Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [544,4,Mod(1,544)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(544, 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("544.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 544 = 2^{5} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 544.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: | \(32.0970390431\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 67x^{5} - 35x^{4} + 893x^{3} + 595x^{2} - 3064x - 2804 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.84285\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 544.1 |
$q$-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 | ||||||||
\(3\) | −3.23405 | −0.622393 | −0.311197 | − | 0.950346i | \(-0.600730\pi\) | ||||
−0.311197 | + | 0.950346i | \(0.600730\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.8262 | 1.32609 | 0.663047 | − | 0.748578i | \(-0.269263\pi\) | ||||
0.663047 | + | 0.748578i | \(0.269263\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −20.4601 | −1.10474 | −0.552371 | − | 0.833598i | \(-0.686277\pi\) | ||||
−0.552371 | + | 0.833598i | \(0.686277\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −16.5409 | −0.612627 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 30.9879 | 0.849381 | 0.424691 | − | 0.905339i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905339i | \(0.360383\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.3781 | 0.968124 | 0.484062 | − | 0.875034i | \(-0.339161\pi\) | ||||
0.484062 | + | 0.875034i | \(0.339161\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −47.9486 | −0.825352 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.0000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −128.769 | −1.55482 | −0.777409 | − | 0.628996i | \(-0.783466\pi\) | ||||
−0.777409 | + | 0.628996i | \(0.783466\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 66.1691 | 0.687584 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −134.304 | −1.21758 | −0.608790 | − | 0.793331i | \(-0.708345\pi\) | ||||
−0.608790 | + | 0.793331i | \(0.708345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 94.8158 | 0.758526 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 140.814 | 1.00369 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 214.969 | 1.37651 | 0.688254 | − | 0.725469i | \(-0.258377\pi\) | ||||
0.688254 | + | 0.725469i | \(0.258377\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 82.5014 | 0.477990 | 0.238995 | − | 0.971021i | \(-0.423182\pi\) | ||||
0.238995 | + | 0.971021i | \(0.423182\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −100.216 | −0.528649 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −303.346 | −1.46499 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −350.245 | −1.55621 | −0.778107 | − | 0.628132i | \(-0.783820\pi\) | ||||
−0.778107 | + | 0.628132i | \(0.783820\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −146.755 | −0.602554 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −226.817 | −0.863973 | −0.431986 | − | 0.901880i | \(-0.642187\pi\) | ||||
−0.431986 | + | 0.901880i | \(0.642187\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −126.462 | −0.448496 | −0.224248 | − | 0.974532i | \(-0.571993\pi\) | ||||
−0.224248 | + | 0.974532i | \(0.571993\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −245.239 | −0.812401 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 172.240 | 0.534550 | 0.267275 | − | 0.963620i | \(-0.413877\pi\) | ||||
0.267275 | + | 0.963620i | \(0.413877\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 75.6165 | 0.220456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 54.9789 | 0.150953 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 619.590 | 1.60580 | 0.802899 | − | 0.596116i | \(-0.203290\pi\) | ||||
0.802899 | + | 0.596116i | \(0.203290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 459.432 | 1.12636 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 416.444 | 0.967708 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −282.706 | −0.623816 | −0.311908 | − | 0.950112i | \(-0.600968\pi\) | ||||
−0.311908 | + | 0.950112i | \(0.600968\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −730.472 | −1.53324 | −0.766618 | − | 0.642104i | \(-0.778062\pi\) | ||||
−0.766618 | + | 0.642104i | \(0.778062\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 338.429 | 0.676795 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 672.784 | 1.28382 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −876.169 | −1.59763 | −0.798814 | − | 0.601578i | \(-0.794539\pi\) | ||||
−0.798814 | + | 0.601578i | \(0.794539\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 434.346 | 0.757814 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −467.038 | −0.780664 | −0.390332 | − | 0.920674i | \(-0.627640\pi\) | ||||
−0.390332 | + | 0.920674i | \(0.627640\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −474.843 | −0.761317 | −0.380659 | − | 0.924716i | \(-0.624303\pi\) | ||||
−0.380659 | + | 0.924716i | \(0.624303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −306.639 | −0.472102 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −634.016 | −0.938348 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1090.67 | −1.55329 | −0.776645 | − | 0.629938i | \(-0.783080\pi\) | ||||
−0.776645 | + | 0.629938i | \(0.783080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.79336 | −0.0120622 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −79.7726 | −0.105496 | −0.0527481 | − | 0.998608i | \(-0.516798\pi\) | ||||
−0.0527481 | + | 0.998608i | \(0.516798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −252.045 | −0.321625 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −695.221 | −0.856730 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 903.357 | 1.07591 | 0.537953 | − | 0.842975i | \(-0.319198\pi\) | ||||
0.537953 | + | 0.842975i | \(0.319198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −928.441 | −1.06953 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −266.814 | −0.297498 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1909.15 | −2.06183 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −289.745 | −0.303290 | −0.151645 | − | 0.988435i | \(-0.548457\pi\) | ||||
−0.151645 | + | 0.988435i | \(0.548457\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −512.568 | −0.520354 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1812.07 | −1.78522 | −0.892610 | − | 0.450829i | \(-0.851128\pi\) | ||||
−0.892610 | + | 0.450829i | \(0.851128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −226.785 | −0.216949 | −0.108475 | − | 0.994099i | \(-0.534597\pi\) | ||||
