\pi\) | ||||
0.231789 | + | 0.972766i | \(0.425542\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −24.2907 | −0.128136 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.88064 | −0.0127993 | −0.00639966 | − | 0.999980i | \(-0.502037\pi\) | ||||
−0.00639966 | + | 0.999980i | \(0.502037\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 131.308 | 0.539131 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 242.307 | 0.922976 | 0.461488 | − | 0.887146i | \(-0.347316\pi\) | ||||
0.461488 | + | 0.887146i | \(0.347316\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 367.006 | 1.30158 | 0.650790 | − | 0.759258i | \(-0.274438\pi\) | ||||
0.650790 | + | 0.759258i | \(0.274438\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.15360 | −0.00713422 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −89.3910 | −0.277426 | −0.138713 | − | 0.990333i | \(-0.544297\pi\) | ||||
−0.138713 | + | 0.990333i | \(0.544297\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −182.444 | −0.500928 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.4127 | 0.0295784 | 0.0147892 | − | 0.999891i | \(-0.495292\pi\) | ||||
0.0147892 | + | 0.999891i | \(0.495292\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.93750 | −0.00475005 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −296.658 | −0.689357 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −400.097 | −0.882851 | −0.441425 | − | 0.897298i | \(-0.645527\pi\) | ||||
−0.441425 | + | 0.897298i | \(0.645527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −480.381 | −1.00830 | −0.504152 | − | 0.863615i | \(-0.668195\pi\) | ||||
−0.504152 | + | 0.863615i | \(0.668195\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.4735 | 0.0199858 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −240.999 | −0.439444 | −0.219722 | − | 0.975562i | \(-0.570515\pi\) | ||||
−0.219722 | + | 0.975562i | \(0.570515\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 641.624 | 1.11946 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −978.496 | −1.63558 | −0.817790 | − | 0.575517i | \(-0.804801\pi\) | ||||
−0.817790 | + | 0.575517i | \(0.804801\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 622.215 | 0.997600 | 0.498800 | − | 0.866717i | \(-0.333774\pi\) | ||||
0.498800 | + | 0.866717i | \(0.333774\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 374.828 | 0.577086 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −545.957 | −0.777531 | −0.388766 | − | 0.921337i | \(-0.627098\pi\) | ||||
−0.388766 | + | 0.921337i | \(0.627098\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 845.995 | 1.11879 | 0.559397 | − | 0.828900i | \(-0.311033\pi\) | ||||
0.559397 | + | 0.828900i | \(0.311033\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.5523 | −0.0185696 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −330.940 | −0.407821 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 203.319 | 0.242154 | 0.121077 | − | 0.992643i | \(-0.461365\pi\) | ||||
0.121077 | + | 0.992643i | \(0.461365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −240.042 | −0.267647 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −23.6623 | −0.0255548 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1199.17 | 1.25523 | 0.627617 | − | 0.778522i | \(-0.284030\pi\) | ||||
0.627617 | + | 0.778522i | \(0.284030\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 72.8722 | 0.0739791 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −367.585 | −0.362139 | −0.181070 | − | 0.983470i | \(-0.557956\pi\) | ||||
−0.181070 | + | 0.983470i | \(0.557956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −945.228 | −0.904233 | −0.452117 | − | 0.891959i | \(-0.649331\pi\) | ||||
−0.452117 | + | 0.891959i | \(0.649331\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −713.157 | −0.644331 | −0.322166 | − | 0.946683i | \(-0.604411\pi\) | ||||
−0.322166 | + | 0.946683i | \(0.604411\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −933.622 | −0.820411 | −0.410205 | − | 0.911993i | \(-0.634543\pi\) | ||||
−0.410205 | + | 0.911993i | \(0.634543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.64192 | 0.00738969 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1191.38 | 0.991822 | 0.495911 | − | 0.868373i | \(-0.334834\pi\) | ||||
0.495911 | + | 0.868373i | \(0.334834\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 51.1779 | 0.0414988 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −393.924 | −0.311267 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1265.44 | −0.950744 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −726.922 | −0.532881 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 59.8085 | 0.0427955 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1196.63 | −0.836090 | −0.418045 | − | 0.908426i | \(-0.637285\pi\) | ||||
−0.418045 | + | 0.908426i | \(0.637285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1101.02 | −0.751467 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −505.508 | −0.337148 | −0.168574 | − | 0.985689i | \(-0.553916\pi\) | ||||
−0.168574 | + | 0.985689i | \(0.553916\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.46080 | 0.00411894 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −739.542 | −0.461192 | −0.230596 | − | 0.973050i | \(-0.574068\pi\) | ||||
−0.230596 | + | 0.973050i | \(0.574068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3095.88 | −1.88913 | −0.944566 | − | 0.328322i | \(-0.893517\pi\) | ||||
−0.944566 | + | 0.328322i | \(0.893517\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 268.173 | 0.160172 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −354.396 | −0.207246 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.3967 | −0.0151181 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2989.16 | −1.64350 | −0.821751 | − | 0.569847i | \(-0.807002\pi\) | ||||
