Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,4,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, 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("2166.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(127.798137072\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.373564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 106x - 348 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-7.85460\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 17.4112 | 1.55730 | 0.778652 | − | 0.627456i | \(-0.215904\pi\) | ||||
0.778652 | + | 0.627456i | \(0.215904\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −0.298020 | −0.0160916 | −0.00804578 | − | 0.999968i | \(-0.502561\pi\) | ||||
−0.00804578 | + | 0.999968i | \(0.502561\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −34.8224 | −1.10118 | ||||||||
\(11\) | 53.7164 | 1.47237 | 0.736187 | − | 0.676778i | \(-0.236624\pi\) | ||||
0.736187 | + | 0.676778i | \(0.236624\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −45.9355 | −0.980017 | −0.490009 | − | 0.871718i | \(-0.663006\pi\) | ||||
−0.490009 | + | 0.871718i | \(0.663006\pi\) | |||||||
\(14\) | 0.596040 | 0.0113784 | ||||||||
\(15\) | −52.2335 | −0.899110 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 87.9427 | 1.25466 | 0.627331 | − | 0.778753i | \(-0.284147\pi\) | ||||
0.627331 | + | 0.778753i | \(0.284147\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 69.6447 | 0.778652 | ||||||||
\(21\) | 0.894059 | 0.00929046 | ||||||||
\(22\) | −107.433 | −1.04113 | ||||||||
\(23\) | −65.1421 | −0.590568 | −0.295284 | − | 0.955410i | \(-0.595414\pi\) | ||||
−0.295284 | + | 0.955410i | \(0.595414\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 178.149 | 1.42519 | ||||||||
\(26\) | 91.8711 | 0.692977 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −1.19208 | −0.00804578 | ||||||||
\(29\) | −37.2750 | −0.238683 | −0.119341 | − | 0.992853i | \(-0.538078\pi\) | ||||
−0.119341 | + | 0.992853i | \(0.538078\pi\) | |||||||
\(30\) | 104.467 | 0.635766 | ||||||||
\(31\) | 176.191 | 1.02080 | 0.510400 | − | 0.859937i | \(-0.329497\pi\) | ||||
0.510400 | + | 0.859937i | \(0.329497\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −161.149 | −0.850075 | ||||||||
\(34\) | −175.885 | −0.887180 | ||||||||
\(35\) | −5.18888 | −0.0250594 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −153.936 | −0.683969 | −0.341984 | − | 0.939706i | \(-0.611099\pi\) | ||||
−0.341984 | + | 0.939706i | \(0.611099\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 137.807 | 0.565813 | ||||||||
\(40\) | −139.289 | −0.550590 | ||||||||
\(41\) | 171.106 | 0.651764 | 0.325882 | − | 0.945410i | \(-0.394339\pi\) | ||||
0.325882 | + | 0.945410i | \(0.394339\pi\) | |||||||
\(42\) | −1.78812 | −0.00656935 | ||||||||
\(43\) | −248.680 | −0.881936 | −0.440968 | − | 0.897523i | \(-0.645365\pi\) | ||||
−0.440968 | + | 0.897523i | \(0.645365\pi\) | |||||||
\(44\) | 214.866 | 0.736187 | ||||||||
\(45\) | 156.701 | 0.519101 | ||||||||
\(46\) | 130.284 | 0.417594 | ||||||||
\(47\) | 372.119 | 1.15488 | 0.577438 | − | 0.816435i | \(-0.304053\pi\) | ||||
0.577438 | + | 0.816435i | \(0.304053\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | −342.911 | −0.999741 | ||||||||
\(50\) | −356.299 | −1.00776 | ||||||||
\(51\) | −263.828 | −0.724379 | ||||||||
\(52\) | −183.742 | −0.490009 | ||||||||
\(53\) | 354.849 | 0.919664 | 0.459832 | − | 0.888006i | \(-0.347910\pi\) | ||||
0.459832 | + | 0.888006i | \(0.347910\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 935.266 | 2.29293 | ||||||||
\(56\) | 2.38416 | 0.00568922 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 74.5500 | 0.168774 | ||||||||
\(59\) | 734.163 | 1.62000 | 0.809999 | − | 0.586431i | \(-0.199467\pi\) | ||||
0.809999 | + | 0.586431i | \(0.199467\pi\) | |||||||
\(60\) | −208.934 | −0.449555 | ||||||||
\(61\) | −172.166 | −0.361371 | −0.180686 | − | 0.983541i | \(-0.557832\pi\) | ||||
−0.180686 | + | 0.983541i | \(0.557832\pi\) | |||||||
\(62\) | −352.381 | −0.721814 | ||||||||
\(63\) | −2.68218 | −0.00536385 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −799.792 | −1.52618 | ||||||||
\(66\) | 322.299 | 0.601094 | ||||||||
\(67\) | 277.911 | 0.506749 | 0.253375 | − | 0.967368i | \(-0.418459\pi\) | ||||
0.253375 | + | 0.967368i | \(0.418459\pi\) | |||||||
\(68\) | 351.771 | 0.627331 | ||||||||
\(69\) | 195.426 | 0.340964 | ||||||||
\(70\) | 10.3778 | 0.0177197 | ||||||||
\(71\) | 868.634 | 1.45194 | 0.725971 | − | 0.687725i | \(-0.241391\pi\) | ||||
0.725971 | + | 0.687725i | \(0.241391\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −844.039 | −1.35325 | −0.676625 | − | 0.736328i | \(-0.736558\pi\) | ||||
−0.676625 | + | 0.736328i | \(0.736558\pi\) | |||||||
\(74\) | 307.871 | 0.483639 | ||||||||
\(75\) | −534.448 | −0.822836 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.0086 | −0.0236928 | ||||||||
\(78\) | −275.613 | −0.400090 | ||||||||
\(79\) | −333.383 | −0.474791 | −0.237396 | − | 0.971413i | \(-0.576294\pi\) | ||||
−0.237396 | + | 0.971413i | \(0.576294\pi\) | |||||||
\(80\) | 278.579 | 0.389326 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −342.213 | −0.460867 | ||||||||
\(83\) | 1415.34 | 1.87173 | 0.935865 | − | 0.352359i | \(-0.114621\pi\) | ||||
0.935865 | + | 0.352359i | \(0.114621\pi\) | |||||||
\(84\) | 3.57624 | 0.00464523 | ||||||||
\(85\) | 1531.19 | 1.95389 | ||||||||
\(86\) | 497.359 | 0.623623 | ||||||||
\(87\) | 111.825 | 0.137803 | ||||||||
\(88\) | −429.731 | −0.520563 | ||||||||
\(89\) | 1329.02 | 1.58287 | 0.791437 | − | 0.611251i | \(-0.209333\pi\) | ||||
0.791437 | + | 0.611251i | \(0.209333\pi\) | |||||||
\(90\) | −313.401 | −0.367060 | ||||||||
\(91\) | 13.6897 | 0.0157700 | ||||||||
\(92\) | −260.568 | −0.295284 | ||||||||
\(93\) | −528.572 | −0.589359 | ||||||||
\(94\) | −744.238 | −0.816620 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 1470.68 | 1.53943 | 0.769716 | − | 0.638387i | \(-0.220398\pi\) | ||||
0.769716 | + | 0.638387i | \(0.220398\pi\) | |||||||
\(98\) | 685.822 | 0.706924 | ||||||||
\(99\) | 483.448 | 0.490791 | ||||||||
\(100\) | 712.597 | 0.712597 | ||||||||
\(101\) | −677.796 | −0.667755 | −0.333877 | − | 0.942617i | \(-0.608357\pi\) | ||||
−0.333877 | + | 0.942617i | \(0.608357\pi\) | |||||||
\(102\) | 527.656 | 0.512214 | ||||||||
\(103\) | −1646.65 | −1.57523 | −0.787617 | − | 0.616165i | \(-0.788685\pi\) | ||||
−0.787617 | + | 0.616165i | \(0.788685\pi\) | |||||||
\(104\) | 367.484 | 0.346488 | ||||||||
\(105\) | 15.5666 | 0.0144681 | ||||||||
\(106\) | −709.697 | −0.650301 | ||||||||
\(107\) | −1960.88 | −1.77164 | −0.885819 | − | 0.464030i | \(-0.846403\pi\) | ||||
−0.885819 | + | 0.464030i | \(0.846403\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −352.283 | −0.309565 | −0.154782 | − | 0.987949i | \(-0.549468\pi\) | ||||
−0.154782 | + | 0.987949i | \(0.549468\pi\) | |||||||
\(110\) | −1870.53 | −1.62135 | ||||||||
\(111\) | 461.807 | 0.394890 | ||||||||
\(112\) | −4.76832 | −0.00402289 | ||||||||