−0.108475 | + | 0.994099i | \(0.534597\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 981.035 | 0.911802 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 468.440 | 0.423232 | 0.211616 | − | 0.977353i | \(-0.432127\pi\) | ||||
0.211616 | + | 0.977353i | \(0.432127\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1908.40 | −1.67699 | −0.838494 | − | 0.544910i | \(-0.816564\pi\) | ||||
−0.838494 | + | 0.544910i | \(0.816564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1132.71 | 0.968577 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 487.589 | 0.405916 | 0.202958 | − | 0.979187i | \(-0.434944\pi\) | ||||
0.202958 | + | 0.979187i | \(0.434944\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1991.22 | −1.61463 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −750.595 | −0.593098 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 347.822 | 0.267939 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −370.752 | −0.278551 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 733.538 | 0.537731 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −447.517 | −0.320217 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1123.73 | −0.785154 | −0.392577 | − | 0.919719i | \(-0.628416\pi\) | ||||
−0.392577 | + | 0.919719i | \(0.628416\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 408.986 | 0.279141 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 518.217 | 0.345624 | 0.172812 | − | 0.984955i | \(-0.444715\pi\) | ||||
0.172812 | + | 0.984955i | \(0.444715\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2634.62 | 1.71767 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2087.73 | 1.33099 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 372.303 | 0.232175 | 0.116087 | − | 0.993239i | \(-0.462965\pi\) | ||||
0.116087 | + | 0.993239i | \(0.462965\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2403.34 | 1.46654 | 0.733269 | − | 0.679938i | \(-0.237993\pi\) | ||||
0.733269 | + | 0.679938i | \(0.237993\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −557.034 | −0.332700 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1406.17 | 0.822306 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3187.17 | 1.82538 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −244.548 | −0.137211 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1027.59 | 0.564987 | 0.282494 | − | 0.959269i | \(-0.408838\pi\) | ||||
0.282494 | + | 0.959269i | \(0.408838\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3152.28 | −1.69887 | −0.849433 | − | 0.527696i | \(-0.823056\pi\) | ||||
−0.849433 | + | 0.527696i | \(0.823056\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 281.196 | 0.148584 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1223.18 | 0.633860 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1158.66 | −0.588989 | −0.294495 | − | 0.955653i | \(-0.595151\pi\) | ||||
−0.294495 | + | 0.955653i | \(0.595151\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2003.79 | −0.999437 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2747.88 | 1.34511 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 402.407 | 0.193368 | 0.0966838 | − | 0.995315i | \(-0.469176\pi\) | ||||
0.0966838 | + | 0.995315i | \(0.469176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1485.83 | −0.701039 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −396.122 | −0.183550 | −0.0917749 | − | 0.995780i | \(-0.529254\pi\) | ||||
−0.0917749 | + | 0.995780i | \(0.529254\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −137.831 | −0.0627361 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2129.95 | 0.952522 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1119.31 | 0.491906 | 0.245953 | − | 0.969282i | \(-0.420899\pi\) | ||||
0.245953 | + | 0.969282i | \(0.420899\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1939.94 | −0.837976 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 914.284 | 0.388259 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4245.20 | 1.77263 | 0.886316 | − | 0.463082i | \(-0.153256\pi\) | ||||
0.886316 | + | 0.463082i | \(0.153256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2349.81 | 0.964974 | 0.482487 | − | 0.875903i | \(-0.339734\pi\) | ||||
0.482487 | + | 0.875903i | \(0.339734\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2362.38 | 0.954276 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5192.80 | −2.06369 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −526.794 | −0.206005 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2881.06 | −1.10882 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4004.90 | 1.51720 | 0.758598 | − | 0.651559i | \(-0.225885\pi\) | ||||
0.758598 | + | 0.651559i | \(0.225885\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2939.05 | 1.09615 | 0.548076 | − | 0.836429i | \(-0.315360\pi\) | ||||
0.548076 | + | 0.836429i | \(0.315360\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2175.82 | −0.799043 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1408.64 | 0.509449 | 0.254724 | − | 0.967014i | \(-0.418015\pi\) | ||||
0.254724 | + | 0.967014i | \(0.418015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1138.15 | 0.405435 | 0.202718 | − | 0.979237i | \(-0.435023\pi\) | ||||
0.202718 | + | 0.979237i | \(0.435023\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2833.58 | 0.994353 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4398.29 | −1.52069 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3362.83 | −1.14571 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2221.51 | 0.745922 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3990.26 | −1.32063 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4428.15 | 1.44477 | 0.722385 | − | 0.691491i | \(-0.243046\pi\) | ||||
0.722385 | + | 0.691491i | \(0.243046\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1510.42 | 0.485880 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1874.96 | −0.594748 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1687.99 | −0.528056 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1535.67 | 0.473839 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −771.427 | −0.234805 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3443.70 | 1.03411 | 0.517056 | − | 0.855951i | \(-0.327028\pi\) | ||||
0.517056 | + | 0.855951i | \(0.327028\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1568.34 | −0.464693 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5689.39 | −1.66352 | −0.831758 | − | 0.555139i | \(-0.812665\pi\) | ||||