−0.821751 | + | 0.569847i | \(0.807002\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1769.68 | −0.953741 | −0.476871 | − | 0.878974i | \(-0.658229\pi\) | ||||
−0.476871 | + | 0.878974i | \(0.658229\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 547.333 | 0.289211 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.1464 | −0.00992179 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2328.02 | −1.18341 | −0.591707 | − | 0.806153i | \(-0.701546\pi\) | ||||
−0.591707 | + | 0.806153i | \(0.701546\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −34.2381 | −0.0170771 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2597.36 | −1.24810 | −0.624051 | − | 0.781384i | \(-0.714514\pi\) | ||||
−0.624051 | + | 0.781384i | \(0.714514\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.81250 | 0.00274244 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3276.61 | 1.51827 | 0.759137 | − | 0.650931i | \(-0.225621\pi\) | ||||
0.759137 | + | 0.650931i | \(0.225621\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −281.247 | −0.128014 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 889.974 | 0.398000 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 230.036 | 0.101094 | 0.0505471 | − | 0.998722i | \(-0.483904\pi\) | ||||
0.0505471 | + | 0.998722i | \(0.483904\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1200.29 | 0.509714 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3730.56 | −1.55774 | −0.778869 | − | 0.627186i | \(-0.784206\pi\) | ||||
−0.778869 | + | 0.627186i | \(0.784206\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1649.91 | 0.677550 | 0.338775 | − | 0.940867i | \(-0.389987\pi\) | ||||
0.338775 | + | 0.940867i | \(0.389987\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1441.14 | 0.582144 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.689305 | 0.000273939 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 492.412 | 0.192560 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1809.65 | 0.685560 | 0.342780 | − | 0.939416i | \(-0.388632\pi\) | ||||
0.342780 | + | 0.939416i | \(0.388632\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4367.23 | 1.62881 | 0.814404 | − | 0.580298i | \(-0.197064\pi\) | ||||
0.814404 | + | 0.580298i | \(0.197064\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −31.4205 | −0.0115388 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 398.287 | 0.144044 | 0.0720222 | − | 0.997403i | \(-0.477055\pi\) | ||||
0.0720222 | + | 0.997403i | \(0.477055\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4343.35 | −1.54720 | −0.773598 | − | 0.633677i | \(-0.781545\pi\) | ||||
−0.773598 | + | 0.633677i | \(0.781545\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 722.998 | 0.253713 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −57.9814 | −0.0197541 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1924.87 | −0.646319 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 800.672 | 0.264993 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2723.91 | −0.888728 | −0.444364 | − | 0.895846i | \(-0.646570\pi\) | ||||
−0.444364 | + | 0.895846i | \(0.646570\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2935.49 | 0.944302 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −87.8205 | −0.0278572 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1866.65 | −0.575965 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2661.82 | −0.810197 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4896.87 | 1.47049 | 0.735243 | − | 0.677803i | \(-0.237068\pi\) | ||||
0.735243 | + | 0.677803i | \(0.237068\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1124.48 | −0.333181 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3231.55 | −0.944869 | −0.472434 | − | 0.881366i | \(-0.656625\pi\) | ||||
−0.472434 | + | 0.881366i | \(0.656625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5918.53 | −1.70789 | −0.853947 | − | 0.520360i | \(-0.825798\pi\) | ||||
−0.853947 | + | 0.520360i | \(0.825798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −521.944 | −0.146754 | −0.0733771 | − | 0.997304i | \(-0.523378\pi\) | ||||
−0.0733771 | + | 0.997304i | \(0.523378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.3903 | 0.00593765 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1637.87 | 0.448908 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6626.70 | −1.79350 | −0.896748 | − | 0.442542i | \(-0.854077\pi\) | ||||
−0.896748 | + | 0.442542i | \(0.854077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2025.39 | −0.541357 | −0.270678 | − | 0.962670i | \(-0.587248\pi\) | ||||
−0.270678 | + | 0.962670i | \(0.587248\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4328.17 | −1.11496 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2537.98 | −0.645936 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3352.64 | −0.843096 | −0.421548 | − | 0.906806i | \(-0.638513\pi\) | ||||
−0.421548 | + | 0.906806i | \(0.638513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1731.73 | −0.430327 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 43.6569 | 0.0107212 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6826.73 | −1.65696 | −0.828482 | − | 0.560015i | \(-0.810795\pi\) | ||||
−0.828482 | + | 0.560015i | \(0.810795\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 992.819 | 0.235456 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1794.16 | −0.420657 | −0.210329 | − | 0.977631i | \(-0.567453\pi\) | ||||
