Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,4,Mod(1,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2160.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(127.444125612\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.5637.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 23x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 135) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.20067\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.4013 | −1.31755 | −0.658774 | − | 0.752341i | \(-0.728925\pi\) | ||||
−0.658774 | + | 0.752341i | \(0.728925\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.9839 | 0.794451 | 0.397226 | − | 0.917721i | \(-0.369973\pi\) | ||||
0.397226 | + | 0.917721i | \(0.369973\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −65.3919 | −1.39511 | −0.697556 | − | 0.716530i | \(-0.745729\pi\) | ||||
−0.697556 | + | 0.716530i | \(0.745729\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 68.1718 | 0.972593 | 0.486296 | − | 0.873794i | \(-0.338347\pi\) | ||||
0.486296 | + | 0.873794i | \(0.338347\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −104.424 | −1.26087 | −0.630435 | − | 0.776242i | \(-0.717124\pi\) | ||||
−0.630435 | + | 0.776242i | \(0.717124\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 154.807 | 1.40345 | 0.701727 | − | 0.712446i | \(-0.252413\pi\) | ||||
0.701727 | + | 0.712446i | \(0.252413\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −205.658 | −1.31689 | −0.658443 | − | 0.752631i | \(-0.728785\pi\) | ||||
−0.658443 | + | 0.752631i | \(0.728785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.2497 | 0.105734 | 0.0528668 | − | 0.998602i | \(-0.483164\pi\) | ||||
0.0528668 | + | 0.998602i | \(0.483164\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 122.007 | 0.589226 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −337.613 | −1.50009 | −0.750044 | − | 0.661387i | \(-0.769968\pi\) | ||||
−0.750044 | + | 0.661387i | \(0.769968\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −195.969 | −0.746469 | −0.373234 | − | 0.927737i | \(-0.621751\pi\) | ||||
−0.373234 | + | 0.927737i | \(0.621751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −334.882 | −1.18765 | −0.593826 | − | 0.804594i | \(-0.702383\pi\) | ||||
−0.593826 | + | 0.804594i | \(0.702383\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.00398 | 0.0155299 | 0.00776496 | − | 0.999970i | \(-0.497528\pi\) | ||||
0.00776496 | + | 0.999970i | \(0.497528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 252.425 | 0.735934 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −319.965 | −0.829256 | −0.414628 | − | 0.909991i | \(-0.636088\pi\) | ||||
−0.414628 | + | 0.909991i | \(0.636088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −144.919 | −0.355289 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −430.611 | −0.950182 | −0.475091 | − | 0.879937i | \(-0.657585\pi\) | ||||
−0.475091 | + | 0.879937i | \(0.657585\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 594.581 | 1.24800 | 0.624002 | − | 0.781422i | \(-0.285505\pi\) | ||||
0.624002 | + | 0.781422i | \(0.285505\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 326.960 | 0.623913 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −195.876 | −0.357166 | −0.178583 | − | 0.983925i | \(-0.557151\pi\) | ||||
−0.178583 | + | 0.983925i | \(0.557151\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −425.955 | −0.711994 | −0.355997 | − | 0.934487i | \(-0.615859\pi\) | ||||
−0.355997 | + | 0.934487i | \(0.615859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 929.193 | 1.48978 | 0.744889 | − | 0.667188i | \(-0.232502\pi\) | ||||
0.744889 | + | 0.667188i | \(0.232502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −707.245 | −1.04673 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −24.4296 | −0.0347917 | −0.0173959 | − | 0.999849i | \(-0.505538\pi\) | ||||
−0.0173959 | + | 0.999849i | \(0.505538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 545.859 | 0.721877 | 0.360938 | − | 0.932590i | \(-0.382456\pi\) | ||||
0.360938 | + | 0.932590i | \(0.382456\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −340.859 | −0.434957 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −84.1332 | −0.100203 | −0.0501017 | − | 0.998744i | \(-0.515955\pi\) | ||||
−0.0501017 | + | 0.998744i | \(0.515955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1595.65 | 1.83813 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 522.121 | 0.563879 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 827.613 | 0.866303 | 0.433152 | − | 0.901321i | \(-0.357401\pi\) | ||||