−0.831758 | + | 0.555139i | \(0.812665\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3137.13 | −0.905272 | −0.452636 | − | 0.891695i | \(-0.649516\pi\) | ||||
−0.452636 | + | 0.891695i | \(0.649516\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2050.44 | 0.584021 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4024.42 | 1.13154 | 0.565769 | − | 0.824564i | \(-0.308580\pi\) | ||||
0.565769 | + | 0.824564i | \(0.308580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2553.67 | 0.708864 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3527.28 | 0.966757 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2002.37 | 0.541936 | 0.270968 | − | 0.962588i | \(-0.412656\pi\) | ||||
0.270968 | + | 0.962588i | \(0.412656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4487.69 | −1.19949 | −0.599746 | − | 0.800190i | \(-0.704732\pi\) | ||||
−0.599746 | + | 0.800190i | \(0.704732\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3773.53 | −0.996181 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1121.10 | 0.292346 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5843.27 | −1.50526 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 257.989 | 0.0656601 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1958.20 | 0.492432 | 0.246216 | − | 0.969215i | \(-0.420813\pi\) | ||||
0.246216 | + | 0.969215i | \(0.420813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4161.80 | −1.03419 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 815.127 | 0.200177 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 331.844 | 0.0805442 | 0.0402721 | − | 0.999189i | \(-0.487178\pi\) | ||||
0.0402721 | + | 0.999189i | \(0.487178\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7166.05 | 1.71922 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3555.79 | −0.843286 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2516.26 | 0.589960 | 0.294980 | − | 0.955503i | \(-0.404687\pi\) | ||||
0.294980 | + | 0.955503i | \(0.404687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9186.16 | 2.12944 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2921.50 | −0.669637 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3807.69 | −0.863044 | −0.431522 | − | 0.902102i | \(-0.642023\pi\) | ||||
−0.431522 | + | 0.902102i | \(0.642023\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3855.07 | 0.864128 | 0.432064 | − | 0.901843i | \(-0.357785\pi\) | ||||
0.432064 | + | 0.901843i | \(0.357785\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3002.62 | 0.665667 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2938.14 | 0.644278 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6652.57 | −1.44301 | −0.721506 | − | 0.692408i | \(-0.756550\pi\) | ||||
−0.721506 | + | 0.692408i | \(0.756550\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1364.65 | −0.292829 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2986.58 | −0.634038 | −0.317019 | − | 0.948419i | \(-0.602682\pi\) | ||||
−0.317019 | + | 0.948419i | \(0.602682\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2793.41 | 0.586752 | 0.293376 | − | 0.955997i | \(-0.405221\pi\) | ||||
0.293376 | + | 0.955997i | \(0.405221\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6174.28 | 1.28327 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4640.71 | 0.954467 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 937.050 | 0.188766 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2906.62 | −0.579544 | −0.289772 | − | 0.957096i | \(-0.593579\pi\) | ||||
−0.289772 | + | 0.957096i | \(0.593579\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4191.45 | −0.827239 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4363.51 | 0.852514 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6094.46 | −1.17877 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2587.44 | 0.495473 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5860.31 | 1.11111 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10830.1 | −2.03322 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8551.47 | 1.58977 | 0.794883 | − | 0.606763i | \(-0.207532\pi\) | ||||
0.794883 | + | 0.606763i | \(0.207532\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 733.434 | 0.135028 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −257.113 | −0.0468796 | −0.0234398 | − | 0.999725i | \(-0.507462\pi\) | ||||
−0.0234398 | + | 0.999725i | \(0.507462\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2077.26 | 0.375123 | 0.187561 | − | 0.982253i | \(-0.439942\pi\) | ||||
0.187561 | + | 0.982253i | \(0.439942\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5017.61 | 0.897494 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3599.66 | 0.637782 | 0.318891 | − | 0.947791i | \(-0.396690\pi\) | ||||
0.318891 | + | 0.947791i | \(0.396690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6661.43 | 1.16918 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1514.96 | −0.263417 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2189.07 | 0.377099 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4302.56 | 0.734348 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6171.87 | 1.04375 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3524.06 | −0.590540 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8288.14 | −1.37631 | −0.688153 | − | 0.725565i | \(-0.741578\pi\) | ||||
−0.688153 | + | 0.725565i | \(0.741578\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5793.37 | 0.953378 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12990.2 | −2.11861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5660.61 | 0.914994 | 0.457497 | − | 0.889211i | \(-0.348746\pi\) | ||||
0.457497 | + | 0.889211i | \(0.348746\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1576.89 | −0.252639 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2556.54 | 0.405996 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5470.70 | 0.861195 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6439.70 | 1.00493 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10900.4 | 1.68635 | 0.843173 | − | 0.537642i | \(-0.180685\pi\) | ||||
0.843173 | + | 0.537642i | \(0.180685\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10560.8 | −1.61978 | −0.809892 | − | 0.586579i | \(-0.800474\pi\) | ||||
−0.809892 | + | 0.586579i | \(0.800474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6389.85 | 0.971694 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7233.45 | −1.09064 | −0.545322 | − | 0.838226i | \(-0.683593\pi\) | ||||
