Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(1,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1150.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.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: | \(67.8521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 68x^{2} - 111x + 342 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.74869\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 4.74869 | 0.913886 | 0.456943 | − | 0.889496i | \(-0.348944\pi\) | ||||
0.456943 | + | 0.889496i | \(0.348944\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 9.49738 | 0.646215 | ||||||||
\(7\) | −29.3684 | −1.58574 | −0.792872 | − | 0.609388i | \(-0.791415\pi\) | ||||
−0.792872 | + | 0.609388i | \(0.791415\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −4.44993 | −0.164812 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −38.1645 | −1.04609 | −0.523047 | − | 0.852304i | \(-0.675205\pi\) | ||||
−0.523047 | + | 0.852304i | \(0.675205\pi\) | |||||||
\(12\) | 18.9948 | 0.456943 | ||||||||
\(13\) | 22.5396 | 0.480874 | 0.240437 | − | 0.970665i | \(-0.422709\pi\) | ||||
0.240437 | + | 0.970665i | \(0.422709\pi\) | |||||||
\(14\) | −58.7368 | −1.12129 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 104.049 | 1.48444 | 0.742221 | − | 0.670155i | \(-0.233772\pi\) | ||||
0.742221 | + | 0.670155i | \(0.233772\pi\) | |||||||
\(18\) | −8.89986 | −0.116540 | ||||||||
\(19\) | 142.000 | 1.71458 | 0.857289 | − | 0.514835i | \(-0.172147\pi\) | ||||
0.857289 | + | 0.514835i | \(0.172147\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −139.461 | −1.44919 | ||||||||
\(22\) | −76.3291 | −0.739701 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 37.9895 | 0.323108 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 45.0792 | 0.340029 | ||||||||
\(27\) | −149.346 | −1.06451 | ||||||||
\(28\) | −117.474 | −0.792872 | ||||||||
\(29\) | 241.429 | 1.54594 | 0.772969 | − | 0.634444i | \(-0.218771\pi\) | ||||
0.772969 | + | 0.634444i | \(0.218771\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 99.2706 | 0.575146 | 0.287573 | − | 0.957759i | \(-0.407152\pi\) | ||||
0.287573 | + | 0.957759i | \(0.407152\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −181.232 | −0.956011 | ||||||||
\(34\) | 208.097 | 1.04966 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −17.7997 | −0.0824061 | ||||||||
\(37\) | −59.9452 | −0.266349 | −0.133175 | − | 0.991093i | \(-0.542517\pi\) | ||||
−0.133175 | + | 0.991093i | \(0.542517\pi\) | |||||||
\(38\) | 284.000 | 1.21239 | ||||||||
\(39\) | 107.034 | 0.439464 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 249.248 | 0.949414 | 0.474707 | − | 0.880144i | \(-0.342554\pi\) | ||||
0.474707 | + | 0.880144i | \(0.342554\pi\) | |||||||
\(42\) | −278.923 | −1.02473 | ||||||||
\(43\) | 163.863 | 0.581136 | 0.290568 | − | 0.956854i | \(-0.406156\pi\) | ||||
0.290568 | + | 0.956854i | \(0.406156\pi\) | |||||||
\(44\) | −152.658 | −0.523047 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 205.591 | 0.638052 | 0.319026 | − | 0.947746i | \(-0.396644\pi\) | ||||
0.319026 | + | 0.947746i | \(0.396644\pi\) | |||||||
\(48\) | 75.9791 | 0.228472 | ||||||||
\(49\) | 519.502 | 1.51458 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 494.095 | 1.35661 | ||||||||
\(52\) | 90.1584 | 0.240437 | ||||||||
\(53\) | −491.274 | −1.27324 | −0.636620 | − | 0.771178i | \(-0.719668\pi\) | ||||
−0.636620 | + | 0.771178i | \(0.719668\pi\) | |||||||
\(54\) | −298.692 | −0.752719 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −234.947 | −0.560645 | ||||||||
\(57\) | 674.313 | 1.56693 | ||||||||
\(58\) | 482.858 | 1.09314 | ||||||||
\(59\) | 433.734 | 0.957074 | 0.478537 | − | 0.878067i | \(-0.341167\pi\) | ||||
0.478537 | + | 0.878067i | \(0.341167\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 660.902 | 1.38721 | 0.693605 | − | 0.720355i | \(-0.256021\pi\) | ||||
0.693605 | + | 0.720355i | \(0.256021\pi\) | |||||||
\(62\) | 198.541 | 0.406690 | ||||||||
\(63\) | 130.687 | 0.261350 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −362.463 | −0.676002 | ||||||||
\(67\) | 323.564 | 0.589995 | 0.294997 | − | 0.955498i | \(-0.404681\pi\) | ||||
0.294997 | + | 0.955498i | \(0.404681\pi\) | |||||||
\(68\) | 416.195 | 0.742221 | ||||||||
\(69\) | 109.220 | 0.190558 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 893.243 | 1.49308 | 0.746538 | − | 0.665342i | \(-0.231714\pi\) | ||||
0.746538 | + | 0.665342i | \(0.231714\pi\) | |||||||
\(72\) | −35.5994 | −0.0582699 | ||||||||
\(73\) | −196.273 | −0.314685 | −0.157343 | − | 0.987544i | \(-0.550293\pi\) | ||||
−0.157343 | + | 0.987544i | \(0.550293\pi\) | |||||||
\(74\) | −119.890 | −0.188337 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 567.999 | 0.857289 | ||||||||
\(77\) | 1120.83 | 1.65884 | ||||||||
\(78\) | 214.067 | 0.310748 | ||||||||
\(79\) | −500.211 | −0.712381 | −0.356191 | − | 0.934413i | \(-0.615925\pi\) | ||||
−0.356191 | + | 0.934413i | \(0.615925\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −589.050 | −0.808025 | ||||||||
\(82\) | 498.496 | 0.671337 | ||||||||
\(83\) | −800.944 | −1.05922 | −0.529609 | − | 0.848242i | \(-0.677661\pi\) | ||||
−0.529609 | + | 0.848242i | \(0.677661\pi\) | |||||||
\(84\) | −557.846 | −0.724595 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 327.726 | 0.410925 | ||||||||
\(87\) | 1146.47 | 1.41281 | ||||||||
\(88\) | −305.316 | −0.369850 | ||||||||
\(89\) | −729.016 | −0.868264 | −0.434132 | − | 0.900849i | \(-0.642945\pi\) | ||||
−0.434132 | + | 0.900849i | \(0.642945\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −661.952 | −0.762543 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 471.405 | 0.525618 | ||||||||
\(94\) | 411.181 | 0.451171 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 151.958 | 0.161554 | ||||||||
\(97\) | −1139.96 | −1.19325 | −0.596626 | − | 0.802520i | \(-0.703492\pi\) | ||||
−0.596626 | + | 0.802520i | \(0.703492\pi\) | |||||||
\(98\) | 1039.00 | 1.07097 | ||||||||
\(99\) | 169.829 | 0.172409 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1669.38 | −1.64465 | −0.822326 | − | 0.569017i | \(-0.807324\pi\) | ||||
−0.822326 | + | 0.569017i | \(0.807324\pi\) | |||||||
\(102\) | 988.190 | 0.959269 | ||||||||
\(103\) | 1110.63 | 1.06246 | 0.531229 | − | 0.847228i | \(-0.321730\pi\) | ||||
0.531229 | + | 0.847228i | \(0.321730\pi\) | |||||||
\(104\) | 180.317 | 0.170015 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −982.549 | −0.900317 | ||||||||
\(107\) | −39.1892 | −0.0354071 | −0.0177036 | − | 0.999843i | \(-0.505636\pi\) | ||||
−0.0177036 | + | 0.999843i | \(0.505636\pi\) | |||||||
\(108\) | −597.384 | −0.532253 | ||||||||
\(109\) | 807.545 | 0.709622 | 0.354811 | − | 0.934938i | \(-0.384545\pi\) | ||||
0.354811 | + | 0.934938i | \(0.384545\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −284.661 | −0.243413 | ||||||||
