Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,4,Mod(1,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.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: | \(40.8883236340\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 45x^{6} + 77x^{5} + 540x^{4} - 915x^{3} - 1452x^{2} + 2660x - 672 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.50363\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.50363 | −1.23872 | −0.619361 | − | 0.785107i | \(-0.712608\pi\) | ||||
−0.619361 | + | 0.785107i | \(0.712608\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.27544 | 0.534430 | ||||||||
\(5\) | 15.3058 | 1.36899 | 0.684495 | − | 0.729017i | \(-0.260023\pi\) | ||||
0.684495 | + | 0.729017i | \(0.260023\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 13.0495 | 0.576711 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −53.6258 | −1.69580 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.90915 | 0.126069 | 0.0630347 | − | 0.998011i | \(-0.479922\pi\) | ||||
0.0630347 | + | 0.998011i | \(0.479922\pi\) | |||||||
\(14\) | 24.5254 | 0.468193 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.9241 | −1.24881 | ||||||||
\(17\) | −73.2134 | −1.04452 | −0.522260 | − | 0.852786i | \(-0.674911\pi\) | ||||
−0.522260 | + | 0.852786i | \(0.674911\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 80.3384 | 0.970046 | 0.485023 | − | 0.874501i | \(-0.338811\pi\) | ||||
0.485023 | + | 0.874501i | \(0.338811\pi\) | |||||||
\(20\) | 65.4390 | 0.731630 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −38.5400 | −0.373489 | ||||||||
\(23\) | −190.324 | −1.72544 | −0.862722 | − | 0.505678i | \(-0.831242\pi\) | ||||
−0.862722 | + | 0.505678i | \(0.831242\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 109.267 | 0.874134 | ||||||||
\(26\) | −20.7035 | −0.156165 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −29.9281 | −0.201996 | ||||||||
\(29\) | −285.553 | −1.82848 | −0.914238 | − | 0.405177i | \(-0.867210\pi\) | ||||
−0.914238 | + | 0.405177i | \(0.867210\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 85.3709 | 0.494615 | 0.247307 | − | 0.968937i | \(-0.420454\pi\) | ||||
0.247307 | + | 0.968937i | \(0.420454\pi\) | |||||||
\(32\) | 175.629 | 0.970222 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 256.513 | 1.29387 | ||||||||
\(35\) | −107.140 | −0.517430 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −149.061 | −0.662309 | −0.331154 | − | 0.943577i | \(-0.607438\pi\) | ||||
−0.331154 | + | 0.943577i | \(0.607438\pi\) | |||||||
\(38\) | −281.476 | −1.20162 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 199.732 | 0.789512 | ||||||||
\(41\) | 13.9250 | 0.0530420 | 0.0265210 | − | 0.999648i | \(-0.491557\pi\) | ||||
0.0265210 | + | 0.999648i | \(0.491557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −148.052 | −0.525065 | −0.262532 | − | 0.964923i | \(-0.584558\pi\) | ||||
−0.262532 | + | 0.964923i | \(0.584558\pi\) | |||||||
\(44\) | 47.0299 | 0.161137 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 666.824 | 2.13735 | ||||||||
\(47\) | 94.7888 | 0.294178 | 0.147089 | − | 0.989123i | \(-0.453010\pi\) | ||||
0.147089 | + | 0.989123i | \(0.453010\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −382.831 | −1.08281 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 25.2642 | 0.0673754 | ||||||||
\(53\) | 105.750 | 0.274074 | 0.137037 | − | 0.990566i | \(-0.456242\pi\) | ||||
0.137037 | + | 0.990566i | \(0.456242\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 168.364 | 0.412766 | ||||||||
\(56\) | −91.3463 | −0.217976 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1000.47 | 2.26497 | ||||||||
\(59\) | 184.187 | 0.406424 | 0.203212 | − | 0.979135i | \(-0.434862\pi\) | ||||
0.203212 | + | 0.979135i | \(0.434862\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −189.128 | −0.396972 | −0.198486 | − | 0.980104i | \(-0.563602\pi\) | ||||
−0.198486 | + | 0.980104i | \(0.563602\pi\) | |||||||
\(62\) | −299.108 | −0.612690 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 24.0535 | 0.0469795 | ||||||||
\(65\) | 90.4441 | 0.172588 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −193.756 | −0.353299 | −0.176649 | − | 0.984274i | \(-0.556526\pi\) | ||||
−0.176649 | + | 0.984274i | \(0.556526\pi\) | |||||||
\(68\) | −313.020 | −0.558224 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 375.381 | 0.640951 | ||||||||
\(71\) | 356.265 | 0.595505 | 0.297752 | − | 0.954643i | \(-0.403763\pi\) | ||||
0.297752 | + | 0.954643i | \(0.403763\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 655.740 | 1.05135 | 0.525675 | − | 0.850686i | \(-0.323813\pi\) | ||||
0.525675 | + | 0.850686i | \(0.323813\pi\) | |||||||
\(74\) | 522.254 | 0.820416 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 343.482 | 0.518422 | ||||||||
\(77\) | −77.0000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 110.189 | 0.156927 | 0.0784634 | − | 0.996917i | \(-0.474999\pi\) | ||||
0.0784634 | + | 0.996917i | \(0.474999\pi\) | |||||||
\(80\) | −1223.30 | −1.70961 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −48.7881 | −0.0657042 | ||||||||
\(83\) | −1278.27 | −1.69047 | −0.845233 | − | 0.534399i | \(-0.820538\pi\) | ||||
−0.845233 | + | 0.534399i | \(0.820538\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1120.59 | −1.42994 | ||||||||
\(86\) | 518.721 | 0.650409 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 143.544 | 0.173885 | ||||||||
\(89\) | 255.120 | 0.303850 | 0.151925 | − | 0.988392i | \(-0.451453\pi\) | ||||
0.151925 | + | 0.988392i | \(0.451453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −41.3640 | −0.0476498 | ||||||||
\(92\) | −813.718 | −0.922130 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −332.105 | −0.364405 | ||||||||
\(95\) | 1229.64 | 1.32798 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 372.537 | 0.389953 | 0.194976 | − | 0.980808i | \(-0.437537\pi\) | ||||
0.194976 | + | 0.980808i | \(0.437537\pi\) | |||||||
\(98\) | −171.678 | −0.176960 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 467.164 | 0.467164 | ||||||||
\(101\) | −1143.78 | −1.12684 | −0.563419 | − | 0.826171i | \(-0.690514\pi\) | ||||
−0.563419 | + | 0.826171i | \(0.690514\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 471.721 | 0.451263 | 0.225631 | − | 0.974213i | \(-0.427556\pi\) | ||||
0.225631 | + | 0.974213i | \(0.427556\pi\) | |||||||
\(104\) | 77.1113 | 0.0727056 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −370.510 | −0.339501 | ||||||||
\(107\) | −1562.49 | −1.41170 | −0.705849 | − | 0.708363i | \(-0.749434\pi\) | ||||
−0.705849 | + | 0.708363i | \(0.749434\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −895.894 | −0.787258 | −0.393629 | − | 0.919269i | \(-0.628781\pi\) | ||||