0.433152 | + | 0.901321i | \(0.357401\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 823.576 | 0.811375 | 0.405688 | − | 0.914012i | \(-0.367032\pi\) | ||||
0.405688 | + | 0.914012i | \(0.367032\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1171.19 | −1.12040 | −0.560198 | − | 0.828359i | \(-0.689275\pi\) | ||||
−0.560198 | + | 0.828359i | \(0.689275\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1023.21 | −0.924460 | −0.462230 | − | 0.886760i | \(-0.652951\pi\) | ||||
−0.462230 | + | 0.886760i | \(0.652951\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −403.647 | −0.354700 | −0.177350 | − | 0.984148i | \(-0.556753\pi\) | ||||
−0.177350 | + | 0.984148i | \(0.556753\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1082.20 | 0.900931 | 0.450465 | − | 0.892794i | \(-0.351258\pi\) | ||||
0.450465 | + | 0.892794i | \(0.351258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −774.033 | −0.627643 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1663.48 | −1.28144 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −490.935 | −0.368847 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 774.132 | 0.540890 | 0.270445 | − | 0.962735i | \(-0.412829\pi\) | ||||
0.270445 | + | 0.962735i | \(0.412829\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1214.04 | 0.809702 | 0.404851 | − | 0.914383i | \(-0.367323\pi\) | ||||
0.404851 | + | 0.914383i | \(0.367323\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2548.09 | 1.66126 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2300.15 | 1.43441 | 0.717207 | − | 0.696860i | \(-0.245420\pi\) | ||||
0.717207 | + | 0.696860i | \(0.245420\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1355.93 | 0.827396 | 0.413698 | − | 0.910414i | \(-0.364237\pi\) | ||||
0.413698 | + | 0.910414i | \(0.364237\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1895.31 | −1.10835 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1028.29 | 0.588929 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 259.845 | 0.142868 | 0.0714340 | − | 0.997445i | \(-0.477242\pi\) | ||||
0.0714340 | + | 0.997445i | \(0.477242\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 508.304 | 0.273941 | 0.136971 | − | 0.990575i | \(-0.456263\pi\) | ||||
0.136971 | + | 0.990575i | \(0.456263\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −91.2485 | −0.0472855 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.3052 | −0.0118468 | −0.00592342 | − | 0.999982i | \(-0.501885\pi\) | ||||
−0.00592342 | + | 0.999982i | \(0.501885\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3777.49 | −1.84912 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4032.10 | 1.93754 | 0.968769 | − | 0.247964i | \(-0.0797616\pi\) | ||||
0.968769 | + | 0.247964i | \(0.0797616\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 671.911 | 0.311341 | 0.155671 | − | 0.987809i | \(-0.450246\pi\) | ||||
0.155671 | + | 0.987809i | \(0.450246\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2079.10 | 0.946337 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1633.53 | 0.717889 | 0.358944 | − | 0.933359i | \(-0.383137\pi\) | ||||
0.358944 | + | 0.933359i | \(0.383137\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −610.034 | −0.263510 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −341.260 | −0.142497 | −0.0712485 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712485 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1695.92 | −0.696447 | −0.348223 | − | 0.937412i | \(-0.613215\pi\) | ||||
−0.348223 | + | 0.937412i | \(0.613215\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1688.07 | 0.670860 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1975.88 | 0.772678 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 726.451 | 0.275205 | 0.137603 | − | 0.990488i | \(-0.456060\pi\) | ||||
0.137603 | + | 0.990488i | \(0.456060\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4247.26 | 1.58406 | 0.792032 | − | 0.610479i | \(-0.209023\pi\) | ||||
0.792032 | + | 0.610479i | \(0.209023\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2678.52 | 0.968713 | 0.484357 | − | 0.874871i | \(-0.339054\pi\) | ||||
0.484357 | + | 0.874871i | \(0.339054\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1486.48 | −0.529517 | −0.264759 | − | 0.964315i | \(-0.585292\pi\) | ||||