\(112\) | −469.894 | −0.396436 | ||||||||
\(113\) | −1066.58 | −0.887923 | −0.443961 | − | 0.896046i | \(-0.646427\pi\) | ||||
−0.443961 | + | 0.896046i | \(0.646427\pi\) | |||||||
\(114\) | 1348.63 | 1.10799 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 965.715 | 0.772969 | ||||||||
\(117\) | −100.300 | −0.0792539 | ||||||||
\(118\) | 867.468 | 0.676753 | ||||||||
\(119\) | −3055.74 | −2.35395 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 125.532 | 0.0943139 | ||||||||
\(122\) | 1321.80 | 0.980906 | ||||||||
\(123\) | 1183.60 | 0.867657 | ||||||||
\(124\) | 397.082 | 0.287573 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 261.374 | 0.184802 | ||||||||
\(127\) | 641.707 | 0.448364 | 0.224182 | − | 0.974547i | \(-0.428029\pi\) | ||||
0.224182 | + | 0.974547i | \(0.428029\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 778.134 | 0.531092 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2389.92 | 1.59396 | 0.796979 | − | 0.604007i | \(-0.206430\pi\) | ||||
0.796979 | + | 0.604007i | \(0.206430\pi\) | |||||||
\(132\) | −724.926 | −0.478006 | ||||||||
\(133\) | −4170.31 | −2.71888 | ||||||||
\(134\) | 647.128 | 0.417189 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 832.390 | 0.524830 | ||||||||
\(137\) | −899.291 | −0.560814 | −0.280407 | − | 0.959881i | \(-0.590470\pi\) | ||||
−0.280407 | + | 0.959881i | \(0.590470\pi\) | |||||||
\(138\) | 218.440 | 0.134745 | ||||||||
\(139\) | 309.341 | 0.188762 | 0.0943811 | − | 0.995536i | \(-0.469913\pi\) | ||||
0.0943811 | + | 0.995536i | \(0.469913\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 976.286 | 0.583107 | ||||||||
\(142\) | 1786.49 | 1.05576 | ||||||||
\(143\) | −860.214 | −0.503040 | ||||||||
\(144\) | −71.1989 | −0.0412030 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −392.546 | −0.222516 | ||||||||
\(147\) | 2466.96 | 1.38416 | ||||||||
\(148\) | −239.781 | −0.133175 | ||||||||
\(149\) | 2560.87 | 1.40802 | 0.704010 | − | 0.710190i | \(-0.251391\pi\) | ||||
0.704010 | + | 0.710190i | \(0.251391\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2463.15 | −1.32747 | −0.663737 | − | 0.747966i | \(-0.731031\pi\) | ||||
−0.663737 | + | 0.747966i | \(0.731031\pi\) | |||||||
\(152\) | 1136.00 | 0.606195 | ||||||||
\(153\) | −463.009 | −0.244654 | ||||||||
\(154\) | 2241.66 | 1.17298 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 428.135 | 0.219732 | ||||||||
\(157\) | 566.720 | 0.288084 | 0.144042 | − | 0.989572i | \(-0.453990\pi\) | ||||
0.144042 | + | 0.989572i | \(0.453990\pi\) | |||||||
\(158\) | −1000.42 | −0.503730 | ||||||||
\(159\) | −2332.91 | −1.16360 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −675.473 | −0.330650 | ||||||||
\(162\) | −1178.10 | −0.571360 | ||||||||
\(163\) | −960.902 | −0.461740 | −0.230870 | − | 0.972985i | \(-0.574157\pi\) | ||||
−0.230870 | + | 0.972985i | \(0.574157\pi\) | |||||||
\(164\) | 996.992 | 0.474707 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1601.89 | −0.748980 | ||||||||
\(167\) | 4224.70 | 1.95759 | 0.978794 | − | 0.204847i | \(-0.0656696\pi\) | ||||
0.978794 | + | 0.204847i | \(0.0656696\pi\) | |||||||
\(168\) | −1115.69 | −0.512366 | ||||||||
\(169\) | −1688.97 | −0.768760 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −631.889 | −0.282583 | ||||||||
\(172\) | 655.451 | 0.290568 | ||||||||
\(173\) | −3448.98 | −1.51573 | −0.757865 | − | 0.652412i | \(-0.773757\pi\) | ||||
−0.757865 | + | 0.652412i | \(0.773757\pi\) | |||||||
\(174\) | 2292.94 | 0.999008 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −610.633 | −0.261524 | ||||||||
\(177\) | 2059.67 | 0.874657 | ||||||||
\(178\) | −1458.03 | −0.613955 | ||||||||
\(179\) | 1457.82 | 0.608728 | 0.304364 | − | 0.952556i | \(-0.401556\pi\) | ||||
0.304364 | + | 0.952556i | \(0.401556\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3634.97 | −1.49274 | −0.746368 | − | 0.665534i | \(-0.768204\pi\) | ||||
−0.746368 | + | 0.665534i | \(0.768204\pi\) | |||||||
\(182\) | −1323.90 | −0.539199 | ||||||||
\(183\) | 3138.42 | 1.26775 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 942.811 | 0.371668 | ||||||||
\(187\) | −3970.97 | −1.55287 | ||||||||
\(188\) | 822.362 | 0.319026 | ||||||||
\(189\) | 4386.05 | 1.68803 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 448.811 | 0.170025 | 0.0850127 | − | 0.996380i | \(-0.472907\pi\) | ||||
0.0850127 | + | 0.996380i | \(0.472907\pi\) | |||||||
\(192\) | 303.916 | 0.114236 | ||||||||
\(193\) | −4259.35 | −1.58857 | −0.794286 | − | 0.607544i | \(-0.792155\pi\) | ||||
−0.794286 | + | 0.607544i | \(0.792155\pi\) | |||||||
\(194\) | −2279.92 | −0.843756 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2078.01 | 0.757292 | ||||||||
\(197\) | 1767.37 | 0.639189 | 0.319594 | − | 0.947554i | \(-0.396453\pi\) | ||||
0.319594 | + | 0.947554i | \(0.396453\pi\) | |||||||
\(198\) | 339.659 | 0.121912 | ||||||||
\(199\) | 1004.29 | 0.357750 | 0.178875 | − | 0.983872i | \(-0.442754\pi\) | ||||
0.178875 | + | 0.983872i | \(0.442754\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1536.51 | 0.539188 | ||||||||
\(202\) | −3338.76 | −1.16294 | ||||||||
\(203\) | −7090.37 | −2.45146 | ||||||||
\(204\) | 1976.38 | 0.678305 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2221.25 | 0.751272 | ||||||||
\(207\) | −102.348 | −0.0343657 | ||||||||
\(208\) | 360.634 | 0.120218 | ||||||||
\(209\) | −5419.36 | −1.79361 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5395.17 | 1.76028 | 0.880140 | − | 0.474714i | \(-0.157449\pi\) | ||||
0.880140 | + | 0.474714i | \(0.157449\pi\) | |||||||
\(212\) | −1965.10 | −0.636620 | ||||||||
\(213\) | 4241.74 | 1.36450 | ||||||||
\(214\) | −78.3783 | −0.0250366 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1194.77 | −0.376360 | ||||||||
\(217\) | −2915.42 | −0.912034 | ||||||||
\(218\) | 1615.09 | 0.501779 | ||||||||
\(219\) | −932.041 | −0.287587 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2345.22 | 0.713830 | ||||||||
\(222\) | −569.322 | −0.172119 | ||||||||
\(223\) | 1504.79 | 0.451876 | 0.225938 | − | 0.974142i | \(-0.427455\pi\) | ||||
0.225938 | + | 0.974142i | \(0.427455\pi\) | |||||||
\(224\) | −939.788 | −0.280323 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2133.16 | −0.627856 | ||||||||
\(227\) | 1779.44 | 0.520288 | 0.260144 | − | 0.965570i | \(-0.416230\pi\) | ||||
0.260144 | + | 0.965570i | \(0.416230\pi\) | |||||||
\(228\) | 2697.25 | 0.783465 | ||||||||
\(229\) | 3976.16 | 1.14739 | 0.573694 | − | 0.819070i | \(-0.305510\pi\) | ||||
0.573694 | + | 0.819070i | \(0.305510\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5322.48 | 1.51599 | ||||||||
\(232\) | 1931.43 | 0.546572 | ||||||||
\(233\) | 2311.12 | 0.649815 | 0.324907 | − | 0.945746i | \(-0.394667\pi\) | ||||
0.324907 | + | 0.945746i | \(0.394667\pi\) | |||||||
\(234\) | −200.599 | −0.0560410 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1734.94 | 0.478537 | ||||||||
