Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,4,Mod(1,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, 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("608.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.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: | \(35.8731612835\) |
Analytic rank: | \(0\) |
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: |
\( x^{7} - 3x^{6} - 121x^{5} + 402x^{4} + 4234x^{3} - 14542x^{2} - 40996x + 141664 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.39349\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 608.1 |
$q$-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 | ||||||||
\(3\) | −9.45545 | −1.81970 | −0.909851 | − | 0.414935i | \(-0.863804\pi\) | ||||
−0.909851 | + | 0.414935i | \(0.863804\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −11.5945 | −1.03704 | −0.518521 | − | 0.855065i | \(-0.673517\pi\) | ||||
−0.518521 | + | 0.855065i | \(0.673517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.9032 | 0.858694 | 0.429347 | − | 0.903140i | \(-0.358744\pi\) | ||||
0.429347 | + | 0.903140i | \(0.358744\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 62.4055 | 2.31131 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.4189 | −0.532274 | −0.266137 | − | 0.963935i | \(-0.585747\pi\) | ||||
−0.266137 | + | 0.963935i | \(0.585747\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −69.4979 | −1.48271 | −0.741355 | − | 0.671113i | \(-0.765817\pi\) | ||||
−0.741355 | + | 0.671113i | \(0.765817\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 109.631 | 1.88711 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −112.461 | −1.60446 | −0.802230 | − | 0.597015i | \(-0.796353\pi\) | ||||
−0.802230 | + | 0.597015i | \(0.796353\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −150.372 | −1.56257 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 57.3974 | 0.520356 | 0.260178 | − | 0.965561i | \(-0.416219\pi\) | ||||
0.260178 | + | 0.965561i | \(0.416219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.43209 | 0.0754567 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −334.775 | −2.38620 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −59.8778 | −0.383415 | −0.191707 | − | 0.981452i | \(-0.561402\pi\) | ||||
−0.191707 | + | 0.981452i | \(0.561402\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −223.000 | −1.29200 | −0.645998 | − | 0.763339i | \(-0.723559\pi\) | ||||
−0.645998 | + | 0.763339i | \(0.723559\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 183.614 | 0.968580 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −184.390 | −0.890502 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −258.002 | −1.14636 | −0.573180 | − | 0.819429i | \(-0.694291\pi\) | ||||
−0.573180 | + | 0.819429i | \(0.694291\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 657.133 | 2.69809 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −305.175 | −1.16245 | −0.581224 | − | 0.813743i | \(-0.697426\pi\) | ||||
−0.581224 | + | 0.813743i | \(0.697426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 322.813 | 1.14485 | 0.572424 | − | 0.819958i | \(-0.306003\pi\) | ||||
0.572424 | + | 0.819958i | \(0.306003\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −723.559 | −2.39693 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −213.936 | −0.663952 | −0.331976 | − | 0.943288i | \(-0.607715\pi\) | ||||
−0.331976 | + | 0.943288i | \(0.607715\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −90.0873 | −0.262645 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1063.37 | 2.91964 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 348.651 | 0.903603 | 0.451802 | − | 0.892118i | \(-0.350782\pi\) | ||||
0.451802 | + | 0.892118i | \(0.350782\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 225.152 | 0.551990 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 179.654 | 0.417468 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −56.3816 | −0.124411 | −0.0622056 | − | 0.998063i | \(-0.519813\pi\) | ||||
−0.0622056 | + | 0.998063i | \(0.519813\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 87.2763 | 0.183190 | 0.0915950 | − | 0.995796i | \(-0.470803\pi\) | ||||
0.0915950 | + | 0.995796i | \(0.470803\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 992.449 | 1.98471 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 805.792 | 1.53763 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1074.10 | 1.95854 | 0.979272 | − | 0.202549i | \(-0.0649224\pi\) | ||||
0.979272 | + | 0.202549i | \(0.0649224\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −542.718 | −0.946892 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 725.349 | 1.21244 | 0.606219 | − | 0.795298i | \(-0.292685\pi\) | ||||
0.606219 | + | 0.795298i | \(0.292685\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 889.389 | 1.42596 | 0.712980 | − | 0.701184i | \(-0.247345\pi\) | ||||
0.712980 | + | 0.701184i | \(0.247345\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −89.1846 | −0.137309 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −308.823 | −0.457060 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1258.90 | −1.79288 | −0.896439 | − | 0.443168i | \(-0.853855\pi\) | ||||
−0.896439 | + | 0.443168i | \(0.853855\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1480.50 | 2.03086 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 227.650 | 0.301058 | 0.150529 | − | 0.988606i | \(-0.451902\pi\) | ||||
0.150529 | + | 0.988606i | \(0.451902\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1303.93 | 1.66389 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 566.171 | 0.697700 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −927.529 | −1.10470 | −0.552348 | − | 0.833614i | \(-0.686268\pi\) | ||||
−0.552348 | + | 0.833614i | \(0.686268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1105.24 | −1.27319 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2108.56 | 2.35105 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 220.295 | 0.237914 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 603.489 | 0.631701 | 0.315851 | − | 0.948809i | \(-0.397710\pi\) | ||||
0.315851 | + | 0.948809i | \(0.397710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1211.84 | −1.23025 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1035.55 | −1.02021 | −0.510106 | − | 0.860112i | \(-0.670394\pi\) | ||||
−0.510106 | + | 0.860112i | \(0.670394\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 666.961 | 0.638035 | 0.319018 | − | 0.947749i | \(-0.396647\pi\) | ||||