−0.393629 | + | 0.919269i | \(0.628781\pi\) | |||||||
\(110\) | −589.884 | −0.511302 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 559.469 | 0.472008 | ||||||||
\(113\) | −341.558 | −0.284345 | −0.142173 | − | 0.989842i | \(-0.545409\pi\) | ||||
−0.142173 | + | 0.989842i | \(0.545409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2913.05 | −2.36212 | ||||||||
\(116\) | −1220.87 | −0.977194 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −645.322 | −0.503447 | ||||||||
\(119\) | 512.493 | 0.394792 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 662.634 | 0.491738 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 364.998 | 0.264337 | ||||||||
\(125\) | −240.809 | −0.172309 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2446.85 | −1.70963 | −0.854813 | − | 0.518935i | \(-0.826329\pi\) | ||||
−0.854813 | + | 0.518935i | \(0.826329\pi\) | |||||||
\(128\) | −1489.31 | −1.02842 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −316.883 | −0.213788 | ||||||||
\(131\) | −2075.09 | −1.38398 | −0.691989 | − | 0.721908i | \(-0.743265\pi\) | ||||
−0.691989 | + | 0.721908i | \(0.743265\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −562.368 | −0.366643 | ||||||||
\(134\) | 678.849 | 0.437639 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −955.396 | −0.602386 | ||||||||
\(137\) | −199.066 | −0.124141 | −0.0620707 | − | 0.998072i | \(-0.519770\pi\) | ||||
−0.0620707 | + | 0.998072i | \(0.519770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2358.20 | 1.43899 | 0.719495 | − | 0.694497i | \(-0.244373\pi\) | ||||
0.719495 | + | 0.694497i | \(0.244373\pi\) | |||||||
\(140\) | −458.073 | −0.276530 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1248.22 | −0.737664 | ||||||||
\(143\) | 65.0006 | 0.0380114 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4370.61 | −2.50317 | ||||||||
\(146\) | −2297.47 | −1.30233 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −637.300 | −0.353958 | ||||||||
\(149\) | 616.754 | 0.339104 | 0.169552 | − | 0.985521i | \(-0.445768\pi\) | ||||
0.169552 | + | 0.985521i | \(0.445768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −997.331 | −0.537494 | −0.268747 | − | 0.963211i | \(-0.586610\pi\) | ||||
−0.268747 | + | 0.963211i | \(0.586610\pi\) | |||||||
\(152\) | 1048.37 | 0.559436 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 269.780 | 0.141165 | ||||||||
\(155\) | 1306.67 | 0.677123 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3181.76 | 1.61740 | 0.808701 | − | 0.588220i | \(-0.200171\pi\) | ||||
0.808701 | + | 0.588220i | \(0.200171\pi\) | |||||||
\(158\) | −386.061 | −0.194388 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2688.14 | 1.32822 | ||||||||
\(161\) | 1332.27 | 0.652157 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2715.81 | −1.30502 | −0.652511 | − | 0.757779i | \(-0.726284\pi\) | ||||
−0.652511 | + | 0.757779i | \(0.726284\pi\) | |||||||
\(164\) | 59.5356 | 0.0283473 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4478.60 | 2.09402 | ||||||||
\(167\) | 193.315 | 0.0895759 | 0.0447880 | − | 0.998997i | \(-0.485739\pi\) | ||||
0.0447880 | + | 0.998997i | \(0.485739\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2162.08 | −0.984106 | ||||||||
\(170\) | 3926.13 | 1.77129 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −632.990 | −0.280611 | ||||||||
\(173\) | −2560.26 | −1.12516 | −0.562580 | − | 0.826743i | \(-0.690191\pi\) | ||||
−0.562580 | + | 0.826743i | \(0.690191\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −764.868 | −0.330392 | ||||||||
\(176\) | −879.165 | −0.376532 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −893.847 | −0.376386 | ||||||||
\(179\) | −2783.34 | −1.16221 | −0.581107 | − | 0.813827i | \(-0.697380\pi\) | ||||
−0.581107 | + | 0.813827i | \(0.697380\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3055.72 | 1.25486 | 0.627430 | − | 0.778673i | \(-0.284107\pi\) | ||||
0.627430 | + | 0.778673i | \(0.284107\pi\) | |||||||
\(182\) | 144.924 | 0.0590248 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2483.62 | −0.995083 | ||||||||
\(185\) | −2281.49 | −0.906694 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −805.347 | −0.314935 | ||||||||
\(188\) | 405.264 | 0.157218 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4308.21 | −1.64500 | ||||||||
\(191\) | −3141.28 | −1.19003 | −0.595014 | − | 0.803715i | \(-0.702854\pi\) | ||||
−0.595014 | + | 0.803715i | \(0.702854\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1695.74 | −0.632446 | −0.316223 | − | 0.948685i | \(-0.602415\pi\) | ||||
−0.316223 | + | 0.948685i | \(0.602415\pi\) | |||||||
\(194\) | −1305.23 | −0.483043 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 209.497 | 0.0763472 | ||||||||
\(197\) | 3061.85 | 1.10735 | 0.553675 | − | 0.832733i | \(-0.313225\pi\) | ||||
0.553675 | + | 0.832733i | \(0.313225\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 66.9619 | 0.0238533 | 0.0119266 | − | 0.999929i | \(-0.496204\pi\) | ||||
0.0119266 | + | 0.999929i | \(0.496204\pi\) | |||||||
\(200\) | 1425.87 | 0.504123 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4007.40 | 1.39584 | ||||||||
\(203\) | 1998.87 | 0.691099 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 213.133 | 0.0726140 | ||||||||
\(206\) | −1652.74 | −0.558989 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −472.284 | −0.157437 | ||||||||
\(209\) | 883.722 | 0.292480 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −913.636 | −0.298092 | −0.149046 | − | 0.988830i | \(-0.547620\pi\) | ||||
−0.149046 | + | 0.988830i | \(0.547620\pi\) | |||||||
\(212\) | 452.130 | 0.146474 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5474.39 | 1.74870 | ||||||||
\(215\) | −2266.06 | −0.718809 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −597.596 | −0.186947 | ||||||||
\(218\) | 3138.89 | 0.975193 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 719.829 | 0.220595 | ||||||||
\(221\) | −432.629 | −0.131682 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 153.648 | 0.0461391 | 0.0230695 | − | 0.999734i | \(-0.492656\pi\) | ||||
0.0230695 | + | 0.999734i | \(0.492656\pi\) | |||||||
\(224\) | −1229.40 | −0.366710 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1196.69 | 0.352225 | ||||||||
\(227\) | −497.228 | −0.145384 | −0.0726921 | − | 0.997354i | \(-0.523159\pi\) | ||||
−0.0726921 | + | 0.997354i | \(0.523159\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3374.79 | 0.973854 | 0.486927 | − | 0.873443i | \(-0.338118\pi\) | ||||
0.486927 | + | 0.873443i | \(0.338118\pi\) | |||||||
\(230\) | 10206.3 | 2.92600 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3726.32 | −1.05450 | ||||||||