−0.210329 | + | 0.977631i | \(0.567453\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.73094 | −0.000633057 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −609.956 | −0.139808 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1466.66 | 0.332431 | 0.166216 | − | 0.986089i | \(-0.446845\pi\) | ||||
0.166216 | + | 0.986089i | \(0.446845\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1756.51 | 0.393729 | 0.196865 | − | 0.980431i | \(-0.436924\pi\) | ||||
0.196865 | + | 0.980431i | \(0.436924\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1011.65 | −0.221836 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7708.00 | 1.67194 | 0.835972 | − | 0.548771i | \(-0.184904\pi\) | ||||
0.835972 | + | 0.548771i | \(0.184904\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 720.125 | 0.154526 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6837.65 | 1.45160 | 0.725800 | − | 0.687905i | \(-0.241470\pi\) | ||||
0.725800 | + | 0.687905i | \(0.241470\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3248.60 | −0.682365 | −0.341182 | − | 0.939997i | \(-0.610827\pi\) | ||||
−0.341182 | + | 0.939997i | \(0.610827\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 70.9870 | 0.0147541 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1214.56 | −0.247214 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3597.52 | −0.724710 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9674.19 | 1.92892 | 0.964458 | − | 0.264237i | \(-0.0851200\pi\) | ||||
0.964458 | + | 0.264237i | \(0.0851200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 95.7388 | 0.0188953 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −218.617 | −0.0427119 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9361.15 | 1.81060 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1102.76 | 0.209081 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 114.950 | 0.0215804 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4959.70 | −0.922035 | −0.461018 | − | 0.887391i | \(-0.652516\pi\) | ||||
−0.461018 | + | 0.887391i | \(0.652516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2835.68 | 0.522059 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6757.74 | 1.23214 | 0.616071 | − | 0.787690i | \(-0.288723\pi\) | ||||
0.616071 | + | 0.787690i | \(0.288723\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3382.02 | −0.610744 | −0.305372 | − | 0.952233i | \(-0.598781\pi\) | ||||
−0.305372 | + | 0.952233i | \(0.598781\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 867.009 | 0.153615 | 0.0768077 | − | 0.997046i | \(-0.475527\pi\) | ||||
0.0768077 | + | 0.997046i | \(0.475527\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 893.196 | 0.156769 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2139.47 | 0.372005 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6013.73 | 1.03595 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5468.66 | 0.933374 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2800.87 | 0.473664 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1379.21 | −0.229028 | −0.114514 | − | 0.993422i | \(-0.536531\pi\) | ||||
−0.114514 | + | 0.993422i | \(0.536531\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −25.9258 | −0.00426644 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 57.6685 | 0.00940527 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2109.75 | −0.341025 | −0.170513 | − | 0.985355i | \(-0.554542\pi\) | ||||
−0.170513 | + | 0.985355i | \(0.554542\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3574.15 | −0.572629 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 647.865 | 0.102885 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −153.534 | −0.0239593 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4188.30 | −0.647953 | −0.323976 | − | 0.946065i | \(-0.605020\pi\) | ||||
−0.323976 | + | 0.946065i | \(0.605020\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10456.8 | −1.60385 | −0.801923 | − | 0.597428i | \(-0.796190\pi\) | ||||
−0.801923 | + | 0.597428i | \(0.796190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1181.77 | 0.179710 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4581.24 | 0.690750 | 0.345375 | − | 0.938465i | \(-0.387752\pi\) | ||||
0.345375 | + | 0.938465i | \(0.387752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 234.143 | 0.0350057 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7780.68 | −1.14387 | −0.571934 | − | 0.820300i | \(-0.693807\pi\) | ||||
−0.571934 | + | 0.820300i | \(0.693807\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2919.45 | 0.425638 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3796.32 | 0.548912 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −148.889 | −0.0213513 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4126.59 | 0.586938 | 0.293469 | − | 0.955969i | \(-0.405190\pi\) | ||||
0.293469 | + | 0.955969i | \(0.405190\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2180.76 | 0.307659 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5129.82 | −0.712097 | −0.356048 | − | 0.934468i | \(-0.615876\pi\) | ||||
−0.356048 | + | 0.934468i | \(0.615876\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −179.426 | −0.0247080 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4828.33 | −0.659607 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1017.94 | −0.137963 | −0.0689815 | − | 0.997618i | \(-0.521975\pi\) | ||||
−0.0689815 | + | 0.997618i | \(0.521975\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3589.88 | 0.482717 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10366.6 | 1.38305 | 0.691525 | − | 0.722352i | \(-0.256939\pi\) | ||||
0.691525 | + | 0.722352i | \(0.256939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3303.06 | 0.433860 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13006.6 | 1.69527 | 0.847637 | − | 0.530576i | \(-0.178024\pi\) | ||||