\(237\) | −2375.35 | −0.651035 | ||||||||
\(238\) | −6111.49 | −1.66449 | ||||||||
\(239\) | 824.267 | 0.223085 | 0.111543 | − | 0.993760i | \(-0.464421\pi\) | ||||
0.111543 | + | 0.993760i | \(0.464421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3641.83 | 0.973406 | 0.486703 | − | 0.873567i | \(-0.338199\pi\) | ||||
0.486703 | + | 0.873567i | \(0.338199\pi\) | |||||||
\(242\) | 251.064 | 0.0666900 | ||||||||
\(243\) | 1235.13 | 0.326063 | ||||||||
\(244\) | 2643.61 | 0.693605 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2367.20 | 0.613526 | ||||||||
\(247\) | 3200.62 | 0.824496 | ||||||||
\(248\) | 794.165 | 0.203345 | ||||||||
\(249\) | −3803.44 | −0.968004 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7767.51 | −1.95331 | −0.976655 | − | 0.214813i | \(-0.931086\pi\) | ||||
−0.976655 | + | 0.214813i | \(0.931086\pi\) | |||||||
\(252\) | 522.749 | 0.130675 | ||||||||
\(253\) | −877.784 | −0.218126 | ||||||||
\(254\) | 1283.41 | 0.317042 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1501.17 | 0.364359 | 0.182179 | − | 0.983265i | \(-0.441685\pi\) | ||||
0.182179 | + | 0.983265i | \(0.441685\pi\) | |||||||
\(258\) | 1556.27 | 0.375539 | ||||||||
\(259\) | 1760.49 | 0.422362 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1074.34 | −0.254789 | ||||||||
\(262\) | 4779.84 | 1.12710 | ||||||||
\(263\) | 5430.98 | 1.27334 | 0.636671 | − | 0.771136i | \(-0.280311\pi\) | ||||
0.636671 | + | 0.771136i | \(0.280311\pi\) | |||||||
\(264\) | −1449.85 | −0.338001 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8340.61 | −1.92254 | ||||||||
\(267\) | −3461.87 | −0.793494 | ||||||||
\(268\) | 1294.26 | 0.294997 | ||||||||
\(269\) | −5014.20 | −1.13651 | −0.568255 | − | 0.822852i | \(-0.692381\pi\) | ||||
−0.568255 | + | 0.822852i | \(0.692381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7215.54 | 1.61739 | 0.808695 | − | 0.588228i | \(-0.200174\pi\) | ||||
0.808695 | + | 0.588228i | \(0.200174\pi\) | |||||||
\(272\) | 1664.78 | 0.371111 | ||||||||
\(273\) | −3143.41 | −0.696877 | ||||||||
\(274\) | −1798.58 | −0.396556 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 436.880 | 0.0952792 | ||||||||
\(277\) | 7439.60 | 1.61373 | 0.806863 | − | 0.590738i | \(-0.201163\pi\) | ||||
0.806863 | + | 0.590738i | \(0.201163\pi\) | |||||||
\(278\) | 618.681 | 0.133475 | ||||||||
\(279\) | −441.747 | −0.0947910 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2605.59 | −0.553155 | −0.276578 | − | 0.960992i | \(-0.589200\pi\) | ||||
−0.276578 | + | 0.960992i | \(0.589200\pi\) | |||||||
\(282\) | 1952.57 | 0.412319 | ||||||||
\(283\) | 7162.57 | 1.50449 | 0.752245 | − | 0.658884i | \(-0.228971\pi\) | ||||
0.752245 | + | 0.658884i | \(0.228971\pi\) | |||||||
\(284\) | 3572.97 | 0.746538 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1720.43 | −0.355703 | ||||||||
\(287\) | −7320.01 | −1.50553 | ||||||||
\(288\) | −142.398 | −0.0291349 | ||||||||
\(289\) | 5913.13 | 1.20357 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5413.32 | −1.09050 | ||||||||
\(292\) | −785.093 | −0.157343 | ||||||||
\(293\) | −9310.55 | −1.85641 | −0.928205 | − | 0.372069i | \(-0.878649\pi\) | ||||
−0.928205 | + | 0.372069i | \(0.878649\pi\) | |||||||
\(294\) | 4933.91 | 0.978747 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −479.562 | −0.0941687 | ||||||||
\(297\) | 5699.72 | 1.11357 | ||||||||
\(298\) | 5121.74 | 0.995620 | ||||||||
\(299\) | 518.411 | 0.100269 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4812.39 | −0.921533 | ||||||||
\(302\) | −4926.31 | −0.938666 | ||||||||
\(303\) | −7927.38 | −1.50302 | ||||||||
\(304\) | 2272.00 | 0.428645 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −926.018 | −0.172997 | ||||||||
\(307\) | −3359.07 | −0.624470 | −0.312235 | − | 0.950005i | \(-0.601078\pi\) | ||||
−0.312235 | + | 0.950005i | \(0.601078\pi\) | |||||||
\(308\) | 4483.32 | 0.829419 | ||||||||
\(309\) | 5274.02 | 0.970966 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5509.20 | −1.00450 | −0.502248 | − | 0.864724i | \(-0.667493\pi\) | ||||
−0.502248 | + | 0.864724i | \(0.667493\pi\) | |||||||
\(312\) | 856.269 | 0.155374 | ||||||||
\(313\) | −2401.42 | −0.433661 | −0.216831 | − | 0.976209i | \(-0.569572\pi\) | ||||
−0.216831 | + | 0.976209i | \(0.569572\pi\) | |||||||
\(314\) | 1133.44 | 0.203706 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2000.84 | −0.356191 | ||||||||
\(317\) | 1057.36 | 0.187341 | 0.0936704 | − | 0.995603i | \(-0.470140\pi\) | ||||
0.0936704 | + | 0.995603i | \(0.470140\pi\) | |||||||
\(318\) | −4665.82 | −0.822787 | ||||||||
\(319\) | −9214.02 | −1.61720 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −186.097 | −0.0323581 | ||||||||
\(322\) | −1350.95 | −0.233805 | ||||||||
\(323\) | 14774.9 | 2.54519 | ||||||||
\(324\) | −2356.20 | −0.404012 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1921.80 | −0.326500 | ||||||||
\(327\) | 3834.78 | 0.648514 | ||||||||
\(328\) | 1993.98 | 0.335669 | ||||||||
\(329\) | −6037.86 | −1.01179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9680.21 | −1.60747 | −0.803735 | − | 0.594987i | \(-0.797157\pi\) | ||||
−0.803735 | + | 0.594987i | \(0.797157\pi\) | |||||||
\(332\) | −3203.78 | −0.529609 | ||||||||
\(333\) | 266.752 | 0.0438976 | ||||||||
\(334\) | 8449.40 | 1.38422 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2231.38 | −0.362297 | ||||||||
\(337\) | −467.694 | −0.0755991 | −0.0377996 | − | 0.999285i | \(-0.512035\pi\) | ||||
−0.0377996 | + | 0.999285i | \(0.512035\pi\) | |||||||
\(338\) | −3377.93 | −0.543596 | ||||||||
\(339\) | −5064.85 | −0.811460 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3788.62 | −0.601657 | ||||||||
\(342\) | −1263.78 | −0.199817 | ||||||||
\(343\) | −5183.59 | −0.815998 | ||||||||
\(344\) | 1310.90 | 0.205463 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6897.96 | −1.07178 | ||||||||
\(347\) | −3371.55 | −0.521597 | −0.260798 | − | 0.965393i | \(-0.583986\pi\) | ||||
−0.260798 | + | 0.965393i | \(0.583986\pi\) | |||||||
\(348\) | 4585.88 | 0.706406 | ||||||||
\(349\) | 10958.7 | 1.68082 | 0.840412 | − | 0.541947i | \(-0.182313\pi\) | ||||
0.840412 | + | 0.541947i | \(0.182313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3366.20 | −0.511893 | ||||||||
\(352\) | −1221.27 | −0.184925 | ||||||||
\(353\) | 1584.76 | 0.238947 | 0.119474 | − | 0.992837i | \(-0.461879\pi\) | ||||
0.119474 | + | 0.992837i | \(0.461879\pi\) | |||||||
\(354\) | 4119.34 | 0.618476 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2916.06 | −0.434132 | ||||||||
\(357\) | −14510.8 | −2.15124 | ||||||||
\(358\) | 2915.63 | 0.430436 | ||||||||
\(359\) | 5130.67 | 0.754280 | 0.377140 | − | 0.926156i | \(-0.376908\pi\) | ||||
0.377140 | + | 0.926156i | \(0.376908\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13304.9 | 1.93978 | ||||||||
\(362\) | −7269.94 | −1.05552 | ||||||||
\(363\) | 596.112 | 0.0861922 | ||||||||