\(233\) | −4849.94 | −1.36365 | −0.681825 | − | 0.731516i | \(-0.738813\pi\) | ||||
−0.681825 | + | 0.731516i | \(0.738813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1450.82 | 0.402727 | ||||||||
\(236\) | 787.479 | 0.217206 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1795.59 | −0.489037 | ||||||||
\(239\) | −7350.07 | −1.98927 | −0.994637 | − | 0.103430i | \(-0.967018\pi\) | ||||
−0.994637 | + | 0.103430i | \(0.967018\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 919.171 | 0.245680 | 0.122840 | − | 0.992426i | \(-0.460800\pi\) | ||||
0.122840 | + | 0.992426i | \(0.460800\pi\) | |||||||
\(242\) | −423.940 | −0.112611 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −808.604 | −0.212154 | ||||||||
\(245\) | 749.983 | 0.195570 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 474.731 | 0.122293 | ||||||||
\(248\) | 1114.05 | 0.285250 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 843.706 | 0.213443 | ||||||||
\(251\) | 4350.71 | 1.09408 | 0.547041 | − | 0.837106i | \(-0.315754\pi\) | ||||
0.547041 | + | 0.837106i | \(0.315754\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2093.56 | −0.520241 | ||||||||
\(254\) | 8572.86 | 2.11775 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5025.56 | 1.22694 | ||||||||
\(257\) | 4128.98 | 1.00217 | 0.501087 | − | 0.865397i | \(-0.332934\pi\) | ||||
0.501087 | + | 0.865397i | \(0.332934\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1043.42 | 0.250329 | ||||||||
\(260\) | 386.689 | 0.0922362 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7270.34 | 1.71436 | ||||||||
\(263\) | 6853.69 | 1.60691 | 0.803454 | − | 0.595367i | \(-0.202993\pi\) | ||||
0.803454 | + | 0.595367i | \(0.202993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1618.59 | 0.375205 | ||||||||
\(266\) | 1970.33 | 0.454169 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −828.392 | −0.188814 | ||||||||
\(269\) | 7519.13 | 1.70427 | 0.852136 | − | 0.523320i | \(-0.175307\pi\) | ||||
0.852136 | + | 0.523320i | \(0.175307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5354.31 | −1.20019 | −0.600095 | − | 0.799929i | \(-0.704870\pi\) | ||||
−0.600095 | + | 0.799929i | \(0.704870\pi\) | |||||||
\(272\) | 5851.51 | 1.30441 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 697.455 | 0.153777 | ||||||||
\(275\) | 1201.93 | 0.263561 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6529.96 | 1.41642 | 0.708208 | − | 0.706004i | \(-0.249504\pi\) | ||||
0.708208 | + | 0.706004i | \(0.249504\pi\) | |||||||
\(278\) | −8262.26 | −1.78251 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1398.13 | −0.298407 | ||||||||
\(281\) | −1530.30 | −0.324876 | −0.162438 | − | 0.986719i | \(-0.551936\pi\) | ||||
−0.162438 | + | 0.986719i | \(0.551936\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5563.44 | −1.16860 | −0.584298 | − | 0.811540i | \(-0.698630\pi\) | ||||
−0.584298 | + | 0.811540i | \(0.698630\pi\) | |||||||
\(284\) | 1523.19 | 0.318256 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −227.738 | −0.0470855 | ||||||||
\(287\) | −97.4751 | −0.0200480 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 447.195 | 0.0910228 | ||||||||
\(290\) | 15313.0 | 3.10073 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2803.58 | 0.561873 | ||||||||
\(293\) | −4599.78 | −0.917140 | −0.458570 | − | 0.888658i | \(-0.651638\pi\) | ||||
−0.458570 | + | 0.888658i | \(0.651638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2819.12 | 0.556391 | ||||||||
\(296\) | −1945.16 | −0.381961 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2160.88 | −0.420055 | ||||||||
\(299\) | −1124.65 | −0.217526 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1036.37 | 0.198456 | ||||||||
\(302\) | 3494.28 | 0.665806 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6420.97 | −1.21141 | ||||||||
\(305\) | −2894.74 | −0.543451 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5902.91 | 1.09738 | 0.548692 | − | 0.836025i | \(-0.315126\pi\) | ||||
0.548692 | + | 0.836025i | \(0.315126\pi\) | |||||||
\(308\) | −329.209 | −0.0609040 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4578.08 | −0.838766 | ||||||||
\(311\) | −1759.91 | −0.320886 | −0.160443 | − | 0.987045i | \(-0.551292\pi\) | ||||
−0.160443 | + | 0.987045i | \(0.551292\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2376.13 | −0.429095 | −0.214548 | − | 0.976714i | \(-0.568828\pi\) | ||||
−0.214548 | + | 0.976714i | \(0.568828\pi\) | |||||||
\(314\) | −11147.7 | −2.00351 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 471.106 | 0.0838664 | ||||||||
\(317\) | −1891.58 | −0.335147 | −0.167573 | − | 0.985860i | \(-0.553593\pi\) | ||||
−0.167573 | + | 0.985860i | \(0.553593\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3141.08 | −0.551307 | ||||||||
\(320\) | 368.158 | 0.0643145 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4667.77 | −0.807841 | ||||||||
\(323\) | −5881.84 | −1.01323 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 645.674 | 0.110202 | ||||||||
\(326\) | 9515.20 | 1.61656 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 181.714 | 0.0305899 | ||||||||
\(329\) | −663.522 | −0.111189 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8905.72 | −1.47886 | −0.739430 | − | 0.673234i | \(-0.764905\pi\) | ||||
−0.739430 | + | 0.673234i | \(0.764905\pi\) | |||||||
\(332\) | −5465.18 | −0.903436 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −677.306 | −0.110960 | ||||||||
\(335\) | −2965.58 | −0.483663 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10164.2 | 1.64297 | 0.821484 | − | 0.570232i | \(-0.193147\pi\) | ||||
0.821484 | + | 0.570232i | \(0.193147\pi\) | |||||||
\(338\) | 7575.14 | 1.21903 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4791.01 | −0.764203 | ||||||||
\(341\) | 939.079 | 0.149132 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −1932.01 | −0.302811 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8970.20 | 1.39376 | ||||||||
\(347\) | −7678.94 | −1.18797 | −0.593987 | − | 0.804475i | \(-0.702447\pi\) | ||||
−0.593987 | + | 0.804475i | \(0.702447\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8494.69 | 1.30289 | 0.651447 | − | 0.758694i | \(-0.274162\pi\) | ||||
0.651447 | + | 0.758694i | \(0.274162\pi\) | |||||||
\(350\) | 2679.82 | 0.409263 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1931.92 | 0.292533 | ||||||||
\(353\) | −1477.92 | −0.222838 | −0.111419 | − | 0.993774i | \(-0.535540\pi\) | ||||
−0.111419 | + | 0.993774i | \(0.535540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5452.91 | 0.815240 | ||||||||
\(356\) | 1090.75 | 0.162387 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9751.78 | 1.43966 | ||||||||
