Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2254,4,Mod(1,2254)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2254, 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("2254.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2254 = 2 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2254.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: | \(132.990305153\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 92x^{3} - 28x^{2} + 1593x - 1782 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 322) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.26012\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2254.1 |
$q$-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 | ||||||||
\(3\) | 0.260120 | 0.0500601 | 0.0250301 | − | 0.999687i | \(-0.492032\pi\) | ||||
0.0250301 | + | 0.999687i | \(0.492032\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −15.2484 | −1.36386 | −0.681931 | − | 0.731416i | \(-0.738860\pi\) | ||||
−0.681931 | + | 0.731416i | \(0.738860\pi\) | |||||||
\(6\) | 0.520240 | 0.0353978 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −26.9323 | −0.997494 | ||||||||
\(10\) | −30.4969 | −0.964397 | ||||||||
\(11\) | 63.1379 | 1.73062 | 0.865309 | − | 0.501238i | \(-0.167122\pi\) | ||||
0.865309 | + | 0.501238i | \(0.167122\pi\) | |||||||
\(12\) | 1.04048 | 0.0250301 | ||||||||
\(13\) | −40.8864 | −0.872295 | −0.436148 | − | 0.899875i | \(-0.643657\pi\) | ||||
−0.436148 | + | 0.899875i | \(0.643657\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.96643 | −0.0682751 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 57.0717 | 0.814231 | 0.407115 | − | 0.913377i | \(-0.366535\pi\) | ||||
0.407115 | + | 0.913377i | \(0.366535\pi\) | |||||||
\(18\) | −53.8647 | −0.705335 | ||||||||
\(19\) | −34.4579 | −0.416062 | −0.208031 | − | 0.978122i | \(-0.566706\pi\) | ||||
−0.208031 | + | 0.978122i | \(0.566706\pi\) | |||||||
\(20\) | −60.9938 | −0.681931 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 126.276 | 1.22373 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 2.08096 | 0.0176989 | ||||||||
\(25\) | 107.515 | 0.860121 | ||||||||
\(26\) | −81.7727 | −0.616806 | ||||||||
\(27\) | −14.0289 | −0.0999948 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 180.951 | 1.15868 | 0.579340 | − | 0.815086i | \(-0.303310\pi\) | ||||
0.579340 | + | 0.815086i | \(0.303310\pi\) | |||||||
\(30\) | −7.93285 | −0.0482778 | ||||||||
\(31\) | 5.92805 | 0.0343455 | 0.0171727 | − | 0.999853i | \(-0.494533\pi\) | ||||
0.0171727 | + | 0.999853i | \(0.494533\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 16.4234 | 0.0866350 | ||||||||
\(34\) | 114.143 | 0.575748 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −107.729 | −0.498747 | ||||||||
\(37\) | −161.864 | −0.719196 | −0.359598 | − | 0.933107i | \(-0.617086\pi\) | ||||
−0.359598 | + | 0.933107i | \(0.617086\pi\) | |||||||
\(38\) | −68.9158 | −0.294200 | ||||||||
\(39\) | −10.6354 | −0.0436672 | ||||||||
\(40\) | −121.988 | −0.482198 | ||||||||
\(41\) | 104.432 | 0.397792 | 0.198896 | − | 0.980021i | \(-0.436264\pi\) | ||||
0.198896 | + | 0.980021i | \(0.436264\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.5725 | 0.0587742 | 0.0293871 | − | 0.999568i | \(-0.490644\pi\) | ||||
0.0293871 | + | 0.999568i | \(0.490644\pi\) | |||||||
\(44\) | 252.552 | 0.865309 | ||||||||
\(45\) | 410.676 | 1.36044 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | −333.754 | −1.03581 | −0.517904 | − | 0.855439i | \(-0.673287\pi\) | ||||
−0.517904 | + | 0.855439i | \(0.673287\pi\) | |||||||
\(48\) | 4.16192 | 0.0125150 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 215.030 | 0.608198 | ||||||||
\(51\) | 14.8455 | 0.0407605 | ||||||||
\(52\) | −163.545 | −0.436148 | ||||||||
\(53\) | 296.103 | 0.767412 | 0.383706 | − | 0.923455i | \(-0.374648\pi\) | ||||
0.383706 | + | 0.923455i | \(0.374648\pi\) | |||||||
\(54\) | −28.0578 | −0.0707070 | ||||||||
\(55\) | −962.756 | −2.36033 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.96319 | −0.0208281 | ||||||||
\(58\) | 361.902 | 0.819311 | ||||||||
\(59\) | 805.644 | 1.77773 | 0.888864 | − | 0.458171i | \(-0.151495\pi\) | ||||
0.888864 | + | 0.458171i | \(0.151495\pi\) | |||||||
\(60\) | −15.8657 | −0.0341376 | ||||||||
\(61\) | −715.603 | −1.50202 | −0.751012 | − | 0.660288i | \(-0.770434\pi\) | ||||
−0.751012 | + | 0.660288i | \(0.770434\pi\) | |||||||
\(62\) | 11.8561 | 0.0242859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 623.454 | 1.18969 | ||||||||
\(66\) | 32.8469 | 0.0612602 | ||||||||
\(67\) | 301.232 | 0.549275 | 0.274637 | − | 0.961548i | \(-0.411442\pi\) | ||||
0.274637 | + | 0.961548i | \(0.411442\pi\) | |||||||
\(68\) | 228.287 | 0.407115 | ||||||||
\(69\) | 5.98276 | 0.0104383 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −871.046 | −1.45597 | −0.727987 | − | 0.685591i | \(-0.759544\pi\) | ||||
−0.727987 | + | 0.685591i | \(0.759544\pi\) | |||||||
\(72\) | −215.459 | −0.352667 | ||||||||
\(73\) | −894.771 | −1.43459 | −0.717295 | − | 0.696770i | \(-0.754620\pi\) | ||||
−0.717295 | + | 0.696770i | \(0.754620\pi\) | |||||||
\(74\) | −323.728 | −0.508548 | ||||||||
\(75\) | 27.9668 | 0.0430578 | ||||||||
\(76\) | −137.832 | −0.208031 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −21.2707 | −0.0308774 | ||||||||
\(79\) | −1246.19 | −1.77477 | −0.887386 | − | 0.461028i | \(-0.847481\pi\) | ||||
−0.887386 | + | 0.461028i | \(0.847481\pi\) | |||||||
\(80\) | −243.975 | −0.340966 | ||||||||
\(81\) | 723.524 | 0.992488 | ||||||||
\(82\) | 208.863 | 0.281281 | ||||||||
\(83\) | 1223.93 | 1.61860 | 0.809300 | − | 0.587395i | \(-0.199846\pi\) | ||||
0.809300 | + | 0.587395i | \(0.199846\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −870.255 | −1.11050 | ||||||||
\(86\) | 33.1451 | 0.0415596 | ||||||||
\(87\) | 47.0690 | 0.0580037 | ||||||||
\(88\) | 505.104 | 0.611866 | ||||||||
\(89\) | 86.3579 | 0.102853 | 0.0514265 | − | 0.998677i | \(-0.483623\pi\) | ||||
0.0514265 | + | 0.998677i | \(0.483623\pi\) | |||||||
\(90\) | 821.353 | 0.961980 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 1.54200 | 0.00171934 | ||||||||
\(94\) | −667.507 | −0.732426 | ||||||||
\(95\) | 525.429 | 0.567452 | ||||||||
\(96\) | 8.32384 | 0.00884946 | ||||||||
\(97\) | −343.939 | −0.360018 | −0.180009 | − | 0.983665i | \(-0.557613\pi\) | ||||
−0.180009 | + | 0.983665i | \(0.557613\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1700.45 | −1.72628 | ||||||||
\(100\) | 430.061 | 0.430061 | ||||||||
\(101\) | −458.505 | −0.451713 | −0.225856 | − | 0.974161i | \(-0.572518\pi\) | ||||
−0.225856 | + | 0.974161i | \(0.572518\pi\) | |||||||
\(102\) | 29.6910 | 0.0288220 | ||||||||
\(103\) | 574.886 | 0.549954 | 0.274977 | − | 0.961451i | \(-0.411330\pi\) | ||||
0.274977 | + | 0.961451i | \(0.411330\pi\) | |||||||
\(104\) | −327.091 | −0.308403 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 592.205 | 0.542642 | ||||||||
\(107\) | −1451.76 | −1.31165 | −0.655825 | − | 0.754913i | \(-0.727679\pi\) | ||||