\(113\) | 2216.11 | 1.84490 | 0.922452 | − | 0.386111i | \(-0.126182\pi\) | ||||
0.922452 | + | 0.386111i | \(0.126182\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1134.20 | −0.919693 | ||||||||
\(116\) | −149.100 | −0.119341 | ||||||||
\(117\) | −413.420 | −0.326672 | ||||||||
\(118\) | −1468.33 | −1.14551 | ||||||||
\(119\) | −26.2087 | −0.0201895 | ||||||||
\(120\) | 417.868 | 0.317883 | ||||||||
\(121\) | 1554.45 | 1.16788 | ||||||||
\(122\) | 344.333 | 0.255528 | ||||||||
\(123\) | −513.319 | −0.376296 | ||||||||
\(124\) | 704.763 | 0.510400 | ||||||||
\(125\) | 925.392 | 0.662156 | ||||||||
\(126\) | 5.36436 | 0.00379282 | ||||||||
\(127\) | −2438.78 | −1.70399 | −0.851996 | − | 0.523549i | \(-0.824608\pi\) | ||||
−0.851996 | + | 0.523549i | \(0.824608\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 746.039 | 0.509186 | ||||||||
\(130\) | 1599.58 | 1.07918 | ||||||||
\(131\) | −1533.40 | −1.02270 | −0.511351 | − | 0.859372i | \(-0.670855\pi\) | ||||
−0.511351 | + | 0.859372i | \(0.670855\pi\) | |||||||
\(132\) | −644.597 | −0.425038 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −555.821 | −0.358326 | ||||||||
\(135\) | −470.102 | −0.299703 | ||||||||
\(136\) | −703.542 | −0.443590 | ||||||||
\(137\) | −1087.94 | −0.678461 | −0.339230 | − | 0.940703i | \(-0.610167\pi\) | ||||
−0.339230 | + | 0.940703i | \(0.610167\pi\) | |||||||
\(138\) | −390.852 | −0.241098 | ||||||||
\(139\) | −49.3719 | −0.0301271 | −0.0150635 | − | 0.999887i | \(-0.504795\pi\) | ||||
−0.0150635 | + | 0.999887i | \(0.504795\pi\) | |||||||
\(140\) | −20.7555 | −0.0125297 | ||||||||
\(141\) | −1116.36 | −0.666768 | ||||||||
\(142\) | −1737.27 | −1.02668 | ||||||||
\(143\) | −2467.49 | −1.44295 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −649.002 | −0.371701 | ||||||||
\(146\) | 1688.08 | 0.956892 | ||||||||
\(147\) | 1028.73 | 0.577201 | ||||||||
\(148\) | −615.742 | −0.341984 | ||||||||
\(149\) | 2565.82 | 1.41074 | 0.705369 | − | 0.708840i | \(-0.250781\pi\) | ||||
0.705369 | + | 0.708840i | \(0.250781\pi\) | |||||||
\(150\) | 1068.90 | 0.581833 | ||||||||
\(151\) | 46.8825 | 0.0252665 | 0.0126333 | − | 0.999920i | \(-0.495979\pi\) | ||||
0.0126333 | + | 0.999920i | \(0.495979\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 791.485 | 0.418221 | ||||||||
\(154\) | 32.0171 | 0.0167533 | ||||||||
\(155\) | 3067.69 | 1.58969 | ||||||||
\(156\) | 551.226 | 0.282907 | ||||||||
\(157\) | 2888.34 | 1.46824 | 0.734122 | − | 0.679017i | \(-0.237594\pi\) | ||||
0.734122 | + | 0.679017i | \(0.237594\pi\) | |||||||
\(158\) | 666.766 | 0.335728 | ||||||||
\(159\) | −1064.55 | −0.530968 | ||||||||
\(160\) | −557.158 | −0.275295 | ||||||||
\(161\) | 19.4136 | 0.00950315 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −183.569 | −0.0882099 | −0.0441050 | − | 0.999027i | \(-0.514044\pi\) | ||||
−0.0441050 | + | 0.999027i | \(0.514044\pi\) | |||||||
\(164\) | 684.426 | 0.325882 | ||||||||
\(165\) | −2805.80 | −1.32383 | ||||||||
\(166\) | −2830.68 | −1.32351 | ||||||||
\(167\) | −3522.58 | −1.63225 | −0.816125 | − | 0.577876i | \(-0.803882\pi\) | ||||
−0.816125 | + | 0.577876i | \(0.803882\pi\) | |||||||
\(168\) | −7.15247 | −0.00328468 | ||||||||
\(169\) | −86.9273 | −0.0395664 | ||||||||
\(170\) | −3062.37 | −1.38161 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −994.718 | −0.440968 | ||||||||
\(173\) | 3142.83 | 1.38118 | 0.690592 | − | 0.723245i | \(-0.257350\pi\) | ||||
0.690592 | + | 0.723245i | \(0.257350\pi\) | |||||||
\(174\) | −223.650 | −0.0974418 | ||||||||
\(175\) | −53.0920 | −0.0229336 | ||||||||
\(176\) | 859.463 | 0.368093 | ||||||||
\(177\) | −2202.49 | −0.935307 | ||||||||
\(178\) | −2658.04 | −1.11926 | ||||||||
\(179\) | −325.374 | −0.135864 | −0.0679318 | − | 0.997690i | \(-0.521640\pi\) | ||||
−0.0679318 | + | 0.997690i | \(0.521640\pi\) | |||||||
\(180\) | 626.803 | 0.259551 | ||||||||
\(181\) | 2639.37 | 1.08388 | 0.541942 | − | 0.840416i | \(-0.317689\pi\) | ||||
0.541942 | + | 0.840416i | \(0.317689\pi\) | |||||||
\(182\) | −27.3794 | −0.0111511 | ||||||||
\(183\) | 516.499 | 0.208638 | ||||||||
\(184\) | 521.136 | 0.208797 | ||||||||
\(185\) | −2680.20 | −1.06515 | ||||||||
\(186\) | 1057.14 | 0.416740 | ||||||||
\(187\) | 4723.97 | 1.84733 | ||||||||
\(188\) | 1488.48 | 0.577438 | ||||||||
\(189\) | 8.04653 | 0.00309682 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3801.94 | −1.44031 | −0.720154 | − | 0.693814i | \(-0.755929\pi\) | ||||
−0.720154 | + | 0.693814i | \(0.755929\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | −2534.43 | −0.945245 | −0.472623 | − | 0.881265i | \(-0.656693\pi\) | ||||
−0.472623 | + | 0.881265i | \(0.656693\pi\) | |||||||
\(194\) | −2941.36 | −1.08854 | ||||||||
\(195\) | 2399.38 | 0.881143 | ||||||||
\(196\) | −1371.64 | −0.499871 | ||||||||
\(197\) | −4115.93 | −1.48857 | −0.744284 | − | 0.667864i | \(-0.767209\pi\) | ||||
−0.744284 | + | 0.667864i | \(0.767209\pi\) | |||||||
\(198\) | −966.896 | −0.347042 | ||||||||
\(199\) | 1531.33 | 0.545493 | 0.272747 | − | 0.962086i | \(-0.412068\pi\) | ||||
0.272747 | + | 0.962086i | \(0.412068\pi\) | |||||||
\(200\) | −1425.19 | −0.503882 | ||||||||
\(201\) | −833.732 | −0.292572 | ||||||||
\(202\) | 1355.59 | 0.472174 | ||||||||
\(203\) | 11.1087 | 0.00384077 | ||||||||
\(204\) | −1055.31 | −0.362190 | ||||||||
\(205\) | 2979.17 | 1.01499 | ||||||||
\(206\) | 3293.30 | 1.11386 | ||||||||
\(207\) | −586.278 | −0.196856 | ||||||||
\(208\) | −734.968 | −0.245004 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −31.1333 | −0.0102305 | ||||||||
\(211\) | 1431.90 | 0.467185 | 0.233593 | − | 0.972335i | \(-0.424952\pi\) | ||||
0.233593 | + | 0.972335i | \(0.424952\pi\) | |||||||
\(212\) | 1419.39 | 0.459832 | ||||||||
\(213\) | −2605.90 | −0.838279 | ||||||||
\(214\) | 3921.76 | 1.25274 | ||||||||
\(215\) | −4329.80 | −1.37344 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −52.5083 | −0.0164263 | ||||||||
\(218\) | 704.566 | 0.218895 | ||||||||
\(219\) | 2532.12 | 0.781299 | ||||||||
\(220\) | 3741.07 | 1.14647 | ||||||||
\(221\) | −4039.70 | −1.22959 | ||||||||
\(222\) | −923.613 | −0.279229 | ||||||||
\(223\) | 3138.32 | 0.942409 | 0.471205 | − | 0.882024i | \(-0.343819\pi\) | ||||
0.471205 | + | 0.882024i | \(0.343819\pi\) | |||||||
\(224\) | 9.53663 | 0.00284461 | ||||||||
\(225\) | 1603.34 | 0.475065 | ||||||||
\(226\) | −4432.22 | −1.30454 | ||||||||
\(227\) | −3887.66 | −1.13671 | −0.568355 | − | 0.822784i | \(-0.692420\pi\) | ||||
−0.568355 | + | 0.822784i | \(0.692420\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −458.623 | −0.132344 | −0.0661718 | − | 0.997808i | \(-0.521079\pi\) | ||||
−0.0661718 | + | 0.997808i | \(0.521079\pi\) | |||||||
\(230\) | 2268.40 | 0.650321 | ||||||||
\(231\) | 48.0257 | 0.0136790 | ||||||||
\(232\) | 298.200 | 0.0843871 | ||||||||
\(233\) | 4351.86 | 1.22360 | 0.611802 | − | 0.791011i | \(-0.290445\pi\) | ||||
0.611802 | + | 0.791011i | \(0.290445\pi\) | |||||||
\(234\) | 826.839 | 0.230992 | ||||||||
\(235\) | 6479.03 | 1.79849 | ||||||||
\(236\) | 2936.65 | 0.809999 | ||||||||
