Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 40x^{4} - 88x^{3} - 8x^{2} + 48x - 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.215317\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 6.36242 | 1.22445 | 0.612225 | − | 0.790684i | \(-0.290275\pi\) | ||||
0.612225 | + | 0.790684i | \(0.290275\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.72860 | −0.780710 | −0.390355 | − | 0.920664i | \(-0.627648\pi\) | ||||
−0.390355 | + | 0.920664i | \(0.627648\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.76166 | −0.473085 | −0.236543 | − | 0.971621i | \(-0.576014\pi\) | ||||
−0.236543 | + | 0.971621i | \(0.576014\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 13.4804 | 0.499276 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.5540 | −1.08418 | −0.542090 | − | 0.840320i | \(-0.682367\pi\) | ||||
−0.542090 | + | 0.840320i | \(0.682367\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 27.6290 | 0.589455 | 0.294727 | − | 0.955581i | \(-0.404771\pi\) | ||||
0.294727 | + | 0.955581i | \(0.404771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −55.5351 | −0.955940 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 134.762 | 1.92263 | 0.961313 | − | 0.275459i | \(-0.0888299\pi\) | ||||
0.961313 | + | 0.275459i | \(0.0888299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 161.056 | 1.94467 | 0.972336 | − | 0.233585i | \(-0.0750456\pi\) | ||||
0.972336 | + | 0.233585i | \(0.0750456\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −55.7454 | −0.579269 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −163.135 | −1.47895 | −0.739477 | − | 0.673181i | \(-0.764927\pi\) | ||||
−0.739477 | + | 0.673181i | \(0.764927\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −48.8115 | −0.390492 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −86.0171 | −0.613111 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −200.241 | −1.16014 | −0.580069 | − | 0.814568i | \(-0.696974\pi\) | ||||
−0.580069 | + | 0.814568i | \(0.696974\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −251.659 | −1.32752 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 76.4771 | 0.369342 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 208.370 | 0.925833 | 0.462917 | − | 0.886402i | \(-0.346803\pi\) | ||||
0.462917 | + | 0.886402i | \(0.346803\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 175.788 | 0.721758 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −83.2931 | −0.317273 | −0.158637 | − | 0.987337i | \(-0.550710\pi\) | ||||
−0.158637 | + | 0.987337i | \(0.550710\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 334.050 | 1.18470 | 0.592351 | − | 0.805680i | \(-0.298200\pi\) | ||||
0.592351 | + | 0.805680i | \(0.298200\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −117.665 | −0.389790 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −277.727 | −0.861928 | −0.430964 | − | 0.902369i | \(-0.641826\pi\) | ||||
−0.430964 | + | 0.902369i | \(0.641826\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −266.233 | −0.776190 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 857.414 | 2.35416 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 185.468 | 0.480678 | 0.240339 | − | 0.970689i | \(-0.422741\pi\) | ||||
0.240339 | + | 0.970689i | \(0.422741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 345.251 | 0.846430 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1024.71 | 2.38115 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −190.892 | −0.421220 | −0.210610 | − | 0.977570i | \(-0.567545\pi\) | ||||
−0.210610 | + | 0.977570i | \(0.567545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −622.436 | −1.30647 | −0.653235 | − | 0.757155i | \(-0.726589\pi\) | ||||
−0.653235 | + | 0.757155i | \(0.726589\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −118.111 | −0.236200 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −241.163 | −0.460193 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −627.283 | −1.14380 | −0.571901 | − | 0.820322i | \(-0.693794\pi\) | ||||
−0.571901 | + | 0.820322i | \(0.693794\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1037.93 | −1.81090 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 872.996 | 1.45923 | 0.729616 | − | 0.683857i | \(-0.239699\pi\) | ||||
0.729616 | + | 0.683857i | \(0.239699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −359.712 | −0.576728 | −0.288364 | − | 0.957521i | \(-0.593111\pi\) | ||||
−0.288364 | + | 0.957521i | \(0.593111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −310.560 | −0.478138 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 346.559 | 0.512910 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −165.772 | −0.236086 | −0.118043 | − | 0.993008i | \(-0.537662\pi\) | ||||
−0.118043 | + | 0.993008i | \(0.537662\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −911.250 | −1.25000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 565.467 | 0.747808 | 0.373904 | − | 0.927467i | \(-0.378019\pi\) | ||||
0.373904 | + | 0.927467i | \(0.378019\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1176.29 | −1.50101 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 184.510 | 0.227375 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.8167 | 0.0188378 | 0.00941890 | − | 0.999956i | \(-0.497002\pi\) | ||||
0.00941890 | + | 0.999956i | \(0.497002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −242.076 | −0.278862 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1274.02 | −1.42053 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1405.79 | −1.51823 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1436.13 | −1.50327 | −0.751634 | − | 0.659580i | \(-0.770734\pi\) | ||||
−0.751634 | + | 0.659580i | \(0.770734\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −533.206 | −0.541305 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −618.989 | −0.609819 | −0.304910 | − | 0.952381i | \(-0.598626\pi\) | ||||
−0.304910 | + | 0.952381i | \(0.598626\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1112.51 | −1.06426 | −0.532128 | − | 0.846664i | \(-0.678608\pi\) | ||||
−0.532128 | + | 0.846664i | \(0.678608\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 486.580 | 0.452241 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −985.275 | −0.890188 | −0.445094 | − | 0.895484i | \(-0.646830\pi\) | ||||
−0.445094 | + | 0.895484i | \(0.646830\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −510.618 | −0.448700 | −0.224350 | − | 0.974509i | \(-0.572026\pi\) | ||||