−0.655825 | + | 0.754913i | \(0.727679\pi\) | |||||||
\(108\) | −56.1155 | −0.0499974 | ||||||||
\(109\) | −1812.89 | −1.59306 | −0.796530 | − | 0.604598i | \(-0.793334\pi\) | ||||
−0.796530 | + | 0.604598i | \(0.793334\pi\) | |||||||
\(110\) | −1925.51 | −1.66900 | ||||||||
\(111\) | −42.1040 | −0.0360030 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1693.79 | −1.41007 | −0.705035 | − | 0.709173i | \(-0.749069\pi\) | ||||
−0.705035 | + | 0.709173i | \(0.749069\pi\) | |||||||
\(114\) | −17.9264 | −0.0147277 | ||||||||
\(115\) | −350.714 | −0.284385 | ||||||||
\(116\) | 723.804 | 0.579340 | ||||||||
\(117\) | 1101.17 | 0.870109 | ||||||||
\(118\) | 1611.29 | 1.25704 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −31.7314 | −0.0241389 | ||||||||
\(121\) | 2655.40 | 1.99504 | ||||||||
\(122\) | −1431.21 | −1.06209 | ||||||||
\(123\) | 27.1647 | 0.0199135 | ||||||||
\(124\) | 23.7122 | 0.0171727 | ||||||||
\(125\) | 266.616 | 0.190775 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 251.950 | 0.176039 | 0.0880194 | − | 0.996119i | \(-0.471946\pi\) | ||||
0.0880194 | + | 0.996119i | \(0.471946\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 4.31085 | 0.00294224 | ||||||||
\(130\) | 1246.91 | 0.841238 | ||||||||
\(131\) | 1844.44 | 1.23015 | 0.615074 | − | 0.788469i | \(-0.289126\pi\) | ||||
0.615074 | + | 0.788469i | \(0.289126\pi\) | |||||||
\(132\) | 65.6938 | 0.0433175 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 602.465 | 0.388396 | ||||||||
\(135\) | 213.919 | 0.136379 | ||||||||
\(136\) | 456.574 | 0.287874 | ||||||||
\(137\) | −1169.93 | −0.729592 | −0.364796 | − | 0.931087i | \(-0.618861\pi\) | ||||
−0.364796 | + | 0.931087i | \(0.618861\pi\) | |||||||
\(138\) | 11.9655 | 0.00738096 | ||||||||
\(139\) | 1618.44 | 0.987585 | 0.493792 | − | 0.869580i | \(-0.335610\pi\) | ||||
0.493792 | + | 0.869580i | \(0.335610\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −86.8160 | −0.0518526 | ||||||||
\(142\) | −1742.09 | −1.02953 | ||||||||
\(143\) | −2581.48 | −1.50961 | ||||||||
\(144\) | −430.917 | −0.249373 | ||||||||
\(145\) | −2759.22 | −1.58028 | ||||||||
\(146\) | −1789.54 | −1.01441 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −647.455 | −0.359598 | ||||||||
\(149\) | −1745.63 | −0.959785 | −0.479892 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479892 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(150\) | 55.9337 | 0.0304464 | ||||||||
\(151\) | −2520.41 | −1.35833 | −0.679167 | − | 0.733984i | \(-0.737659\pi\) | ||||
−0.679167 | + | 0.733984i | \(0.737659\pi\) | |||||||
\(152\) | −275.663 | −0.147100 | ||||||||
\(153\) | −1537.07 | −0.812190 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −90.3936 | −0.0468425 | ||||||||
\(156\) | −42.5414 | −0.0218336 | ||||||||
\(157\) | −1122.56 | −0.570635 | −0.285318 | − | 0.958433i | \(-0.592099\pi\) | ||||
−0.285318 | + | 0.958433i | \(0.592099\pi\) | |||||||
\(158\) | −2492.37 | −1.25495 | ||||||||
\(159\) | 77.0222 | 0.0384167 | ||||||||
\(160\) | −487.950 | −0.241099 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1447.05 | 0.701795 | ||||||||
\(163\) | 149.438 | 0.0718091 | 0.0359045 | − | 0.999355i | \(-0.488569\pi\) | ||||
0.0359045 | + | 0.999355i | \(0.488569\pi\) | |||||||
\(164\) | 417.726 | 0.198896 | ||||||||
\(165\) | −250.432 | −0.118158 | ||||||||
\(166\) | 2447.86 | 1.14452 | ||||||||
\(167\) | −1950.78 | −0.903927 | −0.451963 | − | 0.892037i | \(-0.649276\pi\) | ||||
−0.451963 | + | 0.892037i | \(0.649276\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −525.306 | −0.239101 | ||||||||
\(170\) | −1740.51 | −0.785241 | ||||||||
\(171\) | 928.032 | 0.415020 | ||||||||
\(172\) | 66.2902 | 0.0293871 | ||||||||
\(173\) | −2850.79 | −1.25284 | −0.626420 | − | 0.779486i | \(-0.715480\pi\) | ||||
−0.626420 | + | 0.779486i | \(0.715480\pi\) | |||||||
\(174\) | 94.1379 | 0.0410148 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1010.21 | 0.432655 | ||||||||
\(177\) | 209.564 | 0.0889933 | ||||||||
\(178\) | 172.716 | 0.0727280 | ||||||||
\(179\) | 1847.62 | 0.771493 | 0.385747 | − | 0.922605i | \(-0.373944\pi\) | ||||
0.385747 | + | 0.922605i | \(0.373944\pi\) | |||||||
\(180\) | 1642.71 | 0.680222 | ||||||||
\(181\) | −3260.42 | −1.33892 | −0.669461 | − | 0.742847i | \(-0.733475\pi\) | ||||
−0.669461 | + | 0.742847i | \(0.733475\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −186.143 | −0.0751915 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 2468.17 | 0.980884 | ||||||||
\(186\) | 3.08401 | 0.00121576 | ||||||||
\(187\) | 3603.39 | 1.40912 | ||||||||
\(188\) | −1335.01 | −0.517904 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1050.86 | 0.401249 | ||||||||
\(191\) | 1616.13 | 0.612247 | 0.306123 | − | 0.951992i | \(-0.400968\pi\) | ||||
0.306123 | + | 0.951992i | \(0.400968\pi\) | |||||||
\(192\) | 16.6477 | 0.00625751 | ||||||||
\(193\) | −4746.87 | −1.77040 | −0.885200 | − | 0.465211i | \(-0.845979\pi\) | ||||
−0.885200 | + | 0.465211i | \(0.845979\pi\) | |||||||
\(194\) | −687.878 | −0.254571 | ||||||||
\(195\) | 162.173 | 0.0595560 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1471.77 | −0.532280 | −0.266140 | − | 0.963934i | \(-0.585748\pi\) | ||||
−0.266140 | + | 0.963934i | \(0.585748\pi\) | |||||||
\(198\) | −3400.90 | −1.22067 | ||||||||
\(199\) | −3296.74 | −1.17437 | −0.587184 | − | 0.809453i | \(-0.699764\pi\) | ||||
−0.587184 | + | 0.809453i | \(0.699764\pi\) | |||||||
\(200\) | 860.121 | 0.304099 | ||||||||
\(201\) | 78.3566 | 0.0274967 | ||||||||
\(202\) | −917.011 | −0.319409 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 59.3820 | 0.0203802 | ||||||||
\(205\) | −1592.42 | −0.542533 | ||||||||
\(206\) | 1149.77 | 0.388876 | ||||||||
\(207\) | −619.444 | −0.207992 | ||||||||
\(208\) | −654.182 | −0.218074 | ||||||||
\(209\) | −2175.60 | −0.720045 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2436.09 | −0.794821 | −0.397410 | − | 0.917641i | \(-0.630091\pi\) | ||||
−0.397410 | + | 0.917641i | \(0.630091\pi\) | |||||||
\(212\) | 1184.41 | 0.383706 | ||||||||
\(213\) | −226.577 | −0.0728862 | ||||||||
\(214\) | −2903.51 | −0.927477 | ||||||||
\(215\) | −252.706 | −0.0801599 | ||||||||
\(216\) | −112.231 | −0.0353535 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3625.79 | −1.12646 | ||||||||
\(219\) | −232.748 | −0.0718157 | ||||||||
\(220\) | −3851.02 | −1.18016 | ||||||||
\(221\) | −2333.45 | −0.710250 | ||||||||
\(222\) | −84.2080 | −0.0254580 | ||||||||
\(223\) | −1464.12 | −0.439662 | −0.219831 | − | 0.975538i | \(-0.570551\pi\) | ||||
−0.219831 | + | 0.975538i | \(0.570551\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2895.64 | −0.857966 | ||||||||
\(226\) | −3387.57 | −0.997070 | ||||||||
\(227\) | 3419.39 | 0.999794 | 0.499897 | − | 0.866085i | \(-0.333371\pi\) | ||||
0.499897 | + | 0.866085i | \(0.333371\pi\) | |||||||
\(228\) | −35.8527 | −0.0104141 | ||||||||
\(229\) | 3437.40 | 0.991922 | 0.495961 | − | 0.868345i | \(-0.334816\pi\) | ||||
0.495961 | + | 0.868345i | \(0.334816\pi\) | |||||||