0.319018 | + | 0.947749i | \(0.396647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1743.49 | 1.62045 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1369.29 | −1.23714 | −0.618572 | − | 0.785728i | \(-0.712289\pi\) | ||||
−0.618572 | + | 0.785728i | \(0.712289\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1326.45 | 1.16560 | 0.582800 | − | 0.812615i | \(-0.301957\pi\) | ||||
0.582800 | + | 0.812615i | \(0.301957\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2439.53 | 2.08603 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1204.31 | −1.00258 | −0.501291 | − | 0.865279i | \(-0.667141\pi\) | ||||
−0.501291 | + | 0.865279i | \(0.667141\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −665.493 | −0.539631 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4337.05 | −3.42701 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1788.49 | −1.37774 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −953.907 | −0.716685 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2885.57 | 2.11531 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1339.95 | 0.958790 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 375.658 | 0.262475 | 0.131237 | − | 0.991351i | \(-0.458105\pi\) | ||||
0.131237 | + | 0.991351i | \(0.458105\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3052.34 | −2.08328 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2063.01 | −1.37592 | −0.687962 | − | 0.725747i | \(-0.741495\pi\) | ||||
−0.687962 | + | 0.725747i | \(0.741495\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −302.161 | −0.196998 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3881.54 | 2.47459 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1905.46 | 1.18828 | 0.594141 | − | 0.804361i | \(-0.297492\pi\) | ||||
0.594141 | + | 0.804361i | \(0.297492\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1869.18 | 1.14059 | 0.570293 | − | 0.821441i | \(-0.306830\pi\) | ||||
0.570293 | + | 0.821441i | \(0.306830\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2022.86 | 1.20819 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1349.57 | 0.789208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 694.252 | 0.397617 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 851.816 | 0.477936 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2041.70 | 1.12257 | 0.561284 | − | 0.827623i | \(-0.310308\pi\) | ||||
0.561284 | + | 0.827623i | \(0.310308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1970.09 | 1.06175 | 0.530874 | − | 0.847451i | \(-0.321864\pi\) | ||||
0.530874 | + | 0.847451i | \(0.321864\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7018.19 | −3.70841 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2585.56 | 1.33986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 945.030 | 0.480392 | 0.240196 | − | 0.970724i | \(-0.422788\pi\) | ||||
0.240196 | + | 0.970724i | \(0.422788\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3296.66 | −1.64429 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 912.803 | 0.446826 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −345.511 | −0.166028 | −0.0830139 | − | 0.996548i | \(-0.526455\pi\) | ||||
−0.0830139 | + | 0.996548i | \(0.526455\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2128.91 | −1.00446 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1554.01 | 0.720079 | 0.360040 | − | 0.932937i | \(-0.382763\pi\) | ||||
0.360040 | + | 0.932937i | \(0.382763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2632.95 | 1.19843 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1185.70 | −0.530252 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2065.34 | −0.907658 | −0.453829 | − | 0.891089i | \(-0.649942\pi\) | ||||
−0.453829 | + | 0.891089i | \(0.649942\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 150.001 | 0.0647942 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 533.113 | 0.226391 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3565.91 | −1.48899 | −0.744493 | − | 0.667631i | \(-0.767309\pi\) | ||||
−0.744493 | + | 0.667631i | \(0.767309\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1620.30 | 0.665393 | 0.332697 | − | 0.943034i | \(-0.392042\pi\) | ||||
0.332697 | + | 0.943034i | \(0.392042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −825.237 | −0.333351 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2991.41 | 1.18882 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2183.87 | 0.854012 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5324.00 | −2.04902 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2138.73 | −0.810226 | −0.405113 | − | 0.914267i | \(-0.632768\pi\) | ||||
−0.405113 | + | 0.914267i | \(0.632768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3704.25 | −1.38154 | −0.690772 | − | 0.723073i | \(-0.742729\pi\) | ||||
−0.690772 | + | 0.723073i | \(0.742729\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7619.12 | −2.79803 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −520.563 | −0.188267 | −0.0941334 | − | 0.995560i | \(-0.530008\pi\) | ||||
−0.0941334 | + | 0.995560i | \(0.530008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −67.7611 | −0.0241380 | −0.0120690 | − | 0.999927i | \(-0.503842\pi\) | ||||
−0.0120690 | + | 0.999927i | \(0.503842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10156.1 | −3.56397 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −952.250 | −0.329236 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3538.35 | 1.20551 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3581.91 | 1.20271 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 368.959 | 0.122112 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −860.566 | −0.280776 | −0.140388 | − | 0.990097i | \(-0.544835\pi\) | ||||
−0.140388 | + | 0.990097i | \(0.544835\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6858.50 | −2.20628 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3742.85 | −1.18726 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3546.41 | −1.10943 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8409.57 | −2.59482 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7815.80 | 2.37895 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6297.10 | 1.89096 | 0.945482 | − | 0.325674i | \(-0.105591\pi\) | ||||
0.945482 | + | 0.325674i | \(0.105591\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 588.614 | 0.174404 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8392 | 0.00316928 | 0.00158464 | − | 0.999999i | \(-0.499496\pi\) | ||||