−0.224350 | + | 0.974509i | \(0.572026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1325.74 | 1.13364 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1119.33 | 0.931836 | 0.465918 | − | 0.884828i | \(-0.345724\pi\) | ||||
0.465918 | + | 0.884828i | \(0.345724\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1423.94 | 1.15463 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 372.452 | 0.294301 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1180.74 | −0.909566 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 233.519 | 0.175446 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −529.946 | −0.388485 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1517.13 | 1.08557 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2342.91 | −1.63700 | −0.818502 | − | 0.574503i | \(-0.805195\pi\) | ||||
−0.818502 | + | 0.574503i | \(0.805195\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2125.37 | 1.45061 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1140.68 | −0.760778 | −0.380389 | − | 0.924827i | \(-0.624210\pi\) | ||||
−0.380389 | + | 0.924827i | \(0.624210\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1411.12 | −0.919996 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 750.809 | 0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1859.11 | −1.15937 | −0.579687 | − | 0.814839i | \(-0.696825\pi\) | ||||
−0.579687 | + | 0.814839i | \(0.696825\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2724.85 | −1.66272 | −0.831362 | − | 0.555731i | \(-0.812438\pi\) | ||||
−0.831362 | + | 0.555731i | \(0.812438\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1767.02 | −1.05539 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1092.84 | −0.639075 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −253.129 | −0.144974 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1693.89 | −0.950406 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 765.729 | 0.421013 | 0.210506 | − | 0.977592i | \(-0.432489\pi\) | ||||
0.210506 | + | 0.977592i | \(0.432489\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3074.79 | 1.65710 | 0.828551 | − | 0.559913i | \(-0.189165\pi\) | ||||
0.828551 | + | 0.559913i | \(0.189165\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1816.65 | 0.959920 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1747.82 | 0.905731 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1934.86 | 0.983560 | 0.491780 | − | 0.870720i | \(-0.336346\pi\) | ||||
0.491780 | + | 0.870720i | \(0.336346\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1180.02 | 0.588566 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1429.33 | 0.699672 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 684.358 | 0.328853 | 0.164427 | − | 0.986389i | \(-0.447423\pi\) | ||||
0.164427 | + | 0.986389i | \(0.447423\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2196.63 | 1.03641 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2994.75 | −1.38767 | −0.693834 | − | 0.720135i | \(-0.744080\pi\) | ||||
−0.693834 | + | 0.720135i | \(0.744080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1433.64 | −0.652543 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2171.11 | 0.970928 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2563.06 | 1.12639 | 0.563197 | − | 0.826323i | \(-0.309571\pi\) | ||||
0.563197 | + | 0.826323i | \(0.309571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 427.670 | 0.184736 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1214.53 | −0.515762 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1480.22 | −0.618085 | −0.309042 | − | 0.951048i | \(-0.600008\pi\) | ||||
−0.309042 | + | 0.951048i | \(0.600008\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2998.88 | −1.23152 | −0.615759 | − | 0.787935i | \(-0.711150\pi\) | ||||
−0.615759 | + | 0.787935i | \(0.711150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3960.20 | −1.59971 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1818.78 | −0.722807 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5330.38 | −2.08447 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 753.653 | 0.290054 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −423.297 | −0.160360 | −0.0801799 | − | 0.996780i | \(-0.525549\pi\) | ||||
−0.0801799 | + | 0.996780i | \(0.525549\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 306.989 | 0.114495 | 0.0572476 | − | 0.998360i | \(-0.481768\pi\) | ||||
0.0572476 | + | 0.998360i | \(0.481768\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1534.38 | −0.563483 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2904.54 | −1.05046 | −0.525229 | − | 0.850961i | \(-0.676020\pi\) | ||||
−0.525229 | + | 0.850961i | \(0.676020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 266.678 | 0.0949963 | 0.0474982 | − | 0.998871i | \(-0.484875\pi\) | ||||
0.0474982 | + | 0.998871i | \(0.484875\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3991.04 | −1.40053 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −254.088 | −0.0878497 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 727.033 | 0.247698 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2199.13 | −0.738406 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6370.41 | −2.10838 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −919.255 | −0.299925 | −0.149962 | − | 0.988692i | \(-0.547915\pi\) | ||||
−0.149962 | + | 0.988692i | \(0.547915\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5554.37 | 1.78676 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2915.79 | −0.924909 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1754.44 | 0.548844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2288.64 | −0.706174 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3723.35 | 1.13330 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2349.53 | −0.705542 | −0.352771 | − | 0.935710i | \(-0.614761\pi\) | ||||
−0.352771 | + | 0.935710i | \(0.614761\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −658.001 | −0.194963 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1026.17 | −0.300042 | −0.150021 | − | 0.988683i | \(-0.547934\pi\) | ||||
−0.150021 | + | 0.988683i | \(0.547934\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 471.496 | 0.136058 | 0.0680292 | − | 0.997683i | \(-0.478329\pi\) | ||||
0.0680292 | + | 0.997683i | \(0.478329\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2204.95 | 0.628032 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1412.43 | 0.397131 | 0.198566 | − | 0.980088i | \(-0.436372\pi\) | ||||