\(230\) | −701.429 | −0.201091 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1447.61 | 0.409656 | ||||||||
\(233\) | 3049.48 | 0.857415 | 0.428708 | − | 0.903443i | \(-0.358969\pi\) | ||||
0.428708 | + | 0.903443i | \(0.358969\pi\) | |||||||
\(234\) | 2202.33 | 0.615260 | ||||||||
\(235\) | 5089.22 | 1.41270 | ||||||||
\(236\) | 3222.58 | 0.888864 | ||||||||
\(237\) | −324.158 | −0.0888453 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1961.10 | 0.530767 | 0.265383 | − | 0.964143i | \(-0.414501\pi\) | ||||
0.265383 | + | 0.964143i | \(0.414501\pi\) | |||||||
\(240\) | −63.4628 | −0.0170688 | ||||||||
\(241\) | −6121.70 | −1.63624 | −0.818119 | − | 0.575049i | \(-0.804983\pi\) | ||||
−0.818119 | + | 0.575049i | \(0.804983\pi\) | |||||||
\(242\) | 5310.80 | 1.41071 | ||||||||
\(243\) | 566.983 | 0.149679 | ||||||||
\(244\) | −2862.41 | −0.751012 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 54.3295 | 0.0140810 | ||||||||
\(247\) | 1408.86 | 0.362929 | ||||||||
\(248\) | 47.4244 | 0.0121430 | ||||||||
\(249\) | 318.369 | 0.0810273 | ||||||||
\(250\) | 533.233 | 0.134898 | ||||||||
\(251\) | −4112.95 | −1.03429 | −0.517145 | − | 0.855898i | \(-0.673005\pi\) | ||||
−0.517145 | + | 0.855898i | \(0.673005\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1452.17 | 0.360859 | ||||||||
\(254\) | 503.899 | 0.124478 | ||||||||
\(255\) | −226.371 | −0.0555917 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2135.52 | 0.518328 | 0.259164 | − | 0.965833i | \(-0.416553\pi\) | ||||
0.259164 | + | 0.965833i | \(0.416553\pi\) | |||||||
\(258\) | 8.62170 | 0.00208048 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2493.81 | 0.594845 | ||||||||
\(261\) | −4873.43 | −1.15578 | ||||||||
\(262\) | 3688.88 | 0.869846 | ||||||||
\(263\) | 7005.80 | 1.64257 | 0.821286 | − | 0.570517i | \(-0.193257\pi\) | ||||
0.821286 | + | 0.570517i | \(0.193257\pi\) | |||||||
\(264\) | 131.388 | 0.0306301 | ||||||||
\(265\) | −4515.10 | −1.04664 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.4634 | 0.00514883 | ||||||||
\(268\) | 1204.93 | 0.274637 | ||||||||
\(269\) | −6566.34 | −1.48831 | −0.744157 | − | 0.668004i | \(-0.767149\pi\) | ||||
−0.744157 | + | 0.668004i | \(0.767149\pi\) | |||||||
\(270\) | 427.837 | 0.0964346 | ||||||||
\(271\) | 5759.43 | 1.29100 | 0.645499 | − | 0.763761i | \(-0.276649\pi\) | ||||
0.645499 | + | 0.763761i | \(0.276649\pi\) | |||||||
\(272\) | 913.147 | 0.203558 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2339.87 | −0.515900 | ||||||||
\(275\) | 6788.29 | 1.48854 | ||||||||
\(276\) | 23.9310 | 0.00521913 | ||||||||
\(277\) | 356.886 | 0.0774123 | 0.0387061 | − | 0.999251i | \(-0.487676\pi\) | ||||
0.0387061 | + | 0.999251i | \(0.487676\pi\) | |||||||
\(278\) | 3236.88 | 0.698328 | ||||||||
\(279\) | −159.656 | −0.0342594 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −925.745 | −0.196531 | −0.0982657 | − | 0.995160i | \(-0.531329\pi\) | ||||
−0.0982657 | + | 0.995160i | \(0.531329\pi\) | |||||||
\(282\) | −173.632 | −0.0366654 | ||||||||
\(283\) | −6928.18 | −1.45526 | −0.727629 | − | 0.685971i | \(-0.759378\pi\) | ||||
−0.727629 | + | 0.685971i | \(0.759378\pi\) | |||||||
\(284\) | −3484.19 | −0.727987 | ||||||||
\(285\) | 136.675 | 0.0284067 | ||||||||
\(286\) | −5162.96 | −1.06746 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −861.835 | −0.176334 | ||||||||
\(289\) | −1655.82 | −0.337028 | ||||||||
\(290\) | −5518.44 | −1.11743 | ||||||||
\(291\) | −89.4655 | −0.0180225 | ||||||||
\(292\) | −3579.08 | −0.717295 | ||||||||
\(293\) | −148.190 | −0.0295472 | −0.0147736 | − | 0.999891i | \(-0.504703\pi\) | ||||
−0.0147736 | + | 0.999891i | \(0.504703\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12284.8 | −2.42458 | ||||||||
\(296\) | −1294.91 | −0.254274 | ||||||||
\(297\) | −885.755 | −0.173053 | ||||||||
\(298\) | −3491.27 | −0.678670 | ||||||||
\(299\) | −940.386 | −0.181886 | ||||||||
\(300\) | 111.867 | 0.0215289 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5040.83 | −0.960487 | ||||||||
\(303\) | −119.266 | −0.0226128 | ||||||||
\(304\) | −551.326 | −0.104016 | ||||||||
\(305\) | 10911.8 | 2.04856 | ||||||||
\(306\) | −3074.15 | −0.574305 | ||||||||
\(307\) | 10096.8 | 1.87705 | 0.938527 | − | 0.345207i | \(-0.112191\pi\) | ||||
0.938527 | + | 0.345207i | \(0.112191\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 149.539 | 0.0275308 | ||||||||
\(310\) | −180.787 | −0.0331227 | ||||||||
\(311\) | 1063.81 | 0.193965 | 0.0969826 | − | 0.995286i | \(-0.469081\pi\) | ||||
0.0969826 | + | 0.995286i | \(0.469081\pi\) | |||||||
\(312\) | −85.0829 | −0.0154387 | ||||||||
\(313\) | −1953.88 | −0.352844 | −0.176422 | − | 0.984315i | \(-0.556452\pi\) | ||||
−0.176422 | + | 0.984315i | \(0.556452\pi\) | |||||||
\(314\) | −2245.11 | −0.403500 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4984.75 | −0.887386 | ||||||||
\(317\) | −2939.51 | −0.520819 | −0.260409 | − | 0.965498i | \(-0.583858\pi\) | ||||
−0.260409 | + | 0.965498i | \(0.583858\pi\) | |||||||
\(318\) | 154.044 | 0.0271647 | ||||||||
\(319\) | 11424.9 | 2.00523 | ||||||||
\(320\) | −975.901 | −0.170483 | ||||||||
\(321\) | −377.631 | −0.0656614 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1966.57 | −0.338771 | ||||||||
\(324\) | 2894.10 | 0.496244 | ||||||||
\(325\) | −4395.90 | −0.750280 | ||||||||
\(326\) | 298.876 | 0.0507767 | ||||||||
\(327\) | −471.570 | −0.0797488 | ||||||||
\(328\) | 835.452 | 0.140641 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −500.864 | −0.0835505 | ||||||||
\(331\) | −8808.46 | −1.46271 | −0.731354 | − | 0.681998i | \(-0.761111\pi\) | ||||
−0.731354 | + | 0.681998i | \(0.761111\pi\) | |||||||
\(332\) | 4895.72 | 0.809300 | ||||||||
\(333\) | 4359.37 | 0.717393 | ||||||||
\(334\) | −3901.56 | −0.639173 | ||||||||
\(335\) | −4593.33 | −0.749135 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3966.73 | 0.641191 | 0.320596 | − | 0.947216i | \(-0.396117\pi\) | ||||
0.320596 | + | 0.947216i | \(0.396117\pi\) | |||||||
\(338\) | −1050.61 | −0.169070 | ||||||||
\(339\) | −440.587 | −0.0705883 | ||||||||
\(340\) | −3481.02 | −0.555250 | ||||||||
\(341\) | 374.285 | 0.0594389 | ||||||||
\(342\) | 1856.06 | 0.293463 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 132.580 | 0.0207798 | ||||||||
\(345\) | −91.2278 | −0.0142363 | ||||||||
\(346\) | −5701.57 | −0.885891 | ||||||||
\(347\) | 5747.24 | 0.889129 | 0.444565 | − | 0.895747i | \(-0.353358\pi\) | ||||
0.444565 | + | 0.895747i | \(0.353358\pi\) | |||||||
\(348\) | 188.276 | 0.0290018 | ||||||||
\(349\) | −8367.21 | −1.28334 | −0.641671 | − | 0.766980i | \(-0.721759\pi\) | ||||
−0.641671 | + | 0.766980i | \(0.721759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 573.590 | 0.0872249 | ||||||||
\(352\) | 2020.41 | 0.305933 | ||||||||
\(353\) | −4056.10 | −0.611571 | −0.305785 | − | 0.952100i | \(-0.598919\pi\) | ||||
−0.305785 | + | 0.952100i | \(0.598919\pi\) | |||||||
\(354\) | 419.128 | 0.0629278 | ||||||||
\(355\) | 13282.1 | 1.98575 | ||||||||