0.00158464 | + | 0.999999i | \(0.499496\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4424.48 | 1.27676 | 0.638379 | − | 0.769722i | \(-0.279605\pi\) | ||||
0.638379 | + | 0.769722i | \(0.279605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2920.06 | 0.831713 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2410.23 | −0.677681 | −0.338840 | − | 0.940844i | \(-0.610035\pi\) | ||||
−0.338840 | + | 0.940844i | \(0.610035\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2480.47 | 0.688546 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11903.5 | 3.26250 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2833.55 | 0.766893 | 0.383446 | − | 0.923563i | \(-0.374737\pi\) | ||||
0.383446 | + | 0.923563i | \(0.374737\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3255.23 | 0.870074 | 0.435037 | − | 0.900413i | \(-0.356735\pi\) | ||||
0.435037 | + | 0.900413i | \(0.356735\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4959.84 | −1.30936 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1044.52 | 0.272374 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1320.46 | 0.340157 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2152.53 | −0.547836 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4125.96 | −1.03756 | −0.518782 | − | 0.854907i | \(-0.673614\pi\) | ||||
−0.518782 | + | 0.854907i | \(0.673614\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1114.59 | −0.276972 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12329.2 | −3.02779 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6627.29 | 1.60856 | 0.804278 | − | 0.594253i | \(-0.202552\pi\) | ||||
0.804278 | + | 0.594253i | \(0.202552\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4103.07 | −0.984372 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3736.70 | −0.886192 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −823.636 | −0.193109 | −0.0965543 | − | 0.995328i | \(-0.530782\pi\) | ||||
−0.0965543 | + | 0.995328i | \(0.530782\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4042.43 | −0.937075 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8770.20 | 2.01022 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5760.24 | −1.30561 | −0.652803 | − | 0.757527i | \(-0.726407\pi\) | ||||
−0.652803 | + | 0.757527i | \(0.726407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8413.28 | 1.88587 | 0.942934 | − | 0.332980i | \(-0.108054\pi\) | ||||
0.942934 | + | 0.332980i | \(0.108054\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10450.5 | 2.31683 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −183.161 | −0.0401636 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4635.95 | −1.00558 | −0.502792 | − | 0.864407i | \(-0.667694\pi\) | ||||
−0.502792 | + | 0.864407i | \(0.667694\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13916.4 | −2.98621 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4108.20 | −0.872153 | −0.436076 | − | 0.899910i | \(-0.643632\pi\) | ||||
−0.436076 | + | 0.899910i | \(0.643632\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5079.96 | 1.06704 | 0.533519 | − | 0.845788i | \(-0.320869\pi\) | ||||
0.533519 | + | 0.845788i | \(0.320869\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2082.99 | −0.432932 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4853.27 | −0.998187 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7734.49 | 1.57429 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5706.26 | −1.14951 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7988.86 | 1.59288 | 0.796441 | − | 0.604716i | \(-0.206714\pi\) | ||||
0.796441 | + | 0.604716i | \(0.206714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 653.716 | 0.129020 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6500.95 | 1.27011 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3988.99 | −0.771537 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5133.77 | 0.983074 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9791.62 | 1.85648 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1011.92 | −0.189976 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7003.80 | −1.30205 | −0.651023 | − | 0.759058i | \(-0.725660\pi\) | ||||
−0.651023 | + | 0.759058i | \(0.725660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6306.42 | −1.16103 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2835.42 | 0.516983 | 0.258492 | − | 0.966013i | \(-0.416775\pi\) | ||||
0.258492 | + | 0.966013i | \(0.416775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 669.394 | 0.120883 | 0.0604415 | − | 0.998172i | \(-0.480749\pi\) | ||||
0.0604415 | + | 0.998172i | \(0.480749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11506.9 | −2.05823 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5609.44 | 0.993872 | 0.496936 | − | 0.867787i | \(-0.334458\pi\) | ||||
0.496936 | + | 0.867787i | \(0.334458\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1162.76 | 0.204082 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12947.3 | 2.25123 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2136.76 | 0.368088 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −655.510 | −0.111880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12542.1 | −2.12105 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3402.27 | −0.570131 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10139.4 | −1.68373 | −0.841864 | − | 0.539689i | \(-0.818542\pi\) | ||||
−0.841864 | + | 0.539689i | \(0.818542\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16100.8 | −2.64960 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12453.7 | −2.03109 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 946.788 | 0.153041 | 0.0765205 | − | 0.997068i | \(-0.475619\pi\) | ||||
0.0765205 | + | 0.997068i | \(0.475619\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11387.3 | 1.82440 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4330.40 | 0.687696 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6887.49 | −1.08423 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6292.53 | 0.981967 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6022.07 | 0.931648 | 0.465824 | − | 0.884878i | \(-0.345758\pi\) | ||||
0.465824 | + | 0.884878i | \(0.345758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2271.70 | 0.348427 | 0.174214 | − | 0.984708i | \(-0.444262\pi\) | ||||
0.174214 | + | 0.984708i | \(0.444262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23266.1 | 3.53805 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3519.71 | 0.530695 | 0.265348 | − | 0.964153i | \(-0.414513\pi\) | ||||