0.198566 | + | 0.980088i | \(0.436372\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2424.17 | 0.672916 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1054.71 | −0.289075 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −64.0933 | −0.0173467 | −0.00867333 | − | 0.999962i | \(-0.502761\pi\) | ||||
−0.00867333 | + | 0.999962i | \(0.502761\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3629.05 | −0.969991 | −0.484995 | − | 0.874517i | \(-0.661179\pi\) | ||||
−0.484995 | + | 0.874517i | \(0.661179\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3475.29 | −0.917450 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2323.84 | 0.605979 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4449.82 | 1.14630 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3597.74 | 0.915653 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1919.48 | −0.482696 | −0.241348 | − | 0.970439i | \(-0.577589\pi\) | ||||
−0.241348 | + | 0.970439i | \(0.577589\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6452.63 | 1.60345 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7484.03 | −1.83791 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4978.66 | 1.20841 | 0.604203 | − | 0.796831i | \(-0.293492\pi\) | ||||
0.604203 | + | 0.796831i | \(0.293492\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1825.67 | −0.437998 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 390.933 | 0.0927132 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6142.46 | 1.44015 | 0.720077 | − | 0.693894i | \(-0.244107\pi\) | ||||
0.720077 | + | 0.693894i | \(0.244107\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1618.87 | −0.375270 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 100.632 | 0.0230659 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8276.23 | 1.87588 | 0.937938 | − | 0.346803i | \(-0.112733\pi\) | ||||
0.937938 | + | 0.346803i | \(0.112733\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3102.84 | −0.695514 | −0.347757 | − | 0.937585i | \(-0.613057\pi\) | ||||
−0.347757 | + | 0.937585i | \(0.613057\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1540.19 | −0.341453 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1930.69 | 0.423364 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −934.063 | −0.202608 | −0.101304 | − | 0.994856i | \(-0.532301\pi\) | ||||
−0.101304 | + | 0.994856i | \(0.532301\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2699.33 | −0.579229 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −728.824 | −0.154726 | −0.0773630 | − | 0.997003i | \(-0.524650\pi\) | ||||
−0.0773630 | + | 0.997003i | \(0.524650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4414.80 | −0.927323 | −0.463662 | − | 0.886012i | \(-0.653465\pi\) | ||||
−0.463662 | + | 0.886012i | \(0.653465\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8944.26 | −1.85899 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 729.786 | 0.150097 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13247.9 | 2.69649 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9137.28 | −1.84068 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8255.06 | 1.64596 | 0.822979 | − | 0.568072i | \(-0.192311\pi\) | ||||
0.822979 | + | 0.568072i | \(0.192311\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1666.22 | 0.328850 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3402.32 | 0.664723 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4507.26 | −0.871777 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2926.84 | −0.560465 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3938.27 | −0.746693 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5432.99 | 1.01997 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −966.478 | −0.179674 | −0.0898368 | − | 0.995956i | \(-0.528635\pi\) | ||||
−0.0898368 | + | 0.995956i | \(0.528635\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7078.23 | −1.30313 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6837.36 | 1.24666 | 0.623330 | − | 0.781959i | \(-0.285779\pi\) | ||||
0.623330 | + | 0.781959i | \(0.285779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9633.46 | 1.73967 | 0.869833 | − | 0.493346i | \(-0.164226\pi\) | ||||
0.869833 | + | 0.493346i | \(0.164226\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1030.95 | 0.184404 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7832.86 | −1.38781 | −0.693907 | − | 0.720065i | \(-0.744112\pi\) | ||||
−0.693907 | + | 0.720065i | \(0.744112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1147.07 | −0.201327 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6268.74 | −1.08999 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21704.3 | 3.73888 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1348.61 | −0.230177 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3248.77 | −0.549411 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2433.35 | 0.407766 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3002.68 | 0.498617 | 0.249308 | − | 0.968424i | \(-0.419797\pi\) | ||||
0.249308 | + | 0.968424i | \(0.419797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2808.92 | 0.462246 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5475.30 | 0.892978 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6707.78 | −1.08426 | −0.542131 | − | 0.840294i | \(-0.682382\pi\) | ||||
−0.542131 | + | 0.840294i | \(0.682382\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7121.64 | 1.14099 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7920.31 | 1.25780 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5337.90 | 0.840290 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9059.70 | 1.41379 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9319.21 | −1.44173 | −0.720866 | − | 0.693074i | \(-0.756256\pi\) | ||||
−0.720866 | + | 0.693074i | \(0.756256\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5673.56 | −0.870197 | −0.435098 | − | 0.900383i | \(-0.643286\pi\) | ||||
−0.435098 | + | 0.900383i | \(0.643286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2376.57 | −0.361401 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6621.49 | −0.998375 | −0.499188 | − | 0.866494i | \(-0.666368\pi\) | ||||
−0.499188 | + | 0.866494i | \(0.666368\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7620.03 | −1.13924 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7512.38 | −1.11372 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2432.83 | −0.357660 | −0.178830 | − | 0.983880i | \(-0.557231\pi\) | ||||