\(359\) | −1354.69 | −0.199158 | −0.0995791 | − | 0.995030i | \(-0.531750\pi\) | ||||
−0.0995791 | + | 0.995030i | \(0.531750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −404.749 | −0.0590100 | ||||||||
\(362\) | −10706.1 | −1.55442 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −176.850 | −0.0254655 | ||||||||
\(365\) | 10036.6 | 1.43929 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2054.98 | −0.292286 | −0.146143 | − | 0.989263i | \(-0.546686\pi\) | ||||
−0.146143 | + | 0.989263i | \(0.546686\pi\) | |||||||
\(368\) | 15211.5 | 2.15476 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7993.50 | 1.12314 | ||||||||
\(371\) | −740.253 | −0.103590 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6632.28 | 0.920661 | 0.460330 | − | 0.887748i | \(-0.347731\pi\) | ||||
0.460330 | + | 0.887748i | \(0.347731\pi\) | |||||||
\(374\) | 2821.64 | 0.390116 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1236.94 | 0.169656 | ||||||||
\(377\) | −1687.37 | −0.230515 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −578.193 | −0.0783636 | −0.0391818 | − | 0.999232i | \(-0.512475\pi\) | ||||
−0.0391818 | + | 0.999232i | \(0.512475\pi\) | |||||||
\(380\) | 5257.26 | 0.709715 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11005.9 | 1.47411 | ||||||||
\(383\) | 5643.47 | 0.752918 | 0.376459 | − | 0.926433i | \(-0.377142\pi\) | ||||
0.376459 | + | 0.926433i | \(0.377142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1178.54 | −0.156011 | ||||||||
\(386\) | 5941.25 | 0.783424 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1592.76 | 0.208403 | ||||||||
\(389\) | 13487.4 | 1.75794 | 0.878970 | − | 0.476877i | \(-0.158231\pi\) | ||||
0.878970 | + | 0.476877i | \(0.158231\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13934.2 | 1.80226 | ||||||||
\(392\) | 639.424 | 0.0823873 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10727.6 | −1.37170 | ||||||||
\(395\) | 1686.53 | 0.214831 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15505.0 | −1.96014 | −0.980068 | − | 0.198664i | \(-0.936340\pi\) | ||||
−0.980068 | + | 0.198664i | \(0.936340\pi\) | |||||||
\(398\) | −234.610 | −0.0295476 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8733.05 | −1.09163 | ||||||||
\(401\) | 11389.7 | 1.41839 | 0.709196 | − | 0.705011i | \(-0.249058\pi\) | ||||
0.709196 | + | 0.705011i | \(0.249058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 504.469 | 0.0623558 | ||||||||
\(404\) | −4890.18 | −0.602217 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7003.31 | −0.856079 | ||||||||
\(407\) | −1639.67 | −0.199694 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13512.3 | 1.63360 | 0.816798 | − | 0.576924i | \(-0.195747\pi\) | ||||
0.816798 | + | 0.576924i | \(0.195747\pi\) | |||||||
\(410\) | −746.740 | −0.0899485 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2016.82 | 0.241169 | ||||||||
\(413\) | −1289.31 | −0.153614 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19564.9 | −2.31423 | ||||||||
\(416\) | 1037.82 | 0.122315 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3096.24 | −0.362301 | ||||||||
\(419\) | −8247.54 | −0.961620 | −0.480810 | − | 0.876825i | \(-0.659657\pi\) | ||||
−0.480810 | + | 0.876825i | \(0.659657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2630.75 | 0.304549 | 0.152275 | − | 0.988338i | \(-0.451340\pi\) | ||||
0.152275 | + | 0.988338i | \(0.451340\pi\) | |||||||
\(422\) | 3201.05 | 0.369252 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1379.99 | 0.158062 | ||||||||
\(425\) | −7999.79 | −0.913051 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1323.89 | 0.150041 | ||||||||
\(428\) | −6680.34 | −0.754454 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7939.43 | 0.890404 | ||||||||
\(431\) | 10428.7 | 1.16551 | 0.582753 | − | 0.812649i | \(-0.301976\pi\) | ||||
0.582753 | + | 0.812649i | \(0.301976\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8822.44 | −0.979167 | −0.489583 | − | 0.871956i | \(-0.662851\pi\) | ||||
−0.489583 | + | 0.871956i | \(0.662851\pi\) | |||||||
\(434\) | 2093.76 | 0.231575 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3830.35 | −0.420735 | ||||||||
\(437\) | −15290.3 | −1.67376 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16899.6 | −1.83730 | −0.918652 | − | 0.395068i | \(-0.870721\pi\) | ||||
−0.918652 | + | 0.395068i | \(0.870721\pi\) | |||||||
\(440\) | 2197.06 | 0.238047 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1515.77 | 0.163117 | ||||||||
\(443\) | −9130.18 | −0.979206 | −0.489603 | − | 0.871946i | \(-0.662858\pi\) | ||||
−0.489603 | + | 0.871946i | \(0.662858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3904.81 | 0.415968 | ||||||||
\(446\) | −538.325 | −0.0571534 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −168.375 | −0.0177566 | ||||||||
\(449\) | −6461.47 | −0.679143 | −0.339572 | − | 0.940580i | \(-0.610282\pi\) | ||||
−0.339572 | + | 0.940580i | \(0.610282\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 153.175 | 0.0159928 | ||||||||
\(452\) | −1460.31 | −0.151963 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1742.11 | 0.180090 | ||||||||
\(455\) | −633.109 | −0.0652321 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9239.47 | −0.945743 | −0.472871 | − | 0.881132i | \(-0.656782\pi\) | ||||
−0.472871 | + | 0.881132i | \(0.656782\pi\) | |||||||
\(458\) | −11824.0 | −1.20633 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12454.6 | −1.26239 | ||||||||
\(461\) | −7393.95 | −0.747007 | −0.373504 | − | 0.927629i | \(-0.621844\pi\) | ||||
−0.373504 | + | 0.927629i | \(0.621844\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3360.31 | −0.337293 | −0.168646 | − | 0.985677i | \(-0.553940\pi\) | ||||
−0.168646 | + | 0.985677i | \(0.553940\pi\) | |||||||
\(464\) | 22822.6 | 2.28343 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16992.4 | 1.68918 | ||||||||
\(467\) | 10685.1 | 1.05878 | 0.529389 | − | 0.848379i | \(-0.322421\pi\) | ||||
0.529389 | + | 0.848379i | \(0.322421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1356.29 | 0.133534 | ||||||||
\(470\) | −5083.13 | −0.498866 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2403.54 | 0.234389 | ||||||||
\(473\) | −1628.58 | −0.158313 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8778.31 | 0.847951 | ||||||||
\(476\) | 2191.14 | 0.210989 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25751.9 | 2.46416 | ||||||||
\(479\) | 18204.4 | 1.73649 | 0.868247 | − | 0.496133i | \(-0.165247\pi\) | ||||
0.868247 | + | 0.496133i | \(0.165247\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −880.821 | −0.0834969 | ||||||||
\(482\) | −3220.44 | −0.304330 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 517.329 | 0.0485846 | ||||||||