0.847637 | + | 0.530576i | \(0.178024\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13006.8 | −1.68230 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1516.52 | 0.194653 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 130.641 | 0.0166412 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1954.49 | −0.247086 | −0.123543 | − | 0.992339i | \(-0.539426\pi\) | ||||
−0.123543 | + | 0.992339i | \(0.539426\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10846.1 | 1.35069 | 0.675345 | − | 0.737502i | \(-0.263995\pi\) | ||||
0.675345 | + | 0.737502i | \(0.263995\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3502.15 | −0.432890 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.3824 | −0.00237807 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.3243 | −0.00284065 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5900.36 | 0.713335 | 0.356667 | − | 0.934231i | \(-0.383913\pi\) | ||||
0.356667 | + | 0.934231i | \(0.383913\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2218.63 | 0.266269 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −202.437 | −0.0239452 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9287.65 | 1.09069 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8994.03 | 1.04866 | 0.524328 | − | 0.851516i | \(-0.324316\pi\) | ||||
0.524328 | + | 0.851516i | \(0.324316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8032.54 | 0.929886 | 0.464943 | − | 0.885341i | \(-0.346075\pi\) | ||||
0.464943 | + | 0.885341i | \(0.346075\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −804.519 | −0.0924753 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7598.37 | −0.867235 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1063.19 | 0.119653 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7285.93 | −0.814271 | −0.407136 | − | 0.913368i | \(-0.633472\pi\) | ||||
−0.407136 | + | 0.913368i | \(0.633472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11152.5 | −1.23777 | −0.618887 | − | 0.785480i | \(-0.712416\pi\) | ||||
−0.618887 | + | 0.785480i | \(0.712416\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 79.1902 | 0.00872845 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21149.2 | −2.31511 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10898.9 | −1.18491 | −0.592457 | − | 0.805602i | \(-0.701842\pi\) | ||||
−0.592457 | + | 0.805602i | \(0.701842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17184.4 | 1.84302 | 0.921509 | − | 0.388356i | \(-0.126957\pi\) | ||||
0.921509 | + | 0.388356i | \(0.126957\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −48.6519 | −0.00518274 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8967.49 | 0.948876 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5273.80 | 0.554312 | 0.277156 | − | 0.960825i | \(-0.410608\pi\) | ||||
0.277156 | + | 0.960825i | \(0.410608\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1961.94 | 0.204843 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5309.05 | 0.550643 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4945.05 | 0.506170 | 0.253085 | − | 0.967444i | \(-0.418555\pi\) | ||||
0.253085 | + | 0.967444i | \(0.418555\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1642.00 | −0.166976 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6611.17 | 0.667924 | 0.333962 | − | 0.942587i | \(-0.391614\pi\) | ||||
0.333962 | + | 0.942587i | \(0.391614\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4339.15 | −0.435545 | −0.217772 | − | 0.976000i | \(-0.569879\pi\) | ||||
−0.217772 | + | 0.976000i | \(0.569879\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 57.4393 | 0.00572835 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12296.5 | 1.21844 | 0.609221 | − | 0.793001i | \(-0.291482\pi\) | ||||
0.609221 | + | 0.793001i | \(0.291482\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6984.05 | 0.683244 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2971.62 | 0.288869 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12355.1 | −1.19345 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 102.714 | 0.00985948 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3899.71 | 0.371988 | 0.185994 | − | 0.982551i | \(-0.440449\pi\) | ||||
0.185994 | + | 0.982551i | \(0.440449\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 126.084 | 0.0119520 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −286.949 | −0.0268653 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9992.44 | 0.929776 | 0.464888 | − | 0.885370i | \(-0.346095\pi\) | ||||
0.464888 | + | 0.885370i | \(0.346095\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7792.07 | 0.720592 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18654.9 | −1.71463 | −0.857317 | − | 0.514788i | \(-0.827870\pi\) | ||||
−0.857317 | + | 0.514788i | \(0.827870\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6708.67 | 0.612867 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.4375 | −0.00158335 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17669.0 | 1.58512 | 0.792558 | − | 0.609796i | \(-0.208749\pi\) | ||||
0.792558 | + | 0.609796i | \(0.208749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9829.84 | −0.876576 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11137.5 | −0.987270 | −0.493635 | − | 0.869669i | \(-0.664332\pi\) | ||||
−0.493635 | + | 0.869669i | \(0.664332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 87.9590 | 0.00775074 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 843.741 | 0.0739090 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10872.5 | −0.946786 | −0.473393 | − | 0.880851i | \(-0.656971\pi\) | ||||