−0.264759 | + | 0.964315i | \(0.585292\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5018.32 | 1.73506 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 979.845 | 0.333831 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3026.62 | −1.00170 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4827.41 | 1.57504 | 0.787519 | − | 0.616291i | \(-0.211365\pi\) | ||||
0.787519 | + | 0.616291i | \(0.211365\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1674.41 | 0.531134 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −445.317 | −0.139309 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4457.88 | −1.35688 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2774.48 | −0.833153 | −0.416576 | − | 0.909101i | \(-0.636770\pi\) | ||||
−0.416576 | + | 0.909101i | \(0.636770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5101.34 | 1.49158 | 0.745788 | − | 0.666184i | \(-0.232073\pi\) | ||||
0.745788 | + | 0.666184i | \(0.232073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4097.83 | −1.18250 | −0.591249 | − | 0.806489i | \(-0.701365\pi\) | ||||
−0.591249 | + | 0.806489i | \(0.701365\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 357.613 | 0.100549 | 0.0502747 | − | 0.998735i | \(-0.483990\pi\) | ||||
0.0502747 | + | 0.998735i | \(0.483990\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.0199 | −0.00694519 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 351.682 | 0.0951818 | 0.0475909 | − | 0.998867i | \(-0.484846\pi\) | ||||
0.0475909 | + | 0.998867i | \(0.484846\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6165.53 | −1.64795 | −0.823976 | − | 0.566624i | \(-0.808249\pi\) | ||||
−0.823976 | + | 0.566624i | \(0.808249\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1262.13 | −0.329120 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6828.50 | 1.75906 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3245.53 | −0.816160 | −0.408080 | − | 0.912946i | \(-0.633802\pi\) | ||||
−0.408080 | + | 0.912946i | \(0.633802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4486.90 | 1.11498 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3552.19 | 0.862178 | 0.431089 | − | 0.902309i | \(-0.358129\pi\) | ||||
0.431089 | + | 0.902309i | \(0.358129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8238.22 | 1.97644 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4416.59 | −1.03551 | −0.517754 | − | 0.855530i | \(-0.673232\pi\) | ||||
−0.517754 | + | 0.855530i | \(0.673232\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1599.83 | 0.370855 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3419.93 | −0.775155 | −0.387578 | − | 0.921837i | \(-0.626688\pi\) | ||||
−0.387578 | + | 0.921837i | \(0.626688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −716.407 | −0.160585 | −0.0802927 | − | 0.996771i | \(-0.525585\pi\) | ||||
−0.0802927 | + | 0.996771i | \(0.525585\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 724.597 | 0.158890 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 657.529 | 0.142625 | 0.0713124 | − | 0.997454i | \(-0.477281\pi\) | ||||
0.0713124 | + | 0.997454i | \(0.477281\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1513.91 | 0.321397 | 0.160698 | − | 0.987004i | \(-0.448625\pi\) | ||||
0.160698 | + | 0.987004i | \(0.448625\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3906.38 | −0.820532 | −0.410266 | − | 0.911966i | \(-0.634564\pi\) | ||||
−0.410266 | + | 0.911966i | \(0.634564\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4781.91 | 0.983509 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −265.611 | −0.0540629 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8048.76 | −1.60483 | −0.802413 | − | 0.596770i | \(-0.796451\pi\) | ||||
−0.802413 | + | 0.596770i | \(0.796451\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2153.05 | 0.424934 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10123.1 | −1.95797 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8171.57 | 1.56479 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2972.91 | −0.558125 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −101.564 | −0.0188814 | −0.00944068 | − | 0.999955i | \(-0.503005\pi\) | ||||
−0.00944068 | + | 0.999955i | \(0.503005\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7684.59 | 1.40113 | 0.700567 | − | 0.713586i | \(-0.252930\pi\) | ||||
0.700567 | + | 0.713586i | \(0.252930\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1345.15 | −0.242915 | −0.121457 | − | 0.992597i | \(-0.538757\pi\) | ||||