\(364\) | −2647.81 | −0.381271 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6276.84 | 0.896437 | ||||||||
\(367\) | −2811.27 | −0.399856 | −0.199928 | − | 0.979811i | \(-0.564071\pi\) | ||||
−0.199928 | + | 0.979811i | \(0.564071\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | −1109.14 | −0.156475 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14427.9 | 2.01903 | ||||||||
\(372\) | 1885.62 | 0.262809 | ||||||||
\(373\) | 1952.42 | 0.271026 | 0.135513 | − | 0.990776i | \(-0.456732\pi\) | ||||
0.135513 | + | 0.990776i | \(0.456732\pi\) | |||||||
\(374\) | −7941.94 | −1.09804 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1644.72 | 0.225586 | ||||||||
\(377\) | 5441.71 | 0.743401 | ||||||||
\(378\) | 8772.10 | 1.19362 | ||||||||
\(379\) | 9609.27 | 1.30236 | 0.651181 | − | 0.758923i | \(-0.274274\pi\) | ||||
0.651181 | + | 0.758923i | \(0.274274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3047.27 | 0.409754 | ||||||||
\(382\) | 897.623 | 0.120226 | ||||||||
\(383\) | −5027.44 | −0.670732 | −0.335366 | − | 0.942088i | \(-0.608860\pi\) | ||||
−0.335366 | + | 0.942088i | \(0.608860\pi\) | |||||||
\(384\) | 607.833 | 0.0807769 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8518.70 | −1.12329 | ||||||||
\(387\) | −729.178 | −0.0957783 | ||||||||
\(388\) | −4559.84 | −0.596626 | ||||||||
\(389\) | 5892.29 | 0.767997 | 0.383999 | − | 0.923334i | \(-0.374547\pi\) | ||||
0.383999 | + | 0.923334i | \(0.374547\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2393.12 | 0.309528 | ||||||||
\(392\) | 4156.02 | 0.535486 | ||||||||
\(393\) | 11349.0 | 1.45670 | ||||||||
\(394\) | 3534.75 | 0.451975 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 679.318 | 0.0862046 | ||||||||
\(397\) | 2454.41 | 0.310285 | 0.155143 | − | 0.987892i | \(-0.450416\pi\) | ||||
0.155143 | + | 0.987892i | \(0.450416\pi\) | |||||||
\(398\) | 2008.58 | 0.252967 | ||||||||
\(399\) | −19803.5 | −2.48475 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9458.39 | 1.17788 | 0.588939 | − | 0.808177i | \(-0.299546\pi\) | ||||
0.588939 | + | 0.808177i | \(0.299546\pi\) | |||||||
\(402\) | 3073.01 | 0.381264 | ||||||||
\(403\) | 2237.52 | 0.276573 | ||||||||
\(404\) | −6677.53 | −0.822326 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14180.7 | −1.73345 | ||||||||
\(407\) | 2287.78 | 0.278627 | ||||||||
\(408\) | 3952.76 | 0.479634 | ||||||||
\(409\) | −5857.25 | −0.708123 | −0.354062 | − | 0.935222i | \(-0.615200\pi\) | ||||
−0.354062 | + | 0.935222i | \(0.615200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4270.45 | −0.512521 | ||||||||
\(412\) | 4442.51 | 0.531229 | ||||||||
\(413\) | −12738.1 | −1.51767 | ||||||||
\(414\) | −204.697 | −0.0243002 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 721.267 | 0.0850073 | ||||||||
\(417\) | 1468.96 | 0.172507 | ||||||||
\(418\) | −10838.7 | −1.26827 | ||||||||
\(419\) | −5252.61 | −0.612426 | −0.306213 | − | 0.951963i | \(-0.599062\pi\) | ||||
−0.306213 | + | 0.951963i | \(0.599062\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −203.517 | −0.0235602 | −0.0117801 | − | 0.999931i | \(-0.503750\pi\) | ||||
−0.0117801 | + | 0.999931i | \(0.503750\pi\) | |||||||
\(422\) | 10790.3 | 1.24471 | ||||||||
\(423\) | −914.863 | −0.105159 | ||||||||
\(424\) | −3930.20 | −0.450158 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8483.47 | 0.964849 | ||||||||
\(427\) | −19409.6 | −2.19976 | ||||||||
\(428\) | −156.757 | −0.0177036 | ||||||||
\(429\) | −4084.89 | −0.459721 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3107.72 | 0.347317 | 0.173659 | − | 0.984806i | \(-0.444441\pi\) | ||||
0.173659 | + | 0.984806i | \(0.444441\pi\) | |||||||
\(432\) | −2389.54 | −0.266126 | ||||||||
\(433\) | 5713.46 | 0.634114 | 0.317057 | − | 0.948406i | \(-0.397305\pi\) | ||||
0.317057 | + | 0.948406i | \(0.397305\pi\) | |||||||
\(434\) | −5830.83 | −0.644905 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3230.18 | 0.354811 | ||||||||
\(437\) | 3266.00 | 0.357514 | ||||||||
\(438\) | −1864.08 | −0.203354 | ||||||||
\(439\) | −4587.14 | −0.498706 | −0.249353 | − | 0.968413i | \(-0.580218\pi\) | ||||
−0.249353 | + | 0.968413i | \(0.580218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2311.75 | −0.249622 | ||||||||
\(442\) | 4690.43 | 0.504754 | ||||||||
\(443\) | −5268.01 | −0.564990 | −0.282495 | − | 0.959269i | \(-0.591162\pi\) | ||||
−0.282495 | + | 0.959269i | \(0.591162\pi\) | |||||||
\(444\) | −1138.64 | −0.121707 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3009.58 | 0.319525 | ||||||||
\(447\) | 12160.8 | 1.28677 | ||||||||
\(448\) | −1879.58 | −0.198218 | ||||||||
\(449\) | 16866.8 | 1.77282 | 0.886409 | − | 0.462902i | \(-0.153192\pi\) | ||||
0.886409 | + | 0.462902i | \(0.153192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9512.43 | −0.993177 | ||||||||
\(452\) | −4266.31 | −0.443961 | ||||||||
\(453\) | −11696.8 | −1.21316 | ||||||||
\(454\) | 3558.87 | 0.367899 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5394.51 | 0.553993 | ||||||||
\(457\) | −9124.25 | −0.933948 | −0.466974 | − | 0.884271i | \(-0.654656\pi\) | ||||
−0.466974 | + | 0.884271i | \(0.654656\pi\) | |||||||
\(458\) | 7952.31 | 0.811326 | ||||||||
\(459\) | −15539.3 | −1.58020 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6011.92 | 0.607382 | 0.303691 | − | 0.952771i | \(-0.401781\pi\) | ||||
0.303691 | + | 0.952771i | \(0.401781\pi\) | |||||||
\(462\) | 10645.0 | 1.07197 | ||||||||
\(463\) | 8584.09 | 0.861634 | 0.430817 | − | 0.902439i | \(-0.358225\pi\) | ||||
0.430817 | + | 0.902439i | \(0.358225\pi\) | |||||||
\(464\) | 3862.86 | 0.386484 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4622.25 | 0.459488 | ||||||||
\(467\) | −3954.09 | −0.391806 | −0.195903 | − | 0.980623i | \(-0.562764\pi\) | ||||
−0.195903 | + | 0.980623i | \(0.562764\pi\) | |||||||
\(468\) | −401.198 | −0.0396269 | ||||||||
\(469\) | −9502.56 | −0.935581 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2691.18 | 0.263276 | ||||||||
\(472\) | 3469.87 | 0.338377 | ||||||||
\(473\) | −6253.75 | −0.607923 | ||||||||
\(474\) | −4750.69 | −0.460351 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12223.0 | −1.17697 | ||||||||
\(477\) | 2186.14 | 0.209845 | ||||||||
\(478\) | 1648.53 | 0.157745 | ||||||||
\(479\) | −95.3377 | −0.00909413 | −0.00454707 | − | 0.999990i | \(-0.501447\pi\) | ||||
−0.00454707 | + | 0.999990i | \(0.501447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1351.14 | −0.128080 | ||||||||
\(482\) | 7283.66 | 0.688302 | ||||||||
\(483\) | −3207.61 | −0.302177 | ||||||||
\(484\) | 502.127 | 0.0471570 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2470.25 | 0.230561 | ||||||||
\(487\) | −13915.2 | −1.29478 | −0.647391 | − | 0.762158i | \(-0.724140\pi\) | ||||
−0.647391 | + | 0.762158i | \(0.724140\pi\) | |||||||
\(488\) | 5287.22 | 0.490453 | ||||||||