\(237\) | 1000.15 | 0.274121 | ||||||||
\(238\) | 52.4174 | 0.0142761 | ||||||||
\(239\) | −68.9788 | −0.0186689 | −0.00933445 | − | 0.999956i | \(-0.502971\pi\) | ||||
−0.00933445 | + | 0.999956i | \(0.502971\pi\) | |||||||
\(240\) | −835.737 | −0.224777 | ||||||||
\(241\) | −39.6721 | −0.0106038 | −0.00530188 | − | 0.999986i | \(-0.501688\pi\) | ||||
−0.00530188 | + | 0.999986i | \(0.501688\pi\) | |||||||
\(242\) | −3108.91 | −0.825819 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −688.666 | −0.180686 | ||||||||
\(245\) | −5970.49 | −1.55690 | ||||||||
\(246\) | 1026.64 | 0.266082 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1409.53 | −0.360907 | ||||||||
\(249\) | −4246.01 | −1.08064 | ||||||||
\(250\) | −1850.78 | −0.468215 | ||||||||
\(251\) | −5883.34 | −1.47950 | −0.739748 | − | 0.672884i | \(-0.765055\pi\) | ||||
−0.739748 | + | 0.672884i | \(0.765055\pi\) | |||||||
\(252\) | −10.7287 | −0.00268193 | ||||||||
\(253\) | −3499.20 | −0.869536 | ||||||||
\(254\) | 4877.56 | 1.20490 | ||||||||
\(255\) | −4593.56 | −1.12808 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −3076.70 | −0.746767 | −0.373384 | − | 0.927677i | \(-0.621803\pi\) | ||||
−0.373384 | + | 0.927677i | \(0.621803\pi\) | |||||||
\(258\) | −1492.08 | −0.360049 | ||||||||
\(259\) | 45.8758 | 0.0110061 | ||||||||
\(260\) | −3199.17 | −0.763092 | ||||||||
\(261\) | −335.475 | −0.0795609 | ||||||||
\(262\) | 3066.81 | 0.723160 | ||||||||
\(263\) | −1610.93 | −0.377698 | −0.188849 | − | 0.982006i | \(-0.560476\pi\) | ||||
−0.188849 | + | 0.982006i | \(0.560476\pi\) | |||||||
\(264\) | 1289.19 | 0.300547 | ||||||||
\(265\) | 6178.33 | 1.43220 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3987.06 | −0.913873 | ||||||||
\(268\) | 1111.64 | 0.253375 | ||||||||
\(269\) | 5892.43 | 1.33557 | 0.667784 | − | 0.744355i | \(-0.267243\pi\) | ||||
0.667784 | + | 0.744355i | \(0.267243\pi\) | |||||||
\(270\) | 940.204 | 0.211922 | ||||||||
\(271\) | 2430.30 | 0.544761 | 0.272380 | − | 0.962190i | \(-0.412189\pi\) | ||||
0.272380 | + | 0.962190i | \(0.412189\pi\) | |||||||
\(272\) | 1407.08 | 0.313665 | ||||||||
\(273\) | −41.0691 | −0.00910481 | ||||||||
\(274\) | 2175.88 | 0.479744 | ||||||||
\(275\) | 9569.54 | 2.09842 | ||||||||
\(276\) | 781.705 | 0.170482 | ||||||||
\(277\) | 1573.19 | 0.341241 | 0.170621 | − | 0.985337i | \(-0.445423\pi\) | ||||
0.170621 | + | 0.985337i | \(0.445423\pi\) | |||||||
\(278\) | 98.7437 | 0.0213031 | ||||||||
\(279\) | 1585.72 | 0.340267 | ||||||||
\(280\) | 41.5110 | 0.00885985 | ||||||||
\(281\) | 3250.35 | 0.690035 | 0.345017 | − | 0.938596i | \(-0.387873\pi\) | ||||
0.345017 | + | 0.938596i | \(0.387873\pi\) | |||||||
\(282\) | 2232.71 | 0.471476 | ||||||||
\(283\) | 1283.72 | 0.269643 | 0.134822 | − | 0.990870i | \(-0.456954\pi\) | ||||
0.134822 | + | 0.990870i | \(0.456954\pi\) | |||||||
\(284\) | 3474.54 | 0.725971 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4934.98 | 1.02032 | ||||||||
\(287\) | −50.9931 | −0.0104879 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | 2820.93 | 0.574176 | ||||||||
\(290\) | 1298.00 | 0.262833 | ||||||||
\(291\) | −4412.04 | −0.888791 | ||||||||
\(292\) | −3376.15 | −0.676625 | ||||||||
\(293\) | 5208.20 | 1.03845 | 0.519226 | − | 0.854637i | \(-0.326220\pi\) | ||||
0.519226 | + | 0.854637i | \(0.326220\pi\) | |||||||
\(294\) | −2057.47 | −0.408143 | ||||||||
\(295\) | 12782.6 | 2.52283 | ||||||||
\(296\) | 1231.48 | 0.241819 | ||||||||
\(297\) | −1450.34 | −0.283358 | ||||||||
\(298\) | −5131.63 | −0.997542 | ||||||||
\(299\) | 2992.33 | 0.578766 | ||||||||
\(300\) | −2137.79 | −0.411418 | ||||||||
\(301\) | 74.1114 | 0.0141917 | ||||||||
\(302\) | −93.7651 | −0.0178661 | ||||||||
\(303\) | 2033.39 | 0.385528 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2997.62 | −0.562765 | ||||||||
\(306\) | −1582.97 | −0.295727 | ||||||||
\(307\) | 479.565 | 0.0891538 | 0.0445769 | − | 0.999006i | \(-0.485806\pi\) | ||||
0.0445769 | + | 0.999006i | \(0.485806\pi\) | |||||||
\(308\) | −64.0342 | −0.0118464 | ||||||||
\(309\) | 4939.95 | 0.909462 | ||||||||
\(310\) | −6135.38 | −1.12408 | ||||||||
\(311\) | 1642.23 | 0.299428 | 0.149714 | − | 0.988729i | \(-0.452165\pi\) | ||||
0.149714 | + | 0.988729i | \(0.452165\pi\) | |||||||
\(312\) | −1102.45 | −0.200045 | ||||||||
\(313\) | 8018.68 | 1.44806 | 0.724029 | − | 0.689769i | \(-0.242288\pi\) | ||||
0.724029 | + | 0.689769i | \(0.242288\pi\) | |||||||
\(314\) | −5776.67 | −1.03821 | ||||||||
\(315\) | −46.6999 | −0.00835315 | ||||||||
\(316\) | −1333.53 | −0.237396 | ||||||||
\(317\) | 3071.10 | 0.544132 | 0.272066 | − | 0.962279i | \(-0.412293\pi\) | ||||
0.272066 | + | 0.962279i | \(0.412293\pi\) | |||||||
\(318\) | 2129.09 | 0.375451 | ||||||||
\(319\) | −2002.28 | −0.351430 | ||||||||
\(320\) | 1114.32 | 0.194663 | ||||||||
\(321\) | 5882.64 | 1.02286 | ||||||||
\(322\) | −38.8272 | −0.00671974 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −8183.38 | −1.39671 | ||||||||
\(326\) | 367.138 | 0.0623738 | ||||||||
\(327\) | 1056.85 | 0.178727 | ||||||||
\(328\) | −1368.85 | −0.230434 | ||||||||
\(329\) | −110.899 | −0.0185837 | ||||||||
\(330\) | 5611.60 | 0.936086 | ||||||||
\(331\) | −2172.26 | −0.360719 | −0.180360 | − | 0.983601i | \(-0.557726\pi\) | ||||
−0.180360 | + | 0.983601i | \(0.557726\pi\) | |||||||
\(332\) | 5661.35 | 0.935865 | ||||||||
\(333\) | −1385.42 | −0.227990 | ||||||||
\(334\) | 7045.17 | 1.15417 | ||||||||
\(335\) | 4838.75 | 0.789162 | ||||||||
\(336\) | 14.3049 | 0.00232262 | ||||||||
\(337\) | −9700.80 | −1.56806 | −0.784030 | − | 0.620722i | \(-0.786839\pi\) | ||||
−0.784030 | + | 0.620722i | \(0.786839\pi\) | |||||||
\(338\) | 173.855 | 0.0279777 | ||||||||
\(339\) | −6648.33 | −1.06516 | ||||||||
\(340\) | 6124.75 | 0.976945 | ||||||||
\(341\) | 9464.34 | 1.50300 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 204.415 | 0.0321789 | ||||||||
\(344\) | 1989.44 | 0.311812 | ||||||||
\(345\) | 3402.60 | 0.530985 | ||||||||
\(346\) | −6285.65 | −0.976644 | ||||||||
\(347\) | −483.729 | −0.0748356 | −0.0374178 | − | 0.999300i | \(-0.511913\pi\) | ||||
−0.0374178 | + | 0.999300i | \(0.511913\pi\) | |||||||
\(348\) | 447.300 | 0.0689017 | ||||||||
\(349\) | 11947.6 | 1.83250 | 0.916250 | − | 0.400607i | \(-0.131201\pi\) | ||||
0.916250 | + | 0.400607i | \(0.131201\pi\) | |||||||
\(350\) | 106.184 | 0.0162165 | ||||||||
\(351\) | 1240.26 | 0.188604 | ||||||||
\(352\) | −1718.93 | −0.260281 | ||||||||
\(353\) | 7542.02 | 1.13717 | 0.568585 | − | 0.822624i | \(-0.307491\pi\) | ||||
0.568585 | + | 0.822624i | \(0.307491\pi\) | |||||||
\(354\) | 4404.98 | 0.661362 | ||||||||
\(355\) | 15123.9 | 2.26111 | ||||||||
\(356\) | 5316.08 | 0.791437 | ||||||||
\(357\) | 78.6260 | 0.0116564 | ||||||||
\(358\) | 650.748 | 0.0960701 | ||||||||
\(359\) | 8295.22 | 1.21951 | 0.609756 | − | 0.792589i | \(-0.291267\pi\) | ||||
0.609756 | + | 0.792589i | \(0.291267\pi\) | |||||||
\(360\) | −1253.61 | −0.183530 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −5278.75 | −0.766422 | ||||||||