−0.178830 | + | 0.983880i | \(0.557231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19080.0 | 2.78175 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1485.74 | 0.214825 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3139.78 | 0.450257 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6367.01 | −0.905600 | −0.452800 | − | 0.891612i | \(-0.649575\pi\) | ||||
−0.452800 | + | 0.891612i | \(0.649575\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1122.83 | −0.158407 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1625.00 | −0.227402 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6083.32 | 0.844456 | 0.422228 | − | 0.906490i | \(-0.361248\pi\) | ||||
0.422228 | + | 0.906490i | \(0.361248\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9652.63 | 1.32923 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 801.242 | 0.109459 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3131.84 | 0.424464 | 0.212232 | − | 0.977219i | \(-0.431927\pi\) | ||||
0.212232 | + | 0.977219i | \(0.431927\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14906.6 | −2.00443 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2584.17 | −0.344765 | −0.172383 | − | 0.985030i | \(-0.555147\pi\) | ||||
−0.172383 | + | 0.985030i | \(0.555147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3024.97 | −0.400434 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4503.15 | 0.591493 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2718.60 | −0.354341 | −0.177170 | − | 0.984180i | \(-0.556694\pi\) | ||||
−0.177170 | + | 0.984180i | \(0.556694\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21984.4 | −2.84348 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7257.51 | −0.931534 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1446.96 | 0.184315 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8139.31 | −1.02897 | −0.514484 | − | 0.857500i | \(-0.672017\pi\) | ||||
−0.514484 | + | 0.857500i | \(0.672017\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8978.14 | −1.12649 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8000.82 | −0.996364 | −0.498182 | − | 0.867072i | \(-0.665999\pi\) | ||||
−0.498182 | + | 0.867072i | \(0.665999\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5532.45 | −0.683849 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7953.93 | 0.975887 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8241.87 | −1.00377 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3305.16 | −0.399583 | −0.199792 | − | 0.979838i | \(-0.564027\pi\) | ||||
−0.199792 | + | 0.979838i | \(0.564027\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11828.4 | −1.41960 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1672.53 | 0.199273 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4935.74 | −0.583821 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17336.6 | −2.03592 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1456.05 | −0.169768 | −0.0848841 | − | 0.996391i | \(-0.527052\pi\) | ||||
−0.0848841 | + | 0.996391i | \(0.527052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9020.41 | 1.04425 | 0.522123 | − | 0.852870i | \(-0.325140\pi\) | ||||
0.522123 | + | 0.852870i | \(0.325140\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3743.88 | −0.430340 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6577.95 | −0.750770 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5453.57 | 0.618072 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6953.10 | −0.782515 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10391.1 | 1.16130 | 0.580650 | − | 0.814153i | \(-0.302798\pi\) | ||||
0.580650 | + | 0.814153i | \(0.302798\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12704.4 | 1.41001 | 0.705003 | − | 0.709204i | \(-0.250946\pi\) | ||||
0.705003 | + | 0.709204i | \(0.250946\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1610.52 | −0.177514 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26273.8 | −2.87608 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6317.12 | −0.686788 | −0.343394 | − | 0.939192i | \(-0.611577\pi\) | ||||
−0.343394 | + | 0.939192i | \(0.611577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3588.94 | −0.387533 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12564.4 | −1.34752 | −0.673760 | − | 0.738951i | \(-0.735322\pi\) | ||||
−0.673760 | + | 0.738951i | \(0.735322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −138.057 | −0.0147069 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4871.89 | 0.515509 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 502.664 | 0.0528334 | 0.0264167 | − | 0.999651i | \(-0.491590\pi\) | ||||
0.0264167 | + | 0.999651i | \(0.491590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3294.58 | 0.343981 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19563.1 | 2.02904 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2112.99 | 0.217711 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12772.7 | 1.30739 | 0.653697 | − | 0.756756i | \(-0.273217\pi\) | ||||
0.653697 | + | 0.756756i | \(0.273217\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11591.9 | −1.17878 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5821.63 | 0.588157 | 0.294078 | − | 0.955781i | \(-0.404987\pi\) | ||||
0.294078 | + | 0.955781i | \(0.404987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8530.04 | −0.856208 | −0.428104 | − | 0.903729i | \(-0.640818\pi\) | ||||
−0.428104 | + | 0.903729i | \(0.640818\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11120.4 | 1.10902 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19333.8 | 1.91576 | 0.957880 | − | 0.287169i | \(-0.0927140\pi\) | ||||
0.957880 | + | 0.287169i | \(0.0927140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5496.04 | 0.541116 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12310.4 | 1.20432 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13213.0 | −1.28443 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7861.39 | −0.759380 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2500.19 | 0.239991 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15650.9 | 1.49292 | 0.746458 | − | 0.665433i | \(-0.231753\pi\) | ||||
0.746458 | + | 0.665433i | \(0.231753\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5757.06 | 0.545737 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9094.02 | 0.856713 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12535.4 | 1.17362 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20860.9 | −1.94106 | −0.970532 | − | 0.240971i | \(-0.922534\pi\) | ||||