\(489\) | −4563.03 | −0.421978 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6291.33 | 0.578256 | 0.289128 | − | 0.957290i | \(-0.406635\pi\) | ||||
0.289128 | + | 0.957290i | \(0.406635\pi\) | |||||||
\(492\) | 4734.41 | 0.433828 | ||||||||
\(493\) | 25120.3 | 2.29486 | ||||||||
\(494\) | 6401.24 | 0.583007 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1588.33 | 0.143786 | ||||||||
\(497\) | −26233.1 | −2.36764 | ||||||||
\(498\) | −7606.87 | −0.684482 | ||||||||
\(499\) | −638.332 | −0.0572658 | −0.0286329 | − | 0.999590i | \(-0.509115\pi\) | ||||
−0.0286329 | + | 0.999590i | \(0.509115\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20061.8 | 1.78901 | ||||||||
\(502\) | −15535.0 | −1.38120 | ||||||||
\(503\) | −15063.4 | −1.33527 | −0.667637 | − | 0.744487i | \(-0.732694\pi\) | ||||
−0.667637 | + | 0.744487i | \(0.732694\pi\) | |||||||
\(504\) | 1045.50 | 0.0924011 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1755.57 | −0.154238 | ||||||||
\(507\) | −8020.38 | −0.702559 | ||||||||
\(508\) | 2566.83 | 0.224182 | ||||||||
\(509\) | −13623.1 | −1.18631 | −0.593157 | − | 0.805087i | \(-0.702119\pi\) | ||||
−0.593157 | + | 0.805087i | \(0.702119\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5764.23 | 0.499010 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −21207.1 | −1.82518 | ||||||||
\(514\) | 3002.33 | 0.257640 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3112.54 | 0.265546 | ||||||||
\(517\) | −7846.27 | −0.667463 | ||||||||
\(518\) | 3520.99 | 0.298655 | ||||||||
\(519\) | −16378.2 | −1.38520 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21659.4 | −1.82133 | −0.910666 | − | 0.413143i | \(-0.864431\pi\) | ||||
−0.910666 | + | 0.413143i | \(0.864431\pi\) | |||||||
\(522\) | −2148.68 | −0.180163 | ||||||||
\(523\) | 3813.85 | 0.318868 | 0.159434 | − | 0.987209i | \(-0.449033\pi\) | ||||
0.159434 | + | 0.987209i | \(0.449033\pi\) | |||||||
\(524\) | 9559.69 | 0.796979 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10862.0 | 0.900388 | ||||||||
\(527\) | 10329.0 | 0.853771 | ||||||||
\(528\) | −2899.71 | −0.239003 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1930.09 | −0.157737 | ||||||||
\(532\) | −16681.2 | −1.35944 | ||||||||
\(533\) | 5617.95 | 0.456549 | ||||||||
\(534\) | −6923.74 | −0.561085 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2588.51 | 0.208595 | ||||||||
\(537\) | 6922.72 | 0.556308 | ||||||||
\(538\) | −10028.4 | −0.803634 | ||||||||
\(539\) | −19826.6 | −1.58440 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9727.32 | 0.773031 | 0.386516 | − | 0.922283i | \(-0.373679\pi\) | ||||
0.386516 | + | 0.922283i | \(0.373679\pi\) | |||||||
\(542\) | 14431.1 | 1.14367 | ||||||||
\(543\) | −17261.3 | −1.36419 | ||||||||
\(544\) | 3329.56 | 0.262415 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6286.81 | −0.492767 | ||||||||
\(547\) | −782.647 | −0.0611766 | −0.0305883 | − | 0.999532i | \(-0.509738\pi\) | ||||
−0.0305883 | + | 0.999532i | \(0.509738\pi\) | |||||||
\(548\) | −3597.16 | −0.280407 | ||||||||
\(549\) | −2940.97 | −0.228629 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34282.8 | 2.65063 | ||||||||
\(552\) | 873.759 | 0.0673726 | ||||||||
\(553\) | 14690.4 | 1.12965 | ||||||||
\(554\) | 14879.2 | 1.14108 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1237.36 | 0.0943811 | ||||||||
\(557\) | −3472.87 | −0.264184 | −0.132092 | − | 0.991237i | \(-0.542169\pi\) | ||||
−0.132092 | + | 0.991237i | \(0.542169\pi\) | |||||||
\(558\) | −883.494 | −0.0670274 | ||||||||
\(559\) | 3693.40 | 0.279453 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18856.9 | −1.41914 | ||||||||
\(562\) | −5211.18 | −0.391140 | ||||||||
\(563\) | −7544.75 | −0.564784 | −0.282392 | − | 0.959299i | \(-0.591128\pi\) | ||||
−0.282392 | + | 0.959299i | \(0.591128\pi\) | |||||||
\(564\) | 3905.14 | 0.291554 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14325.1 | 1.06383 | ||||||||
\(567\) | 17299.5 | 1.28132 | ||||||||
\(568\) | 7145.94 | 0.527882 | ||||||||
\(569\) | 13222.5 | 0.974193 | 0.487096 | − | 0.873348i | \(-0.338056\pi\) | ||||
0.487096 | + | 0.873348i | \(0.338056\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4069.49 | 0.298254 | 0.149127 | − | 0.988818i | \(-0.452354\pi\) | ||||
0.149127 | + | 0.988818i | \(0.452354\pi\) | |||||||
\(572\) | −3440.85 | −0.251520 | ||||||||
\(573\) | 2131.27 | 0.155384 | ||||||||
\(574\) | −14640.0 | −1.06457 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −284.795 | −0.0206015 | ||||||||
\(577\) | −846.627 | −0.0610841 | −0.0305421 | − | 0.999533i | \(-0.509723\pi\) | ||||
−0.0305421 | + | 0.999533i | \(0.509723\pi\) | |||||||
\(578\) | 11826.3 | 0.851051 | ||||||||
\(579\) | −20226.3 | −1.45177 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23522.4 | 1.67965 | ||||||||
\(582\) | −10826.6 | −0.771097 | ||||||||
\(583\) | 18749.3 | 1.33193 | ||||||||
\(584\) | −1570.19 | −0.111258 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18621.1 | −1.31268 | ||||||||
\(587\) | −4702.77 | −0.330672 | −0.165336 | − | 0.986237i | \(-0.552871\pi\) | ||||
−0.165336 | + | 0.986237i | \(0.552871\pi\) | |||||||
\(588\) | 9867.82 | 0.692079 | ||||||||
\(589\) | 14096.4 | 0.986133 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8392.71 | 0.584146 | ||||||||
\(592\) | −959.123 | −0.0665874 | ||||||||
\(593\) | 14016.5 | 0.970640 | 0.485320 | − | 0.874337i | \(-0.338703\pi\) | ||||
0.485320 | + | 0.874337i | \(0.338703\pi\) | |||||||
\(594\) | 11399.4 | 0.787415 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10243.5 | 0.704010 | ||||||||
\(597\) | 4769.07 | 0.326943 | ||||||||
\(598\) | 1036.82 | 0.0709010 | ||||||||
\(599\) | 12885.0 | 0.878910 | 0.439455 | − | 0.898265i | \(-0.355172\pi\) | ||||
0.439455 | + | 0.898265i | \(0.355172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4753.41 | −0.322622 | −0.161311 | − | 0.986904i | \(-0.551572\pi\) | ||||
−0.161311 | + | 0.986904i | \(0.551572\pi\) | |||||||
\(602\) | −9624.77 | −0.651622 | ||||||||
\(603\) | −1439.84 | −0.0972383 | ||||||||
\(604\) | −9852.61 | −0.663737 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15854.8 | −1.06280 | ||||||||
\(607\) | 6800.06 | 0.454705 | 0.227352 | − | 0.973813i | \(-0.426993\pi\) | ||||
0.227352 | + | 0.973813i | \(0.426993\pi\) | |||||||
\(608\) | 4543.99 | 0.303097 | ||||||||
\(609\) | −33670.0 | −2.24036 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4633.93 | 0.306823 | ||||||||
\(612\) | −1852.04 | −0.122327 | ||||||||
\(613\) | −20842.3 | −1.37327 | −0.686634 | − | 0.727003i | \(-0.740913\pi\) | ||||
−0.686634 | + | 0.727003i | \(0.740913\pi\) | |||||||
\(614\) | −6718.14 | −0.441567 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8966.65 | 0.586488 | ||||||||
\(617\) | −18917.7 | −1.23436 | −0.617179 | − | 0.786823i | \(-0.711724\pi\) | ||||
−0.617179 | + | 0.786823i | \(0.711724\pi\) | |||||||