\(485\) | 5701.97 | 0.533841 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6213.98 | −0.578197 | −0.289099 | − | 0.957299i | \(-0.593356\pi\) | ||||
−0.289099 | + | 0.957299i | \(0.593356\pi\) | |||||||
\(488\) | −2468.02 | −0.228938 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2627.67 | −0.242257 | ||||||||
\(491\) | −17022.7 | −1.56461 | −0.782306 | − | 0.622894i | \(-0.785957\pi\) | ||||
−0.782306 | + | 0.622894i | \(0.785957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20906.3 | 1.90988 | ||||||||
\(494\) | −1663.28 | −0.151487 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6823.19 | −0.617682 | ||||||||
\(497\) | −2493.85 | −0.225080 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20595.2 | −1.84763 | −0.923814 | − | 0.382843i | \(-0.874945\pi\) | ||||
−0.923814 | + | 0.382843i | \(0.874945\pi\) | |||||||
\(500\) | −1029.56 | −0.0920871 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15243.3 | −1.35526 | ||||||||
\(503\) | −19173.9 | −1.69965 | −0.849824 | − | 0.527067i | \(-0.823292\pi\) | ||||
−0.849824 | + | 0.527067i | \(0.823292\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17506.5 | −1.54263 | ||||||||
\(506\) | 7335.07 | 0.644434 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10461.4 | −0.913677 | ||||||||
\(509\) | −3120.30 | −0.271719 | −0.135859 | − | 0.990728i | \(-0.543380\pi\) | ||||
−0.135859 | + | 0.990728i | \(0.543380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4590.18 | −0.397373 | ||||||||
\(512\) | −5693.25 | −0.491423 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14466.4 | −1.24141 | ||||||||
\(515\) | 7220.06 | 0.617774 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1042.68 | 0.0886980 | ||||||||
\(518\) | −3655.78 | −0.310088 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1180.25 | 0.0995333 | ||||||||
\(521\) | 7932.70 | 0.667059 | 0.333530 | − | 0.942740i | \(-0.391760\pi\) | ||||
0.333530 | + | 0.942740i | \(0.391760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4156.12 | −0.347484 | −0.173742 | − | 0.984791i | \(-0.555586\pi\) | ||||
−0.173742 | + | 0.984791i | \(0.555586\pi\) | |||||||
\(524\) | −8871.91 | −0.739640 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24012.8 | −1.99051 | ||||||||
\(527\) | −6250.29 | −0.516635 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24056.1 | 1.97716 | ||||||||
\(530\) | −5670.95 | −0.464774 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2404.37 | −0.195945 | ||||||||
\(533\) | 82.2850 | 0.00668698 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23915.1 | −1.93260 | ||||||||
\(536\) | −2528.41 | −0.203751 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26344.3 | −2.11112 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21965.6 | −1.74561 | −0.872804 | − | 0.488070i | \(-0.837701\pi\) | ||||
−0.872804 | + | 0.488070i | \(0.837701\pi\) | |||||||
\(542\) | 18759.5 | 1.48670 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12858.4 | −1.01342 | ||||||||
\(545\) | −13712.4 | −1.07775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11875.0 | 0.928224 | 0.464112 | − | 0.885776i | \(-0.346373\pi\) | ||||
0.464112 | + | 0.885776i | \(0.346373\pi\) | |||||||
\(548\) | −851.096 | −0.0663449 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4211.14 | −0.326479 | ||||||||
\(551\) | −22940.8 | −1.77371 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −771.322 | −0.0593127 | ||||||||
\(554\) | −22878.6 | −1.75455 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10082.3 | 0.769040 | ||||||||
\(557\) | −2292.04 | −0.174357 | −0.0871786 | − | 0.996193i | \(-0.527785\pi\) | ||||
−0.0871786 | + | 0.996193i | \(0.527785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −874.864 | −0.0661946 | ||||||||
\(560\) | 8563.11 | 0.646174 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5361.62 | 0.402431 | ||||||||
\(563\) | 7686.51 | 0.575395 | 0.287698 | − | 0.957721i | \(-0.407110\pi\) | ||||
0.287698 | + | 0.957721i | \(0.407110\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5227.80 | −0.389266 | ||||||||
\(566\) | 19492.3 | 1.44756 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4649.07 | 0.343434 | ||||||||
\(569\) | 1044.55 | 0.0769592 | 0.0384796 | − | 0.999259i | \(-0.487749\pi\) | ||||
0.0384796 | + | 0.999259i | \(0.487749\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1085.27 | −0.0795399 | −0.0397700 | − | 0.999209i | \(-0.512663\pi\) | ||||
−0.0397700 | + | 0.999209i | \(0.512663\pi\) | |||||||
\(572\) | 277.907 | 0.0203144 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 341.517 | 0.0248339 | ||||||||
\(575\) | −20796.1 | −1.50827 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12880.9 | −0.929354 | −0.464677 | − | 0.885480i | \(-0.653830\pi\) | ||||
−0.464677 | + | 0.885480i | \(0.653830\pi\) | |||||||
\(578\) | −1566.81 | −0.112752 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −18686.3 | −1.33777 | ||||||||
\(581\) | 8947.91 | 0.638936 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1163.25 | 0.0826365 | ||||||||
\(584\) | 8557.06 | 0.606325 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16115.9 | 1.13608 | ||||||||
\(587\) | 4693.01 | 0.329985 | 0.164993 | − | 0.986295i | \(-0.447240\pi\) | ||||
0.164993 | + | 0.986295i | \(0.447240\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6858.55 | 0.479799 | ||||||||
\(590\) | −9877.15 | −0.689213 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11913.5 | 0.827101 | ||||||||
\(593\) | −13825.6 | −0.957418 | −0.478709 | − | 0.877974i | \(-0.658895\pi\) | ||||
−0.478709 | + | 0.877974i | \(0.658895\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7844.11 | 0.540466 | ||||||||
\(596\) | 2636.90 | 0.181227 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3940.36 | 0.269454 | ||||||||
\(599\) | −13616.7 | −0.928823 | −0.464411 | − | 0.885620i | \(-0.653734\pi\) | ||||
−0.464411 | + | 0.885620i | \(0.653734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25768.9 | 1.74898 | 0.874490 | − | 0.485044i | \(-0.161196\pi\) | ||||
0.874490 | + | 0.485044i | \(0.161196\pi\) | |||||||
\(602\) | −3631.05 | −0.245831 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4264.03 | −0.287253 | ||||||||
\(605\) | 1852.00 | 0.124454 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19103.1 | 1.27738 | 0.638691 | − | 0.769463i | \(-0.279476\pi\) | ||||
0.638691 | + | 0.769463i | \(0.279476\pi\) | |||||||
\(608\) | 14109.7 | 0.941161 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10142.1 | 0.673184 | ||||||||
\(611\) | 560.121 | 0.0370869 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6915.62 | −0.455659 | −0.227830 | − | 0.973701i | \(-0.573163\pi\) | ||||