\(363\) | −4663.36 | −0.674278 | ||||||||
\(364\) | 54.7588 | 0.00788500 | ||||||||
\(365\) | −14695.7 | −2.10742 | ||||||||
\(366\) | −1033.00 | −0.147529 | ||||||||
\(367\) | −2998.67 | −0.426510 | −0.213255 | − | 0.976997i | \(-0.568407\pi\) | ||||
−0.213255 | + | 0.976997i | \(0.568407\pi\) | |||||||
\(368\) | −1042.27 | −0.147642 | ||||||||
\(369\) | 1539.96 | 0.217255 | ||||||||
\(370\) | 5360.40 | 0.753173 | ||||||||
\(371\) | −105.752 | −0.0147988 | ||||||||
\(372\) | −2114.29 | −0.294679 | ||||||||
\(373\) | −6597.74 | −0.915866 | −0.457933 | − | 0.888987i | \(-0.651410\pi\) | ||||
−0.457933 | + | 0.888987i | \(0.651410\pi\) | |||||||
\(374\) | −9447.94 | −1.30626 | ||||||||
\(375\) | −2776.18 | −0.382296 | ||||||||
\(376\) | −2976.95 | −0.408310 | ||||||||
\(377\) | 1712.25 | 0.233913 | ||||||||
\(378\) | −16.0931 | −0.00218978 | ||||||||
\(379\) | −6283.53 | −0.851618 | −0.425809 | − | 0.904813i | \(-0.640010\pi\) | ||||
−0.425809 | + | 0.904813i | \(0.640010\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7316.35 | 0.983800 | ||||||||
\(382\) | 7603.88 | 1.01845 | ||||||||
\(383\) | −3098.49 | −0.413383 | −0.206691 | − | 0.978406i | \(-0.566270\pi\) | ||||
−0.206691 | + | 0.978406i | \(0.566270\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −278.728 | −0.0368969 | ||||||||
\(386\) | 5068.86 | 0.668389 | ||||||||
\(387\) | −2238.12 | −0.293979 | ||||||||
\(388\) | 5882.72 | 0.769716 | ||||||||
\(389\) | 10304.6 | 1.34309 | 0.671546 | − | 0.740963i | \(-0.265631\pi\) | ||||
0.671546 | + | 0.740963i | \(0.265631\pi\) | |||||||
\(390\) | −4798.75 | −0.623062 | ||||||||
\(391\) | −5728.77 | −0.740963 | ||||||||
\(392\) | 2743.29 | 0.353462 | ||||||||
\(393\) | 4600.21 | 0.590458 | ||||||||
\(394\) | 8231.86 | 1.05258 | ||||||||
\(395\) | −5804.59 | −0.739394 | ||||||||
\(396\) | 1933.79 | 0.245396 | ||||||||
\(397\) | 10609.4 | 1.34124 | 0.670620 | − | 0.741801i | \(-0.266028\pi\) | ||||
0.670620 | + | 0.741801i | \(0.266028\pi\) | |||||||
\(398\) | −3062.66 | −0.385722 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2850.39 | 0.356299 | ||||||||
\(401\) | −13842.3 | −1.72382 | −0.861908 | − | 0.507065i | \(-0.830730\pi\) | ||||
−0.861908 | + | 0.507065i | \(0.830730\pi\) | |||||||
\(402\) | 1667.46 | 0.206879 | ||||||||
\(403\) | −8093.41 | −1.00040 | ||||||||
\(404\) | −2711.18 | −0.333877 | ||||||||
\(405\) | 1410.31 | 0.173034 | ||||||||
\(406\) | −22.2174 | −0.00271584 | ||||||||
\(407\) | −8268.87 | −1.00706 | ||||||||
\(408\) | 2110.63 | 0.256107 | ||||||||
\(409\) | 3161.28 | 0.382189 | 0.191095 | − | 0.981572i | \(-0.438796\pi\) | ||||
0.191095 | + | 0.981572i | \(0.438796\pi\) | |||||||
\(410\) | −5958.33 | −0.717710 | ||||||||
\(411\) | 3263.83 | 0.391710 | ||||||||
\(412\) | −6586.60 | −0.787617 | ||||||||
\(413\) | −218.795 | −0.0260683 | ||||||||
\(414\) | 1172.56 | 0.139198 | ||||||||
\(415\) | 24642.7 | 2.91485 | ||||||||
\(416\) | 1469.94 | 0.173244 | ||||||||
\(417\) | 148.116 | 0.0173939 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7703.02 | 0.898132 | 0.449066 | − | 0.893499i | \(-0.351757\pi\) | ||||
0.449066 | + | 0.893499i | \(0.351757\pi\) | |||||||
\(420\) | 62.2665 | 0.00723404 | ||||||||
\(421\) | 4734.35 | 0.548071 | 0.274036 | − | 0.961720i | \(-0.411641\pi\) | ||||
0.274036 | + | 0.961720i | \(0.411641\pi\) | |||||||
\(422\) | −2863.80 | −0.330350 | ||||||||
\(423\) | 3349.07 | 0.384958 | ||||||||
\(424\) | −2838.79 | −0.325150 | ||||||||
\(425\) | 15666.9 | 1.78814 | ||||||||
\(426\) | 5211.80 | 0.592753 | ||||||||
\(427\) | 51.3090 | 0.00581503 | ||||||||
\(428\) | −7843.52 | −0.885819 | ||||||||
\(429\) | 7402.48 | 0.833088 | ||||||||
\(430\) | 8659.61 | 0.971171 | ||||||||
\(431\) | 9552.77 | 1.06761 | 0.533806 | − | 0.845607i | \(-0.320761\pi\) | ||||
0.533806 | + | 0.845607i | \(0.320761\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | 15829.3 | 1.75684 | 0.878418 | − | 0.477894i | \(-0.158600\pi\) | ||||
0.878418 | + | 0.477894i | \(0.158600\pi\) | |||||||
\(434\) | 105.017 | 0.0116151 | ||||||||
\(435\) | 1947.01 | 0.214602 | ||||||||
\(436\) | −1409.13 | −0.154782 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −5064.23 | −0.552462 | ||||||||
\(439\) | 12163.0 | 1.32234 | 0.661169 | − | 0.750237i | \(-0.270061\pi\) | ||||
0.661169 | + | 0.750237i | \(0.270061\pi\) | |||||||
\(440\) | −7482.13 | −0.810674 | ||||||||
\(441\) | −3086.20 | −0.333247 | ||||||||
\(442\) | 8079.39 | 0.869451 | ||||||||
\(443\) | 10738.1 | 1.15165 | 0.575826 | − | 0.817573i | \(-0.304681\pi\) | ||||
0.575826 | + | 0.817573i | \(0.304681\pi\) | |||||||
\(444\) | 1847.23 | 0.197445 | ||||||||
\(445\) | 23139.8 | 2.46501 | ||||||||
\(446\) | −6276.64 | −0.666384 | ||||||||
\(447\) | −7697.45 | −0.814490 | ||||||||
\(448\) | −19.0733 | −0.00201144 | ||||||||
\(449\) | 11902.2 | 1.25101 | 0.625503 | − | 0.780222i | \(-0.284894\pi\) | ||||
0.625503 | + | 0.780222i | \(0.284894\pi\) | |||||||
\(450\) | −3206.69 | −0.335921 | ||||||||
\(451\) | 9191.23 | 0.959641 | ||||||||
\(452\) | 8864.45 | 0.922452 | ||||||||
\(453\) | −140.648 | −0.0145876 | ||||||||
\(454\) | 7775.32 | 0.803775 | ||||||||
\(455\) | 238.354 | 0.0245587 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14980.8 | −1.53342 | −0.766709 | − | 0.641995i | \(-0.778107\pi\) | ||||
−0.766709 | + | 0.641995i | \(0.778107\pi\) | |||||||
\(458\) | 917.247 | 0.0935811 | ||||||||
\(459\) | −2374.45 | −0.241460 | ||||||||
\(460\) | −4536.80 | −0.459847 | ||||||||
\(461\) | 1153.32 | 0.116520 | 0.0582598 | − | 0.998301i | \(-0.481445\pi\) | ||||
0.0582598 | + | 0.998301i | \(0.481445\pi\) | |||||||
\(462\) | −96.0513 | −0.00967254 | ||||||||
\(463\) | 9780.17 | 0.981691 | 0.490846 | − | 0.871247i | \(-0.336688\pi\) | ||||
0.490846 | + | 0.871247i | \(0.336688\pi\) | |||||||
\(464\) | −596.400 | −0.0596707 | ||||||||
\(465\) | −9203.07 | −0.917811 | ||||||||
\(466\) | −8703.71 | −0.865218 | ||||||||
\(467\) | 14300.1 | 1.41698 | 0.708492 | − | 0.705719i | \(-0.249376\pi\) | ||||
0.708492 | + | 0.705719i | \(0.249376\pi\) | |||||||
\(468\) | −1653.68 | −0.163336 | ||||||||
\(469\) | −82.8229 | −0.00815438 | ||||||||
\(470\) | −12958.1 | −1.27173 | ||||||||
\(471\) | −8665.01 | −0.847691 | ||||||||
\(472\) | −5873.31 | −0.572756 | ||||||||
\(473\) | −13358.2 | −1.29854 | ||||||||
\(474\) | −2000.30 | −0.193833 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −104.835 | −0.0100947 | ||||||||
\(477\) | 3193.64 | 0.306555 | ||||||||
\(478\) | 137.958 | 0.0132009 | ||||||||
\(479\) | −1760.50 | −0.167932 | −0.0839658 | − | 0.996469i | \(-0.526759\pi\) | ||||
−0.0839658 | + | 0.996469i | \(0.526759\pi\) | |||||||
\(480\) | 1671.47 | 0.158942 | ||||||||
\(481\) | 7071.11 | 0.670301 | ||||||||
\(482\) | 79.3442 | 0.00749799 | ||||||||
\(483\) | −58.2409 | −0.00548665 | ||||||||
\(484\) | 6217.82 | 0.583942 | ||||||||
\(485\) | 25606.3 | 2.39736 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | −8313.61 | −0.773564 | −0.386782 | − | 0.922171i | \(-0.626413\pi\) | ||||
−0.386782 | + | 0.922171i | \(0.626413\pi\) | |||||||