\(618\) | 10548.0 | 0.686577 | ||||||||
\(619\) | −28044.8 | −1.82103 | −0.910513 | − | 0.413480i | \(-0.864313\pi\) | ||||
−0.910513 | + | 0.413480i | \(0.864313\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3434.96 | −0.221965 | ||||||||
\(622\) | −11018.4 | −0.710285 | ||||||||
\(623\) | 21410.0 | 1.37684 | ||||||||
\(624\) | 1712.54 | 0.109866 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4802.83 | −0.306645 | ||||||||
\(627\) | −25734.9 | −1.63916 | ||||||||
\(628\) | 2266.88 | 0.144042 | ||||||||
\(629\) | −6237.22 | −0.395380 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25796.2 | −1.62746 | −0.813732 | − | 0.581241i | \(-0.802567\pi\) | ||||
−0.813732 | + | 0.581241i | \(0.802567\pi\) | |||||||
\(632\) | −4001.69 | −0.251865 | ||||||||
\(633\) | 25620.0 | 1.60870 | ||||||||
\(634\) | 2114.71 | 0.132470 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9331.64 | −0.581798 | ||||||||
\(637\) | 11709.4 | 0.728324 | ||||||||
\(638\) | −18428.0 | −1.14353 | ||||||||
\(639\) | −3974.87 | −0.246077 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26482.3 | −1.63181 | −0.815903 | − | 0.578188i | \(-0.803760\pi\) | ||||
−0.815903 | + | 0.578188i | \(0.803760\pi\) | |||||||
\(642\) | −372.195 | −0.0228806 | ||||||||
\(643\) | −30458.1 | −1.86804 | −0.934020 | − | 0.357219i | \(-0.883725\pi\) | ||||
−0.934020 | + | 0.357219i | \(0.883725\pi\) | |||||||
\(644\) | −2701.89 | −0.165325 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 29549.8 | 1.79972 | ||||||||
\(647\) | 6746.24 | 0.409926 | 0.204963 | − | 0.978770i | \(-0.434293\pi\) | ||||
0.204963 | + | 0.978770i | \(0.434293\pi\) | |||||||
\(648\) | −4712.40 | −0.285680 | ||||||||
\(649\) | −16553.3 | −1.00119 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13844.4 | −0.833495 | ||||||||
\(652\) | −3843.61 | −0.230870 | ||||||||
\(653\) | −12976.2 | −0.777640 | −0.388820 | − | 0.921314i | \(-0.627117\pi\) | ||||
−0.388820 | + | 0.921314i | \(0.627117\pi\) | |||||||
\(654\) | 7669.57 | 0.458569 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3987.97 | 0.237354 | ||||||||
\(657\) | 873.401 | 0.0518640 | ||||||||
\(658\) | −12075.7 | −0.715442 | ||||||||
\(659\) | −6538.56 | −0.386504 | −0.193252 | − | 0.981149i | \(-0.561903\pi\) | ||||
−0.193252 | + | 0.981149i | \(0.561903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25177.1 | −1.48151 | −0.740753 | − | 0.671777i | \(-0.765531\pi\) | ||||
−0.740753 | + | 0.671777i | \(0.765531\pi\) | |||||||
\(662\) | −19360.4 | −1.13665 | ||||||||
\(663\) | 11136.7 | 0.652359 | ||||||||
\(664\) | −6407.55 | −0.374490 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 533.504 | 0.0310403 | ||||||||
\(667\) | 5552.86 | 0.322350 | ||||||||
\(668\) | 16898.8 | 0.978794 | ||||||||
\(669\) | 7145.79 | 0.412963 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25223.0 | −1.45115 | ||||||||
\(672\) | −4462.77 | −0.256183 | ||||||||
\(673\) | −18339.3 | −1.05041 | −0.525207 | − | 0.850975i | \(-0.676012\pi\) | ||||
−0.525207 | + | 0.850975i | \(0.676012\pi\) | |||||||
\(674\) | −935.388 | −0.0534567 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6755.86 | −0.384380 | ||||||||
\(677\) | −31876.9 | −1.80965 | −0.904823 | − | 0.425789i | \(-0.859997\pi\) | ||||
−0.904823 | + | 0.425789i | \(0.859997\pi\) | |||||||
\(678\) | −10129.7 | −0.573789 | ||||||||
\(679\) | 33478.8 | 1.89219 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8450.00 | 0.475484 | ||||||||
\(682\) | −7577.23 | −0.425436 | ||||||||
\(683\) | 28843.7 | 1.61592 | 0.807959 | − | 0.589239i | \(-0.200572\pi\) | ||||
0.807959 | + | 0.589239i | \(0.200572\pi\) | |||||||
\(684\) | −2527.56 | −0.141292 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10367.2 | −0.576998 | ||||||||
\(687\) | 18881.5 | 1.04858 | ||||||||
\(688\) | 2621.80 | 0.145284 | ||||||||
\(689\) | −11073.1 | −0.612268 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18327.7 | −1.00900 | −0.504499 | − | 0.863413i | \(-0.668323\pi\) | ||||
−0.504499 | + | 0.863413i | \(0.668323\pi\) | |||||||
\(692\) | −13795.9 | −0.757865 | ||||||||
\(693\) | −4987.62 | −0.273397 | ||||||||
\(694\) | −6743.09 | −0.368825 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9171.77 | 0.499504 | ||||||||
\(697\) | 25933.9 | 1.40935 | ||||||||
\(698\) | 21917.5 | 1.18852 | ||||||||
\(699\) | 10974.8 | 0.593857 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8329.48 | −0.448788 | −0.224394 | − | 0.974499i | \(-0.572040\pi\) | ||||
−0.224394 | + | 0.974499i | \(0.572040\pi\) | |||||||
\(702\) | −6732.40 | −0.361963 | ||||||||
\(703\) | −8512.20 | −0.456677 | ||||||||
\(704\) | −2442.53 | −0.130762 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3169.52 | 0.168961 | ||||||||
\(707\) | 49027.1 | 2.60800 | ||||||||
\(708\) | 8238.68 | 0.437328 | ||||||||
\(709\) | −6169.85 | −0.326818 | −0.163409 | − | 0.986558i | \(-0.552249\pi\) | ||||
−0.163409 | + | 0.986558i | \(0.552249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2225.90 | 0.117409 | ||||||||
\(712\) | −5832.12 | −0.306978 | ||||||||
\(713\) | 2283.22 | 0.119926 | ||||||||
\(714\) | −29021.6 | −1.52115 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5831.27 | 0.304364 | ||||||||
\(717\) | 3914.19 | 0.203875 | ||||||||
\(718\) | 10261.3 | 0.533356 | ||||||||
\(719\) | 28740.8 | 1.49075 | 0.745377 | − | 0.666644i | \(-0.232270\pi\) | ||||
0.745377 | + | 0.666644i | \(0.232270\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32617.3 | −1.68479 | ||||||||
\(722\) | 26609.9 | 1.37163 | ||||||||
\(723\) | 17293.9 | 0.889583 | ||||||||
\(724\) | −14539.9 | −0.746368 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1192.22 | 0.0609471 | ||||||||
\(727\) | −11174.0 | −0.570041 | −0.285021 | − | 0.958521i | \(-0.592000\pi\) | ||||
−0.285021 | + | 0.958521i | \(0.592000\pi\) | |||||||
\(728\) | −5295.62 | −0.269600 | ||||||||
\(729\) | 21769.6 | 1.10601 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17049.7 | 0.862663 | ||||||||
\(732\) | 12553.7 | 0.633876 | ||||||||
\(733\) | 23560.7 | 1.18722 | 0.593612 | − | 0.804751i | \(-0.297701\pi\) | ||||
0.593612 | + | 0.804751i | \(0.297701\pi\) | |||||||
\(734\) | −5622.54 | −0.282741 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −12348.7 | −0.617191 | ||||||||
\(738\) | −2218.27 | −0.110645 | ||||||||
\(739\) | 22713.6 | 1.13063 | 0.565313 | − | 0.824877i | \(-0.308755\pi\) | ||||
0.565313 | + | 0.824877i | \(0.308755\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15198.8 | 0.753495 | ||||||||
\(742\) | 28855.9 | 1.42767 | ||||||||
\(743\) | 15882.7 | 0.784224 | 0.392112 | − | 0.919917i | \(-0.371745\pi\) | ||||
0.392112 | + | 0.919917i | \(0.371745\pi\) | |||||||
\(744\) | 3771.24 | 0.185834 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3904.84 | 0.191644 | ||||||||
\(747\) | 3564.14 | 0.174572 | ||||||||
\(748\) | −15883.9 | −0.776433 | ||||||||