−0.545322 | + | 0.838226i | \(0.683593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6924.39 | −1.03523 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1124.87 | −0.166764 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6170.33 | −0.907124 | −0.453562 | − | 0.891225i | \(-0.649847\pi\) | ||||
−0.453562 | + | 0.891225i | \(0.649847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9722.34 | 1.41746 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1199.03 | 0.173368 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7040.11 | −1.00958 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −723.148 | −0.102856 | −0.0514278 | − | 0.998677i | \(-0.516377\pi\) | ||||
−0.0514278 | + | 0.998677i | \(0.516377\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3751.76 | 0.529293 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12676.9 | −1.77399 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1008.46 | 0.139989 | 0.0699946 | − | 0.997547i | \(-0.477702\pi\) | ||||
0.0699946 | + | 0.997547i | \(0.477702\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1447.29 | 0.199301 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9754.88 | 1.33263 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3084.08 | 0.417991 | 0.208996 | − | 0.977917i | \(-0.432981\pi\) | ||||
0.208996 | + | 0.977917i | \(0.432981\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3634.19 | 0.488675 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4733.10 | −0.631462 | −0.315731 | − | 0.948849i | \(-0.602250\pi\) | ||||
−0.315731 | + | 0.948849i | \(0.602250\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9400.03 | −1.24434 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2091.80 | 0.274761 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10092.8 | 1.31549 | 0.657747 | − | 0.753239i | \(-0.271510\pi\) | ||||
0.657747 | + | 0.753239i | \(0.271510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2283.17 | 0.295306 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1675.94 | −0.215114 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16170.5 | −2.05981 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3901.46 | −0.493221 | −0.246611 | − | 0.969115i | \(-0.579317\pi\) | ||||
−0.246611 | + | 0.969115i | \(0.579317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8520.49 | −1.06907 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15577.8 | −1.93994 | −0.969971 | − | 0.243222i | \(-0.921796\pi\) | ||||
−0.969971 | + | 0.243222i | \(0.921796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3743.75 | 0.462753 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −130.372 | −0.0159956 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10853.3 | −1.32182 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10459.9 | −1.26457 | −0.632285 | − | 0.774736i | \(-0.717883\pi\) | ||||
−0.632285 | + | 0.774736i | \(0.717883\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1204.05 | −0.144504 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5784.19 | 0.689156 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1182.72 | −0.139898 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7772.53 | −0.912764 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5093.23 | −0.593844 | −0.296922 | − | 0.954902i | \(-0.595960\pi\) | ||||
−0.296922 | + | 0.954902i | \(0.595960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1453.23 | −0.168233 | −0.0841167 | − | 0.996456i | \(-0.526807\pi\) | ||||
−0.0841167 | + | 0.996456i | \(0.526807\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2849.01 | −0.327479 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1611.87 | −0.183970 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14945.5 | 1.69383 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4547.62 | −0.511798 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17568.3 | −1.96342 | −0.981712 | − | 0.190371i | \(-0.939031\pi\) | ||||
−0.981712 | + | 0.190371i | \(0.939031\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4995.28 | 0.554407 | 0.277203 | − | 0.960811i | \(-0.410592\pi\) | ||||
0.277203 | + | 0.960811i | \(0.410592\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10307.5 | −1.13610 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17294.1 | 1.89311 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8289.59 | 0.901232 | 0.450616 | − | 0.892718i | \(-0.351204\pi\) | ||||
0.450616 | + | 0.892718i | \(0.351204\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1250.77 | −0.135057 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −874.185 | −0.0937557 | −0.0468779 | − | 0.998901i | \(-0.514927\pi\) | ||||
−0.0468779 | + | 0.998901i | \(0.514927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13393.3 | 1.42675 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3323.26 | −0.351644 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6982.97 | −0.733957 | −0.366979 | − | 0.930229i | \(-0.619608\pi\) | ||||
−0.366979 | + | 0.930229i | \(0.619608\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7028.58 | −0.733842 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10194.6 | 1.05736 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13765.2 | −1.41829 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10742.1 | 1.09955 | 0.549777 | − | 0.835312i | \(-0.314713\pi\) | ||||
0.549777 | + | 0.835312i | \(0.314713\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2393.83 | −0.243430 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9758.03 | 0.985850 | 0.492925 | − | 0.870072i | \(-0.335928\pi\) | ||||
0.492925 | + | 0.870072i | \(0.335928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1328.79 | −0.133379 | −0.0666893 | − | 0.997774i | \(-0.521244\pi\) | ||||
−0.0666893 | + | 0.997774i | \(0.521244\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3955.83 | −0.394510 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7604.91 | −0.753562 | −0.376781 | − | 0.926302i | \(-0.622969\pi\) | ||||
−0.376781 | + | 0.926302i | \(0.622969\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17926.5 | 1.76497 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3747.17 | 0.366583 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3918.80 | −0.380944 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12209.3 | −1.17937 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10248.6 | −0.983754 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14081.3 | 1.34319 | 0.671596 | − | 0.740917i | \(-0.265609\pi\) | ||||