\(488\) | 1377.33 | 0.127764 | ||||||||
\(489\) | 550.706 | 0.0509280 | ||||||||
\(490\) | 11941.0 | 1.10089 | ||||||||
\(491\) | 5072.82 | 0.466259 | 0.233130 | − | 0.972446i | \(-0.425103\pi\) | ||||
0.233130 | + | 0.972446i | \(0.425103\pi\) | |||||||
\(492\) | −2053.28 | −0.188148 | ||||||||
\(493\) | −3278.07 | −0.299466 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8417.40 | 0.764311 | ||||||||
\(496\) | 2819.05 | 0.255200 | ||||||||
\(497\) | −258.870 | −0.0233640 | ||||||||
\(498\) | 8492.03 | 0.764130 | ||||||||
\(499\) | 7893.74 | 0.708161 | 0.354080 | − | 0.935215i | \(-0.384794\pi\) | ||||
0.354080 | + | 0.935215i | \(0.384794\pi\) | |||||||
\(500\) | 3701.57 | 0.331078 | ||||||||
\(501\) | 10567.8 | 0.942380 | ||||||||
\(502\) | 11766.7 | 1.04616 | ||||||||
\(503\) | 14575.6 | 1.29203 | 0.646016 | − | 0.763323i | \(-0.276434\pi\) | ||||
0.646016 | + | 0.763323i | \(0.276434\pi\) | |||||||
\(504\) | 21.4574 | 0.00189641 | ||||||||
\(505\) | −11801.2 | −1.03990 | ||||||||
\(506\) | 6998.40 | 0.614855 | ||||||||
\(507\) | 260.782 | 0.0228437 | ||||||||
\(508\) | −9755.13 | −0.851996 | ||||||||
\(509\) | −4331.64 | −0.377204 | −0.188602 | − | 0.982054i | \(-0.560396\pi\) | ||||
−0.188602 | + | 0.982054i | \(0.560396\pi\) | |||||||
\(510\) | 9187.12 | 0.797672 | ||||||||
\(511\) | 251.540 | 0.0217759 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6153.40 | 0.528044 | ||||||||
\(515\) | −28670.1 | −2.45312 | ||||||||
\(516\) | 2984.15 | 0.254593 | ||||||||
\(517\) | 19988.9 | 1.70041 | ||||||||
\(518\) | −91.7517 | −0.00778250 | ||||||||
\(519\) | −9428.48 | −0.797427 | ||||||||
\(520\) | 6398.33 | 0.539588 | ||||||||
\(521\) | −13878.8 | −1.16707 | −0.583535 | − | 0.812088i | \(-0.698331\pi\) | ||||
−0.583535 | + | 0.812088i | \(0.698331\pi\) | |||||||
\(522\) | 670.950 | 0.0562580 | ||||||||
\(523\) | −4580.75 | −0.382987 | −0.191494 | − | 0.981494i | \(-0.561333\pi\) | ||||
−0.191494 | + | 0.981494i | \(0.561333\pi\) | |||||||
\(524\) | −6133.61 | −0.511351 | ||||||||
\(525\) | 159.276 | 0.0132407 | ||||||||
\(526\) | 3221.87 | 0.267073 | ||||||||
\(527\) | 15494.7 | 1.28076 | ||||||||
\(528\) | −2578.39 | −0.212519 | ||||||||
\(529\) | −7923.51 | −0.651230 | ||||||||
\(530\) | −12356.7 | −1.01272 | ||||||||
\(531\) | 6607.47 | 0.539999 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7859.87 | −0.638740 | ||||||||
\(534\) | 7974.12 | 0.646205 | ||||||||
\(535\) | −34141.2 | −2.75898 | ||||||||
\(536\) | −2223.29 | −0.179163 | ||||||||
\(537\) | 976.122 | 0.0784409 | ||||||||
\(538\) | −11784.9 | −0.944389 | ||||||||
\(539\) | −18420.0 | −1.47199 | ||||||||
\(540\) | −1880.41 | −0.149852 | ||||||||
\(541\) | −4696.29 | −0.373215 | −0.186608 | − | 0.982435i | \(-0.559749\pi\) | ||||
−0.186608 | + | 0.982435i | \(0.559749\pi\) | |||||||
\(542\) | −4860.60 | −0.385204 | ||||||||
\(543\) | −7918.12 | −0.625781 | ||||||||
\(544\) | −2814.17 | −0.221795 | ||||||||
\(545\) | −6133.66 | −0.482086 | ||||||||
\(546\) | 82.1382 | 0.00643808 | ||||||||
\(547\) | −8293.13 | −0.648243 | −0.324121 | − | 0.946016i | \(-0.605069\pi\) | ||||
−0.324121 | + | 0.946016i | \(0.605069\pi\) | |||||||
\(548\) | −4351.77 | −0.339230 | ||||||||
\(549\) | −1549.50 | −0.120457 | ||||||||
\(550\) | −19139.1 | −1.48381 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1563.41 | −0.120549 | ||||||||
\(553\) | 99.3547 | 0.00764013 | ||||||||
\(554\) | −3146.38 | −0.241294 | ||||||||
\(555\) | 8040.60 | 0.614963 | ||||||||
\(556\) | −197.487 | −0.0150635 | ||||||||
\(557\) | −11787.1 | −0.896654 | −0.448327 | − | 0.893870i | \(-0.647980\pi\) | ||||
−0.448327 | + | 0.893870i | \(0.647980\pi\) | |||||||
\(558\) | −3171.43 | −0.240605 | ||||||||
\(559\) | 11423.2 | 0.864313 | ||||||||
\(560\) | −83.0220 | −0.00626486 | ||||||||
\(561\) | −14171.9 | −1.06656 | ||||||||
\(562\) | −6500.71 | −0.487928 | ||||||||
\(563\) | −9868.41 | −0.738728 | −0.369364 | − | 0.929285i | \(-0.620424\pi\) | ||||
−0.369364 | + | 0.929285i | \(0.620424\pi\) | |||||||
\(564\) | −4465.43 | −0.333384 | ||||||||
\(565\) | 38585.1 | 2.87308 | ||||||||
\(566\) | −2567.43 | −0.190667 | ||||||||
\(567\) | −24.1396 | −0.00178795 | ||||||||
\(568\) | −6949.07 | −0.513339 | ||||||||
\(569\) | 16579.6 | 1.22154 | 0.610768 | − | 0.791810i | \(-0.290861\pi\) | ||||
0.610768 | + | 0.791810i | \(0.290861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9453.06 | −0.692817 | −0.346408 | − | 0.938084i | \(-0.612599\pi\) | ||||
−0.346408 | + | 0.938084i | \(0.612599\pi\) | |||||||
\(572\) | −9869.97 | −0.721476 | ||||||||
\(573\) | 11405.8 | 0.831562 | ||||||||
\(574\) | 101.986 | 0.00741607 | ||||||||
\(575\) | −11605.0 | −0.841674 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −23284.1 | −1.67995 | −0.839974 | − | 0.542627i | \(-0.817430\pi\) | ||||
−0.839974 | + | 0.542627i | \(0.817430\pi\) | |||||||
\(578\) | −5641.85 | −0.406004 | ||||||||
\(579\) | 7603.29 | 0.545738 | ||||||||
\(580\) | −2596.01 | −0.185851 | ||||||||
\(581\) | −421.799 | −0.0301190 | ||||||||
\(582\) | 8824.07 | 0.628470 | ||||||||
\(583\) | 19061.2 | 1.35409 | ||||||||
\(584\) | 6752.31 | 0.478446 | ||||||||
\(585\) | −7198.13 | −0.508728 | ||||||||
\(586\) | −10416.4 | −0.734296 | ||||||||
\(587\) | −18491.4 | −1.30021 | −0.650103 | − | 0.759846i | \(-0.725274\pi\) | ||||
−0.650103 | + | 0.759846i | \(0.725274\pi\) | |||||||
\(588\) | 4114.93 | 0.288600 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −25565.3 | −1.78391 | ||||||||
\(591\) | 12347.8 | 0.859425 | ||||||||
\(592\) | −2462.97 | −0.170992 | ||||||||
\(593\) | −4642.52 | −0.321493 | −0.160747 | − | 0.986996i | \(-0.551390\pi\) | ||||
−0.160747 | + | 0.986996i | \(0.551390\pi\) | |||||||
\(594\) | 2900.69 | 0.200365 | ||||||||
\(595\) | −456.324 | −0.0314411 | ||||||||
\(596\) | 10263.3 | 0.705369 | ||||||||
\(597\) | −4593.99 | −0.314941 | ||||||||
\(598\) | −5984.67 | −0.409250 | ||||||||
\(599\) | 13658.6 | 0.931675 | 0.465838 | − | 0.884870i | \(-0.345753\pi\) | ||||
0.465838 | + | 0.884870i | \(0.345753\pi\) | |||||||
\(600\) | 4275.58 | 0.290917 | ||||||||
\(601\) | −9070.65 | −0.615640 | −0.307820 | − | 0.951445i | \(-0.599599\pi\) | ||||
−0.307820 | + | 0.951445i | \(0.599599\pi\) | |||||||
\(602\) | −148.223 | −0.0100351 | ||||||||
\(603\) | 2501.20 | 0.168916 | ||||||||
\(604\) | 187.530 | 0.0126333 | ||||||||
\(605\) | 27064.9 | 1.81875 | ||||||||
\(606\) | −4066.78 | −0.272610 | ||||||||
\(607\) | 9500.94 | 0.635307 | 0.317653 | − | 0.948207i | \(-0.397105\pi\) | ||||
0.317653 | + | 0.948207i | \(0.397105\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33.3261 | −0.00221747 | ||||||||
\(610\) | 5995.24 | 0.397935 | ||||||||
\(611\) | −17093.5 | −1.13180 | ||||||||
\(612\) | 3165.94 | 0.209110 | ||||||||
\(613\) | 12685.1 | 0.835802 | 0.417901 | − | 0.908493i | \(-0.362766\pi\) | ||||
0.417901 | + | 0.908493i | \(0.362766\pi\) | |||||||
\(614\) | −959.130 | −0.0630413 | ||||||||
\(615\) | −8937.50 | −0.586008 | ||||||||
\(616\) | 128.068 | 0.00837666 | ||||||||