−0.227830 | + | 0.973701i | \(0.573163\pi\) | |||||||
\(614\) | −20681.6 | −1.35935 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1004.81 | −0.0657223 | ||||||||
\(617\) | −16084.3 | −1.04948 | −0.524742 | − | 0.851261i | \(-0.675838\pi\) | ||||
−0.524742 | + | 0.851261i | \(0.675838\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12041.5 | 0.781891 | 0.390945 | − | 0.920414i | \(-0.372148\pi\) | ||||
0.390945 | + | 0.920414i | \(0.372148\pi\) | |||||||
\(620\) | 5586.58 | 0.361875 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6166.09 | 0.397488 | ||||||||
\(623\) | −1785.84 | −0.114845 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17344.1 | −1.11002 | ||||||||
\(626\) | 8325.09 | 0.531530 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13603.4 | 0.864389 | ||||||||
\(629\) | 10913.2 | 0.691795 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19654.5 | 1.23999 | 0.619994 | − | 0.784607i | \(-0.287135\pi\) | ||||
0.619994 | + | 0.784607i | \(0.287135\pi\) | |||||||
\(632\) | 1437.91 | 0.0905014 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6627.39 | 0.415153 | ||||||||
\(635\) | −37450.9 | −2.34046 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 289.548 | 0.0180099 | ||||||||
\(638\) | 11005.2 | 0.682915 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −22795.0 | −1.40789 | ||||||||
\(641\) | −9941.56 | −0.612586 | −0.306293 | − | 0.951937i | \(-0.599089\pi\) | ||||
−0.306293 | + | 0.951937i | \(0.599089\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15162.4 | 0.929930 | 0.464965 | − | 0.885329i | \(-0.346067\pi\) | ||||
0.464965 | + | 0.885329i | \(0.346067\pi\) | |||||||
\(644\) | 5696.03 | 0.348532 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20607.8 | 1.25511 | ||||||||
\(647\) | −7769.45 | −0.472100 | −0.236050 | − | 0.971741i | \(-0.575853\pi\) | ||||
−0.236050 | + | 0.971741i | \(0.575853\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2026.05 | 0.122542 | ||||||||
\(650\) | −2262.20 | −0.136509 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11611.3 | −0.697443 | ||||||||
\(653\) | 17240.5 | 1.03319 | 0.516594 | − | 0.856230i | \(-0.327200\pi\) | ||||
0.516594 | + | 0.856230i | \(0.327200\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31760.8 | −1.89465 | ||||||||
\(656\) | −1112.94 | −0.0662396 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2324.74 | 0.137732 | ||||||||
\(659\) | 26820.8 | 1.58542 | 0.792709 | − | 0.609600i | \(-0.208670\pi\) | ||||
0.792709 | + | 0.609600i | \(0.208670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33944.1 | 1.99738 | 0.998692 | − | 0.0511251i | \(-0.0162807\pi\) | ||||
0.998692 | + | 0.0511251i | \(0.0162807\pi\) | |||||||
\(662\) | 31202.4 | 1.83189 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16680.8 | −0.974910 | ||||||||
\(665\) | −8607.49 | −0.501931 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54347.5 | 3.15494 | ||||||||
\(668\) | 826.508 | 0.0478721 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10390.3 | 0.599123 | ||||||||
\(671\) | −2080.40 | −0.119692 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9225.59 | −0.528411 | −0.264205 | − | 0.964466i | \(-0.585110\pi\) | ||||
−0.264205 | + | 0.964466i | \(0.585110\pi\) | |||||||
\(674\) | −35611.7 | −2.03518 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9243.86 | −0.525936 | ||||||||
\(677\) | −23388.8 | −1.32778 | −0.663889 | − | 0.747831i | \(-0.731095\pi\) | ||||
−0.663889 | + | 0.747831i | \(0.731095\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2607.76 | −0.147388 | ||||||||
\(680\) | −14623.1 | −0.824661 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3290.19 | −0.184733 | ||||||||
\(683\) | −8866.19 | −0.496713 | −0.248357 | − | 0.968669i | \(-0.579891\pi\) | ||||
−0.248357 | + | 0.968669i | \(0.579891\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3046.86 | −0.169948 | ||||||||
\(686\) | 1201.75 | 0.0668847 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11833.0 | 0.655709 | ||||||||
\(689\) | 624.895 | 0.0345524 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26611.8 | 1.46507 | 0.732534 | − | 0.680731i | \(-0.238338\pi\) | ||||
0.732534 | + | 0.680731i | \(0.238338\pi\) | |||||||
\(692\) | −10946.2 | −0.601320 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26904.2 | 1.47157 | ||||||||
\(695\) | 36094.0 | 1.96996 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1019.50 | −0.0554034 | ||||||||
\(698\) | −29762.3 | −1.61392 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3270.15 | −0.176571 | ||||||||
\(701\) | −19326.3 | −1.04129 | −0.520644 | − | 0.853774i | \(-0.674308\pi\) | ||||
−0.520644 | + | 0.853774i | \(0.674308\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11975.3 | −0.642470 | ||||||||
\(704\) | 264.589 | 0.0141649 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5178.09 | 0.276034 | ||||||||
\(707\) | 8006.48 | 0.425905 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24749.2 | 1.31097 | 0.655484 | − | 0.755209i | \(-0.272465\pi\) | ||||
0.655484 | + | 0.755209i | \(0.272465\pi\) | |||||||
\(710\) | −19105.0 | −1.00986 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3329.18 | 0.175234 | ||||||||
\(713\) | −16248.1 | −0.853430 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 994.885 | 0.0520372 | ||||||||
\(716\) | −11900.0 | −0.621122 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4746.34 | 0.246702 | ||||||||
\(719\) | 3517.02 | 0.182424 | 0.0912119 | − | 0.995832i | \(-0.470926\pi\) | ||||
0.0912119 | + | 0.995832i | \(0.470926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3302.05 | −0.170561 | ||||||||
\(722\) | 1418.09 | 0.0730969 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13064.5 | 0.670635 | ||||||||
\(725\) | −31201.4 | −1.59833 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27443.7 | 1.40004 | 0.700021 | − | 0.714123i | \(-0.253174\pi\) | ||||
0.700021 | + | 0.714123i | \(0.253174\pi\) | |||||||
\(728\) | −539.779 | −0.0274801 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −35164.6 | −1.78288 | ||||||||
\(731\) | 10839.4 | 0.548441 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24925.8 | −1.25601 | −0.628005 | − | 0.778210i | \(-0.716128\pi\) | ||||
−0.628005 | + | 0.778210i | \(0.716128\pi\) | |||||||
\(734\) | 7199.88 | 0.362061 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33426.4 | −1.67406 | ||||||||
\(737\) | −2131.31 | −0.106524 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37245.9 | 1.85401 | 0.927004 | − | 0.375053i | \(-0.122375\pi\) | ||||
0.927004 | + | 0.375053i | \(0.122375\pi\) | |||||||
\(740\) | −9754.38 | −0.484565 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2593.57 | 0.128319 | ||||||||