\(356\) | 345.431 | 0.0514265 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3695.23 | 0.545528 | ||||||||
\(359\) | −2580.13 | −0.379315 | −0.189658 | − | 0.981850i | \(-0.560738\pi\) | ||||
−0.189658 | + | 0.981850i | \(0.560738\pi\) | |||||||
\(360\) | 3285.41 | 0.480990 | ||||||||
\(361\) | −5671.65 | −0.826892 | ||||||||
\(362\) | −6520.83 | −0.946761 | ||||||||
\(363\) | 690.722 | 0.0998720 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13643.9 | 1.95658 | ||||||||
\(366\) | −372.285 | −0.0531684 | ||||||||
\(367\) | −938.253 | −0.133451 | −0.0667254 | − | 0.997771i | \(-0.521255\pi\) | ||||
−0.0667254 | + | 0.997771i | \(0.521255\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | −2812.59 | −0.396795 | ||||||||
\(370\) | 4936.34 | 0.693590 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.16802 | 0.000859669 0 | ||||||||
\(373\) | 10951.6 | 1.52025 | 0.760125 | − | 0.649777i | \(-0.225138\pi\) | ||||
0.760125 | + | 0.649777i | \(0.225138\pi\) | |||||||
\(374\) | 7206.78 | 0.996401 | ||||||||
\(375\) | 69.3522 | 0.00955023 | ||||||||
\(376\) | −2670.03 | −0.366213 | ||||||||
\(377\) | −7398.42 | −1.01071 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9520.76 | 1.29037 | 0.645183 | − | 0.764028i | \(-0.276781\pi\) | ||||
0.645183 | + | 0.764028i | \(0.276781\pi\) | |||||||
\(380\) | 2101.72 | 0.283726 | ||||||||
\(381\) | 65.5371 | 0.00881252 | ||||||||
\(382\) | 3232.26 | 0.432924 | ||||||||
\(383\) | 3099.25 | 0.413484 | 0.206742 | − | 0.978396i | \(-0.433714\pi\) | ||||
0.206742 | + | 0.978396i | \(0.433714\pi\) | |||||||
\(384\) | 33.2954 | 0.00442473 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9493.74 | −1.25186 | ||||||||
\(387\) | −446.337 | −0.0586269 | ||||||||
\(388\) | −1375.76 | −0.180009 | ||||||||
\(389\) | 4368.35 | 0.569368 | 0.284684 | − | 0.958621i | \(-0.408111\pi\) | ||||
0.284684 | + | 0.958621i | \(0.408111\pi\) | |||||||
\(390\) | 324.345 | 0.0421125 | ||||||||
\(391\) | 1312.65 | 0.169779 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 479.775 | 0.0615813 | ||||||||
\(394\) | −2943.54 | −0.376379 | ||||||||
\(395\) | 19002.4 | 2.42054 | ||||||||
\(396\) | −6801.81 | −0.863141 | ||||||||
\(397\) | −6306.06 | −0.797210 | −0.398605 | − | 0.917123i | \(-0.630505\pi\) | ||||
−0.398605 | + | 0.917123i | \(0.630505\pi\) | |||||||
\(398\) | −6593.47 | −0.830404 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1720.24 | 0.215030 | ||||||||
\(401\) | −83.0874 | −0.0103471 | −0.00517355 | − | 0.999987i | \(-0.501647\pi\) | ||||
−0.00517355 | + | 0.999987i | \(0.501647\pi\) | |||||||
\(402\) | 156.713 | 0.0194431 | ||||||||
\(403\) | −242.376 | −0.0299594 | ||||||||
\(404\) | −1834.02 | −0.225856 | ||||||||
\(405\) | −11032.6 | −1.35362 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10219.7 | −1.24465 | ||||||||
\(408\) | 118.764 | 0.0144110 | ||||||||
\(409\) | −1594.33 | −0.192750 | −0.0963749 | − | 0.995345i | \(-0.530725\pi\) | ||||
−0.0963749 | + | 0.995345i | \(0.530725\pi\) | |||||||
\(410\) | −3184.84 | −0.383629 | ||||||||
\(411\) | −304.323 | −0.0365235 | ||||||||
\(412\) | 2299.55 | 0.274977 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1238.89 | −0.147072 | ||||||||
\(415\) | −18663.0 | −2.20755 | ||||||||
\(416\) | −1308.36 | −0.154201 | ||||||||
\(417\) | 420.988 | 0.0494386 | ||||||||
\(418\) | −4351.20 | −0.509149 | ||||||||
\(419\) | 3260.67 | 0.380177 | 0.190089 | − | 0.981767i | \(-0.439122\pi\) | ||||
0.190089 | + | 0.981767i | \(0.439122\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7104.66 | −0.822471 | −0.411235 | − | 0.911529i | \(-0.634903\pi\) | ||||
−0.411235 | + | 0.911529i | \(0.634903\pi\) | |||||||
\(422\) | −4872.18 | −0.562023 | ||||||||
\(423\) | 8988.76 | 1.03321 | ||||||||
\(424\) | 2368.82 | 0.271321 | ||||||||
\(425\) | 6136.08 | 0.700337 | ||||||||
\(426\) | −453.153 | −0.0515384 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5807.02 | −0.655825 | ||||||||
\(429\) | −671.495 | −0.0755712 | ||||||||
\(430\) | −505.411 | −0.0566816 | ||||||||
\(431\) | 10760.4 | 1.20258 | 0.601290 | − | 0.799031i | \(-0.294654\pi\) | ||||
0.601290 | + | 0.799031i | \(0.294654\pi\) | |||||||
\(432\) | −224.462 | −0.0249987 | ||||||||
\(433\) | 11537.4 | 1.28049 | 0.640245 | − | 0.768171i | \(-0.278833\pi\) | ||||
0.640245 | + | 0.768171i | \(0.278833\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −717.729 | −0.0791091 | ||||||||
\(436\) | −7251.57 | −0.796530 | ||||||||
\(437\) | −792.532 | −0.0867550 | ||||||||
\(438\) | −465.496 | −0.0507814 | ||||||||
\(439\) | 10785.2 | 1.17255 | 0.586277 | − | 0.810111i | \(-0.300593\pi\) | ||||
0.586277 | + | 0.810111i | \(0.300593\pi\) | |||||||
\(440\) | −7702.05 | −0.834501 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4666.91 | −0.502222 | ||||||||
\(443\) | 2483.46 | 0.266349 | 0.133175 | − | 0.991093i | \(-0.457483\pi\) | ||||
0.133175 | + | 0.991093i | \(0.457483\pi\) | |||||||
\(444\) | −168.416 | −0.0180015 | ||||||||
\(445\) | −1316.82 | −0.140277 | ||||||||
\(446\) | −2928.24 | −0.310888 | ||||||||
\(447\) | −454.074 | −0.0480469 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3010.79 | −0.316454 | −0.158227 | − | 0.987403i | \(-0.550578\pi\) | ||||
−0.158227 | + | 0.987403i | \(0.550578\pi\) | |||||||
\(450\) | −5791.27 | −0.606674 | ||||||||
\(451\) | 6593.59 | 0.688426 | ||||||||
\(452\) | −6775.14 | −0.705035 | ||||||||
\(453\) | −655.610 | −0.0679983 | ||||||||
\(454\) | 6838.79 | 0.706961 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −71.7055 | −0.00736385 | ||||||||
\(457\) | −12906.5 | −1.32110 | −0.660549 | − | 0.750783i | \(-0.729677\pi\) | ||||
−0.660549 | + | 0.750783i | \(0.729677\pi\) | |||||||
\(458\) | 6874.81 | 0.701395 | ||||||||
\(459\) | −800.652 | −0.0814188 | ||||||||
\(460\) | −1402.86 | −0.142193 | ||||||||
\(461\) | −1928.01 | −0.194786 | −0.0973931 | − | 0.995246i | \(-0.531050\pi\) | ||||
−0.0973931 | + | 0.995246i | \(0.531050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2880.38 | 0.289121 | 0.144560 | − | 0.989496i | \(-0.453823\pi\) | ||||
0.144560 | + | 0.989496i | \(0.453823\pi\) | |||||||
\(464\) | 2895.22 | 0.289670 | ||||||||
\(465\) | −23.5132 | −0.00234494 | ||||||||
\(466\) | 6098.95 | 0.606284 | ||||||||
\(467\) | −6861.47 | −0.679895 | −0.339947 | − | 0.940444i | \(-0.610409\pi\) | ||||
−0.339947 | + | 0.940444i | \(0.610409\pi\) | |||||||
\(468\) | 4404.66 | 0.435055 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10178.4 | 0.998929 | ||||||||
\(471\) | −291.999 | −0.0285661 | ||||||||
\(472\) | 6445.16 | 0.628522 | ||||||||
\(473\) | 1046.36 | 0.101716 | ||||||||
\(474\) | −648.316 | −0.0628231 | ||||||||
\(475\) | −3704.75 | −0.357864 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7974.73 | −0.765488 | ||||||||
\(478\) | 3922.21 | 0.375309 | ||||||||
\(479\) | 4580.05 | 0.436885 | 0.218443 | − | 0.975850i | \(-0.429902\pi\) | ||||
0.218443 | + | 0.975850i | \(0.429902\pi\) | |||||||
\(480\) | −126.926 | −0.0120695 | ||||||||
\(481\) | 6618.02 | 0.627351 | ||||||||