\(617\) | −17506.1 | −1.14225 | −0.571125 | − | 0.820863i | \(-0.693493\pi\) | ||||
−0.571125 | + | 0.820863i | \(0.693493\pi\) | |||||||
\(618\) | −9879.89 | −0.643087 | ||||||||
\(619\) | −11070.4 | −0.718834 | −0.359417 | − | 0.933177i | \(-0.617024\pi\) | ||||
−0.359417 | + | 0.933177i | \(0.617024\pi\) | |||||||
\(620\) | 12270.8 | 0.794847 | ||||||||
\(621\) | 1758.84 | 0.113655 | ||||||||
\(622\) | −3284.45 | −0.211727 | ||||||||
\(623\) | −396.074 | −0.0254709 | ||||||||
\(624\) | 2204.91 | 0.141453 | ||||||||
\(625\) | −6156.50 | −0.394016 | ||||||||
\(626\) | −16037.4 | −1.02393 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11553.3 | 0.734122 | ||||||||
\(629\) | −13537.5 | −0.858149 | ||||||||
\(630\) | 93.3998 | 0.00590657 | ||||||||
\(631\) | −14996.3 | −0.946108 | −0.473054 | − | 0.881033i | \(-0.656848\pi\) | ||||
−0.473054 | + | 0.881033i | \(0.656848\pi\) | |||||||
\(632\) | 2667.06 | 0.167864 | ||||||||
\(633\) | −4295.70 | −0.269730 | ||||||||
\(634\) | −6142.19 | −0.384760 | ||||||||
\(635\) | −42462.1 | −2.65363 | ||||||||
\(636\) | −4258.18 | −0.265484 | ||||||||
\(637\) | 15751.8 | 0.979763 | ||||||||
\(638\) | 4004.56 | 0.248499 | ||||||||
\(639\) | 7817.71 | 0.483981 | ||||||||
\(640\) | −2228.63 | −0.137647 | ||||||||
\(641\) | 5497.70 | 0.338762 | 0.169381 | − | 0.985551i | \(-0.445823\pi\) | ||||
0.169381 | + | 0.985551i | \(0.445823\pi\) | |||||||
\(642\) | −11765.3 | −0.723268 | ||||||||
\(643\) | 4295.23 | 0.263433 | 0.131716 | − | 0.991287i | \(-0.457951\pi\) | ||||
0.131716 | + | 0.991287i | \(0.457951\pi\) | |||||||
\(644\) | 77.6545 | 0.00475158 | ||||||||
\(645\) | 12989.4 | 0.792958 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8674.61 | −0.527101 | −0.263550 | − | 0.964646i | \(-0.584893\pi\) | ||||
−0.263550 | + | 0.964646i | \(0.584893\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | 39436.6 | 2.38524 | ||||||||
\(650\) | 16366.8 | 0.987626 | ||||||||
\(651\) | 157.525 | 0.00948370 | ||||||||
\(652\) | −734.275 | −0.0441050 | ||||||||
\(653\) | 4186.04 | 0.250861 | 0.125430 | − | 0.992102i | \(-0.459969\pi\) | ||||
0.125430 | + | 0.992102i | \(0.459969\pi\) | |||||||
\(654\) | −2113.70 | −0.126379 | ||||||||
\(655\) | −26698.4 | −1.59266 | ||||||||
\(656\) | 2737.70 | 0.162941 | ||||||||
\(657\) | −7596.35 | −0.451083 | ||||||||
\(658\) | 221.798 | 0.0131407 | ||||||||
\(659\) | −701.546 | −0.0414694 | −0.0207347 | − | 0.999785i | \(-0.506601\pi\) | ||||
−0.0207347 | + | 0.999785i | \(0.506601\pi\) | |||||||
\(660\) | −11223.2 | −0.661913 | ||||||||
\(661\) | 30247.4 | 1.77986 | 0.889931 | − | 0.456095i | \(-0.150752\pi\) | ||||
0.889931 | + | 0.456095i | \(0.150752\pi\) | |||||||
\(662\) | 4344.52 | 0.255067 | ||||||||
\(663\) | 12119.1 | 0.709904 | ||||||||
\(664\) | −11322.7 | −0.661756 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2770.84 | 0.161213 | ||||||||
\(667\) | 2428.17 | 0.140958 | ||||||||
\(668\) | −14090.3 | −0.816125 | ||||||||
\(669\) | −9414.95 | −0.544100 | ||||||||
\(670\) | −9677.51 | −0.558022 | ||||||||
\(671\) | −9248.16 | −0.532074 | ||||||||
\(672\) | −28.6099 | −0.00164234 | ||||||||
\(673\) | −12697.3 | −0.727259 | −0.363629 | − | 0.931544i | \(-0.618463\pi\) | ||||
−0.363629 | + | 0.931544i | \(0.618463\pi\) | |||||||
\(674\) | 19401.6 | 1.10879 | ||||||||
\(675\) | −4810.03 | −0.274279 | ||||||||
\(676\) | −347.709 | −0.0197832 | ||||||||
\(677\) | 17211.1 | 0.977071 | 0.488535 | − | 0.872544i | \(-0.337531\pi\) | ||||
0.488535 | + | 0.872544i | \(0.337531\pi\) | |||||||
\(678\) | 13296.7 | 0.753179 | ||||||||
\(679\) | −438.291 | −0.0247718 | ||||||||
\(680\) | −12249.5 | −0.690804 | ||||||||
\(681\) | 11663.0 | 0.656279 | ||||||||
\(682\) | −18928.7 | −1.06278 | ||||||||
\(683\) | −3009.45 | −0.168599 | −0.0842996 | − | 0.996440i | \(-0.526865\pi\) | ||||
−0.0842996 | + | 0.996440i | \(0.526865\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18942.4 | −1.05657 | ||||||||
\(686\) | −408.830 | −0.0227539 | ||||||||
\(687\) | 1375.87 | 0.0764086 | ||||||||
\(688\) | −3978.87 | −0.220484 | ||||||||
\(689\) | −16300.2 | −0.901287 | ||||||||
\(690\) | −6805.20 | −0.375463 | ||||||||
\(691\) | −15027.3 | −0.827303 | −0.413652 | − | 0.910435i | \(-0.635747\pi\) | ||||
−0.413652 | + | 0.910435i | \(0.635747\pi\) | |||||||
\(692\) | 12571.3 | 0.690592 | ||||||||
\(693\) | −144.077 | −0.00789759 | ||||||||
\(694\) | 967.458 | 0.0529167 | ||||||||
\(695\) | −859.623 | −0.0469170 | ||||||||
\(696\) | −894.600 | −0.0487209 | ||||||||
\(697\) | 15047.6 | 0.817744 | ||||||||
\(698\) | −23895.3 | −1.29577 | ||||||||
\(699\) | −13055.6 | −0.706448 | ||||||||
\(700\) | −212.368 | −0.0114668 | ||||||||
\(701\) | 6827.82 | 0.367879 | 0.183940 | − | 0.982938i | \(-0.441115\pi\) | ||||
0.183940 | + | 0.982938i | \(0.441115\pi\) | |||||||
\(702\) | −2480.52 | −0.133363 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 3437.85 | 0.184047 | ||||||||
\(705\) | −19437.1 | −1.03836 | ||||||||
\(706\) | −15084.0 | −0.804101 | ||||||||
\(707\) | 201.997 | 0.0107452 | ||||||||
\(708\) | −8809.96 | −0.467653 | ||||||||
\(709\) | 19077.9 | 1.01056 | 0.505280 | − | 0.862956i | \(-0.331389\pi\) | ||||
0.505280 | + | 0.862956i | \(0.331389\pi\) | |||||||
\(710\) | −30247.9 | −1.59885 | ||||||||
\(711\) | −3000.45 | −0.158264 | ||||||||
\(712\) | −10632.2 | −0.559630 | ||||||||
\(713\) | −11477.4 | −0.602851 | ||||||||
\(714\) | −157.252 | −0.00824231 | ||||||||
\(715\) | −42962.0 | −2.24711 | ||||||||
\(716\) | −1301.50 | −0.0679318 | ||||||||
\(717\) | 206.936 | 0.0107785 | ||||||||
\(718\) | −16590.4 | −0.862326 | ||||||||
\(719\) | −26690.8 | −1.38442 | −0.692210 | − | 0.721696i | \(-0.743363\pi\) | ||||
−0.692210 | + | 0.721696i | \(0.743363\pi\) | |||||||
\(720\) | 2507.21 | 0.129775 | ||||||||
\(721\) | 490.734 | 0.0253480 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 119.016 | 0.00612208 | ||||||||
\(724\) | 10557.5 | 0.541942 | ||||||||
\(725\) | −6640.52 | −0.340169 | ||||||||
\(726\) | 9326.73 | 0.476787 | ||||||||
\(727\) | 24306.5 | 1.24000 | 0.619998 | − | 0.784604i | \(-0.287134\pi\) | ||||
0.619998 | + | 0.784604i | \(0.287134\pi\) | |||||||
\(728\) | −109.518 | −0.00557554 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 29391.4 | 1.49017 | ||||||||
\(731\) | −21869.6 | −1.10653 | ||||||||
\(732\) | 2066.00 | 0.104319 | ||||||||
\(733\) | 27102.2 | 1.36568 | 0.682841 | − | 0.730567i | \(-0.260744\pi\) | ||||
0.682841 | + | 0.730567i | \(0.260744\pi\) | |||||||
\(734\) | 5997.34 | 0.301588 | ||||||||
\(735\) | 17911.5 | 0.898877 | ||||||||
\(736\) | 2084.55 | 0.104399 | ||||||||
\(737\) | 14928.4 | 0.746124 | ||||||||
\(738\) | −3079.92 | −0.153622 | ||||||||
\(739\) | 14638.0 | 0.728643 | 0.364321 | − | 0.931273i | \(-0.381301\pi\) | ||||
0.364321 | + | 0.931273i | \(0.381301\pi\) | |||||||
\(740\) | −10720.8 | −0.532573 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 211.504 | 0.0104644 | ||||||||
\(743\) | 19681.2 | 0.971782 | 0.485891 | − | 0.874020i | \(-0.338495\pi\) | ||||
0.485891 | + | 0.874020i | \(0.338495\pi\) | |||||||