0.265348 | + | 0.964153i | \(0.414513\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8410.05 | −1.25735 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16911.0 | 2.50707 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3485.84 | 0.512467 | 0.256234 | − | 0.966615i | \(-0.417518\pi\) | ||||
0.256234 | + | 0.966615i | \(0.417518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9019.62 | 1.30415 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10312.0 | −1.47878 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13100.4 | 1.86331 | 0.931654 | − | 0.363348i | \(-0.118366\pi\) | ||||
0.931654 | + | 0.363348i | \(0.118366\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19044.6 | −2.68678 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5544.68 | 0.775918 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13692.7 | −1.90075 | −0.950377 | − | 0.311101i | \(-0.899302\pi\) | ||||
−0.950377 | + | 0.311101i | \(0.899302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12669.8 | −1.74471 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4161.38 | 0.568493 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3198.56 | −0.433506 | −0.216753 | − | 0.976226i | \(-0.569547\pi\) | ||||
−0.216753 | + | 0.976226i | \(0.569547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3552.02 | −0.477625 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10724.5 | −1.43080 | −0.715400 | − | 0.698716i | \(-0.753755\pi\) | ||||
−0.715400 | + | 0.698716i | \(0.753755\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3580.64 | 0.473991 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20145.3 | 2.64610 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6806.29 | −0.887128 | −0.443564 | − | 0.896243i | \(-0.646286\pi\) | ||||
−0.443564 | + | 0.896243i | \(0.646286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6454.97 | −0.834889 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19506.7 | 2.50377 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14596.3 | 1.85929 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6878.98 | −0.869637 | −0.434819 | − | 0.900518i | \(-0.643188\pi\) | ||||
−0.434819 | + | 0.900518i | \(0.643188\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2857.07 | 0.358477 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10972.1 | 1.36639 | 0.683194 | − | 0.730237i | \(-0.260590\pi\) | ||||
0.683194 | + | 0.730237i | \(0.260590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15498.0 | 1.91566 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17165.6 | −2.10609 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5010.12 | 0.610178 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13952.8 | −1.68685 | −0.843424 | − | 0.537249i | \(-0.819464\pi\) | ||||
−0.843424 | + | 0.537249i | \(0.819464\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18017.0 | −2.16232 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −896.650 | −0.106831 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2639.48 | −0.312210 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17673.9 | −2.07553 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3901.77 | 0.454925 | 0.227463 | − | 0.973787i | \(-0.426957\pi\) | ||||
0.227463 | + | 0.973787i | \(0.426957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5739.67 | 0.664452 | 0.332226 | − | 0.943200i | \(-0.392200\pi\) | ||||
0.332226 | + | 0.943200i | \(0.392200\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13350.8 | −1.53460 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1060.74 | −0.121067 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1387.98 | 0.157304 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12760.8 | −1.43612 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4016.82 | −0.448917 | −0.224459 | − | 0.974484i | \(-0.572061\pi\) | ||||
−0.224459 | + | 0.974484i | \(0.572061\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10619.1 | −1.17857 | −0.589286 | − | 0.807925i | \(-0.700591\pi\) | ||||
−0.589286 | + | 0.807925i | \(0.700591\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6564.46 | −0.723545 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1090.55 | −0.119378 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1594.11 | 0.173309 | 0.0866545 | − | 0.996238i | \(-0.472382\pi\) | ||||
0.0866545 | + | 0.996238i | \(0.472382\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5621.94 | −0.607056 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3512.03 | 0.376662 | 0.188331 | − | 0.982106i | \(-0.439692\pi\) | ||||
0.188331 | + | 0.982106i | \(0.439692\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10754.2 | 1.14562 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19305.2 | −2.04274 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3239.71 | 0.340515 | 0.170258 | − | 0.985400i | \(-0.445540\pi\) | ||||
0.170258 | + | 0.985400i | \(0.445540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5926.16 | 0.618741 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18628.1 | −1.93206 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12814.7 | 1.32036 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7149.11 | −0.731775 | −0.365887 | − | 0.930659i | \(-0.619234\pi\) | ||||
−0.365887 | + | 0.930659i | \(0.619234\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 37649.1 | 3.82856 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1452.36 | −0.146731 | −0.0733657 | − | 0.997305i | \(-0.523374\pi\) | ||||
−0.0733657 | + | 0.997305i | \(0.523374\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4887.26 | 0.490562 | 0.245281 | − | 0.969452i | \(-0.421120\pi\) | ||||
0.245281 | + | 0.969452i | \(0.421120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24447.7 | −2.43814 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15576.4 | −1.54344 | −0.771722 | − | 0.635960i | \(-0.780604\pi\) | ||||
−0.771722 | + | 0.635960i | \(0.780604\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17081.7 | 1.68179 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8935.68 | −0.874171 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6268.66 | −0.609373 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −179.210 | −0.0173110 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21757.8 | 2.08851 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9155.87 | −0.873366 | −0.436683 | − | 0.899616i | \(-0.643847\pi\) | ||||