\(482\) | −12243.4 | −1.15700 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10621.6 | 0.997521 | ||||||||
\(485\) | 5244.54 | 0.491015 | ||||||||
\(486\) | 1133.97 | 0.105839 | ||||||||
\(487\) | 8844.29 | 0.822943 | 0.411471 | − | 0.911423i | \(-0.365015\pi\) | ||||
0.411471 | + | 0.911423i | \(0.365015\pi\) | |||||||
\(488\) | −5724.82 | −0.531046 | ||||||||
\(489\) | 38.8718 | 0.00359477 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4687.22 | −0.430817 | −0.215408 | − | 0.976524i | \(-0.569108\pi\) | ||||
−0.215408 | + | 0.976524i | \(0.569108\pi\) | |||||||
\(492\) | 108.659 | 0.00995675 | ||||||||
\(493\) | 10327.2 | 0.943434 | ||||||||
\(494\) | 2817.72 | 0.256630 | ||||||||
\(495\) | 25929.3 | 2.35441 | ||||||||
\(496\) | 94.8488 | 0.00858637 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 636.738 | 0.0572950 | ||||||||
\(499\) | −10245.1 | −0.919107 | −0.459553 | − | 0.888150i | \(-0.651991\pi\) | ||||
−0.459553 | + | 0.888150i | \(0.651991\pi\) | |||||||
\(500\) | 1066.47 | 0.0953876 | ||||||||
\(501\) | −507.436 | −0.0452507 | ||||||||
\(502\) | −8225.89 | −0.731354 | ||||||||
\(503\) | 10020.9 | 0.888286 | 0.444143 | − | 0.895956i | \(-0.353508\pi\) | ||||
0.444143 | + | 0.895956i | \(0.353508\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6991.50 | 0.616074 | ||||||||
\(506\) | 2904.35 | 0.255166 | ||||||||
\(507\) | −136.643 | −0.0119694 | ||||||||
\(508\) | 1007.80 | 0.0880194 | ||||||||
\(509\) | 15666.6 | 1.36427 | 0.682133 | − | 0.731228i | \(-0.261053\pi\) | ||||
0.682133 | + | 0.731228i | \(0.261053\pi\) | |||||||
\(510\) | −452.741 | −0.0393093 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 483.406 | 0.0416041 | ||||||||
\(514\) | 4271.05 | 0.366513 | ||||||||
\(515\) | −8766.13 | −0.750062 | ||||||||
\(516\) | 17.2434 | 0.00147112 | ||||||||
\(517\) | −21072.5 | −1.79259 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −741.546 | −0.0627173 | ||||||||
\(520\) | 4987.63 | 0.420619 | ||||||||
\(521\) | −12571.8 | −1.05716 | −0.528581 | − | 0.848883i | \(-0.677276\pi\) | ||||
−0.528581 | + | 0.848883i | \(0.677276\pi\) | |||||||
\(522\) | −9746.86 | −0.817258 | ||||||||
\(523\) | −12266.4 | −1.02557 | −0.512785 | − | 0.858517i | \(-0.671386\pi\) | ||||
−0.512785 | + | 0.858517i | \(0.671386\pi\) | |||||||
\(524\) | 7377.76 | 0.615074 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14011.6 | 1.16147 | ||||||||
\(527\) | 338.324 | 0.0279651 | ||||||||
\(528\) | 262.775 | 0.0216587 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −9030.21 | −0.740089 | ||||||||
\(531\) | −21697.9 | −1.77327 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4269.83 | −0.346992 | ||||||||
\(534\) | 44.9268 | 0.00364077 | ||||||||
\(535\) | 22137.0 | 1.78891 | ||||||||
\(536\) | 2409.86 | 0.194198 | ||||||||
\(537\) | 480.602 | 0.0386210 | ||||||||
\(538\) | −13132.7 | −1.05240 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 855.675 | 0.0681896 | ||||||||
\(541\) | −17141.8 | −1.36226 | −0.681131 | − | 0.732161i | \(-0.738512\pi\) | ||||
−0.681131 | + | 0.732161i | \(0.738512\pi\) | |||||||
\(542\) | 11518.9 | 0.912874 | ||||||||
\(543\) | −848.100 | −0.0670266 | ||||||||
\(544\) | 1826.29 | 0.143937 | ||||||||
\(545\) | 27643.8 | 2.17272 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13619.5 | −1.06459 | −0.532294 | − | 0.846560i | \(-0.678670\pi\) | ||||
−0.532294 | + | 0.846560i | \(0.678670\pi\) | |||||||
\(548\) | −4679.73 | −0.364796 | ||||||||
\(549\) | 19272.8 | 1.49826 | ||||||||
\(550\) | 13576.6 | 1.05256 | ||||||||
\(551\) | −6235.19 | −0.482083 | ||||||||
\(552\) | 47.8621 | 0.00369048 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 713.772 | 0.0547387 | ||||||||
\(555\) | 642.021 | 0.0491032 | ||||||||
\(556\) | 6473.76 | 0.493792 | ||||||||
\(557\) | −14755.1 | −1.12243 | −0.561214 | − | 0.827671i | \(-0.689666\pi\) | ||||
−0.561214 | + | 0.827671i | \(0.689666\pi\) | |||||||
\(558\) | −319.313 | −0.0242251 | ||||||||
\(559\) | −677.591 | −0.0512684 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 937.314 | 0.0705409 | ||||||||
\(562\) | −1851.49 | −0.138969 | ||||||||
\(563\) | −21018.7 | −1.57341 | −0.786706 | − | 0.617327i | \(-0.788215\pi\) | ||||
−0.786706 | + | 0.617327i | \(0.788215\pi\) | |||||||
\(564\) | −347.264 | −0.0259263 | ||||||||
\(565\) | 25827.6 | 1.92314 | ||||||||
\(566\) | −13856.4 | −1.02902 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6968.37 | −0.514765 | ||||||||
\(569\) | 13750.9 | 1.01313 | 0.506563 | − | 0.862203i | \(-0.330916\pi\) | ||||
0.506563 | + | 0.862203i | \(0.330916\pi\) | |||||||
\(570\) | 273.349 | 0.0200866 | ||||||||
\(571\) | 10636.3 | 0.779535 | 0.389768 | − | 0.920913i | \(-0.372555\pi\) | ||||
0.389768 | + | 0.920913i | \(0.372555\pi\) | |||||||
\(572\) | −10325.9 | −0.754805 | ||||||||
\(573\) | 420.388 | 0.0306491 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2472.85 | 0.179348 | ||||||||
\(576\) | −1723.67 | −0.124687 | ||||||||
\(577\) | −7290.64 | −0.526019 | −0.263010 | − | 0.964793i | \(-0.584715\pi\) | ||||
−0.263010 | + | 0.964793i | \(0.584715\pi\) | |||||||
\(578\) | −3311.64 | −0.238315 | ||||||||
\(579\) | −1234.76 | −0.0886264 | ||||||||
\(580\) | −11036.9 | −0.790141 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −178.931 | −0.0127439 | ||||||||
\(583\) | 18695.3 | 1.32810 | ||||||||
\(584\) | −7158.17 | −0.507204 | ||||||||
\(585\) | −16791.1 | −1.18671 | ||||||||
\(586\) | −296.379 | −0.0208930 | ||||||||
\(587\) | 6315.96 | 0.444102 | 0.222051 | − | 0.975035i | \(-0.428725\pi\) | ||||
0.222051 | + | 0.975035i | \(0.428725\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −204.268 | −0.0142899 | ||||||||
\(590\) | −24569.7 | −1.71444 | ||||||||
\(591\) | −382.836 | −0.0266460 | ||||||||
\(592\) | −2589.82 | −0.179799 | ||||||||
\(593\) | −19795.1 | −1.37081 | −0.685403 | − | 0.728164i | \(-0.740374\pi\) | ||||
−0.685403 | + | 0.728164i | \(0.740374\pi\) | |||||||
\(594\) | −1771.51 | −0.122367 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6982.54 | −0.479892 | ||||||||
\(597\) | −857.547 | −0.0587890 | ||||||||
\(598\) | −1880.77 | −0.128613 | ||||||||
\(599\) | 27201.1 | 1.85544 | 0.927720 | − | 0.373277i | \(-0.121766\pi\) | ||||
0.927720 | + | 0.373277i | \(0.121766\pi\) | |||||||
\(600\) | 223.735 | 0.0152232 | ||||||||
\(601\) | −11695.1 | −0.793763 | −0.396882 | − | 0.917870i | \(-0.629908\pi\) | ||||
−0.396882 | + | 0.917870i | \(0.629908\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8112.89 | −0.547898 | ||||||||
\(604\) | −10081.7 | −0.679167 | ||||||||
\(605\) | −40490.7 | −2.72096 | ||||||||
\(606\) | −238.533 | −0.0159897 | ||||||||
\(607\) | 4523.78 | 0.302495 | 0.151247 | − | 0.988496i | \(-0.451671\pi\) | ||||
0.151247 | + | 0.988496i | \(0.451671\pi\) | |||||||
\(608\) | −1102.65 | −0.0735501 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21823.7 | 1.44855 | ||||||||
\(611\) | 13646.0 | 0.903530 | ||||||||
\(612\) | −6148.30 | −0.406095 | ||||||||