−0.121457 | + | 0.992597i | \(0.538757\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7622.33 | 1.35051 | 0.675257 | − | 0.737583i | \(-0.264033\pi\) | ||||
0.675257 | + | 0.737583i | \(0.264033\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5960.76 | −1.04620 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7118.78 | −1.22631 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1634.80 | −0.279022 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −122.104 | −0.0204614 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6585.09 | 1.09350 | 0.546751 | − | 0.837295i | \(-0.315864\pi\) | ||||
0.546751 | + | 0.837295i | \(0.315864\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 979.382 | 0.159729 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2946.94 | −0.476351 | −0.238175 | − | 0.971222i | \(-0.576549\pi\) | ||||
−0.238175 | + | 0.971222i | \(0.576549\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 528.947 | 0.0840002 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2210.14 | 0.347919 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8493.48 | −1.31399 | −0.656994 | − | 0.753896i | \(-0.728172\pi\) | ||||
−0.656994 | + | 0.753896i | \(0.728172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5646.54 | 0.866053 | 0.433027 | − | 0.901381i | \(-0.357446\pi\) | ||||
0.433027 | + | 0.901381i | \(0.357446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1221.93 | −0.184240 | −0.0921202 | − | 0.995748i | \(-0.529364\pi\) | ||||
−0.0921202 | + | 0.995748i | \(0.529364\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2129.78 | 0.318414 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4151.44 | 0.610319 | 0.305160 | − | 0.952301i | \(-0.401290\pi\) | ||||
0.305160 | + | 0.952301i | \(0.401290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4045.41 | 0.589796 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4645.96 | −0.666249 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7038.71 | 1.00114 | 0.500569 | − | 0.865696i | \(-0.333124\pi\) | ||||
0.500569 | + | 0.865696i | \(0.333124\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7807.58 | 1.09259 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7119.57 | −0.988303 | −0.494152 | − | 0.869376i | \(-0.664521\pi\) | ||||
−0.494152 | + | 0.869376i | \(0.664521\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13448.4 | 1.83720 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3372.29 | −0.457053 | −0.228526 | − | 0.973538i | \(-0.573391\pi\) | ||||
−0.228526 | + | 0.973538i | \(0.573391\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3958.63 | −0.528138 | −0.264069 | − | 0.964504i | \(-0.585065\pi\) | ||||
−0.264069 | + | 0.964504i | \(0.585065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3536.23 | 0.468111 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9654.01 | 1.25830 | 0.629148 | − | 0.777285i | \(-0.283404\pi\) | ||||
0.629148 | + | 0.777285i | \(0.283404\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10553.4 | 1.36499 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 122.148 | 0.0155593 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10928.3 | 1.38155 | 0.690776 | − | 0.723068i | \(-0.257269\pi\) | ||||
0.690776 | + | 0.723068i | \(0.257269\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4085.57 | 0.508787 | 0.254393 | − | 0.967101i | \(-0.418124\pi\) | ||||
0.254393 | + | 0.967101i | \(0.418124\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1193.38 | −0.147510 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9785.34 | −1.19175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10156.3 | 1.22786 | 0.613930 | − | 0.789361i | \(-0.289588\pi\) | ||||
0.613930 | + | 0.789361i | \(0.289588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10507.5 | 1.25191 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2729.29 | −0.322833 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15878.8 | −1.85139 | −0.925693 | − | 0.378275i | \(-0.876517\pi\) | ||||
−0.925693 | + | 0.378275i | \(0.876517\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2279.85 | −0.263926 | −0.131963 | − | 0.991255i | \(-0.542128\pi\) | ||||
−0.131963 | + | 0.991255i | \(0.542128\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1704.29 | 0.194519 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14508.6 | −1.64431 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1947.38 | 0.217638 | 0.108819 | − | 0.994062i | \(-0.465293\pi\) | ||||