\(743\) | −13860.1 | −0.684357 | −0.342178 | − | 0.939635i | \(-0.611165\pi\) | ||||
−0.342178 | + | 0.939635i | \(0.611165\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9439.90 | 0.464230 | ||||||||
\(746\) | −23237.1 | −1.14044 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3443.22 | −0.168311 | ||||||||
\(749\) | 10937.4 | 0.533572 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20219.8 | 0.982467 | 0.491234 | − | 0.871028i | \(-0.336546\pi\) | ||||
0.491234 | + | 0.871028i | \(0.336546\pi\) | |||||||
\(752\) | −7575.91 | −0.367374 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5911.94 | 0.285544 | ||||||||
\(755\) | −15264.9 | −0.735825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4381.34 | 0.210360 | 0.105180 | − | 0.994453i | \(-0.466458\pi\) | ||||
0.105180 | + | 0.994453i | \(0.466458\pi\) | |||||||
\(758\) | 2025.78 | 0.0970706 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16046.2 | 0.765863 | ||||||||
\(761\) | 14022.2 | 0.667942 | 0.333971 | − | 0.942583i | \(-0.391611\pi\) | ||||
0.333971 | + | 0.942583i | \(0.391611\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6271.26 | 0.297556 | ||||||||
\(764\) | −13430.4 | −0.635987 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19772.6 | −0.932656 | ||||||||
\(767\) | 1088.39 | 0.0512377 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10002.3 | 0.469042 | 0.234521 | − | 0.972111i | \(-0.424648\pi\) | ||||
0.234521 | + | 0.972111i | \(0.424648\pi\) | |||||||
\(770\) | 4129.19 | 0.193254 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7250.04 | −0.337998 | ||||||||
\(773\) | 42649.3 | 1.98446 | 0.992232 | − | 0.124405i | \(-0.0397021\pi\) | ||||
0.992232 | + | 0.124405i | \(0.0397021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9328.20 | 0.432360 | ||||||||
\(776\) | 4861.41 | 0.224890 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −47254.9 | −2.17760 | ||||||||
\(779\) | 1118.71 | 0.0514532 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3918.91 | 0.179551 | ||||||||
\(782\) | −48820.4 | −2.23250 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3916.28 | −0.178402 | ||||||||
\(785\) | 48699.3 | 2.21421 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9129.62 | 0.413514 | 0.206757 | − | 0.978392i | \(-0.433709\pi\) | ||||
0.206757 | + | 0.978392i | \(0.433709\pi\) | |||||||
\(788\) | 13090.8 | 0.591801 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5908.97 | −0.266116 | ||||||||
\(791\) | 2390.90 | 0.107472 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1117.58 | −0.0500461 | ||||||||
\(794\) | 54323.8 | 2.42806 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 286.292 | 0.0127479 | ||||||||
\(797\) | 31429.2 | 1.39684 | 0.698419 | − | 0.715690i | \(-0.253887\pi\) | ||||
0.698419 | + | 0.715690i | \(0.253887\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6939.81 | −0.307275 | ||||||||
\(800\) | 19190.4 | 0.848105 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −39905.4 | −1.75699 | ||||||||
\(803\) | 7213.14 | 0.316994 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20391.4 | 0.892796 | ||||||||
\(806\) | −1767.47 | −0.0772415 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14925.8 | −0.649860 | ||||||||
\(809\) | 18839.2 | 0.818727 | 0.409363 | − | 0.912371i | \(-0.365751\pi\) | ||||
0.409363 | + | 0.912371i | \(0.365751\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10325.1 | 0.447059 | 0.223529 | − | 0.974697i | \(-0.428242\pi\) | ||||
0.223529 | + | 0.974697i | \(0.428242\pi\) | |||||||
\(812\) | 8546.06 | 0.369345 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5744.79 | 0.247365 | ||||||||
\(815\) | −41567.6 | −1.78656 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11894.3 | −0.509337 | ||||||||
\(818\) | −47342.2 | −2.02357 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 911.239 | 0.0388071 | ||||||||
\(821\) | 31707.7 | 1.34788 | 0.673938 | − | 0.738788i | \(-0.264601\pi\) | ||||
0.673938 | + | 0.738788i | \(0.264601\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27144.9 | −1.14971 | −0.574856 | − | 0.818254i | \(-0.694942\pi\) | ||||
−0.574856 | + | 0.818254i | \(0.694942\pi\) | |||||||
\(824\) | 6155.72 | 0.260248 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4517.25 | 0.190285 | ||||||||
\(827\) | −10010.3 | −0.420909 | −0.210455 | − | 0.977604i | \(-0.567494\pi\) | ||||
−0.210455 | + | 0.977604i | \(0.567494\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36122.6 | −1.51338 | −0.756689 | − | 0.653776i | \(-0.773184\pi\) | ||||
−0.756689 | + | 0.653776i | \(0.773184\pi\) | |||||||
\(830\) | 68548.4 | 2.86669 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 142.136 | 0.00592269 | ||||||||
\(833\) | −3587.45 | −0.149217 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2958.84 | 0.122629 | ||||||||
\(836\) | 3778.30 | 0.156310 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 28896.4 | 1.19118 | ||||||||
\(839\) | 6552.24 | 0.269617 | 0.134808 | − | 0.990872i | \(-0.456958\pi\) | ||||
0.134808 | + | 0.990872i | \(0.456958\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57151.4 | 2.34333 | ||||||||
\(842\) | −9217.20 | −0.377251 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3906.20 | −0.159309 | ||||||||
\(845\) | −33092.3 | −1.34723 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −847.000 | −0.0343604 | ||||||||
\(848\) | −8452.01 | −0.342268 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 28028.3 | 1.13102 | ||||||||
\(851\) | 28369.8 | 1.14278 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29048.8 | −1.16601 | −0.583007 | − | 0.812467i | \(-0.698124\pi\) | ||||
−0.583007 | + | 0.812467i | \(0.698124\pi\) | |||||||
\(854\) | −4638.43 | −0.185859 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20389.7 | −0.814141 | ||||||||
\(857\) | 4964.30 | 0.197873 | 0.0989365 | − | 0.995094i | \(-0.468456\pi\) | ||||
0.0989365 | + | 0.995094i | \(0.468456\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21708.3 | 0.862255 | 0.431127 | − | 0.902291i | \(-0.358116\pi\) | ||||
0.431127 | + | 0.902291i | \(0.358116\pi\) | |||||||
\(860\) | −9688.40 | −0.384153 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36538.3 | −1.44374 | ||||||||
\(863\) | −11197.9 | −0.441692 | −0.220846 | − | 0.975309i | \(-0.570882\pi\) | ||||
−0.220846 | + | 0.975309i | \(0.570882\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39186.7 | −1.54033 | ||||||||
\(866\) | 30910.6 | 1.21291 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2554.99 | −0.0999101 | ||||||||
\(869\) | 1212.08 | 0.0473152 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1144.93 | −0.0445402 | ||||||||
\(872\) | −11691.0 | −0.454020 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 53571.6 | 2.07332 | ||||||||