\(613\) | 27979.4 | 1.84352 | 0.921758 | − | 0.387765i | \(-0.126753\pi\) | ||||
0.921758 | + | 0.387765i | \(0.126753\pi\) | |||||||
\(614\) | 20193.6 | 1.32728 | ||||||||
\(615\) | −414.220 | −0.0271593 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27419.8 | 1.78911 | 0.894553 | − | 0.446961i | \(-0.147494\pi\) | ||||
0.894553 | + | 0.446961i | \(0.147494\pi\) | |||||||
\(618\) | 299.079 | 0.0194672 | ||||||||
\(619\) | −4941.83 | −0.320887 | −0.160443 | − | 0.987045i | \(-0.551292\pi\) | ||||
−0.160443 | + | 0.987045i | \(0.551292\pi\) | |||||||
\(620\) | −361.574 | −0.0234213 | ||||||||
\(621\) | −322.664 | −0.0208504 | ||||||||
\(622\) | 2127.62 | 0.137154 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −170.166 | −0.0109168 | ||||||||
\(625\) | −17504.9 | −1.12031 | ||||||||
\(626\) | −3907.77 | −0.249498 | ||||||||
\(627\) | −565.917 | −0.0360455 | ||||||||
\(628\) | −4490.22 | −0.285318 | ||||||||
\(629\) | −9237.84 | −0.585591 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13077.3 | −0.825037 | −0.412519 | − | 0.910949i | \(-0.635351\pi\) | ||||
−0.412519 | + | 0.910949i | \(0.635351\pi\) | |||||||
\(632\) | −9969.49 | −0.627477 | ||||||||
\(633\) | −633.675 | −0.0397888 | ||||||||
\(634\) | −5879.03 | −0.368274 | ||||||||
\(635\) | −3841.84 | −0.240093 | ||||||||
\(636\) | 308.089 | 0.0192084 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22849.7 | 1.41792 | ||||||||
\(639\) | 23459.3 | 1.45233 | ||||||||
\(640\) | −1951.80 | −0.120550 | ||||||||
\(641\) | −1272.72 | −0.0784235 | −0.0392117 | − | 0.999231i | \(-0.512485\pi\) | ||||
−0.0392117 | + | 0.999231i | \(0.512485\pi\) | |||||||
\(642\) | −755.262 | −0.0464296 | ||||||||
\(643\) | −113.036 | −0.00693269 | −0.00346634 | − | 0.999994i | \(-0.501103\pi\) | ||||
−0.00346634 | + | 0.999994i | \(0.501103\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −65.7338 | −0.00401281 | ||||||||
\(646\) | −3933.14 | −0.239547 | ||||||||
\(647\) | 1829.78 | 0.111184 | 0.0555919 | − | 0.998454i | \(-0.482295\pi\) | ||||
0.0555919 | + | 0.998454i | \(0.482295\pi\) | |||||||
\(648\) | 5788.19 | 0.350898 | ||||||||
\(649\) | 50866.7 | 3.07657 | ||||||||
\(650\) | −8791.81 | −0.530528 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 597.751 | 0.0359045 | ||||||||
\(653\) | 1936.86 | 0.116072 | 0.0580361 | − | 0.998314i | \(-0.481516\pi\) | ||||
0.0580361 | + | 0.998314i | \(0.481516\pi\) | |||||||
\(654\) | −943.139 | −0.0563909 | ||||||||
\(655\) | −28124.8 | −1.67775 | ||||||||
\(656\) | 1670.90 | 0.0994480 | ||||||||
\(657\) | 24098.3 | 1.43099 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22889.3 | −1.35302 | −0.676509 | − | 0.736434i | \(-0.736508\pi\) | ||||
−0.676509 | + | 0.736434i | \(0.736508\pi\) | |||||||
\(660\) | −1001.73 | −0.0590791 | ||||||||
\(661\) | −17818.0 | −1.04847 | −0.524237 | − | 0.851573i | \(-0.675649\pi\) | ||||
−0.524237 | + | 0.851573i | \(0.675649\pi\) | |||||||
\(662\) | −17616.9 | −1.03429 | ||||||||
\(663\) | −606.978 | −0.0355552 | ||||||||
\(664\) | 9791.45 | 0.572262 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8718.74 | 0.507274 | ||||||||
\(667\) | 4161.87 | 0.241602 | ||||||||
\(668\) | −7803.11 | −0.451963 | ||||||||
\(669\) | −380.847 | −0.0220095 | ||||||||
\(670\) | −9186.65 | −0.529718 | ||||||||
\(671\) | −45181.7 | −2.59943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20993.6 | 1.20244 | 0.601222 | − | 0.799082i | \(-0.294681\pi\) | ||||
0.601222 | + | 0.799082i | \(0.294681\pi\) | |||||||
\(674\) | 7933.46 | 0.453391 | ||||||||
\(675\) | −1508.32 | −0.0860076 | ||||||||
\(676\) | −2101.22 | −0.119551 | ||||||||
\(677\) | −5364.75 | −0.304555 | −0.152278 | − | 0.988338i | \(-0.548661\pi\) | ||||
−0.152278 | + | 0.988338i | \(0.548661\pi\) | |||||||
\(678\) | −881.175 | −0.0499134 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6962.04 | −0.392621 | ||||||||
\(681\) | 889.453 | 0.0500498 | ||||||||
\(682\) | 748.570 | 0.0420297 | ||||||||
\(683\) | −31720.5 | −1.77709 | −0.888543 | − | 0.458793i | \(-0.848282\pi\) | ||||
−0.888543 | + | 0.458793i | \(0.848282\pi\) | |||||||
\(684\) | 3712.13 | 0.207510 | ||||||||
\(685\) | 17839.7 | 0.995063 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 894.138 | 0.0496557 | ||||||||
\(688\) | 265.161 | 0.0146935 | ||||||||
\(689\) | −12106.6 | −0.669409 | ||||||||
\(690\) | −182.456 | −0.0100666 | ||||||||
\(691\) | 12501.1 | 0.688228 | 0.344114 | − | 0.938928i | \(-0.388179\pi\) | ||||
0.344114 | + | 0.938928i | \(0.388179\pi\) | |||||||
\(692\) | −11403.1 | −0.626420 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11494.5 | 0.628709 | ||||||||
\(695\) | −24678.7 | −1.34693 | ||||||||
\(696\) | 376.552 | 0.0205074 | ||||||||
\(697\) | 5960.09 | 0.323894 | ||||||||
\(698\) | −16734.4 | −0.907460 | ||||||||
\(699\) | 793.230 | 0.0429223 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4917.13 | −0.264932 | −0.132466 | − | 0.991188i | \(-0.542290\pi\) | ||||
−0.132466 | + | 0.991188i | \(0.542290\pi\) | |||||||
\(702\) | 1147.18 | 0.0616773 | ||||||||
\(703\) | 5577.48 | 0.299230 | ||||||||
\(704\) | 4040.83 | 0.216327 | ||||||||
\(705\) | 1323.81 | 0.0707199 | ||||||||
\(706\) | −8112.20 | −0.432446 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 838.257 | 0.0444966 | ||||||||
\(709\) | 2043.21 | 0.108229 | 0.0541145 | − | 0.998535i | \(-0.482766\pi\) | ||||
0.0541145 | + | 0.998535i | \(0.482766\pi\) | |||||||
\(710\) | 26564.2 | 1.40414 | ||||||||
\(711\) | 33562.7 | 1.77032 | ||||||||
\(712\) | 690.863 | 0.0363640 | ||||||||
\(713\) | 136.345 | 0.00716153 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39363.6 | 2.05890 | ||||||||
\(716\) | 7390.46 | 0.385747 | ||||||||
\(717\) | 510.122 | 0.0265703 | ||||||||
\(718\) | −5160.27 | −0.268216 | ||||||||
\(719\) | −24690.8 | −1.28069 | −0.640343 | − | 0.768089i | \(-0.721208\pi\) | ||||
−0.640343 | + | 0.768089i | \(0.721208\pi\) | |||||||
\(720\) | 6570.82 | 0.340111 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11343.3 | −0.584701 | ||||||||
\(723\) | −1592.38 | −0.0819103 | ||||||||
\(724\) | −13041.7 | −0.669461 | ||||||||
\(725\) | 19455.0 | 0.996606 | ||||||||
\(726\) | 1381.44 | 0.0706202 | ||||||||
\(727\) | 23243.0 | 1.18574 | 0.592872 | − | 0.805297i | \(-0.297994\pi\) | ||||
0.592872 | + | 0.805297i | \(0.297994\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19387.7 | −0.984995 | ||||||||
\(730\) | 27287.7 | 1.38351 | ||||||||
\(731\) | 945.823 | 0.0478557 | ||||||||
\(732\) | −744.570 | −0.0375958 | ||||||||
\(733\) | 35315.4 | 1.77954 | 0.889772 | − | 0.456406i | \(-0.150863\pi\) | ||||
0.889772 | + | 0.456406i | \(0.150863\pi\) | |||||||
\(734\) | −1876.51 | −0.0943639 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 19019.2 | 0.950585 | ||||||||
\(738\) | −5625.17 | −0.280576 | ||||||||
\(739\) | 10783.2 | 0.536763 | 0.268382 | − | 0.963313i | \(-0.413511\pi\) | ||||
0.268382 | + | 0.963313i | \(0.413511\pi\) | |||||||
\(740\) | 9872.69 | 0.490442 | ||||||||