0.108819 | + | 0.994062i | \(0.465293\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12636.2 | 1.40244 | 0.701219 | − | 0.712946i | \(-0.252639\pi\) | ||||
0.701219 | + | 0.712946i | \(0.252639\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16165.6 | −1.76957 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15849.8 | 1.72317 | 0.861585 | − | 0.507614i | \(-0.169472\pi\) | ||||
0.861585 | + | 0.507614i | \(0.169472\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17455.6 | 1.87210 | 0.936048 | − | 0.351872i | \(-0.114455\pi\) | ||||
0.936048 | + | 0.351872i | \(0.114455\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 420.666 | 0.0448123 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16068.1 | −1.68887 | −0.844435 | − | 0.535658i | \(-0.820064\pi\) | ||||
−0.844435 | + | 0.535658i | \(0.820064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5679.94 | −0.593033 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7978.25 | −0.822036 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11891.7 | 1.21722 | 0.608612 | − | 0.793468i | \(-0.291727\pi\) | ||||
0.608612 | + | 0.793468i | \(0.291727\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2802.23 | −0.283108 | −0.141554 | − | 0.989931i | \(-0.545210\pi\) | ||||
−0.141554 | + | 0.989931i | \(0.545210\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12933.3 | 1.29819 | 0.649096 | − | 0.760707i | \(-0.275147\pi\) | ||||
0.649096 | + | 0.760707i | \(0.275147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5748.11 | −0.569573 | −0.284787 | − | 0.958591i | \(-0.591923\pi\) | ||||
−0.284787 | + | 0.958591i | \(0.591923\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4779.65 | 0.470583 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9706.17 | −0.943531 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2610.60 | −0.252174 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11217.3 | 1.07000 | 0.535002 | − | 0.844851i | \(-0.320311\pi\) | ||||
0.535002 | + | 0.844851i | \(0.320311\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22077.2 | 2.09279 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4138.07 | −0.387423 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8905.12 | 0.828603 | 0.414301 | − | 0.910140i | \(-0.364026\pi\) | ||||
0.414301 | + | 0.910140i | \(0.364026\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6553.10 | 0.602316 | 0.301158 | − | 0.953574i | \(-0.402627\pi\) | ||||
0.301158 | + | 0.953574i | \(0.402627\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14020.1 | −1.28079 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10393.9 | 0.938087 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4610.09 | 0.413579 | 0.206789 | − | 0.978385i | \(-0.433698\pi\) | ||||
0.206789 | + | 0.978385i | \(0.433698\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13069.1 | −1.15850 | −0.579249 | − | 0.815151i | \(-0.696654\pi\) | ||||
−0.579249 | + | 0.815151i | \(0.696654\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4117.88 | −0.362858 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15930.8 | 1.38727 | 0.693635 | − | 0.720327i | \(-0.256008\pi\) | ||||
0.693635 | + | 0.720327i | \(0.256008\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22673.6 | −1.96286 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5855.95 | 0.501056 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 145.035 | 0.0123378 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3654.38 | 0.307296 | 0.153648 | − | 0.988126i | \(-0.450898\pi\) | ||||
0.153648 | + | 0.988126i | \(0.450898\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5138.66 | 0.429633 | 0.214816 | − | 0.976654i | \(-0.431085\pi\) | ||||
0.214816 | + | 0.976654i | \(0.431085\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1244.11 | 0.102836 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11798.1 | 0.969681 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12814.8 | 1.04141 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5116.04 | 0.413431 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7316.27 | 0.584664 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6932.06 | 0.550892 | 0.275446 | − | 0.961317i | \(-0.411175\pi\) | ||||
0.275446 | + | 0.961317i | \(0.411175\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2018.23 | 0.158627 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3423.11 | 0.267572 | 0.133786 | − | 0.991010i | \(-0.457287\pi\) | ||||