−0.436683 | + | 0.899616i | \(0.643847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17930.6 | 1.69972 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8630.97 | −0.813090 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6997.14 | −0.655101 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4855.86 | −0.451827 | −0.225914 | − | 0.974147i | \(-0.572537\pi\) | ||||
−0.225914 | + | 0.974147i | \(0.572537\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3266.96 | 0.302121 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13319.0 | 1.22419 | 0.612094 | − | 0.790785i | \(-0.290327\pi\) | ||||
0.612094 | + | 0.790785i | \(0.290327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6733.92 | 0.615173 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14050.7 | 1.27582 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11535.4 | 1.04111 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9859.86 | −0.884545 | −0.442273 | − | 0.896881i | \(-0.645828\pi\) | ||||
−0.442273 | + | 0.896881i | \(0.645828\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14693.9 | −1.31033 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9994.26 | 0.885929 | 0.442964 | − | 0.896539i | \(-0.353927\pi\) | ||||
0.442964 | + | 0.896539i | \(0.353927\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12006.7 | 1.05800 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24895.8 | −2.18079 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9489.87 | 0.826387 | 0.413194 | − | 0.910643i | \(-0.364413\pi\) | ||||
0.413194 | + | 0.910643i | \(0.364413\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14144.2 | 1.22446 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6360.72 | 0.547432 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7733.07 | −0.661670 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4154.39 | 0.353404 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19528.7 | 1.65167 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14621.5 | −1.22952 | −0.614759 | − | 0.788715i | \(-0.710747\pi\) | ||||
−0.614759 | + | 0.788715i | \(0.710747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7500.48 | 0.627099 | 0.313550 | − | 0.949572i | \(-0.398482\pi\) | ||||
0.313550 | + | 0.949572i | \(0.398482\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1418.32 | −0.117906 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25078.8 | 2.07296 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8872.54 | −0.729230 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3518.52 | −0.287553 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21209.0 | 1.72358 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15876.2 | 1.28297 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33717.2 | 2.70951 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1749.39 | 0.139799 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2413.87 | −0.191831 | −0.0959153 | − | 0.995390i | \(-0.530578\pi\) | ||||
−0.0959153 | + | 0.995390i | \(0.530578\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15320.7 | −1.21082 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15379.5 | −1.20878 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21120.6 | 1.65092 | 0.825458 | − | 0.564464i | \(-0.190917\pi\) | ||||
0.825458 | + | 0.564464i | \(0.190917\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5446.52 | 0.423410 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1137.68 | 0.0879614 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20020.6 | −1.53953 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −28285.1 | −2.16331 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16059.4 | 1.22165 | 0.610823 | − | 0.791767i | \(-0.290839\pi\) | ||||
0.610823 | + | 0.791767i | \(0.290839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22434.8 | −1.69748 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20649.4 | −1.55405 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19306.8 | −1.44527 | −0.722634 | − | 0.691231i | \(-0.757069\pi\) | ||||
−0.722634 | + | 0.691231i | \(0.757069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13963.3 | 1.03972 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23544.7 | 1.74389 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11379.0 | −0.838373 | −0.419187 | − | 0.907900i | \(-0.637685\pi\) | ||||
−0.419187 | + | 0.907900i | \(0.637685\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16788.6 | 1.23044 | 0.615219 | − | 0.788356i | \(-0.289068\pi\) | ||||
0.615219 | + | 0.788356i | \(0.289068\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20222.7 | 1.47437 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 541.377 | 0.0392643 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4084.31 | 0.294683 | 0.147342 | − | 0.989086i | \(-0.452928\pi\) | ||||
0.147342 | + | 0.989086i | \(0.452928\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35025.4 | 2.51400 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3620.37 | 0.258516 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6770.42 | −0.480964 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 50285.8 | 3.55396 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10687.2 | −0.751458 | −0.375729 | − | 0.926730i | \(-0.622608\pi\) | ||||
−0.375729 | + | 0.926730i | \(0.622608\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4236.99 | 0.296404 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4922.15 | 0.342590 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18697.2 | −1.29477 | −0.647387 | − | 0.762162i | \(-0.724138\pi\) | ||||
−0.647387 | + | 0.762162i | \(0.724138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20736.7 | 1.42877 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 640.712 | 0.0439239 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3455.17 | −0.235683 | −0.117842 | − | 0.993032i | \(-0.537598\pi\) | ||||
−0.117842 | + | 0.993032i | \(0.537598\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15030.6 | −1.02015 | −0.510075 | − | 0.860130i | \(-0.670382\pi\) | ||||
−0.510075 | + | 0.860130i | \(0.670382\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 67029.9 | 4.52681 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11060.1 | 0.743232 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2229.47 | 0.149080 | 0.0745398 | − | 0.997218i | \(-0.476251\pi\) | ||||
0.0745398 | + | 0.997218i | \(0.476251\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9003.95 | 0.599111 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14868.1 | 0.984448 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14821.0 | 0.976534 | 0.488267 | − | 0.872694i | \(-0.337629\pi\) | ||||