\(744\) | 4228.58 | 0.208370 | ||||||||
\(745\) | 44673.9 | 2.19695 | ||||||||
\(746\) | 13195.5 | 0.647615 | ||||||||
\(747\) | 12738.0 | 0.623910 | ||||||||
\(748\) | 18895.9 | 0.923666 | ||||||||
\(749\) | 584.381 | 0.0285084 | ||||||||
\(750\) | 5552.35 | 0.270324 | ||||||||
\(751\) | 7288.23 | 0.354129 | 0.177065 | − | 0.984199i | \(-0.443340\pi\) | ||||
0.177065 | + | 0.984199i | \(0.443340\pi\) | |||||||
\(752\) | 5953.90 | 0.288719 | ||||||||
\(753\) | 17650.0 | 0.854187 | ||||||||
\(754\) | −3424.49 | −0.165402 | ||||||||
\(755\) | 816.280 | 0.0393477 | ||||||||
\(756\) | 32.1861 | 0.00154841 | ||||||||
\(757\) | −25114.6 | −1.20582 | −0.602911 | − | 0.797808i | \(-0.705993\pi\) | ||||
−0.602911 | + | 0.797808i | \(0.705993\pi\) | |||||||
\(758\) | 12567.1 | 0.602185 | ||||||||
\(759\) | 10497.6 | 0.502027 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36270.2 | 1.72772 | 0.863859 | − | 0.503734i | \(-0.168041\pi\) | ||||
0.863859 | + | 0.503734i | \(0.168041\pi\) | |||||||
\(762\) | −14632.7 | −0.695652 | ||||||||
\(763\) | 104.987 | 0.00498138 | ||||||||
\(764\) | −15207.8 | −0.720154 | ||||||||
\(765\) | 13780.7 | 0.651296 | ||||||||
\(766\) | 6196.99 | 0.292306 | ||||||||
\(767\) | −33724.2 | −1.58763 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | −11999.4 | −0.562690 | −0.281345 | − | 0.959607i | \(-0.590781\pi\) | ||||
−0.281345 | + | 0.959607i | \(0.590781\pi\) | |||||||
\(770\) | 557.456 | 0.0260900 | ||||||||
\(771\) | 9230.10 | 0.431146 | ||||||||
\(772\) | −10137.7 | −0.472623 | ||||||||
\(773\) | −27176.5 | −1.26451 | −0.632257 | − | 0.774759i | \(-0.717871\pi\) | ||||
−0.632257 | + | 0.774759i | \(0.717871\pi\) | |||||||
\(774\) | 4476.23 | 0.207874 | ||||||||
\(775\) | 31388.3 | 1.45484 | ||||||||
\(776\) | −11765.4 | −0.544271 | ||||||||
\(777\) | −137.627 | −0.00635439 | ||||||||
\(778\) | −20609.1 | −0.949709 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 9597.50 | 0.440571 | ||||||||
\(781\) | 46659.9 | 2.13780 | ||||||||
\(782\) | 11457.5 | 0.523940 | ||||||||
\(783\) | 1006.43 | 0.0459345 | ||||||||
\(784\) | −5486.58 | −0.249935 | ||||||||
\(785\) | 50289.4 | 2.28650 | ||||||||
\(786\) | −9200.42 | −0.417517 | ||||||||
\(787\) | 549.906 | 0.0249073 | 0.0124536 | − | 0.999922i | \(-0.496036\pi\) | ||||
0.0124536 | + | 0.999922i | \(0.496036\pi\) | |||||||
\(788\) | −16463.7 | −0.744284 | ||||||||
\(789\) | 4832.80 | 0.218064 | ||||||||
\(790\) | 11609.2 | 0.522830 | ||||||||
\(791\) | −660.445 | −0.0296874 | ||||||||
\(792\) | −3867.58 | −0.173521 | ||||||||
\(793\) | 7908.55 | 0.354150 | ||||||||
\(794\) | −21218.9 | −0.948399 | ||||||||
\(795\) | −18535.0 | −0.826879 | ||||||||
\(796\) | 6125.32 | 0.272747 | ||||||||
\(797\) | 30526.9 | 1.35674 | 0.678368 | − | 0.734722i | \(-0.262687\pi\) | ||||
0.678368 | + | 0.734722i | \(0.262687\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32725.2 | 1.44898 | ||||||||
\(800\) | −5700.78 | −0.251941 | ||||||||
\(801\) | 11961.2 | 0.527625 | ||||||||
\(802\) | 27684.5 | 1.21892 | ||||||||
\(803\) | −45338.7 | −1.99249 | ||||||||
\(804\) | −3334.93 | −0.146286 | ||||||||
\(805\) | 338.014 | 0.0147993 | ||||||||
\(806\) | 16186.8 | 0.707390 | ||||||||
\(807\) | −17677.3 | −0.771091 | ||||||||
\(808\) | 5422.37 | 0.236087 | ||||||||
\(809\) | 37891.7 | 1.64673 | 0.823364 | − | 0.567514i | \(-0.192095\pi\) | ||||
0.823364 | + | 0.567514i | \(0.192095\pi\) | |||||||
\(810\) | −2820.61 | −0.122353 | ||||||||
\(811\) | −2925.25 | −0.126658 | −0.0633289 | − | 0.997993i | \(-0.520172\pi\) | ||||
−0.0633289 | + | 0.997993i | \(0.520172\pi\) | |||||||
\(812\) | 44.4348 | 0.00192039 | ||||||||
\(813\) | −7290.90 | −0.314518 | ||||||||
\(814\) | 16537.7 | 0.712097 | ||||||||
\(815\) | −3196.15 | −0.137370 | ||||||||
\(816\) | −4221.25 | −0.181095 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −6322.57 | −0.270249 | ||||||||
\(819\) | 123.207 | 0.00525667 | ||||||||
\(820\) | 11916.7 | 0.507497 | ||||||||
\(821\) | −5014.51 | −0.213164 | −0.106582 | − | 0.994304i | \(-0.533991\pi\) | ||||
−0.106582 | + | 0.994304i | \(0.533991\pi\) | |||||||
\(822\) | −6527.65 | −0.276980 | ||||||||
\(823\) | −6409.06 | −0.271453 | −0.135726 | − | 0.990746i | \(-0.543337\pi\) | ||||
−0.135726 | + | 0.990746i | \(0.543337\pi\) | |||||||
\(824\) | 13173.2 | 0.556929 | ||||||||
\(825\) | −28708.6 | −1.21152 | ||||||||
\(826\) | 437.590 | 0.0184331 | ||||||||
\(827\) | −41427.8 | −1.74194 | −0.870970 | − | 0.491336i | \(-0.836509\pi\) | ||||
−0.870970 | + | 0.491336i | \(0.836509\pi\) | |||||||
\(828\) | −2345.11 | −0.0984279 | ||||||||
\(829\) | −35010.4 | −1.46678 | −0.733390 | − | 0.679808i | \(-0.762063\pi\) | ||||
−0.733390 | + | 0.679808i | \(0.762063\pi\) | |||||||
\(830\) | −49285.4 | −2.06111 | ||||||||
\(831\) | −4719.57 | −0.197016 | ||||||||
\(832\) | −2939.87 | −0.122502 | ||||||||
\(833\) | −30156.6 | −1.25434 | ||||||||
\(834\) | −296.231 | −0.0122993 | ||||||||
\(835\) | −61332.3 | −2.54191 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4757.15 | −0.196453 | ||||||||
\(838\) | −15406.0 | −0.635075 | ||||||||
\(839\) | 2489.62 | 0.102445 | 0.0512223 | − | 0.998687i | \(-0.483688\pi\) | ||||
0.0512223 | + | 0.998687i | \(0.483688\pi\) | |||||||
\(840\) | −124.533 | −0.00511524 | ||||||||
\(841\) | −22999.6 | −0.943031 | ||||||||
\(842\) | −9468.69 | −0.387545 | ||||||||
\(843\) | −9751.06 | −0.398392 | ||||||||
\(844\) | 5727.60 | 0.233593 | ||||||||
\(845\) | −1513.51 | −0.0616169 | ||||||||
\(846\) | −6698.14 | −0.272207 | ||||||||
\(847\) | −463.258 | −0.0187931 | ||||||||
\(848\) | 5677.58 | 0.229916 | ||||||||
\(849\) | −3851.15 | −0.155679 | ||||||||
\(850\) | −31333.9 | −1.26440 | ||||||||
\(851\) | 10027.7 | 0.403930 | ||||||||
\(852\) | −10423.6 | −0.419140 | ||||||||
\(853\) | 619.844 | 0.0248805 | 0.0124402 | − | 0.999923i | \(-0.496040\pi\) | ||||
0.0124402 | + | 0.999923i | \(0.496040\pi\) | |||||||
\(854\) | −102.618 | −0.00411184 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15687.0 | 0.626369 | ||||||||
\(857\) | 40352.1 | 1.60840 | 0.804201 | − | 0.594357i | \(-0.202594\pi\) | ||||
0.804201 | + | 0.594357i | \(0.202594\pi\) | |||||||
\(858\) | −14805.0 | −0.589082 | ||||||||
\(859\) | −32744.2 | −1.30060 | −0.650302 | − | 0.759676i | \(-0.725358\pi\) | ||||
−0.650302 | + | 0.759676i | \(0.725358\pi\) | |||||||
\(860\) | −17319.2 | −0.686721 | ||||||||
\(861\) | 152.979 | 0.00605519 | ||||||||
\(862\) | −19105.5 | −0.754916 | ||||||||
\(863\) | −14658.3 | −0.578186 | −0.289093 | − | 0.957301i | \(-0.593354\pi\) | ||||
−0.289093 | + | 0.957301i | \(0.593354\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | 54720.3 | 2.15092 | ||||||||
\(866\) | −31658.7 | −1.24227 | ||||||||
\(867\) | −8462.78 | −0.331501 | ||||||||
\(868\) | −210.033 | −0.00821313 | ||||||||
\(869\) | −17908.1 | −0.699070 | ||||||||
\(870\) | −3894.01 | −0.151746 | ||||||||
\(871\) | −12766.0 | −0.496623 | ||||||||
\(872\) | 2818.26 | 0.109448 | ||||||||
\(873\) | 13236.1 | 0.513144 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −275.785 | −0.0106551 | ||||||||