0.671596 | + | 0.740917i | \(0.265609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15893.4 | −1.50661 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8886.78 | −0.837189 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4295.81 | −0.402191 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1366.56 | −0.127155 | −0.0635777 | − | 0.997977i | \(-0.520251\pi\) | ||||
−0.0635777 | + | 0.997977i | \(0.520251\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1301.40 | −0.120351 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2574.58 | −0.236638 | −0.118319 | − | 0.992976i | \(-0.537750\pi\) | ||||
−0.118319 | + | 0.992976i | \(0.537750\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3654.47 | −0.333852 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7599.43 | −0.690038 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9555.64 | 0.862433 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11459.0 | 1.02801 | 0.514005 | − | 0.857787i | \(-0.328161\pi\) | ||||
0.514005 | + | 0.857787i | \(0.328161\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1281.08 | 0.114240 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13335.7 | 1.18212 | 0.591062 | − | 0.806626i | \(-0.298709\pi\) | ||||
0.591062 | + | 0.806626i | \(0.298709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26866.0 | −2.36737 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 445.753 | 0.0390465 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5458.78 | 0.475356 | 0.237678 | − | 0.971344i | \(-0.423614\pi\) | ||||
0.237678 | + | 0.971344i | \(0.423614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9715.34 | 0.841059 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18132.4 | −1.56055 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3362.36 | −0.287695 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5337.36 | 0.454037 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3619.91 | −0.306159 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11374.8 | 0.956502 | 0.478251 | − | 0.878223i | \(-0.341271\pi\) | ||||
0.478251 | + | 0.878223i | \(0.341271\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14397.3 | −1.20373 | −0.601865 | − | 0.798598i | \(-0.705576\pi\) | ||||
−0.601865 | + | 0.798598i | \(0.705576\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6273.87 | 0.521551 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1402.52 | −0.115930 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5870.58 | 0.482501 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4676.21 | 0.382166 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10292.5 | −0.836433 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6945.18 | 0.561246 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13729.2 | −1.10327 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2343.20 | 0.187251 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18827.7 | −1.49624 | −0.748122 | − | 0.663561i | \(-0.769044\pi\) | ||||
−0.748122 | + | 0.663561i | \(0.769044\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7599.42 | −0.600593 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28294.3 | −2.22385 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14611.7 | 1.14214 | 0.571072 | − | 0.820900i | \(-0.306528\pi\) | ||||
0.571072 | + | 0.820900i | \(0.306528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12082.7 | 0.939301 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27681.3 | −2.14022 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22315.2 | 1.71599 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16793.8 | 1.28442 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6946.57 | 0.528430 | 0.264215 | − | 0.964464i | \(-0.414887\pi\) | ||||
0.264215 | + | 0.964464i | \(0.414887\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5738.62 | −0.434200 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1703.68 | 0.128216 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9693.48 | 0.725634 | 0.362817 | − | 0.931861i | \(-0.381815\pi\) | ||||
0.362817 | + | 0.931861i | \(0.381815\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7229.09 | 0.538283 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 179.913 | 0.0133256 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24145.1 | 1.77894 | 0.889468 | − | 0.456997i | \(-0.151075\pi\) | ||||
0.889468 | + | 0.456997i | \(0.151075\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13498.2 | 0.989283 | 0.494642 | − | 0.869097i | \(-0.335299\pi\) | ||||
0.494642 | + | 0.869097i | \(0.335299\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12952.1 | −0.944293 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12734.1 | −0.923566 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7282.64 | 0.525443 | 0.262721 | − | 0.964872i | \(-0.415380\pi\) | ||||
0.262721 | + | 0.964872i | \(0.415380\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9505.03 | −0.682238 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1632.16 | 0.116546 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19199.8 | 1.36393 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11128.5 | −0.786504 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4429.97 | −0.311489 | −0.155745 | − | 0.987797i | \(-0.549778\pi\) | ||||
−0.155745 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10623.6 | −0.743187 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4555.61 | −0.317077 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9371.80 | −0.648994 | −0.324497 | − | 0.945887i | \(-0.605195\pi\) | ||||
−0.324497 | + | 0.945887i | \(0.605195\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5156.87 | 0.355313 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3680.85 | −0.252340 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11990.3 | 0.817879 | 0.408940 | − | 0.912561i | \(-0.365899\pi\) | ||||
0.408940 | + | 0.912561i | \(0.365899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1437.02 | −0.0975331 | −0.0487666 | − | 0.998810i | \(-0.515529\pi\) | ||||
−0.0487666 | + | 0.998810i | \(0.515529\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14492.6 | 0.978750 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5496.83 | −0.369385 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26146.2 | −1.74834 | −0.874169 | − | 0.485621i | \(-0.838593\pi\) | ||||
−0.874169 | + | 0.485621i | \(0.838593\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14224.3 | 0.946466 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7815.94 | 0.517511 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12373.7 | −0.815284 | −0.407642 | − | 0.913142i | \(-0.633649\pi\) | ||||