−0.970532 | + | 0.240971i | \(0.922534\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4354.18 | 0.402664 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3936.88 | 0.361851 | 0.180926 | − | 0.983497i | \(-0.442091\pi\) | ||||
0.180926 | + | 0.983497i | \(0.442091\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3908.10 | 0.357023 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4654.14 | 0.422602 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7648.89 | −0.690342 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7186.66 | −0.644728 | −0.322364 | − | 0.946616i | \(-0.604477\pi\) | ||||
−0.322364 | + | 0.946616i | \(0.604477\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19053.9 | −1.69913 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6398.26 | −0.567166 | −0.283583 | − | 0.958948i | \(-0.591523\pi\) | ||||
−0.283583 | + | 0.958948i | \(0.591523\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5402.91 | 0.476092 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9121.41 | −0.799006 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5903.72 | −0.514101 | −0.257051 | − | 0.966398i | \(-0.582751\pi\) | ||||
−0.257051 | + | 0.966398i | \(0.582751\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3151.68 | 0.272841 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13853.6 | −1.19230 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9710.62 | 0.830876 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10985.2 | 0.934485 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16307.3 | 1.37921 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22463.3 | −1.88894 | −0.944469 | − | 0.328601i | \(-0.893423\pi\) | ||||
−0.944469 | + | 0.328601i | \(0.893423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −204.414 | −0.0170906 | −0.00854531 | − | 0.999963i | \(-0.502720\pi\) | ||||
−0.00854531 | + | 0.999963i | \(0.502720\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2721.02 | 0.226200 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26984.9 | −2.23051 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14446.0 | 1.18731 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2573.30 | −0.210305 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2301.31 | −0.187018 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8600.07 | 0.694979 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9417.82 | −0.756813 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10530.6 | 0.841530 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2499.56 | −0.198640 | −0.0993202 | − | 0.995056i | \(-0.531667\pi\) | ||||
−0.0993202 | + | 0.995056i | \(0.531667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19080.1 | −1.50793 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4456.98 | 0.350305 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15423.7 | 1.20562 | 0.602808 | − | 0.797886i | \(-0.294049\pi\) | ||||
0.602808 | + | 0.797886i | \(0.294049\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8390.71 | −0.652289 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4670.62 | 0.361117 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1452.44 | 0.111689 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11571.8 | −0.885041 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5007.02 | 0.380887 | 0.190444 | − | 0.981698i | \(-0.439007\pi\) | ||||
0.190444 | + | 0.981698i | \(0.439007\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9229.48 | 0.698328 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33914.2 | −2.55233 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14132.0 | 1.05789 | 0.528946 | − | 0.848655i | \(-0.322587\pi\) | ||||
0.528946 | + | 0.848655i | \(0.322587\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9770.17 | −0.727494 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7984.06 | 0.591356 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2334.74 | −0.172017 | −0.0860083 | − | 0.996294i | \(-0.527411\pi\) | ||||
−0.0860083 | + | 0.996294i | \(0.527411\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14655.5 | 1.07410 | 0.537052 | − | 0.843549i | \(-0.319538\pi\) | ||||
0.537052 | + | 0.843549i | \(0.319538\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2693.20 | −0.196352 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7962.86 | 0.577520 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3608.50 | −0.260353 | −0.130177 | − | 0.991491i | \(-0.541554\pi\) | ||||
−0.130177 | + | 0.991491i | \(0.541554\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1953.20 | 0.140194 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4954.43 | −0.353777 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7335.98 | −0.521141 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3250.98 | −0.229763 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5916.60 | −0.416021 | −0.208010 | − | 0.978127i | \(-0.566699\pi\) | ||||
−0.208010 | + | 0.978127i | \(0.566699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32249.9 | −2.25609 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18479.9 | −1.28623 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2017.60 | 0.139718 | 0.0698589 | − | 0.997557i | \(-0.477745\pi\) | ||||
0.0698589 | + | 0.997557i | \(0.477745\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10306.2 | 0.710107 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1696.72 | 0.116318 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11250.3 | −0.767403 | −0.383702 | − | 0.923457i | \(-0.625351\pi\) | ||||
−0.383702 | + | 0.923457i | \(0.625351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2924.39 | −0.198483 | −0.0992416 | − | 0.995063i | \(-0.531642\pi\) | ||||
−0.0992416 | + | 0.995063i | \(0.531642\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8456.05 | −0.571073 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2038.29 | −0.136972 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 242.410 | 0.0162094 | 0.00810472 | − | 0.999967i | \(-0.497420\pi\) | ||||
0.00810472 | + | 0.999967i | \(0.497420\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1616.62 | −0.107568 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7673.32 | −0.508068 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13987.6 | −0.921622 | −0.460811 | − | 0.887498i | \(-0.652441\pi\) | ||||