\(741\) | 366.472 | 0.0181683 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4972.73 | −0.245534 | −0.122767 | − | 0.992436i | \(-0.539177\pi\) | ||||
−0.122767 | + | 0.992436i | \(0.539177\pi\) | |||||||
\(744\) | 12.3360 | 0.000607878 0 | ||||||||
\(745\) | 26618.2 | 1.30901 | ||||||||
\(746\) | 21903.2 | 1.07498 | ||||||||
\(747\) | −32963.3 | −1.61454 | ||||||||
\(748\) | 14413.6 | 0.704562 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 138.704 | 0.00675303 | ||||||||
\(751\) | −29604.7 | −1.43847 | −0.719234 | − | 0.694768i | \(-0.755507\pi\) | ||||
−0.719234 | + | 0.694768i | \(0.755507\pi\) | |||||||
\(752\) | −5340.06 | −0.258952 | ||||||||
\(753\) | −1069.86 | −0.0517767 | ||||||||
\(754\) | −14796.8 | −0.714681 | ||||||||
\(755\) | 38432.4 | 1.85258 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9958.05 | −0.478113 | −0.239056 | − | 0.971006i | \(-0.576838\pi\) | ||||
−0.239056 | + | 0.971006i | \(0.576838\pi\) | |||||||
\(758\) | 19041.5 | 0.912426 | ||||||||
\(759\) | 377.739 | 0.0180646 | ||||||||
\(760\) | 4203.44 | 0.200625 | ||||||||
\(761\) | −28654.4 | −1.36494 | −0.682472 | − | 0.730911i | \(-0.739095\pi\) | ||||
−0.682472 | + | 0.730911i | \(0.739095\pi\) | |||||||
\(762\) | 131.074 | 0.00623139 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6464.52 | 0.306123 | ||||||||
\(765\) | 23438.0 | 1.10772 | ||||||||
\(766\) | 6198.50 | 0.292377 | ||||||||
\(767\) | −32939.9 | −1.55070 | ||||||||
\(768\) | 66.5907 | 0.00312876 | ||||||||
\(769\) | −1580.21 | −0.0741011 | −0.0370506 | − | 0.999313i | \(-0.511796\pi\) | ||||
−0.0370506 | + | 0.999313i | \(0.511796\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 555.493 | 0.0259476 | ||||||||
\(772\) | −18987.5 | −0.885200 | ||||||||
\(773\) | −36297.7 | −1.68892 | −0.844461 | − | 0.535617i | \(-0.820079\pi\) | ||||
−0.844461 | + | 0.535617i | \(0.820079\pi\) | |||||||
\(774\) | −892.675 | −0.0414555 | ||||||||
\(775\) | 637.356 | 0.0295413 | ||||||||
\(776\) | −2751.51 | −0.127286 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8736.69 | 0.402604 | ||||||||
\(779\) | −3598.49 | −0.165506 | ||||||||
\(780\) | 648.691 | 0.0297780 | ||||||||
\(781\) | −54996.1 | −2.51974 | ||||||||
\(782\) | 2625.30 | 0.120052 | ||||||||
\(783\) | −2538.54 | −0.115862 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17117.2 | 0.778268 | ||||||||
\(786\) | 959.551 | 0.0435446 | ||||||||
\(787\) | −3840.61 | −0.173956 | −0.0869778 | − | 0.996210i | \(-0.527721\pi\) | ||||
−0.0869778 | + | 0.996210i | \(0.527721\pi\) | |||||||
\(788\) | −5887.07 | −0.266140 | ||||||||
\(789\) | 1822.35 | 0.0822273 | ||||||||
\(790\) | 38004.8 | 1.71158 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13603.6 | −0.610333 | ||||||||
\(793\) | 29258.4 | 1.31021 | ||||||||
\(794\) | −12612.1 | −0.563712 | ||||||||
\(795\) | −1174.47 | −0.0523951 | ||||||||
\(796\) | −13186.9 | −0.587184 | ||||||||
\(797\) | 24193.7 | 1.07526 | 0.537632 | − | 0.843179i | \(-0.319319\pi\) | ||||
0.537632 | + | 0.843179i | \(0.319319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19047.9 | −0.843386 | ||||||||
\(800\) | 3440.49 | 0.152049 | ||||||||
\(801\) | −2325.82 | −0.102595 | ||||||||
\(802\) | −166.175 | −0.00731650 | ||||||||
\(803\) | −56494.0 | −2.48273 | ||||||||
\(804\) | 313.426 | 0.0137484 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −484.753 | −0.0211845 | ||||||||
\(807\) | −1708.04 | −0.0745052 | ||||||||
\(808\) | −3668.04 | −0.159705 | ||||||||
\(809\) | −16476.8 | −0.716063 | −0.358031 | − | 0.933710i | \(-0.616552\pi\) | ||||
−0.358031 | + | 0.933710i | \(0.616552\pi\) | |||||||
\(810\) | −22065.2 | −0.957152 | ||||||||
\(811\) | −2891.58 | −0.125200 | −0.0625999 | − | 0.998039i | \(-0.519939\pi\) | ||||
−0.0625999 | + | 0.998039i | \(0.519939\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1498.14 | 0.0646275 | ||||||||
\(814\) | −20439.5 | −0.880103 | ||||||||
\(815\) | −2278.70 | −0.0979377 | ||||||||
\(816\) | 237.528 | 0.0101901 | ||||||||
\(817\) | −571.055 | −0.0244537 | ||||||||
\(818\) | −3188.66 | −0.136295 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6369.68 | −0.271267 | ||||||||
\(821\) | 36315.1 | 1.54373 | 0.771867 | − | 0.635785i | \(-0.219323\pi\) | ||||
0.771867 | + | 0.635785i | \(0.219323\pi\) | |||||||
\(822\) | −608.646 | −0.0258260 | ||||||||
\(823\) | −18744.4 | −0.793913 | −0.396956 | − | 0.917838i | \(-0.629934\pi\) | ||||
−0.396956 | + | 0.917838i | \(0.629934\pi\) | |||||||
\(824\) | 4599.09 | 0.194438 | ||||||||
\(825\) | 1765.77 | 0.0745166 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25294.4 | 1.06357 | 0.531784 | − | 0.846880i | \(-0.321522\pi\) | ||||
0.531784 | + | 0.846880i | \(0.321522\pi\) | |||||||
\(828\) | −2477.78 | −0.103996 | ||||||||
\(829\) | 39438.4 | 1.65230 | 0.826148 | − | 0.563453i | \(-0.190527\pi\) | ||||
0.826148 | + | 0.563453i | \(0.190527\pi\) | |||||||
\(830\) | −37326.1 | −1.56097 | ||||||||
\(831\) | 92.8332 | 0.00387527 | ||||||||
\(832\) | −2616.73 | −0.109037 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 841.977 | 0.0349584 | ||||||||
\(835\) | 29746.3 | 1.23283 | ||||||||
\(836\) | −8702.40 | −0.360023 | ||||||||
\(837\) | −83.1639 | −0.00343437 | ||||||||
\(838\) | 6521.34 | 0.268826 | ||||||||
\(839\) | 30165.0 | 1.24125 | 0.620627 | − | 0.784106i | \(-0.286878\pi\) | ||||
0.620627 | + | 0.784106i | \(0.286878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8354.24 | 0.342541 | ||||||||
\(842\) | −14209.3 | −0.581574 | ||||||||
\(843\) | −240.805 | −0.00983838 | ||||||||
\(844\) | −9744.35 | −0.397410 | ||||||||
\(845\) | 8010.10 | 0.326101 | ||||||||
\(846\) | 17977.5 | 0.730591 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4737.64 | 0.191853 | ||||||||
\(849\) | −1802.16 | −0.0728503 | ||||||||
\(850\) | 12272.2 | 0.495213 | ||||||||
\(851\) | −3722.87 | −0.149963 | ||||||||
\(852\) | −906.306 | −0.0364431 | ||||||||
\(853\) | −8977.27 | −0.360347 | −0.180173 | − | 0.983635i | \(-0.557666\pi\) | ||||
−0.180173 | + | 0.983635i | \(0.557666\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14151.0 | −0.566030 | ||||||||
\(856\) | −11614.0 | −0.463738 | ||||||||
\(857\) | 40593.6 | 1.61803 | 0.809015 | − | 0.587789i | \(-0.200001\pi\) | ||||
0.809015 | + | 0.587789i | \(0.200001\pi\) | |||||||
\(858\) | −1342.99 | −0.0534369 | ||||||||
\(859\) | 14117.7 | 0.560755 | 0.280377 | − | 0.959890i | \(-0.409540\pi\) | ||||
0.280377 | + | 0.959890i | \(0.409540\pi\) | |||||||
\(860\) | −1010.82 | −0.0400799 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21520.9 | 0.850352 | ||||||||
\(863\) | −7080.02 | −0.279266 | −0.139633 | − | 0.990203i | \(-0.544592\pi\) | ||||
−0.139633 | + | 0.990203i | \(0.544592\pi\) | |||||||
\(864\) | −448.924 | −0.0176767 | ||||||||
\(865\) | 43470.1 | 1.70870 | ||||||||
\(866\) | 23074.8 | 0.905443 | ||||||||
\(867\) | −430.712 | −0.0168717 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −78681.7 | −3.07145 | ||||||||
\(870\) | −1435.46 | −0.0559386 | ||||||||
\(871\) | −12316.3 | −0.479129 | ||||||||
\(872\) | −14503.1 | −0.563232 | ||||||||