−0.473393 | + | 0.880851i | \(0.656971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2669.92 | −0.229786 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 226.182 | 0.0193530 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −723.791 | −0.0615712 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −690.107 | −0.0583667 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20457.2 | 1.72025 | 0.860123 | − | 0.510086i | \(-0.170387\pi\) | ||||
0.860123 | + | 0.510086i | \(0.170387\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14914.1 | −1.24694 | −0.623470 | − | 0.781847i | \(-0.714278\pi\) | ||||
−0.623470 | + | 0.781847i | \(0.714278\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4866.02 | 0.402215 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33575.4 | 2.75955 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3600.87 | −0.294284 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10605.6 | −0.861877 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 170.650 | 0.0137904 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11191.7 | 0.899361 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3615.88 | 0.287355 | 0.143677 | − | 0.989625i | \(-0.454107\pi\) | ||||
0.143677 | + | 0.989625i | \(0.454107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4949.72 | −0.391184 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 223.405 | 0.0175590 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13365.1 | −1.04470 | −0.522350 | − | 0.852731i | \(-0.674945\pi\) | ||||
−0.522350 | + | 0.852731i | \(0.674945\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4323.43 | −0.336101 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10908.4 | 0.843403 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.06792 | −0.000158159 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2933.95 | 0.223188 | 0.111594 | − | 0.993754i | \(-0.464404\pi\) | ||||
0.111594 | + | 0.993754i | \(0.464404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16063.6 | −1.21542 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1477.24 | −0.111175 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −954.247 | −0.0714329 | −0.0357164 | − | 0.999362i | \(-0.511371\pi\) | ||||
−0.0357164 | + | 0.999362i | \(0.511371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −285.085 | −0.0212276 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13258.6 | 0.976853 | 0.488426 | − | 0.872605i | \(-0.337571\pi\) | ||||
0.488426 | + | 0.872605i | \(0.337571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2773.75 | 0.203288 | 0.101644 | − | 0.994821i | \(-0.467590\pi\) | ||||
0.101644 | + | 0.994821i | \(0.467590\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5428.96 | −0.395808 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26722.1 | 1.93807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10361.0 | −0.747546 | −0.373773 | − | 0.927520i | \(-0.621936\pi\) | ||||
−0.373773 | + | 0.927520i | \(0.621936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13101.7 | −0.940393 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 92.4078 | 0.00656456 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 94.2616 | 0.00666194 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4373.97 | −0.307552 | −0.153776 | − | 0.988106i | \(-0.549143\pi\) | ||||
−0.153776 | + | 0.988106i | \(0.549143\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7912.25 | 0.553512 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1194.86 | −0.0831641 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21102.2 | 1.46132 | 0.730662 | − | 0.682740i | \(-0.239212\pi\) | ||||
0.730662 | + | 0.682740i | \(0.239212\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13030.0 | 0.893274 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5381.42 | 0.367076 | 0.183538 | − | 0.983013i | \(-0.441245\pi\) | ||||
0.183538 | + | 0.983013i | \(0.441245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26223.5 | −1.77983 | −0.889915 | − | 0.456126i | \(-0.849237\pi\) | ||||
−0.889915 | + | 0.456126i | \(0.849237\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2168.99 | −0.146481 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 302.806 | 0.0203484 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19022.2 | 1.27197 | 0.635986 | − | 0.771700i | \(-0.280593\pi\) | ||||
0.635986 | + | 0.771700i | \(0.280593\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3912.58 | 0.259061 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 267.855 | 0.0176485 | 0.00882426 | − | 0.999961i | \(-0.497191\pi\) | ||||
0.00882426 | + | 0.999961i | \(0.497191\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 173.944 | 0.0114051 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18568.5 | 1.21157 | 0.605785 | − | 0.795628i | \(-0.292859\pi\) | ||||
0.605785 | + | 0.795628i | \(0.292859\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22873.8 | −1.48526 | −0.742630 | − | 0.669702i | \(-0.766422\pi\) | ||||
−0.742630 | + | 0.669702i | \(0.766422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5774.62 | 0.373152 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15603.5 | 0.998626 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2402.02 | −0.152994 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −175.186 | −0.0111051 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16406.4 | 1.03507 | 0.517535 | − | 0.855662i | \(-0.326850\pi\) | ||||
0.517535 | + | 0.855662i | \(0.326850\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8171.73 | 0.513107 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 286.340 | 0.0178945 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8806.47 | −0.545193 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26155.9 | −1.61169 | −0.805847 | − | 0.592124i | \(-0.798290\pi\) | ||||