\(749\) | 1150.92 | 0.0561466 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30250.6 | −1.46985 | −0.734927 | − | 0.678146i | \(-0.762784\pi\) | ||||
−0.734927 | + | 0.678146i | \(0.762784\pi\) | |||||||
\(752\) | 3289.45 | 0.159513 | ||||||||
\(753\) | −36885.5 | −1.78510 | ||||||||
\(754\) | 10883.4 | 0.525664 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 17544.2 | 0.844017 | ||||||||
\(757\) | 9611.05 | 0.461453 | 0.230726 | − | 0.973019i | \(-0.425890\pi\) | ||||
0.230726 | + | 0.973019i | \(0.425890\pi\) | |||||||
\(758\) | 19218.5 | 0.920908 | ||||||||
\(759\) | −4168.33 | −0.199342 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5892.64 | 0.280694 | 0.140347 | − | 0.990102i | \(-0.455178\pi\) | ||||
0.140347 | + | 0.990102i | \(0.455178\pi\) | |||||||
\(762\) | 6094.54 | 0.289740 | ||||||||
\(763\) | −23716.3 | −1.12528 | ||||||||
\(764\) | 1795.25 | 0.0850127 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10054.9 | −0.474279 | ||||||||
\(767\) | 9776.19 | 0.460232 | ||||||||
\(768\) | 1215.67 | 0.0571179 | ||||||||
\(769\) | 1683.72 | 0.0789553 | 0.0394777 | − | 0.999220i | \(-0.487431\pi\) | ||||
0.0394777 | + | 0.999220i | \(0.487431\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7128.57 | 0.332982 | ||||||||
\(772\) | −17037.4 | −0.794286 | ||||||||
\(773\) | −19880.8 | −0.925048 | −0.462524 | − | 0.886607i | \(-0.653056\pi\) | ||||
−0.462524 | + | 0.886607i | \(0.653056\pi\) | |||||||
\(774\) | −1458.36 | −0.0677255 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9119.68 | −0.421878 | ||||||||
\(777\) | 8360.04 | 0.385991 | ||||||||
\(778\) | 11784.6 | 0.543056 | ||||||||
\(779\) | 35393.2 | 1.62785 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34090.2 | −1.56190 | ||||||||
\(782\) | 4786.24 | 0.218869 | ||||||||
\(783\) | −36056.4 | −1.64566 | ||||||||
\(784\) | 8312.04 | 0.378646 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 22698.0 | 1.03004 | ||||||||
\(787\) | 7622.64 | 0.345258 | 0.172629 | − | 0.984987i | \(-0.444774\pi\) | ||||
0.172629 | + | 0.984987i | \(0.444774\pi\) | |||||||
\(788\) | 7069.50 | 0.319594 | ||||||||
\(789\) | 25790.1 | 1.16369 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31323.7 | 1.40802 | ||||||||
\(792\) | 1358.64 | 0.0609558 | ||||||||
\(793\) | 14896.5 | 0.667074 | ||||||||
\(794\) | 4908.82 | 0.219405 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4017.16 | 0.178875 | ||||||||
\(797\) | 22380.9 | 0.994693 | 0.497347 | − | 0.867552i | \(-0.334308\pi\) | ||||
0.497347 | + | 0.867552i | \(0.334308\pi\) | |||||||
\(798\) | −39607.0 | −1.75698 | ||||||||
\(799\) | 21391.4 | 0.947152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3244.07 | 0.143100 | ||||||||
\(802\) | 18916.8 | 0.832886 | ||||||||
\(803\) | 7490.67 | 0.329191 | ||||||||
\(804\) | 6146.03 | 0.269594 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4475.04 | 0.195566 | ||||||||
\(807\) | −23810.9 | −1.03864 | ||||||||
\(808\) | −13355.1 | −0.581472 | ||||||||
\(809\) | 8117.18 | 0.352762 | 0.176381 | − | 0.984322i | \(-0.443561\pi\) | ||||
0.176381 | + | 0.984322i | \(0.443561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7221.05 | 0.312658 | 0.156329 | − | 0.987705i | \(-0.450034\pi\) | ||||
0.156329 | + | 0.987705i | \(0.450034\pi\) | |||||||
\(812\) | −28361.5 | −1.22573 | ||||||||
\(813\) | 34264.4 | 1.47811 | ||||||||
\(814\) | 4575.56 | 0.197019 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7905.52 | 0.339153 | ||||||||
\(817\) | 23268.5 | 0.996403 | ||||||||
\(818\) | −11714.5 | −0.500719 | ||||||||
\(819\) | 2945.64 | 0.125676 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34803.3 | 1.47947 | 0.739735 | − | 0.672899i | \(-0.234951\pi\) | ||||
0.739735 | + | 0.672899i | \(0.234951\pi\) | |||||||
\(822\) | −8540.91 | −0.362407 | ||||||||
\(823\) | −490.883 | −0.0207911 | −0.0103956 | − | 0.999946i | \(-0.503309\pi\) | ||||
−0.0103956 | + | 0.999946i | \(0.503309\pi\) | |||||||
\(824\) | 8885.01 | 0.375636 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25476.1 | −1.07316 | ||||||||
\(827\) | −30952.0 | −1.30146 | −0.650729 | − | 0.759310i | \(-0.725537\pi\) | ||||
−0.650729 | + | 0.759310i | \(0.725537\pi\) | |||||||
\(828\) | −409.393 | −0.0171829 | ||||||||
\(829\) | 8587.63 | 0.359784 | 0.179892 | − | 0.983686i | \(-0.442425\pi\) | ||||
0.179892 | + | 0.983686i | \(0.442425\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35328.4 | 1.47476 | ||||||||
\(832\) | 1442.53 | 0.0601092 | ||||||||
\(833\) | 54053.5 | 2.24831 | ||||||||
\(834\) | 2937.93 | 0.121981 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −21677.4 | −0.896806 | ||||||||
\(837\) | −14825.7 | −0.612246 | ||||||||
\(838\) | −10505.2 | −0.433051 | ||||||||
\(839\) | 3077.94 | 0.126653 | 0.0633267 | − | 0.997993i | \(-0.479829\pi\) | ||||
0.0633267 | + | 0.997993i | \(0.479829\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33898.9 | 1.38992 | ||||||||
\(842\) | −407.035 | −0.0166596 | ||||||||
\(843\) | −12373.2 | −0.505521 | ||||||||
\(844\) | 21580.7 | 0.880140 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1829.73 | −0.0743585 | ||||||||
\(847\) | −3686.67 | −0.149558 | ||||||||
\(848\) | −7860.39 | −0.318310 | ||||||||
\(849\) | 34012.8 | 1.37493 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1378.74 | −0.0555377 | ||||||||
\(852\) | 16966.9 | 0.682251 | ||||||||
\(853\) | 9193.14 | 0.369012 | 0.184506 | − | 0.982831i | \(-0.440932\pi\) | ||||
0.184506 | + | 0.982831i | \(0.440932\pi\) | |||||||
\(854\) | −38819.3 | −1.55547 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −313.513 | −0.0125183 | ||||||||
\(857\) | −21445.8 | −0.854813 | −0.427407 | − | 0.904059i | \(-0.640573\pi\) | ||||
−0.427407 | + | 0.904059i | \(0.640573\pi\) | |||||||
\(858\) | −8169.78 | −0.325072 | ||||||||
\(859\) | −40276.7 | −1.59979 | −0.799897 | − | 0.600137i | \(-0.795113\pi\) | ||||
−0.799897 | + | 0.600137i | \(0.795113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34760.5 | −1.37588 | ||||||||
\(862\) | 6215.44 | 0.245590 | ||||||||
\(863\) | −43713.4 | −1.72424 | −0.862120 | − | 0.506703i | \(-0.830864\pi\) | ||||
−0.862120 | + | 0.506703i | \(0.830864\pi\) | |||||||
\(864\) | −4779.07 | −0.188180 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11426.9 | 0.448386 | ||||||||
\(867\) | 28079.6 | 1.09992 | ||||||||
\(868\) | −11661.7 | −0.456017 | ||||||||
\(869\) | 19090.3 | 0.745218 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7293.01 | 0.283713 | ||||||||
\(872\) | 6460.36 | 0.250889 | ||||||||
\(873\) | 5072.74 | 0.196662 | ||||||||
\(874\) | 6531.99 | 0.252801 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3728.16 | −0.143793 | ||||||||
\(877\) | −24740.5 | −0.952596 | −0.476298 | − | 0.879284i | \(-0.658022\pi\) | ||||
−0.476298 | + | 0.879284i | \(0.658022\pi\) | |||||||
\(878\) | −9174.27 | −0.352639 | ||||||||