\(875\) | 1685.66 | 0.0651266 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20949.4 | −0.806626 | −0.403313 | − | 0.915062i | \(-0.632141\pi\) | ||||
−0.403313 | + | 0.915062i | \(0.632141\pi\) | |||||||
\(878\) | 59210.2 | 2.27591 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13456.3 | −0.515468 | ||||||||
\(881\) | 35886.4 | 1.37236 | 0.686178 | − | 0.727434i | \(-0.259287\pi\) | ||||
0.686178 | + | 0.727434i | \(0.259287\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7181.51 | −0.273700 | −0.136850 | − | 0.990592i | \(-0.543698\pi\) | ||||
−0.136850 | + | 0.990592i | \(0.543698\pi\) | |||||||
\(884\) | −1849.68 | −0.0703749 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31988.8 | 1.21296 | ||||||||
\(887\) | 25132.3 | 0.951365 | 0.475682 | − | 0.879617i | \(-0.342201\pi\) | ||||
0.475682 | + | 0.879617i | \(0.342201\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17127.9 | 0.646178 | ||||||||
\(890\) | −13681.0 | −0.515268 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 656.912 | 0.0246581 | ||||||||
\(893\) | 7615.18 | 0.285366 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42601.1 | −1.59106 | ||||||||
\(896\) | 10425.1 | 0.388705 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22638.6 | 0.841269 | ||||||||
\(899\) | −24377.9 | −0.904392 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7742.34 | −0.286276 | ||||||||
\(902\) | −536.669 | −0.0198106 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4457.15 | −0.163985 | ||||||||
\(905\) | 46770.1 | 1.71789 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9475.36 | −0.346884 | −0.173442 | − | 0.984844i | \(-0.555489\pi\) | ||||
−0.173442 | + | 0.984844i | \(0.555489\pi\) | |||||||
\(908\) | −2125.87 | −0.0776977 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2218.18 | 0.0808044 | ||||||||
\(911\) | 43008.3 | 1.56414 | 0.782068 | − | 0.623193i | \(-0.214165\pi\) | ||||
0.782068 | + | 0.623193i | \(0.214165\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14061.0 | −0.509694 | ||||||||
\(914\) | 32371.7 | 1.17151 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14428.7 | 0.520457 | ||||||||
\(917\) | 14525.6 | 0.523094 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23979.4 | 0.860727 | 0.430363 | − | 0.902656i | \(-0.358385\pi\) | ||||
0.430363 | + | 0.902656i | \(0.358385\pi\) | |||||||
\(920\) | −38013.8 | −1.36226 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25905.7 | 0.925334 | ||||||||
\(923\) | 2105.22 | 0.0750750 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16287.4 | −0.578947 | ||||||||
\(926\) | 11773.3 | 0.417812 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −50151.4 | −1.77403 | ||||||||
\(929\) | 27635.2 | 0.975975 | 0.487988 | − | 0.872851i | \(-0.337731\pi\) | ||||
0.487988 | + | 0.872851i | \(0.337731\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3936.58 | 0.138578 | ||||||||
\(932\) | −20735.7 | −0.728776 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −37436.8 | −1.31153 | ||||||||
\(935\) | −12326.5 | −0.431143 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5950.96 | −0.207481 | −0.103740 | − | 0.994604i | \(-0.533081\pi\) | ||||
−0.103740 | + | 0.994604i | \(0.533081\pi\) | |||||||
\(938\) | −4751.94 | −0.165412 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6202.88 | 0.215230 | ||||||||
\(941\) | −21970.4 | −0.761122 | −0.380561 | − | 0.924756i | \(-0.624269\pi\) | ||||
−0.380561 | + | 0.924756i | \(0.624269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2650.26 | −0.0915210 | ||||||||
\(944\) | −14720.9 | −0.507549 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5705.94 | 0.196106 | ||||||||
\(947\) | −18563.0 | −0.636976 | −0.318488 | − | 0.947927i | \(-0.603175\pi\) | ||||
−0.318488 | + | 0.947927i | \(0.603175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3874.86 | 0.132543 | ||||||||
\(950\) | −30756.0 | −1.05037 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6687.77 | 0.227681 | ||||||||
\(953\) | 642.345 | 0.0218338 | 0.0109169 | − | 0.999940i | \(-0.496525\pi\) | ||||
0.0109169 | + | 0.999940i | \(0.496525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48079.8 | −1.62914 | ||||||||
\(956\) | −31424.8 | −1.06313 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −63781.5 | −2.15103 | ||||||||
\(959\) | 1393.46 | 0.0469210 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22502.8 | −0.755356 | ||||||||
\(962\) | 3086.07 | 0.103429 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3929.86 | 0.131299 | ||||||||
\(965\) | −25954.6 | −0.865812 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27334.8 | 0.909026 | 0.454513 | − | 0.890740i | \(-0.349813\pi\) | ||||
0.454513 | + | 0.890740i | \(0.349813\pi\) | |||||||
\(968\) | 1578.99 | 0.0524283 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19977.6 | −0.661281 | ||||||||
\(971\) | −53121.2 | −1.75565 | −0.877827 | − | 0.478978i | \(-0.841007\pi\) | ||||
−0.877827 | + | 0.478978i | \(0.841007\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16507.4 | −0.543887 | ||||||||
\(974\) | 21771.5 | 0.716225 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15115.9 | 0.495745 | ||||||||
\(977\) | 11393.0 | 0.373075 | 0.186537 | − | 0.982448i | \(-0.440273\pi\) | ||||
0.186537 | + | 0.982448i | \(0.440273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2806.32 | 0.0916143 | ||||||||
\(980\) | 3206.51 | 0.104519 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 59641.4 | 1.93812 | ||||||||
\(983\) | −50295.2 | −1.63191 | −0.815955 | − | 0.578115i | \(-0.803788\pi\) | ||||
−0.815955 | + | 0.578115i | \(0.803788\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46864.0 | 1.51595 | ||||||||
\(986\) | −73247.9 | −2.36581 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2029.69 | 0.0653572 | ||||||||
\(989\) | 28177.9 | 0.905970 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4361.21 | −0.139797 | −0.0698983 | − | 0.997554i | \(-0.522267\pi\) | ||||
−0.0698983 | + | 0.997554i | \(0.522267\pi\) | |||||||
\(992\) | 14993.6 | 0.479886 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8737.54 | 0.278811 | ||||||||
\(995\) | 1024.90 | 0.0326549 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25946.3 | −0.824199 | −0.412100 | − | 0.911139i | \(-0.635204\pi\) | ||||
−0.412100 | + | 0.911139i | \(0.635204\pi\) | |||||||
\(998\) | 72157.9 | 2.28870 | ||||||||
\(999\) | 0 | 0 |
(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 | 693.4.a.s.1.2 | ✓ | 8 | |
3.2 | odd | 2 | 693.4.a.t.1.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.4.a.s.1.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
693.4.a.t.1.7 | yes | 8 | 3.2 | odd | 2 |