\(876\) | 10128.5 | 0.390650 | ||||||||
\(877\) | −13235.2 | −0.509604 | −0.254802 | − | 0.966993i | \(-0.582010\pi\) | ||||
−0.254802 | + | 0.966993i | \(0.582010\pi\) | |||||||
\(878\) | −24325.9 | −0.935033 | ||||||||
\(879\) | −15624.6 | −0.599550 | ||||||||
\(880\) | 14964.3 | 0.573233 | ||||||||
\(881\) | 4433.78 | 0.169555 | 0.0847775 | − | 0.996400i | \(-0.472982\pi\) | ||||
0.0847775 | + | 0.996400i | \(0.472982\pi\) | |||||||
\(882\) | 6172.40 | 0.235641 | ||||||||
\(883\) | 41092.0 | 1.56609 | 0.783044 | − | 0.621967i | \(-0.213666\pi\) | ||||
0.783044 | + | 0.621967i | \(0.213666\pi\) | |||||||
\(884\) | −16158.8 | −0.614795 | ||||||||
\(885\) | −38347.9 | −1.45656 | ||||||||
\(886\) | −21476.2 | −0.814340 | ||||||||
\(887\) | 19295.4 | 0.730414 | 0.365207 | − | 0.930926i | \(-0.380998\pi\) | ||||
0.365207 | + | 0.930926i | \(0.380998\pi\) | |||||||
\(888\) | −3694.45 | −0.139615 | ||||||||
\(889\) | 726.805 | 0.0274199 | ||||||||
\(890\) | −46279.6 | −1.74303 | ||||||||
\(891\) | 4351.03 | 0.163597 | ||||||||
\(892\) | 12553.3 | 0.471205 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 15394.9 | 0.575931 | ||||||||
\(895\) | −5665.15 | −0.211581 | ||||||||
\(896\) | 38.1465 | 0.00142231 | ||||||||
\(897\) | −8977.00 | −0.334151 | ||||||||
\(898\) | −23804.5 | −0.884594 | ||||||||
\(899\) | −6567.51 | −0.243647 | ||||||||
\(900\) | 6413.37 | 0.237532 | ||||||||
\(901\) | 31206.4 | 1.15387 | ||||||||
\(902\) | −18382.5 | −0.678569 | ||||||||
\(903\) | −222.334 | −0.00819360 | ||||||||
\(904\) | −17728.9 | −0.652272 | ||||||||
\(905\) | 45954.6 | 1.68794 | ||||||||
\(906\) | 281.295 | 0.0103150 | ||||||||
\(907\) | 32079.8 | 1.17441 | 0.587207 | − | 0.809437i | \(-0.300227\pi\) | ||||
0.587207 | + | 0.809437i | \(0.300227\pi\) | |||||||
\(908\) | −15550.6 | −0.568355 | ||||||||
\(909\) | −6100.16 | −0.222585 | ||||||||
\(910\) | −476.708 | −0.0173656 | ||||||||
\(911\) | 2449.21 | 0.0890735 | 0.0445367 | − | 0.999008i | \(-0.485819\pi\) | ||||
0.0445367 | + | 0.999008i | \(0.485819\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 76026.9 | 2.75589 | ||||||||
\(914\) | 29961.6 | 1.08429 | ||||||||
\(915\) | 8992.86 | 0.324912 | ||||||||
\(916\) | −1834.49 | −0.0661718 | ||||||||
\(917\) | 456.985 | 0.0164569 | ||||||||
\(918\) | 4748.91 | 0.170738 | ||||||||
\(919\) | 26639.3 | 0.956201 | 0.478100 | − | 0.878305i | \(-0.341326\pi\) | ||||
0.478100 | + | 0.878305i | \(0.341326\pi\) | |||||||
\(920\) | 9073.60 | 0.325161 | ||||||||
\(921\) | −1438.69 | −0.0514730 | ||||||||
\(922\) | −2306.64 | −0.0823918 | ||||||||
\(923\) | −39901.2 | −1.42293 | ||||||||
\(924\) | 192.103 | 0.00683952 | ||||||||
\(925\) | −27423.5 | −0.974788 | ||||||||
\(926\) | −19560.3 | −0.694161 | ||||||||
\(927\) | −14819.8 | −0.525078 | ||||||||
\(928\) | 1192.80 | 0.0421935 | ||||||||
\(929\) | 4232.31 | 0.149470 | 0.0747350 | − | 0.997203i | \(-0.476189\pi\) | ||||
0.0747350 | + | 0.997203i | \(0.476189\pi\) | |||||||
\(930\) | 18406.1 | 0.648990 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17407.4 | 0.611802 | ||||||||
\(933\) | −4926.68 | −0.172875 | ||||||||
\(934\) | −28600.3 | −1.00196 | ||||||||
\(935\) | 82249.9 | 2.87686 | ||||||||
\(936\) | 3307.36 | 0.115496 | ||||||||
\(937\) | −3428.88 | −0.119548 | −0.0597740 | − | 0.998212i | \(-0.519038\pi\) | ||||
−0.0597740 | + | 0.998212i | \(0.519038\pi\) | |||||||
\(938\) | 165.646 | 0.00576602 | ||||||||
\(939\) | −24056.0 | −0.836037 | ||||||||
\(940\) | 25916.1 | 0.899246 | ||||||||
\(941\) | −22357.8 | −0.774541 | −0.387270 | − | 0.921966i | \(-0.626582\pi\) | ||||
−0.387270 | + | 0.921966i | \(0.626582\pi\) | |||||||
\(942\) | 17330.0 | 0.599408 | ||||||||
\(943\) | −11146.2 | −0.384911 | ||||||||
\(944\) | 11746.6 | 0.405000 | ||||||||
\(945\) | 140.100 | 0.00482269 | ||||||||
\(946\) | 26716.3 | 0.918207 | ||||||||
\(947\) | 18852.7 | 0.646918 | 0.323459 | − | 0.946242i | \(-0.395154\pi\) | ||||
0.323459 | + | 0.946242i | \(0.395154\pi\) | |||||||
\(948\) | 4000.59 | 0.137060 | ||||||||
\(949\) | 38771.4 | 1.32621 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9213.29 | −0.314155 | ||||||||
\(952\) | 209.669 | 0.00713805 | ||||||||
\(953\) | 49446.0 | 1.68071 | 0.840353 | − | 0.542040i | \(-0.182348\pi\) | ||||
0.840353 | + | 0.542040i | \(0.182348\pi\) | |||||||
\(954\) | −6387.27 | −0.216767 | ||||||||
\(955\) | −66196.3 | −2.24300 | ||||||||
\(956\) | −275.915 | −0.00933445 | ||||||||
\(957\) | 6006.84 | 0.202898 | ||||||||
\(958\) | 3521.00 | 0.118746 | ||||||||
\(959\) | 324.228 | 0.0109175 | ||||||||
\(960\) | −3342.95 | −0.112389 | ||||||||
\(961\) | 1252.18 | 0.0420321 | ||||||||
\(962\) | −14142.2 | −0.473974 | ||||||||
\(963\) | −17647.9 | −0.590546 | ||||||||
\(964\) | −158.688 | −0.00530188 | ||||||||
\(965\) | −44127.4 | −1.47203 | ||||||||
\(966\) | 116.482 | 0.00387965 | ||||||||
\(967\) | 10689.7 | 0.355488 | 0.177744 | − | 0.984077i | \(-0.443120\pi\) | ||||
0.177744 | + | 0.984077i | \(0.443120\pi\) | |||||||
\(968\) | −12435.6 | −0.412910 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −51212.5 | −1.69519 | ||||||||
\(971\) | −43553.1 | −1.43943 | −0.719715 | − | 0.694270i | \(-0.755727\pi\) | ||||
−0.719715 | + | 0.694270i | \(0.755727\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 14.7138 | 0.000484792 0 | ||||||||
\(974\) | 16627.2 | 0.546992 | ||||||||
\(975\) | 24550.1 | 0.806394 | ||||||||
\(976\) | −2754.66 | −0.0903428 | ||||||||
\(977\) | −27972.4 | −0.915983 | −0.457991 | − | 0.888957i | \(-0.651431\pi\) | ||||
−0.457991 | + | 0.888957i | \(0.651431\pi\) | |||||||
\(978\) | −1101.41 | −0.0360115 | ||||||||
\(979\) | 71390.2 | 2.33058 | ||||||||
\(980\) | −23882.0 | −0.778450 | ||||||||
\(981\) | −3170.54 | −0.103188 | ||||||||
\(982\) | −10145.6 | −0.329695 | ||||||||
\(983\) | −47151.0 | −1.52989 | −0.764945 | − | 0.644096i | \(-0.777234\pi\) | ||||
−0.764945 | + | 0.644096i | \(0.777234\pi\) | |||||||
\(984\) | 4106.56 | 0.133041 | ||||||||
\(985\) | −71663.2 | −2.31815 | ||||||||
\(986\) | 6556.13 | 0.211754 | ||||||||
\(987\) | 332.697 | 0.0107293 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16199.5 | 0.520843 | ||||||||
\(990\) | −16834.8 | −0.540449 | ||||||||
\(991\) | 23895.1 | 0.765945 | 0.382972 | − | 0.923760i | \(-0.374900\pi\) | ||||
0.382972 | + | 0.923760i | \(0.374900\pi\) | |||||||
\(992\) | −5638.10 | −0.180454 | ||||||||
\(993\) | 6516.77 | 0.208261 | ||||||||
\(994\) | 517.740 | 0.0165208 | ||||||||
\(995\) | 26662.3 | 0.849499 | ||||||||
\(996\) | −16984.1 | −0.540322 | ||||||||
\(997\) | −38584.2 | −1.22565 | −0.612826 | − | 0.790218i | \(-0.709967\pi\) | ||||
−0.612826 | + | 0.790218i | \(0.709967\pi\) | |||||||
\(998\) | −15787.5 | −0.500745 | ||||||||
\(999\) | 4156.26 | 0.131630 |
(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 | 2166.4.a.r.1.3 | ✓ | 3 | |
19.18 | odd | 2 | 2166.4.a.v.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2166.4.a.r.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2166.4.a.v.1.3 | yes | 3 | 19.18 | odd | 2 |