−0.460811 | + | 0.887498i | \(0.652441\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4625.69 | 0.303294 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23904.2 | 1.55972 | 0.779861 | − | 0.625953i | \(-0.215290\pi\) | ||||
0.779861 | + | 0.625953i | \(0.215290\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 360.437 | 0.0234042 | 0.0117021 | − | 0.999932i | \(-0.496275\pi\) | ||||
0.0117021 | + | 0.999932i | \(0.496275\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14032.4 | 0.906764 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −138.580 | −0.00891189 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7141.00 | −0.457024 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −40531.2 | −2.58160 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28080.4 | 1.78003 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6056.06 | 0.382073 | 0.191036 | − | 0.981583i | \(-0.438815\pi\) | ||||
0.191036 | + | 0.981583i | \(0.438815\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5848.69 | −0.367243 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20450.3 | 1.27803 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7355.77 | −0.457529 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11768.4 | 0.728560 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23049.6 | 1.42029 | 0.710143 | − | 0.704057i | \(-0.248630\pi\) | ||||
0.710143 | + | 0.704057i | \(0.248630\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2776.47 | 0.170285 | 0.0851426 | − | 0.996369i | \(-0.472865\pi\) | ||||
0.0851426 | + | 0.996369i | \(0.472865\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18551.5 | −1.13250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16585.2 | 1.00777 | 0.503887 | − | 0.863769i | \(-0.331903\pi\) | ||||
0.503887 | + | 0.863769i | \(0.331903\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7550.53 | 0.456678 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11162.5 | 0.672032 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18704.2 | −1.12091 | −0.560453 | − | 0.828187i | \(-0.689373\pi\) | ||||
−0.560453 | + | 0.828187i | \(0.689373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9956.57 | 0.593947 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4849.08 | −0.287946 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23883.7 | −1.41180 | −0.705901 | − | 0.708310i | \(-0.749458\pi\) | ||||
−0.705901 | + | 0.708310i | \(0.749458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19069.9 | 1.12214 | 0.561068 | − | 0.827770i | \(-0.310391\pi\) | ||||
0.561068 | + | 0.827770i | \(0.310391\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23689.5 | 1.38767 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12317.1 | 0.718250 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4730.91 | −0.274635 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14948.7 | −0.863901 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24619.8 | 1.41645 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31295.3 | −1.79249 | −0.896245 | − | 0.443560i | \(-0.853715\pi\) | ||||
−0.896245 | + | 0.443560i | \(0.853715\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4198.63 | 0.239415 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12955.4 | 0.735474 | 0.367737 | − | 0.929930i | \(-0.380133\pi\) | ||||
0.367737 | + | 0.929930i | \(0.380133\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12582.9 | 0.711174 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6528.95 | −0.367386 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29725.3 | −1.66531 | −0.832655 | − | 0.553791i | \(-0.813180\pi\) | ||||
−0.832655 | + | 0.553791i | \(0.813180\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16227.4 | 0.905135 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2999.86 | 0.166597 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5124.29 | 0.283338 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26123.3 | −1.43817 | −0.719085 | − | 0.694922i | \(-0.755439\pi\) | ||||
−0.719085 | + | 0.694922i | \(0.755439\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4671.77 | 0.256083 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23784.1 | 1.29810 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11224.8 | −0.609998 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8986.50 | 0.486267 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9382.25 | 0.505510 | 0.252755 | − | 0.967530i | \(-0.418663\pi\) | ||||
0.252755 | + | 0.967530i | \(0.418663\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33559.3 | 1.80044 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15423.6 | 0.823951 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5423.38 | 0.288497 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22719.7 | 1.20347 | 0.601733 | − | 0.798697i | \(-0.294477\pi\) | ||||
0.601733 | + | 0.798697i | \(0.294477\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2234.68 | −0.117872 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32666.2 | 1.71579 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9538.95 | 0.498932 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −407.789 | −0.0212401 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3371.69 | 0.174886 | 0.0874430 | − | 0.996170i | \(-0.472130\pi\) | ||||
0.0874430 | + | 0.996170i | \(0.472130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9747.40 | 0.503484 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23089.6 | −1.18770 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1415.53 | −0.0725126 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27147.6 | −1.38493 | −0.692467 | − | 0.721449i | \(-0.743476\pi\) | ||||
−0.692467 | + | 0.721449i | \(0.743476\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2492.44 | 0.126629 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45017.3 | 2.27774 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12826.1 | 0.646305 | 0.323152 | − | 0.946347i | \(-0.395257\pi\) | ||||
0.323152 | + | 0.946347i | \(0.395257\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14785.3 | 0.741991 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24811.5 | 1.24009 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30957.7 | 1.54100 | 0.770500 | − | 0.637440i | \(-0.220007\pi\) | ||||
0.770500 | + | 0.637440i | \(0.220007\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28311.7 | 1.40358 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12335.4 | 0.609076 | 0.304538 | − | 0.952500i | \(-0.401498\pi\) | ||||