0.488267 | + | 0.872694i | \(0.337629\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −33456.7 | −2.19367 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19301.7 | −1.25941 | −0.629706 | − | 0.776833i | \(-0.716825\pi\) | ||||
−0.629706 | + | 0.776833i | \(0.716825\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20550.4 | 1.33440 | 0.667198 | − | 0.744880i | \(-0.267493\pi\) | ||||
0.667198 | + | 0.744880i | \(0.267493\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19215.2 | −1.24167 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14750.7 | −0.948595 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16715.0 | −1.06976 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3488.67 | −0.222207 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29015.2 | 1.83929 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6019.78 | −0.379784 | −0.189892 | − | 0.981805i | \(-0.560814\pi\) | ||||
−0.189892 | + | 0.981805i | \(0.560814\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8137.04 | 0.510929 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4355.56 | −0.272197 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6260.88 | 0.389427 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 45265.8 | 2.80233 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 554.836 | 0.0341883 | 0.0170941 | − | 0.999854i | \(-0.494559\pi\) | ||||
0.0170941 | + | 0.999854i | \(0.494559\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25135.5 | 1.54160 | 0.770800 | − | 0.637077i | \(-0.219857\pi\) | ||||
0.770800 | + | 0.637077i | \(0.219857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 35390.3 | 2.16045 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17081.4 | 1.03792 | 0.518962 | − | 0.854797i | \(-0.326318\pi\) | ||||
0.518962 | + | 0.854797i | \(0.326318\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1094.87 | 0.0662208 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33532.9 | 2.01883 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17375.8 | −1.04130 | −0.520649 | − | 0.853771i | \(-0.674310\pi\) | ||||
−0.520649 | + | 0.853771i | \(0.674310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23919.5 | 1.42689 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 55502.8 | 3.29584 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14944.2 | −0.883377 | −0.441688 | − | 0.897169i | \(-0.645620\pi\) | ||||
−0.441688 | + | 0.897169i | \(0.645620\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2829.77 | −0.166513 | −0.0832565 | − | 0.996528i | \(-0.526532\pi\) | ||||
−0.0832565 | + | 0.996528i | \(0.526532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −73901.9 | −4.32898 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3503.41 | 0.204295 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3436.83 | −0.199512 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −59541.9 | −3.44099 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1694.81 | −0.0975072 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18325.9 | −1.04965 | −0.524823 | − | 0.851211i | \(-0.675869\pi\) | ||||
−0.524823 | + | 0.851211i | \(0.675869\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3157.62 | −0.180055 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12887.9 | 0.731645 | 0.365823 | − | 0.930685i | \(-0.380788\pi\) | ||||
0.365823 | + | 0.930685i | \(0.380788\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9597.42 | 0.542438 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −102.490 | −0.00576714 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21490.8 | −1.20399 | −0.601993 | − | 0.798501i | \(-0.705626\pi\) | ||||
−0.601993 | + | 0.798501i | \(0.705626\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22092.8 | −1.23230 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −41835.4 | −2.32332 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24230.5 | −1.33978 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7795.43 | −0.429164 | −0.214582 | − | 0.976706i | \(-0.568839\pi\) | ||||
−0.214582 | + | 0.976706i | \(0.568839\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19272.2 | −1.05641 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21672.1 | −1.18284 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34320.3 | 1.86510 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22789.8 | 1.23318 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4462.67 | −0.240446 | −0.120223 | − | 0.992747i | \(-0.538361\pi\) | ||||
−0.120223 | + | 0.992747i | \(0.538361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4902.05 | 0.262993 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23454.0 | −1.25295 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16468.6 | −0.876050 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27093.8 | −1.43516 | −0.717581 | − | 0.696475i | \(-0.754751\pi\) | ||||
−0.717581 | + | 0.696475i | \(0.754751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −78562.3 | −4.14390 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12799.6 | −0.672298 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15647.6 | −0.818442 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26792.5 | −1.39552 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5743.87 | −0.297928 | −0.148964 | − | 0.988843i | \(-0.547594\pi\) | ||||
−0.148964 | + | 0.988843i | \(0.547594\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10606.8 | 0.547877 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30779.6 | −1.58327 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −564.772 | −0.0289312 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33173.9 | −1.69237 | −0.846185 | − | 0.532889i | \(-0.821106\pi\) | ||||
−0.846185 | + | 0.532889i | \(0.821106\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6924.11 | 0.351781 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36303.9 | −1.83686 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9406.08 | 0.473972 | 0.236986 | − | 0.971513i | \(-0.423840\pi\) | ||||
0.236986 | + | 0.971513i | \(0.423840\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9876.37 | −0.495640 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20857.9 | −1.04248 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11407.9 | 0.567858 | 0.283929 | − | 0.958845i | \(-0.408362\pi\) | ||||
0.283929 | + | 0.958845i | \(0.408362\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12485.5 | −0.618985 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25469.4 | 1.25758 | 0.628790 | − | 0.777575i | \(-0.283551\pi\) | ||||