−0.407642 | + | 0.913142i | \(0.633649\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10875.6 | 0.713082 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7599.63 | 0.495866 | 0.247933 | − | 0.968777i | \(-0.420249\pi\) | ||||
0.247933 | + | 0.968777i | \(0.420249\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15541.1 | −1.00913 | −0.504563 | − | 0.863375i | \(-0.668346\pi\) | ||||
−0.504563 | + | 0.863375i | \(0.668346\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18911.8 | −1.22207 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18482.8 | −1.18860 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18486.9 | −1.18316 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12904.7 | 0.821953 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5954.16 | 0.377437 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21892.5 | −1.38118 | −0.690591 | − | 0.723246i | \(-0.742649\pi\) | ||||
−0.690591 | + | 0.723246i | \(0.742649\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14320.9 | −0.899215 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16660.6 | −1.04119 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3431.33 | 0.213429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7725.23 | 0.478256 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3967.77 | −0.244489 | −0.122245 | − | 0.992500i | \(-0.539009\pi\) | ||||
−0.122245 | + | 0.992500i | \(0.539009\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16227.4 | 0.995248 | 0.497624 | − | 0.867393i | \(-0.334206\pi\) | ||||
0.497624 | + | 0.867393i | \(0.334206\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6063.70 | 0.370167 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11820.5 | −0.718257 | −0.359129 | − | 0.933288i | \(-0.616926\pi\) | ||||
−0.359129 | + | 0.933288i | \(0.616926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8760.45 | −0.529858 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5459.04 | 0.328658 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25352.4 | 1.51932 | 0.759661 | − | 0.650319i | \(-0.225365\pi\) | ||||
0.759661 | + | 0.650319i | \(0.225365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7683.18 | 0.458331 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7854.34 | 0.466403 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30253.7 | −1.78834 | −0.894170 | − | 0.447727i | \(-0.852234\pi\) | ||||
−0.894170 | + | 0.447727i | \(0.852234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3347.84 | 0.196998 | 0.0984991 | − | 0.995137i | \(-0.468596\pi\) | ||||
0.0984991 | + | 0.995137i | \(0.468596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2494.83 | 0.146141 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 39061.4 | 2.27780 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28871.2 | −1.67601 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11137.1 | −0.643625 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22635.8 | −1.30230 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21301.8 | 1.22009 | 0.610047 | − | 0.792365i | \(-0.291151\pi\) | ||||
0.610047 | + | 0.792365i | \(0.291151\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13351.3 | 0.761324 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3735.64 | −0.212071 | −0.106036 | − | 0.994362i | \(-0.533816\pi\) | ||||
−0.106036 | + | 0.994362i | \(0.533816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5928.22 | 0.335058 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18399.8 | 1.03536 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18135.3 | −1.01600 | −0.508001 | − | 0.861356i | \(-0.669615\pi\) | ||||
−0.508001 | + | 0.861356i | \(0.669615\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5519.83 | 0.307886 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10145.6 | 0.563435 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28115.8 | 1.55461 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13009.6 | −0.716220 | −0.358110 | − | 0.933679i | \(-0.616579\pi\) | ||||
−0.358110 | + | 0.933679i | \(0.616579\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10487.2 | 0.574857 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35632.4 | 1.94477 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3855.89 | 0.209544 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13015.2 | −0.704261 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4773.31 | −0.257183 | −0.128592 | − | 0.991698i | \(-0.541046\pi\) | ||||
−0.128592 | + | 0.991698i | \(0.541046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45100.5 | 2.41963 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8258.69 | −0.441192 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37075.1 | 1.97221 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10193.9 | 0.539972 | 0.269986 | − | 0.962864i | \(-0.412981\pi\) | ||||
0.269986 | + | 0.962864i | \(0.412981\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18040.7 | 0.951587 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11080.3 | −0.581991 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20848.1 | 1.09046 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6475.77 | −0.337297 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12183.9 | 0.631966 | 0.315983 | − | 0.948765i | \(-0.397666\pi\) | ||||
0.315983 | + | 0.948765i | \(0.397666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4640.05 | 0.239673 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14513.4 | 0.746556 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20382.5 | 1.04412 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7370.89 | 0.376026 | 0.188013 | − | 0.982167i | \(-0.439795\pi\) | ||||
0.188013 | + | 0.982167i | \(0.439795\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12441.2 | 0.632078 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2149.86 | 0.108776 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4303.45 | 0.216850 | 0.108425 | − | 0.994105i | \(-0.465419\pi\) | ||||
0.108425 | + | 0.994105i | \(0.465419\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3625.71 | −0.181954 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27150.6 | −1.35700 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9493.89 | −0.472583 | −0.236291 | − | 0.971682i | \(-0.575932\pi\) | ||||
−0.236291 | + | 0.971682i | \(0.575932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18897.4 | 0.936861 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13433.7 | 0.663302 | 0.331651 | − | 0.943402i | \(-0.392394\pi\) | ||||