\(879\) | −44212.9 | −1.69655 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44027.2 | −1.68367 | −0.841835 | − | 0.539735i | \(-0.818524\pi\) | ||||
−0.841835 | + | 0.539735i | \(0.818524\pi\) | |||||||
\(882\) | −4623.50 | −0.176509 | ||||||||
\(883\) | −30245.0 | −1.15269 | −0.576344 | − | 0.817207i | \(-0.695521\pi\) | ||||
−0.576344 | + | 0.817207i | \(0.695521\pi\) | |||||||
\(884\) | 9380.87 | 0.356915 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10536.0 | −0.399509 | ||||||||
\(887\) | 7317.82 | 0.277010 | 0.138505 | − | 0.990362i | \(-0.455770\pi\) | ||||
0.138505 | + | 0.990362i | \(0.455770\pi\) | |||||||
\(888\) | −2277.29 | −0.0860595 | ||||||||
\(889\) | −18845.9 | −0.710991 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22480.8 | 0.845270 | ||||||||
\(892\) | 6019.17 | 0.225938 | ||||||||
\(893\) | 29193.8 | 1.09399 | ||||||||
\(894\) | 24321.6 | 0.909883 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3759.15 | −0.140161 | ||||||||
\(897\) | 2461.77 | 0.0916346 | ||||||||
\(898\) | 33733.7 | 1.25357 | ||||||||
\(899\) | 23966.8 | 0.889140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51116.5 | −1.89005 | ||||||||
\(902\) | −19024.9 | −0.702282 | ||||||||
\(903\) | −22852.5 | −0.842176 | ||||||||
\(904\) | −8532.63 | −0.313928 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −23393.5 | −0.857834 | ||||||||
\(907\) | 35436.0 | 1.29728 | 0.648640 | − | 0.761096i | \(-0.275338\pi\) | ||||
0.648640 | + | 0.761096i | \(0.275338\pi\) | |||||||
\(908\) | 7117.75 | 0.260144 | ||||||||
\(909\) | 7428.63 | 0.271058 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11359.1 | −0.413112 | −0.206556 | − | 0.978435i | \(-0.566225\pi\) | ||||
−0.206556 | + | 0.978435i | \(0.566225\pi\) | |||||||
\(912\) | 10789.0 | 0.391732 | ||||||||
\(913\) | 30567.7 | 1.10804 | ||||||||
\(914\) | −18248.5 | −0.660401 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15904.6 | 0.573694 | ||||||||
\(917\) | −70188.2 | −2.52761 | ||||||||
\(918\) | −31078.5 | −1.11737 | ||||||||
\(919\) | 40517.5 | 1.45435 | 0.727175 | − | 0.686452i | \(-0.240833\pi\) | ||||
0.727175 | + | 0.686452i | \(0.240833\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15951.2 | −0.570695 | ||||||||
\(922\) | 12023.8 | 0.429484 | ||||||||
\(923\) | 20133.3 | 0.717982 | ||||||||
\(924\) | 21289.9 | 0.757995 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17168.2 | 0.609267 | ||||||||
\(927\) | −4942.21 | −0.175106 | ||||||||
\(928\) | 7725.72 | 0.273286 | ||||||||
\(929\) | 16242.2 | 0.573614 | 0.286807 | − | 0.957988i | \(-0.407406\pi\) | ||||
0.286807 | + | 0.957988i | \(0.407406\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 73769.2 | 2.59687 | ||||||||
\(932\) | 9244.50 | 0.324907 | ||||||||
\(933\) | −26161.5 | −0.917994 | ||||||||
\(934\) | −7908.19 | −0.277049 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −802.397 | −0.0280205 | ||||||||
\(937\) | 47445.0 | 1.65417 | 0.827087 | − | 0.562074i | \(-0.189996\pi\) | ||||
0.827087 | + | 0.562074i | \(0.189996\pi\) | |||||||
\(938\) | −19005.1 | −0.661556 | ||||||||
\(939\) | −11403.6 | −0.396317 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48063.5 | −1.66506 | −0.832532 | − | 0.553976i | \(-0.813110\pi\) | ||||
−0.832532 | + | 0.553976i | \(0.813110\pi\) | |||||||
\(942\) | 5382.36 | 0.186164 | ||||||||
\(943\) | 5732.70 | 0.197967 | ||||||||
\(944\) | 6939.74 | 0.239268 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12507.5 | −0.429867 | ||||||||
\(947\) | −13745.4 | −0.471663 | −0.235831 | − | 0.971794i | \(-0.575781\pi\) | ||||
−0.235831 | + | 0.971794i | \(0.575781\pi\) | |||||||
\(948\) | −9501.39 | −0.325518 | ||||||||
\(949\) | −4423.92 | −0.151324 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5021.06 | 0.171208 | ||||||||
\(952\) | −24445.9 | −0.832245 | ||||||||
\(953\) | 13999.1 | 0.475839 | 0.237920 | − | 0.971285i | \(-0.423535\pi\) | ||||
0.237920 | + | 0.971285i | \(0.423535\pi\) | |||||||
\(954\) | 4372.27 | 0.148383 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3297.07 | 0.111543 | ||||||||
\(957\) | −43754.5 | −1.47793 | ||||||||
\(958\) | −190.675 | −0.00643052 | ||||||||
\(959\) | 26410.7 | 0.889308 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19936.4 | −0.669207 | ||||||||
\(962\) | −2702.28 | −0.0905666 | ||||||||
\(963\) | 174.389 | 0.00583552 | ||||||||
\(964\) | 14567.3 | 0.486703 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6415.23 | −0.213671 | ||||||||
\(967\) | 800.187 | 0.0266104 | 0.0133052 | − | 0.999911i | \(-0.495765\pi\) | ||||
0.0133052 | + | 0.999911i | \(0.495765\pi\) | |||||||
\(968\) | 1004.25 | 0.0333450 | ||||||||
\(969\) | 70161.4 | 2.32602 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11363.5 | −0.375563 | −0.187782 | − | 0.982211i | \(-0.560130\pi\) | ||||
−0.187782 | + | 0.982211i | \(0.560130\pi\) | |||||||
\(972\) | 4940.50 | 0.163032 | ||||||||
\(973\) | −9084.84 | −0.299328 | ||||||||
\(974\) | −27830.4 | −0.915549 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10574.4 | 0.346803 | ||||||||
\(977\) | 17444.0 | 0.571220 | 0.285610 | − | 0.958346i | \(-0.407804\pi\) | ||||
0.285610 | + | 0.958346i | \(0.407804\pi\) | |||||||
\(978\) | −9126.06 | −0.298384 | ||||||||
\(979\) | 27822.5 | 0.908286 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3593.52 | −0.116954 | ||||||||
\(982\) | 12582.7 | 0.408889 | ||||||||
\(983\) | 54032.7 | 1.75318 | 0.876590 | − | 0.481237i | \(-0.159812\pi\) | ||||
0.876590 | + | 0.481237i | \(0.159812\pi\) | |||||||
\(984\) | 9468.81 | 0.306763 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 50240.7 | 1.62271 | ||||||||
\(987\) | −28671.9 | −0.924659 | ||||||||
\(988\) | 12802.5 | 0.412248 | ||||||||
\(989\) | 3768.84 | 0.121175 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28869.3 | 0.925392 | 0.462696 | − | 0.886517i | \(-0.346882\pi\) | ||||
0.462696 | + | 0.886517i | \(0.346882\pi\) | |||||||
\(992\) | 3176.66 | 0.101672 | ||||||||
\(993\) | −45968.3 | −1.46904 | ||||||||
\(994\) | −52466.2 | −1.67417 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15213.7 | −0.484002 | ||||||||
\(997\) | −3358.78 | −0.106694 | −0.0533469 | − | 0.998576i | \(-0.516989\pi\) | ||||
−0.0533469 | + | 0.998576i | \(0.516989\pi\) | |||||||
\(998\) | −1276.66 | −0.0404931 | ||||||||
\(999\) | 8952.57 | 0.283530 |
(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 | 1150.4.a.p.1.3 | 4 | ||
5.2 | odd | 4 | 1150.4.b.n.599.6 | 8 | |||
5.3 | odd | 4 | 1150.4.b.n.599.3 | 8 | |||
5.4 | even | 2 | 230.4.a.h.1.2 | ✓ | 4 | ||
15.14 | odd | 2 | 2070.4.a.bj.1.4 | 4 | |||
20.19 | odd | 2 | 1840.4.a.m.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.h.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
1150.4.a.p.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1150.4.b.n.599.3 | 8 | 5.3 | odd | 4 | |||
1150.4.b.n.599.6 | 8 | 5.2 | odd | 4 | |||
1840.4.a.m.1.3 | 4 | 20.19 | odd | 2 | |||
2070.4.a.bj.1.4 | 4 | 15.14 | odd | 2 |