0.628790 | + | 0.777575i | \(0.283551\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23672.5 | −1.16415 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14206.6 | 0.695839 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21776.2 | −1.06233 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23819.5 | 1.15737 | 0.578686 | − | 0.815550i | \(-0.303566\pi\) | ||||
0.578686 | + | 0.815550i | \(0.303566\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39012.8 | 1.88806 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22842.2 | −1.10108 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6611.66 | 0.317444 | 0.158722 | − | 0.987323i | \(-0.449263\pi\) | ||||
0.158722 | + | 0.987323i | \(0.449263\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10539.0 | 0.504006 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29643.4 | 1.41205 | 0.706026 | − | 0.708185i | \(-0.250486\pi\) | ||||
0.706026 | + | 0.708185i | \(0.250486\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21094.8 | 1.00089 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 81372.3 | 3.84578 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3918.40 | 0.184466 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6329.72 | −0.296821 | −0.148411 | − | 0.988926i | \(-0.547416\pi\) | ||||
−0.148411 | + | 0.988926i | \(0.547416\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −62664.0 | −2.92709 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24504.8 | −1.14020 | −0.570101 | − | 0.821575i | \(-0.693096\pi\) | ||||
−0.570101 | + | 0.821575i | \(0.693096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2103.35 | −0.0974898 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 38796.4 | 1.79126 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5798.33 | 0.266684 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14085.5 | −0.645349 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20045.6 | 0.914904 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10957.1 | −0.498187 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33851.3 | 1.53325 | 0.766627 | − | 0.642093i | \(-0.221934\pi\) | ||||
0.766627 | + | 0.642093i | \(0.221934\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7787.84 | 0.351400 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19152.4 | −0.860910 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6065.52 | −0.271618 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 38223.0 | 1.70520 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18282.7 | −0.812556 | −0.406278 | − | 0.913750i | \(-0.633174\pi\) | ||||
−0.406278 | + | 0.913750i | \(0.633174\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24059.4 | 1.06528 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −57882.9 | −2.55330 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17270.9 | −0.759002 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10583.5 | −0.463377 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 54465.7 | 2.37582 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12733.6 | −0.553386 | −0.276693 | − | 0.960958i | \(-0.589238\pi\) | ||||
−0.276693 | + | 0.960958i | \(0.589238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10126.7 | 0.438469 | 0.219234 | − | 0.975672i | \(-0.429644\pi\) | ||||
0.219234 | + | 0.975672i | \(0.429644\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −79551.3 | −3.43172 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4006.03 | 0.172178 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6133.44 | −0.262646 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −68973.1 | −2.94275 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1944.98 | −0.0826802 | −0.0413401 | − | 0.999145i | \(-0.513163\pi\) | ||||
−0.0413401 | + | 0.999145i | \(0.513163\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31712.7 | 1.34318 | 0.671589 | − | 0.740924i | \(-0.265612\pi\) | ||||
0.671589 | + | 0.740924i | \(0.265612\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1731.86 | 0.0730858 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3728.06 | −0.156756 | −0.0783781 | − | 0.996924i | \(-0.524974\pi\) | ||||
−0.0783781 | + | 0.996924i | \(0.524974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13200.4 | 0.553037 | 0.276518 | − | 0.961009i | \(-0.410819\pi\) | ||||
0.276518 | + | 0.961009i | \(0.410819\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43834.9 | 1.82986 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10131.3 | 0.421404 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18018.0 | −0.746753 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 74654.6 | 3.08296 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11445.0 | −0.470949 | −0.235475 | − | 0.971881i | \(-0.575664\pi\) | ||||
−0.235475 | + | 0.971881i | \(0.575664\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20803.7 | −0.852993 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38844.9 | 1.58706 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30527.7 | −1.24282 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15170.2 | −0.615413 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −48033.2 | −1.94169 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14808.7 | −0.596515 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8701.48 | −0.349276 | −0.174638 | − | 0.984633i | \(-0.555876\pi\) | ||||
−0.174638 | + | 0.984633i | \(0.555876\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13747.6 | 0.549894 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −720.765 | −0.0287291 | −0.0143646 | − | 0.999897i | \(-0.504573\pi\) | ||||
−0.0143646 | + | 0.999897i | \(0.504573\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4678.63 | 0.185836 | 0.0929179 | − | 0.995674i | \(-0.470381\pi\) | ||||
0.0929179 | + | 0.995674i | \(0.470381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 45889.9 | 1.81640 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7009.92 | 0.276501 | 0.138250 | − | 0.990397i | \(-0.455852\pi\) | ||||
0.138250 | + | 0.990397i | \(0.455852\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23946.5 | 0.941280 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −73133.0 | −2.86474 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24446.4 | 0.954302 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −74647.8 | −2.90396 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 37661.0 | 1.46006 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21309.5 | 0.823307 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22737.0 | −0.875453 | −0.437727 | − | 0.899108i | \(-0.644216\pi\) | ||||