0.331651 | + | 0.943402i | \(0.392394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15235.2 | 0.749226 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1319.51 | 0.0646297 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9584.34 | −0.467562 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25795.0 | 1.25336 | 0.626679 | − | 0.779277i | \(-0.284414\pi\) | ||||
0.626679 | + | 0.779277i | \(0.284414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6332.92 | −0.306487 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46736.3 | −2.25286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −183.635 | −0.00881683 | −0.00440842 | − | 0.999990i | \(-0.501403\pi\) | ||||
−0.00440842 | + | 0.999990i | \(0.501403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13459.5 | 0.643673 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34650.0 | −1.65054 | −0.825269 | − | 0.564739i | \(-0.808977\pi\) | ||||
−0.825269 | + | 0.564739i | \(0.808977\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39046.1 | 1.85264 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4169.06 | 0.197036 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12828.6 | −0.603931 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10059.9 | 0.471743 | 0.235872 | − | 0.971784i | \(-0.424206\pi\) | ||||
0.235872 | + | 0.971784i | \(0.424206\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1073.20 | −0.0501302 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15739.0 | −0.732331 | −0.366165 | − | 0.930550i | \(-0.619330\pi\) | ||||
−0.366165 | + | 0.930550i | \(0.619330\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7822.44 | 0.362568 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23175.4 | −1.07003 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29206.9 | 1.34332 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14472.5 | −0.663082 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30270.6 | 1.38159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17178.5 | −0.781055 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18685.2 | 0.846322 | 0.423161 | − | 0.906055i | \(-0.360921\pi\) | ||||
0.423161 | + | 0.906055i | \(0.360921\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8137.72 | −0.367187 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9976.13 | −0.448433 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33147.4 | −1.48436 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −29708.5 | −1.32535 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27018.3 | −1.20080 | −0.600399 | − | 0.799701i | \(-0.704991\pi\) | ||||
−0.600399 | + | 0.799701i | \(0.704991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2928.09 | −0.129647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14942.3 | −0.659128 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14714.4 | −0.646649 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40740.5 | 1.78375 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12314.3 | 0.537153 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11420.1 | 0.496305 | 0.248152 | − | 0.968721i | \(-0.420177\pi\) | ||||
0.248152 | + | 0.968721i | \(0.420177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25685.8 | 1.11215 | 0.556073 | − | 0.831133i | \(-0.312307\pi\) | ||||
0.556073 | + | 0.831133i | \(0.312307\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12467.5 | −0.537827 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5966.16 | 0.256424 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16284.4 | 0.697330 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15357.3 | 0.655221 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5672.70 | −0.241143 | −0.120572 | − | 0.992705i | \(-0.538473\pi\) | ||||
−0.120572 | + | 0.992705i | \(0.538473\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13327.2 | −0.564467 | −0.282233 | − | 0.959346i | \(-0.591075\pi\) | ||||
−0.282233 | + | 0.959346i | \(0.591075\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9502.09 | −0.400994 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23460.4 | 0.986454 | 0.493227 | − | 0.869901i | \(-0.335817\pi\) | ||||
0.493227 | + | 0.869901i | \(0.335817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43695.9 | −1.83067 | −0.915333 | − | 0.402699i | \(-0.868072\pi\) | ||||
−0.915333 | + | 0.402699i | \(0.868072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21514.8 | 0.898121 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1285.48 | −0.0534685 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5872.98 | −0.243404 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11617.3 | 0.479753 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1284.76 | −0.0528663 | −0.0264331 | − | 0.999651i | \(-0.508415\pi\) | ||||
−0.0264331 | + | 0.999651i | \(0.508415\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21822.7 | 0.894777 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9658.76 | 0.394621 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2043.51 | −0.0831940 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7585.62 | 0.307727 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9034.02 | −0.365191 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47039.3 | 1.89481 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20512.5 | 0.823371 | 0.411685 | − | 0.911326i | \(-0.364940\pi\) | ||||
0.411685 | + | 0.911326i | \(0.364940\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31579.0 | 1.26313 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31252.6 | 1.24570 | 0.622852 | − | 0.782340i | \(-0.285974\pi\) | ||||
0.622852 | + | 0.782340i | \(0.285974\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34755.4 | −1.38049 | −0.690244 | − | 0.723577i | \(-0.742497\pi\) | ||||
−0.690244 | + | 0.723577i | \(0.742497\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15008.3 | −0.594054 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48390.6 | −1.90873 | −0.954365 | − | 0.298642i | \(-0.903467\pi\) | ||||
−0.954365 | + | 0.298642i | \(0.903467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16595.1 | 0.652314 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −934.641 | −0.0366114 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33797.5 | −1.31934 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39758.9 | −1.54670 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4792.65 | 0.185804 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9156.24 | 0.353757 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 258.763 | 0.00996328 | 0.00498164 | − | 0.999988i | \(-0.498414\pi\) | ||||