−0.805847 | + | 0.592124i | \(0.798290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4898.20 | −0.300414 | −0.150207 | − | 0.988655i | \(-0.547994\pi\) | ||||
−0.150207 | + | 0.988655i | \(0.547994\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 263.461 | 0.0160834 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11929.2 | 0.724863 | 0.362432 | − | 0.932010i | \(-0.381947\pi\) | ||||
0.362432 | + | 0.932010i | \(0.381947\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3239.55 | −0.195938 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7249.87 | 0.434470 | 0.217235 | − | 0.976119i | \(-0.430296\pi\) | ||||
0.217235 | + | 0.976119i | \(0.430296\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 120.962 | 0.00721587 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5599.94 | 0.332533 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12078.7 | −0.713992 | −0.356996 | − | 0.934106i | \(-0.616199\pi\) | ||||
−0.356996 | + | 0.934106i | \(0.616199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1816.64 | 0.106897 | 0.0534486 | − | 0.998571i | \(-0.482979\pi\) | ||||
0.0534486 | + | 0.998571i | \(0.482979\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7985.46 | 0.467767 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23593.2 | −1.36961 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14690.6 | −0.848986 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3889.60 | −0.223780 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21386.6 | −1.22495 | −0.612477 | − | 0.790488i | \(-0.709827\pi\) | ||||
−0.612477 | + | 0.790488i | \(0.709827\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3373.45 | 0.192362 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14029.5 | −0.796449 | −0.398225 | − | 0.917288i | \(-0.630374\pi\) | ||||
−0.398225 | + | 0.917288i | \(0.630374\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9694.64 | 0.545520 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12032.6 | 0.674107 | 0.337053 | − | 0.941486i | \(-0.390570\pi\) | ||||
0.337053 | + | 0.941486i | \(0.390570\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 176.964 | 0.00987074 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17755.6 | 0.986053 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −499.527 | −0.0276204 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10875.1 | −0.598710 | −0.299355 | − | 0.954142i | \(-0.596771\pi\) | ||||
−0.299355 | + | 0.954142i | \(0.596771\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 740.810 | 0.0404324 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14735.9 | 0.800804 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1565.83 | 0.0847285 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31811.2 | 1.71397 | 0.856984 | − | 0.515343i | \(-0.172335\pi\) | ||||
0.856984 | + | 0.515343i | \(0.172335\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −284.855 | −0.0152824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −64.1708 | −0.00342810 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26927.7 | −1.42636 | −0.713180 | − | 0.700981i | \(-0.752746\pi\) | ||||
−0.713180 | + | 0.700981i | \(0.752746\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4913.61 | −0.259177 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17112.9 | −0.898857 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 84.8031 | 0.00443560 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19880.1 | 1.03548 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14549.4 | 0.754661 | 0.377331 | − | 0.926079i | \(-0.376842\pi\) | ||||
0.377331 | + | 0.926079i | \(0.376842\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6076.18 | 0.312552 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13782.8 | −0.706043 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8370.11 | −0.427001 | −0.213501 | − | 0.976943i | \(-0.568487\pi\) | ||||
−0.213501 | + | 0.976943i | \(0.568487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22319.4 | 1.12929 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7667.66 | −0.386373 | −0.193187 | − | 0.981162i | \(-0.561882\pi\) | ||||
−0.193187 | + | 0.981162i | \(0.561882\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1951.35 | −0.0975291 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37924.7 | 1.88780 | 0.943899 | − | 0.330236i | \(-0.107128\pi\) | ||||
0.943899 | + | 0.330236i | \(0.107128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12984.5 | 0.643723 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27008.1 | −1.33356 | −0.666778 | − | 0.745256i | \(-0.732327\pi\) | ||||
−0.666778 | + | 0.745256i | \(0.732327\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 715.273 | 0.0351753 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7613.95 | 0.372932 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17693.1 | −0.859693 | −0.429847 | − | 0.902902i | \(-0.641432\pi\) | ||||
−0.429847 | + | 0.902902i | \(0.641432\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10057.9 | 0.486761 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 423.466 | 0.0204126 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39291.5 | −1.88649 | −0.943247 | − | 0.332093i | \(-0.892245\pi\) | ||||
−0.943247 | + | 0.332093i | \(0.892245\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5195.18 | 0.248449 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21335.0 | −1.01629 | −0.508143 | − | 0.861273i | \(-0.669668\pi\) | ||||