−0.437727 | + | 0.899108i | \(0.644216\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −75538.3 | −2.89857 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7697.02 | 0.294346 | 0.147173 | − | 0.989111i | \(-0.452983\pi\) | ||||
0.147173 | + | 0.989111i | \(0.452983\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7842.91 | −0.298907 | −0.149454 | − | 0.988769i | \(-0.547751\pi\) | ||||
−0.149454 | + | 0.988769i | \(0.547751\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6181.18 | −0.234777 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41079.7 | 1.55504 | 0.777521 | − | 0.628857i | \(-0.216477\pi\) | ||||
0.777521 | + | 0.628857i | \(0.216477\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5974.18 | 0.225385 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28749.6 | −1.08097 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4064.78 | 0.152321 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41344.9 | 1.54414 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37717.7 | 1.40397 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13352.7 | 0.495370 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39209.7 | −1.44979 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −48542.0 | −1.78890 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18786.6 | −0.690041 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38639.4 | −1.41455 | −0.707277 | − | 0.706937i | \(-0.750076\pi\) | ||||
−0.707277 | + | 0.706937i | \(0.750076\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −64624.2 | −2.35803 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18398.0 | 0.669103 | 0.334551 | − | 0.942377i | \(-0.391415\pi\) | ||||
0.334551 | + | 0.942377i | \(0.391415\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4420.70 | −0.160245 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9568.19 | 0.345699 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32808.5 | −1.18150 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24502.3 | 0.879495 | 0.439748 | − | 0.898121i | \(-0.355068\pi\) | ||||
0.439748 | + | 0.898121i | \(0.355068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 66224.1 | 2.36934 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −50410.2 | −1.79770 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2433.50 | −0.0865006 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41622.0 | 1.47470 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47616.6 | −1.68165 | −0.840823 | − | 0.541310i | \(-0.817928\pi\) | ||||
−0.840823 | + | 0.541310i | \(0.817928\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1711.66 | 0.0602549 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26810.1 | −0.940755 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25320.8 | −0.885646 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21360.6 | 0.744739 | 0.372369 | − | 0.928085i | \(-0.378545\pi\) | ||||
0.372369 | + | 0.928085i | \(0.378545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6329.42 | −0.219971 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23923.3 | 0.828776 | 0.414388 | − | 0.910100i | \(-0.363996\pi\) | ||||
0.414388 | + | 0.910100i | \(0.363996\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17516.3 | −0.604887 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 61729.0 | 2.12492 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23330.5 | −0.800569 | −0.400285 | − | 0.916391i | \(-0.631089\pi\) | ||||
−0.400285 | + | 0.916391i | \(0.631089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −61810.7 | −2.11429 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −53039.8 | −1.80855 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25756.2 | −0.875472 | −0.437736 | − | 0.899104i | \(-0.644220\pi\) | ||||
−0.437736 | + | 0.899104i | \(0.644220\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24797.5 | 0.840238 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10994.4 | −0.371368 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30303.0 | 1.02037 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19937.8 | 0.669255 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −85451.3 | −2.85943 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 42948.9 | 1.43272 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2488.74 | 0.0827635 | 0.0413818 | − | 0.999143i | \(-0.486824\pi\) | ||||
0.0413818 | + | 0.999143i | \(0.486824\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20204.0 | −0.669811 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4909.90 | −0.162272 | −0.0811360 | − | 0.996703i | \(-0.525855\pi\) | ||||
−0.0811360 | + | 0.996703i | \(0.525855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29726.0 | 0.979415 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6198.14 | 0.203589 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47452.4 | 1.55388 | 0.776938 | − | 0.629578i | \(-0.216772\pi\) | ||||
0.776938 | + | 0.629578i | \(0.216772\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18011.6 | 0.588000 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 82777.5 | 2.69407 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27802.2 | −0.902088 | −0.451044 | − | 0.892502i | \(-0.648948\pi\) | ||||
−0.451044 | + | 0.892502i | \(0.648948\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6035.66 | 0.195241 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32170.0 | 1.03747 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18528.6 | 0.595728 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26200.5 | −0.839845 | −0.419922 | − | 0.907560i | \(-0.637943\pi\) | ||||
−0.419922 | + | 0.907560i | \(0.637943\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 95873.0 | 3.06388 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 785.655 | 0.0250321 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25254.6 | 0.802227 | 0.401113 | − | 0.916028i | \(-0.368623\pi\) | ||||
0.401113 | + | 0.916028i | \(0.368623\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 86372.7 | 2.73545 |
(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 | 608.4.a.k.1.1 | yes | 7 | |
4.3 | odd | 2 | 608.4.a.j.1.7 | ✓ | 7 | ||
8.3 | odd | 2 | 1216.4.a.bg.1.1 | 7 | |||
8.5 | even | 2 | 1216.4.a.bf.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.4.a.j.1.7 | ✓ | 7 | 4.3 | odd | 2 | ||
608.4.a.k.1.1 | yes | 7 | 1.1 | even | 1 | trivial | |
1216.4.a.bf.1.7 | 7 | 8.5 | even | 2 | |||
1216.4.a.bg.1.1 | 7 | 8.3 | odd | 2 |