0.00498164 | + | 0.999988i | \(0.498414\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9400.15 | 0.360704 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33678.9 | 1.28793 | 0.643967 | − | 0.765053i | \(-0.277287\pi\) | ||||
0.643967 | + | 0.765053i | \(0.277287\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21224.7 | −0.808912 | −0.404456 | − | 0.914557i | \(-0.632539\pi\) | ||||
−0.404456 | + | 0.914557i | \(0.632539\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13555.3 | 0.514868 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 572.377 | 0.0216669 | 0.0108334 | − | 0.999941i | \(-0.496552\pi\) | ||||
0.0108334 | + | 0.999941i | \(0.496552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22991.6 | 0.867394 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −272.487 | −0.0102454 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22179.1 | −0.831127 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62940.1 | 2.35068 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19709.8 | 0.733657 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17735.2 | 0.657957 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10533.0 | −0.389463 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8367.90 | −0.308379 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34838.8 | 1.27965 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43138.1 | −1.57925 | −0.789624 | − | 0.613591i | \(-0.789724\pi\) | ||||
−0.789624 | + | 0.613591i | \(0.789724\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29973.2 | 1.09367 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32501.4 | −1.18202 | −0.591010 | − | 0.806664i | \(-0.701271\pi\) | ||||
−0.591010 | + | 0.806664i | \(0.701271\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2471.98 | −0.0896065 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 35025.1 | 1.26546 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10602.8 | −0.381826 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50933.4 | −1.82822 | −0.914112 | − | 0.405461i | \(-0.867111\pi\) | ||||
−0.914112 | + | 0.405461i | \(0.867111\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27655.9 | −0.989459 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21193.3 | −0.755780 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33208.7 | −1.18043 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3751.23 | 0.132909 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4890.44 | −0.172713 | −0.0863563 | − | 0.996264i | \(-0.527522\pi\) | ||||
−0.0863563 | + | 0.996264i | \(0.527522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9737.03 | −0.342769 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 831.517 | 0.0291776 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7810.34 | −0.273182 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15637.6 | −0.545206 | −0.272603 | − | 0.962127i | \(-0.587885\pi\) | ||||
−0.272603 | + | 0.962127i | \(0.587885\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6717.95 | −0.233474 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1284.81 | −0.0445098 | −0.0222549 | − | 0.999752i | \(-0.507085\pi\) | ||||
−0.0222549 | + | 0.999752i | \(0.507085\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30462.5 | 1.05196 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −42715.2 | −1.47040 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16603.8 | −0.569748 | −0.284874 | − | 0.958565i | \(-0.591952\pi\) | ||||
−0.284874 | + | 0.958565i | \(0.591952\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21547.4 | −0.737049 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11641.5 | −0.396951 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37812.9 | 1.28529 | 0.642643 | − | 0.766165i | \(-0.277838\pi\) | ||||
0.642643 | + | 0.766165i | \(0.277838\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 59377.4 | 2.01195 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21543.4 | −0.727690 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7617.36 | −0.256494 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22984.5 | −0.771526 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7748.43 | −0.259283 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43574.9 | 1.45360 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14492.1 | −0.481937 | −0.240968 | − | 0.970533i | \(-0.577465\pi\) | ||||
−0.240968 | + | 0.970533i | \(0.577465\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7079.55 | −0.234704 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2491.26 | −0.0823360 | −0.0411680 | − | 0.999152i | \(-0.513108\pi\) | ||||
−0.0411680 | + | 0.999152i | \(0.513108\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −49172.7 | −1.62015 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13914.7 | −0.457053 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2404.98 | 0.0787536 | 0.0393768 | − | 0.999224i | \(-0.487463\pi\) | ||||
0.0393768 | + | 0.999224i | \(0.487463\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27993.1 | 0.913854 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31566.7 | 1.02737 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48909.8 | 1.58696 | 0.793479 | − | 0.608597i | \(-0.208268\pi\) | ||||
0.793479 | + | 0.608597i | \(0.208268\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20884.7 | 0.675577 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11397.0 | 0.367548 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16984.4 | 0.546080 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10826.6 | 0.347042 | 0.173521 | − | 0.984830i | \(-0.444486\pi\) | ||||
0.173521 | + | 0.984830i | \(0.444486\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26804.3 | 0.856604 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16874.5 | 0.537645 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2284.06 | 0.0725547 | 0.0362773 | − | 0.999342i | \(-0.488450\pi\) | ||||
0.0362773 | + | 0.999342i | \(0.488450\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49319.2 | −1.56195 |
(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 | 544.4.a.l.1.3 | yes | 7 | |
4.3 | odd | 2 | 544.4.a.k.1.5 | ✓ | 7 | ||
8.3 | odd | 2 | 1088.4.a.bg.1.3 | 7 | |||
8.5 | even | 2 | 1088.4.a.bh.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
544.4.a.k.1.5 | ✓ | 7 | 4.3 | odd | 2 | ||
544.4.a.l.1.3 | yes | 7 | 1.1 | even | 1 | trivial | |
1088.4.a.bg.1.3 | 7 | 8.3 | odd | 2 | |||
1088.4.a.bh.1.5 | 7 | 8.5 | even | 2 |