−0.508143 | + | 0.861273i | \(0.669668\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −130.971 | −0.00618988 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17512.0 | 0.824408 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17085.6 | 0.801201 | 0.400600 | − | 0.916253i | \(-0.368802\pi\) | ||||
0.400600 | + | 0.916253i | \(0.368802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20480.2 | 0.956649 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32736.1 | −1.52320 | −0.761601 | − | 0.648047i | \(-0.775586\pi\) | ||||
−0.761601 | + | 0.648047i | \(0.775586\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9997.15 | −0.463365 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23960.8 | 1.10203 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7922.80 | −0.362996 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2978.46 | −0.135940 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 557.069 | 0.0253282 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10474.6 | −0.474435 | −0.237217 | − | 0.971457i | \(-0.576235\pi\) | ||||
−0.237217 | + | 0.971457i | \(0.576235\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5382.49 | 0.242867 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21026.0 | 0.941556 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.19281 | 0.000365496 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41837.3 | 1.85941 | 0.929706 | − | 0.368302i | \(-0.120061\pi\) | ||||
0.929706 | + | 0.368302i | \(0.120061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5436.29 | −0.240704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1829.87 | 0.0807181 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5038.02 | 0.221405 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4399.99 | −0.191929 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37729.8 | −1.63969 | −0.819846 | − | 0.572584i | \(-0.805941\pi\) | ||||
−0.819846 | + | 0.572584i | \(0.805941\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9550.14 | 0.413503 | 0.206751 | − | 0.978394i | \(-0.433711\pi\) | ||||
0.206751 | + | 0.978394i | \(0.433711\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5269.54 | −0.227320 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 621.518 | 0.0267127 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36291.8 | 1.55409 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41279.7 | −1.75478 | −0.877389 | − | 0.479779i | \(-0.840717\pi\) | ||||
−0.877389 | + | 0.479779i | \(0.840717\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10479.7 | 0.443864 | 0.221932 | − | 0.975062i | \(-0.428764\pi\) | ||||
0.221932 | + | 0.975062i | \(0.428764\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3034.95 | 0.128077 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2353.89 | 0.0989757 | 0.0494879 | − | 0.998775i | \(-0.484241\pi\) | ||||
0.0494879 | + | 0.998775i | \(0.484241\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12428.8 | 0.520712 | 0.260356 | − | 0.965513i | \(-0.416160\pi\) | ||||
0.260356 | + | 0.965513i | \(0.416160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23124.0 | −0.965298 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −784.057 | −0.0324951 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2160.37 | −0.0892156 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44513.6 | 1.83168 | 0.915840 | − | 0.401544i | \(-0.131526\pi\) | ||||
0.915840 | + | 0.401544i | \(0.131526\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12220.0 | −0.501046 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20512.9 | −0.838082 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 67.2993 | 0.00273984 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9745.80 | 0.393963 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 616.097 | 0.0248173 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17576.4 | 0.705516 | 0.352758 | − | 0.935715i | \(-0.385244\pi\) | ||||
0.352758 | + | 0.935715i | \(0.385244\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −212.961 | −0.00851826 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −781.198 | −0.0311379 | −0.0155690 | − | 0.999879i | \(-0.504956\pi\) | ||||
−0.0155690 | + | 0.999879i | \(0.504956\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35266.3 | −1.40078 | −0.700391 | − | 0.713759i | \(-0.746991\pi\) | ||||
−0.700391 | + | 0.713759i | \(0.746991\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3977.79 | −0.156901 | −0.0784506 | − | 0.996918i | \(-0.524997\pi\) | ||||
−0.0784506 | + | 0.996918i | \(0.524997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −55.0450 | −0.00216368 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3643.69 | 0.142729 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4420.57 | −0.172563 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10548.4 | 0.410354 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10792.6 | 0.418411 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15620.3 | −0.601437 | −0.300718 | − | 0.953713i | \(-0.597226\pi\) | ||||
−0.300718 | + | 0.953713i | \(0.597226\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29022.6 | −1.11366 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30711.6 | −1.17446 | −0.587231 | − | 0.809419i | \(-0.699782\pi\) | ||||
−0.587231 | + | 0.809419i | \(0.699782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15042.1 | 0.573279 | 0.286640 | − | 0.958038i | \(-0.407462\pi\) | ||||
0.286640 | + | 0.958038i | \(0.407462\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −287.216 | −0.0109092 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16272.7 | −0.615990 | −0.307995 | − | 0.951388i | \(-0.599658\pi\) | ||||