0.304538 | + | 0.952500i | \(0.401498\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6683.74 | −0.328689 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7622.75 | 0.373362 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8632.65 | 0.421135 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19311.8 | −0.938346 | −0.469173 | − | 0.883106i | \(-0.655448\pi\) | ||||
−0.469173 | + | 0.883106i | \(0.655448\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12212.6 | −0.591036 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26838.6 | −1.29372 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5018.13 | −0.240934 | −0.120467 | − | 0.992717i | \(-0.538439\pi\) | ||||
−0.120467 | + | 0.992717i | \(0.538439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 41054.4 | 1.96335 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34735.3 | −1.65460 | −0.827301 | − | 0.561759i | \(-0.810125\pi\) | ||||
−0.827301 | + | 0.561759i | \(0.810125\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4473.86 | 0.212274 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15856.9 | −0.749419 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5274.15 | −0.248290 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2219.79 | 0.104093 | 0.0520466 | − | 0.998645i | \(-0.483426\pi\) | ||||
0.0520466 | + | 0.998645i | \(0.483426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31676.3 | 1.47963 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20986.4 | 0.976491 | 0.488246 | − | 0.872706i | \(-0.337637\pi\) | ||||
0.488246 | + | 0.872706i | \(0.337637\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9774.04 | 0.453025 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11615.7 | −0.536306 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13414.9 | −0.616993 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34530.5 | −1.58207 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2494.50 | −0.113852 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16888.6 | −0.767875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21717.5 | 0.983665 | 0.491833 | − | 0.870690i | \(-0.336327\pi\) | ||||
0.491833 | + | 0.870690i | \(0.336327\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 39080.9 | 1.76339 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9807.17 | −0.440838 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17197.3 | −0.770106 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10300.0 | −0.459499 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27242.7 | 1.21077 | 0.605387 | − | 0.795931i | \(-0.293018\pi\) | ||||
0.605387 | + | 0.795931i | \(0.293018\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37427.1 | −1.65716 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 213.216 | 0.00940526 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14228.1 | 0.625277 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12476.1 | −0.546241 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 52656.9 | 2.29691 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27019.9 | 1.17425 | 0.587125 | − | 0.809496i | \(-0.300260\pi\) | ||||
0.587125 | + | 0.809496i | \(0.300260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34289.1 | 1.48465 | 0.742327 | − | 0.670038i | \(-0.233722\pi\) | ||||
0.742327 | + | 0.670038i | \(0.233722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19741.6 | −0.851622 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5973.49 | −0.256739 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53800.8 | 2.30386 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3263.30 | −0.139229 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43635.4 | −1.85492 | −0.927458 | − | 0.373928i | \(-0.878011\pi\) | ||||
−0.927458 | + | 0.373928i | \(0.878011\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6114.42 | −0.258974 | −0.129487 | − | 0.991581i | \(-0.541333\pi\) | ||||
−0.129487 | + | 0.991581i | \(0.541333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12283.9 | 0.518387 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14994.4 | 0.630477 | 0.315239 | − | 0.949012i | \(-0.397915\pi\) | ||||
0.315239 | + | 0.949012i | \(0.397915\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6543.43 | −0.274141 | −0.137070 | − | 0.990561i | \(-0.543769\pi\) | ||||
−0.137070 | + | 0.990561i | \(0.543769\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5942.91 | −0.248083 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35878.2 | −1.49232 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26140.0 | 1.08337 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17224.1 | 0.711293 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9312.42 | 0.383195 | 0.191597 | − | 0.981474i | \(-0.438633\pi\) | ||||
0.191597 | + | 0.981474i | \(0.438633\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4637.09 | −0.189454 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12513.6 | 0.509447 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2046.01 | −0.0830009 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28088.8 | −1.13546 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33992.4 | −1.36927 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24580.0 | −0.986638 | −0.493319 | − | 0.869849i | \(-0.664216\pi\) | ||||
−0.493319 | + | 0.869849i | \(0.664216\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18950.7 | −0.758013 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11348.7 | −0.452352 | −0.226176 | − | 0.974086i | \(-0.572622\pi\) | ||||
−0.226176 | + | 0.974086i | \(0.572622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6307.05 | −0.250516 | −0.125258 | − | 0.992124i | \(-0.539976\pi\) | ||||
−0.125258 | + | 0.992124i | \(0.539976\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4643.21 | 0.183787 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4313.70 | −0.170151 | −0.0850753 | − | 0.996375i | \(-0.527113\pi\) | ||||
−0.0850753 | + | 0.996375i | \(0.527113\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22372.0 | −0.879387 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 84288.5 | 3.30171 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6556.94 | 0.255959 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17331.2 | −0.674220 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19359.7 | −0.750545 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13292.6 | −0.513568 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21034.0 | −0.809883 | −0.404941 | − | 0.914343i | \(-0.632708\pi\) | ||||