\(873\) | 9263.09 | 0.359116 | ||||||||
\(874\) | −1585.06 | −0.0613450 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −930.991 | −0.0359079 | ||||||||
\(877\) | −29775.4 | −1.14646 | −0.573229 | − | 0.819395i | \(-0.694309\pi\) | ||||
−0.573229 | + | 0.819395i | \(0.694309\pi\) | |||||||
\(878\) | 21570.5 | 0.829120 | ||||||||
\(879\) | −38.5471 | −0.00147914 | ||||||||
\(880\) | −15404.1 | −0.590082 | ||||||||
\(881\) | −32974.9 | −1.26101 | −0.630506 | − | 0.776184i | \(-0.717153\pi\) | ||||
−0.630506 | + | 0.776184i | \(0.717153\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8286.80 | −0.315825 | −0.157912 | − | 0.987453i | \(-0.550476\pi\) | ||||
−0.157912 | + | 0.987453i | \(0.550476\pi\) | |||||||
\(884\) | −9333.82 | −0.355125 | ||||||||
\(885\) | −3195.53 | −0.121375 | ||||||||
\(886\) | 4966.91 | 0.188337 | ||||||||
\(887\) | 13354.7 | 0.505533 | 0.252767 | − | 0.967527i | \(-0.418659\pi\) | ||||
0.252767 | + | 0.967527i | \(0.418659\pi\) | |||||||
\(888\) | −336.832 | −0.0127290 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2633.65 | −0.0991911 | ||||||||
\(891\) | 45681.8 | 1.71762 | ||||||||
\(892\) | −5856.48 | −0.219831 | ||||||||
\(893\) | 11500.4 | 0.430960 | ||||||||
\(894\) | −908.149 | −0.0339743 | ||||||||
\(895\) | −28173.3 | −1.05221 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −244.613 | −0.00910524 | ||||||||
\(898\) | −6021.57 | −0.223767 | ||||||||
\(899\) | 1072.69 | 0.0397954 | ||||||||
\(900\) | −11582.5 | −0.428983 | ||||||||
\(901\) | 16899.1 | 0.624850 | ||||||||
\(902\) | 13187.2 | 0.486791 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13550.3 | −0.498535 | ||||||||
\(905\) | 49716.3 | 1.82611 | ||||||||
\(906\) | −1311.22 | −0.0480821 | ||||||||
\(907\) | 53901.6 | 1.97329 | 0.986645 | − | 0.162885i | \(-0.0520801\pi\) | ||||
0.986645 | + | 0.162885i | \(0.0520801\pi\) | |||||||
\(908\) | 13677.6 | 0.499897 | ||||||||
\(909\) | 12348.6 | 0.450581 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14861.5 | −0.540488 | −0.270244 | − | 0.962792i | \(-0.587104\pi\) | ||||
−0.270244 | + | 0.962792i | \(0.587104\pi\) | |||||||
\(912\) | −143.411 | −0.00520703 | ||||||||
\(913\) | 77276.5 | 2.80118 | ||||||||
\(914\) | −25813.1 | −0.934158 | ||||||||
\(915\) | 2838.38 | 0.102551 | ||||||||
\(916\) | 13749.6 | 0.495961 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1601.30 | −0.0575718 | ||||||||
\(919\) | 39976.2 | 1.43492 | 0.717460 | − | 0.696599i | \(-0.245304\pi\) | ||||
0.717460 | + | 0.696599i | \(0.245304\pi\) | |||||||
\(920\) | −2805.71 | −0.100545 | ||||||||
\(921\) | 2626.38 | 0.0939655 | ||||||||
\(922\) | −3856.02 | −0.137735 | ||||||||
\(923\) | 35613.9 | 1.27004 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17402.8 | −0.618596 | ||||||||
\(926\) | 5760.77 | 0.204439 | ||||||||
\(927\) | −15483.0 | −0.548576 | ||||||||
\(928\) | 5790.43 | 0.204828 | ||||||||
\(929\) | 7480.52 | 0.264185 | 0.132093 | − | 0.991237i | \(-0.457830\pi\) | ||||
0.132093 | + | 0.991237i | \(0.457830\pi\) | |||||||
\(930\) | −47.0264 | −0.00165812 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12197.9 | 0.428708 | ||||||||
\(933\) | 276.718 | 0.00970992 | ||||||||
\(934\) | −13722.9 | −0.480758 | ||||||||
\(935\) | −54946.1 | −1.92185 | ||||||||
\(936\) | 8809.32 | 0.307630 | ||||||||
\(937\) | 18057.0 | 0.629558 | 0.314779 | − | 0.949165i | \(-0.398070\pi\) | ||||
0.314779 | + | 0.949165i | \(0.398070\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −508.244 | −0.0176634 | ||||||||
\(940\) | 20356.9 | 0.706350 | ||||||||
\(941\) | 18921.5 | 0.655496 | 0.327748 | − | 0.944765i | \(-0.393710\pi\) | ||||
0.327748 | + | 0.944765i | \(0.393710\pi\) | |||||||
\(942\) | −583.999 | −0.0201993 | ||||||||
\(943\) | 2401.93 | 0.0829453 | ||||||||
\(944\) | 12890.3 | 0.444432 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2092.71 | 0.0719238 | ||||||||
\(947\) | −10147.2 | −0.348193 | −0.174097 | − | 0.984729i | \(-0.555701\pi\) | ||||
−0.174097 | + | 0.984729i | \(0.555701\pi\) | |||||||
\(948\) | −1296.63 | −0.0444226 | ||||||||
\(949\) | 36583.9 | 1.25139 | ||||||||
\(950\) | −7409.49 | −0.253048 | ||||||||
\(951\) | −764.626 | −0.0260722 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6284.28 | 0.213607 | 0.106804 | − | 0.994280i | \(-0.465938\pi\) | ||||
0.106804 | + | 0.994280i | \(0.465938\pi\) | |||||||
\(954\) | −15949.5 | −0.541282 | ||||||||
\(955\) | −24643.5 | −0.835020 | ||||||||
\(956\) | 7844.42 | 0.265383 | ||||||||
\(957\) | 2971.84 | 0.100382 | ||||||||
\(958\) | 9160.11 | 0.308925 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −253.851 | −0.00853439 | ||||||||
\(961\) | −29755.9 | −0.998820 | ||||||||
\(962\) | 13236.0 | 0.443604 | ||||||||
\(963\) | 39099.2 | 1.30836 | ||||||||
\(964\) | −24486.8 | −0.818119 | ||||||||
\(965\) | 72382.4 | 2.41458 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10750.9 | −0.357524 | −0.178762 | − | 0.983892i | \(-0.557209\pi\) | ||||
−0.178762 | + | 0.983892i | \(0.557209\pi\) | |||||||
\(968\) | 21243.2 | 0.705354 | ||||||||
\(969\) | −511.544 | −0.0169589 | ||||||||
\(970\) | 10489.1 | 0.347200 | ||||||||
\(971\) | −21337.3 | −0.705198 | −0.352599 | − | 0.935774i | \(-0.614702\pi\) | ||||
−0.352599 | + | 0.935774i | \(0.614702\pi\) | |||||||
\(972\) | 2267.93 | 0.0748394 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 17688.6 | 0.581908 | ||||||||
\(975\) | −1143.46 | −0.0375591 | ||||||||
\(976\) | −11449.6 | −0.375506 | ||||||||
\(977\) | −713.051 | −0.0233496 | −0.0116748 | − | 0.999932i | \(-0.503716\pi\) | ||||
−0.0116748 | + | 0.999932i | \(0.503716\pi\) | |||||||
\(978\) | 77.7435 | 0.00254189 | ||||||||
\(979\) | 5452.46 | 0.177999 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 48825.4 | 1.58907 | ||||||||
\(982\) | −9374.43 | −0.304634 | ||||||||
\(983\) | −31306.7 | −1.01580 | −0.507898 | − | 0.861417i | \(-0.669577\pi\) | ||||
−0.507898 | + | 0.861417i | \(0.669577\pi\) | |||||||
\(984\) | 217.318 | 0.00704049 | ||||||||
\(985\) | 22442.2 | 0.725956 | ||||||||
\(986\) | 20654.4 | 0.667108 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5635.43 | 0.181465 | ||||||||
\(989\) | 381.168 | 0.0122553 | ||||||||
\(990\) | 51858.5 | 1.66482 | ||||||||
\(991\) | 13538.1 | 0.433956 | 0.216978 | − | 0.976176i | \(-0.430380\pi\) | ||||
0.216978 | + | 0.976176i | \(0.430380\pi\) | |||||||
\(992\) | 189.698 | 0.00607148 | ||||||||
\(993\) | −2291.26 | −0.0732234 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 50270.1 | 1.60168 | ||||||||
\(996\) | 1273.48 | 0.0405137 | ||||||||
\(997\) | −44983.5 | −1.42893 | −0.714464 | − | 0.699672i | \(-0.753329\pi\) | ||||
−0.714464 | + | 0.699672i | \(0.753329\pi\) | |||||||
\(998\) | −20490.2 | −0.649907 | ||||||||
\(999\) | 2270.77 | 0.0719158 |
(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 | 2254.4.a.l.1.3 | 5 | ||
7.6 | odd | 2 | 322.4.a.h.1.3 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.4.a.h.1.3 | ✓ | 5 | 7.6 | odd | 2 | ||
2254.4.a.l.1.3 | 5 | 1.1 | even | 1 | trivial |