−0.307995 | + | 0.951388i | \(0.599658\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 655.850 | 0.0246597 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8839.52 | −0.331247 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 892.682 | 0.0333397 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28083.5 | −1.04535 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8826.58 | 0.327456 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 694.062 | 0.0256632 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −394.804 | −0.0145014 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12727.0 | −0.465923 | −0.232961 | − | 0.972486i | \(-0.574842\pi\) | ||||
−0.232961 | + | 0.972486i | \(0.574842\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3308.27 | −0.120713 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23984.8 | −0.872283 | −0.436142 | − | 0.899878i | \(-0.643655\pi\) | ||||
−0.436142 | + | 0.899878i | \(0.643655\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6849.94 | 0.248302 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −344.850 | −0.0124594 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9613.65 | −0.345076 | −0.172538 | − | 0.985003i | \(-0.555197\pi\) | ||||
−0.172538 | + | 0.985003i | \(0.555197\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14879.1 | 0.532337 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42828.1 | 1.52731 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 359.915 | 0.0127934 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8507.05 | −0.301411 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18698.0 | 0.660344 | 0.330172 | − | 0.943921i | \(-0.392893\pi\) | ||||
0.330172 | + | 0.943921i | \(0.392893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20273.2 | −0.711378 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −117.829 | −0.00412129 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6833.17 | −0.238239 | −0.119120 | − | 0.992880i | \(-0.538007\pi\) | ||||
−0.119120 | + | 0.992880i | \(0.538007\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10146.1 | 0.352613 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6888.64 | 0.238643 | 0.119322 | − | 0.992856i | \(-0.461928\pi\) | ||||
0.119322 | + | 0.992856i | \(0.461928\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −51823.4 | −1.78961 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21171.7 | −0.726492 | −0.363246 | − | 0.931693i | \(-0.618332\pi\) | ||||
−0.363246 | + | 0.931693i | \(0.618332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27233.9 | −0.931561 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2601.03 | −0.0886899 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50173.4 | 1.70543 | 0.852715 | − | 0.522376i | \(-0.174954\pi\) | ||||
0.852715 | + | 0.522376i | \(0.174954\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −433.030 | −0.0146728 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2679.59 | −0.0905108 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23388.8 | −0.785096 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6418.41 | −0.214777 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1045.03 | −0.0348608 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30613.9 | 1.01807 | 0.509036 | − | 0.860745i | \(-0.330002\pi\) | ||||
0.509036 | + | 0.860745i | \(0.330002\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18041.2 | −0.598108 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6056.78 | 0.200177 | 0.100088 | − | 0.994979i | \(-0.468087\pi\) | ||||
0.100088 | + | 0.994979i | \(0.468087\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16406.0 | −0.538884 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25920.1 | 0.848779 | 0.424389 | − | 0.905480i | \(-0.360489\pi\) | ||||
0.424389 | + | 0.905480i | \(0.360489\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1646.25 | 0.0537431 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8402.60 | −0.273470 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3354.44 | 0.108840 | 0.0544201 | − | 0.998518i | \(-0.482669\pi\) | ||||
0.0544201 | + | 0.998518i | \(0.482669\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −95.3055 | −0.00308293 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −78493.4 | −2.52371 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8625.53 | −0.276487 | −0.138244 | − | 0.990398i | \(-0.544146\pi\) | ||||
−0.138244 | + | 0.990398i | \(0.544146\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4137.63 | 0.132229 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1039.32 | 0.0331141 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −62201.1 | −1.97586 | −0.987928 | − | 0.154913i | \(-0.950490\pi\) | ||||
−0.987928 | + | 0.154913i | \(0.950490\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 77.7773 | 0.00246323 |
(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 | 1176.4.a.x.1.2 | 3 | ||
4.3 | odd | 2 | 2352.4.a.cj.1.2 | 3 | |||
7.3 | odd | 6 | 168.4.q.e.121.2 | yes | 6 | ||
7.5 | odd | 6 | 168.4.q.e.25.2 | ✓ | 6 | ||
7.6 | odd | 2 | 1176.4.a.y.1.2 | 3 | |||
21.5 | even | 6 | 504.4.s.g.361.2 | 6 | |||
21.17 | even | 6 | 504.4.s.g.289.2 | 6 | |||
28.3 | even | 6 | 336.4.q.l.289.2 | 6 | |||
28.19 | even | 6 | 336.4.q.l.193.2 | 6 | |||
28.27 | even | 2 | 2352.4.a.ch.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.e.25.2 | ✓ | 6 | 7.5 | odd | 6 | ||
168.4.q.e.121.2 | yes | 6 | 7.3 | odd | 6 | ||
336.4.q.l.193.2 | 6 | 28.19 | even | 6 | |||
336.4.q.l.289.2 | 6 | 28.3 | even | 6 | |||
504.4.s.g.289.2 | 6 | 21.17 | even | 6 | |||
504.4.s.g.361.2 | 6 | 21.5 | even | 6 | |||
1176.4.a.x.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1176.4.a.y.1.2 | 3 | 7.6 | odd | 2 | |||
2352.4.a.ch.1.2 | 3 | 28.27 | even | 2 | |||
2352.4.a.cj.1.2 | 3 | 4.3 | odd | 2 |