−0.404941 | + | 0.914343i | \(0.632708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 52522.2 | 2.01539 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10244.5 | 0.391767 | 0.195884 | − | 0.980627i | \(-0.437243\pi\) | ||||
0.195884 | + | 0.980627i | \(0.437243\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2962.63 | 0.112911 | 0.0564555 | − | 0.998405i | \(-0.482020\pi\) | ||||
0.0564555 | + | 0.998405i | \(0.482020\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10601.2 | 0.402661 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16888.9 | −0.639318 | −0.319659 | − | 0.947533i | \(-0.603568\pi\) | ||||
−0.319659 | + | 0.947533i | \(0.603568\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20527.8 | 0.774443 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36043.6 | 1.35522 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −44729.6 | −1.67617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12920.3 | 0.482545 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28677.1 | −1.06745 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5806.98 | −0.215432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24994.0 | 0.924164 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18621.8 | −0.686261 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26176.0 | 0.961458 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24646.4 | −0.902284 | −0.451142 | − | 0.892452i | \(-0.648983\pi\) | ||||
−0.451142 | + | 0.892452i | \(0.648983\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8344.25 | −0.304468 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27585.7 | 1.00324 | 0.501622 | − | 0.865087i | \(-0.332737\pi\) | ||||
0.501622 | + | 0.865087i | \(0.332737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22366.5 | −0.810758 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34567.0 | 1.24891 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9994.28 | 0.359913 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35694.5 | −1.28123 | −0.640616 | − | 0.767861i | \(-0.721321\pi\) | ||||
−0.640616 | + | 0.767861i | \(0.721321\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6149.14 | −0.220001 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24120.0 | 0.860152 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10170.9 | −0.361531 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14997.1 | −0.531358 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24741.4 | 0.873776 | 0.436888 | − | 0.899516i | \(-0.356081\pi\) | ||||
0.436888 | + | 0.899516i | \(0.356081\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42878.5 | −1.50944 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 43502.2 | 1.52647 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46526.8 | 1.62737 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20600.1 | 0.718222 | 0.359111 | − | 0.933295i | \(-0.383080\pi\) | ||||
0.359111 | + | 0.933295i | \(0.383080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 61292.2 | 2.13013 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31347.7 | 1.08598 | 0.542989 | − | 0.839740i | \(-0.317292\pi\) | ||||
0.542989 | + | 0.839740i | \(0.317292\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13588.0 | 0.469233 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6578.34 | −0.226448 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26650.1 | 0.914479 | 0.457240 | − | 0.889343i | \(-0.348838\pi\) | ||||
0.457240 | + | 0.889343i | \(0.348838\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9938.50 | −0.339955 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −49836.0 | −1.69931 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25259.5 | 0.858591 | 0.429295 | − | 0.903164i | \(-0.358762\pi\) | ||||
0.429295 | + | 0.903164i | \(0.358762\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3694.79 | 0.125194 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7298.12 | −0.246515 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16288.9 | 0.548483 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10305.3 | 0.345919 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13281.9 | −0.444449 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2679.59 | −0.0893875 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52945.9 | −1.76073 | −0.880365 | − | 0.474296i | \(-0.842703\pi\) | ||||
−0.880365 | + | 0.474296i | \(0.842703\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 138092. | 4.57807 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38466.0 | −1.27130 | −0.635650 | − | 0.771978i | \(-0.719268\pi\) | ||||
−0.635650 | + | 0.771978i | \(0.719268\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23874.2 | 0.786610 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8580.46 | −0.281841 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12800.3 | 0.419159 | 0.209580 | − | 0.977792i | \(-0.432790\pi\) | ||||
0.209580 | + | 0.977792i | \(0.432790\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −625.613 | −0.0204236 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6883.36 | −0.224025 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46863.4 | −1.52056 | −0.760280 | − | 0.649596i | \(-0.774938\pi\) | ||||
−0.760280 | + | 0.649596i | \(0.774938\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25352.6 | 0.820103 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15482.0 | 0.499288 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −54495.2 | −1.75212 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5189.58 | −0.166350 | −0.0831749 | − | 0.996535i | \(-0.526506\pi\) | ||||
−0.0831749 | + | 0.996535i | \(0.526506\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19104.3 | 0.610531 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2327.72 | −0.0741646 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49632.0 | 1.57659 | 0.788295 | − | 0.615298i | \(-0.210964\pi\) | ||||
0.788295 | + | 0.615298i | \(0.210964\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17923.4 | −0.567639 |
(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 | 1856.4.a.bd.1.5 | 6 | ||
4.3 | odd | 2 | 1856.4.a.bc.1.2 | 6 | |||
8.3 | odd | 2 | 464.4.a.n.1.5 | 6 | |||
8.5 | even | 2 | 232.4.a.e.1.2 | ✓ | 6 | ||
24.5 | odd | 2 | 2088.4.a.l.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.e.1.2 | ✓ | 6 | 8.5 | even | 2 | ||
464.4.a.n.1.5 | 6 | 8.3 | odd | 2 | |||
1856.4.a.bc.1.2 | 6 | 4.3 | odd | 2 | |||
1856.4.a.bd.1.5 | 6 | 1.1 | even | 1 | trivial | ||
2088.4.a.l.1.2 | 6 | 24.5 | odd | 2 |