0.133786 | + | 0.991010i | \(0.457287\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21475.6 | 1.66042 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 596.115 | 0.0458398 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24489.2 | −1.86291 | −0.931455 | − | 0.363856i | \(-0.881460\pi\) | ||||
−0.931455 | + | 0.363856i | \(0.881460\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21898.6 | 1.65691 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10053.1 | 0.752552 | 0.376276 | − | 0.926508i | \(-0.377204\pi\) | ||||
0.376276 | + | 0.926508i | \(0.377204\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5411.02 | −0.402908 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6670.45 | −0.491459 | −0.245729 | − | 0.969338i | \(-0.579027\pi\) | ||||
−0.245729 | + | 0.969338i | \(0.579027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4633.55 | −0.339594 | −0.169797 | − | 0.985479i | \(-0.554311\pi\) | ||||
−0.169797 | + | 0.985479i | \(0.554311\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3870.17 | 0.280691 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7045.15 | 0.508307 | 0.254154 | − | 0.967164i | \(-0.418203\pi\) | ||||
0.254154 | + | 0.967164i | \(0.418203\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13319.7 | −0.951108 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9273.82 | −0.658804 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8001.06 | 0.562588 | 0.281294 | − | 0.959622i | \(-0.409236\pi\) | ||||
0.281294 | + | 0.959622i | \(0.409236\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1905.71 | −0.133316 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6747.53 | 0.467265 | 0.233632 | − | 0.972325i | \(-0.424939\pi\) | ||||
0.233632 | + | 0.972325i | \(0.424939\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8317.41 | 0.573077 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21547.3 | −1.46978 | −0.734890 | − | 0.678186i | \(-0.762766\pi\) | ||||
−0.734890 | + | 0.678186i | \(0.762766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12155.1 | −0.824983 | −0.412492 | − | 0.910961i | \(-0.635341\pi\) | ||||
−0.412492 | + | 0.910961i | \(0.635341\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2454.68 | 0.164953 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16348.9 | −1.09322 | −0.546608 | − | 0.837388i | \(-0.684081\pi\) | ||||
−0.546608 | + | 0.837388i | \(0.684081\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −327.220 | −0.0216660 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29955.5 | −1.97372 | −0.986859 | − | 0.161581i | \(-0.948341\pi\) | ||||
−0.986859 | + | 0.161581i | \(0.948341\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2159.74 | 0.140921 | 0.0704603 | − | 0.997515i | \(-0.477553\pi\) | ||||
0.0704603 | + | 0.997515i | \(0.477553\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22100.8 | −1.43507 | −0.717535 | − | 0.696523i | \(-0.754730\pi\) | ||||
−0.717535 | + | 0.696523i | \(0.754730\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2052.96 | 0.132023 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23015.7 | −1.45898 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18360.1 | −1.15833 | −0.579164 | − | 0.815211i | \(-0.696621\pi\) | ||||
−0.579164 | + | 0.815211i | \(0.696621\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3870.66 | −0.241893 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16506.6 | −1.02671 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21064.5 | −1.29797 | −0.648985 | − | 0.760802i | \(-0.724806\pi\) | ||||
−0.648985 | + | 0.760802i | \(0.724806\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10539.1 | 0.646381 | 0.323190 | − | 0.946334i | \(-0.395245\pi\) | ||||
0.323190 | + | 0.946334i | \(0.395245\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22553.4 | −1.37043 | −0.685213 | − | 0.728343i | \(-0.740291\pi\) | ||||
−0.685213 | + | 0.728343i | \(0.740291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12480.8 | −0.754873 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22624.0 | 1.35582 | 0.677908 | − | 0.735147i | \(-0.262887\pi\) | ||||
0.677908 | + | 0.735147i | \(0.262887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6070.19 | −0.362110 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6376.60 | −0.376930 | −0.188465 | − | 0.982080i | \(-0.560351\pi\) | ||||
−0.188465 | + | 0.982080i | \(0.560351\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22097.5 | −1.30029 | −0.650146 | − | 0.759809i | \(-0.725292\pi\) | ||||
−0.650146 | + | 0.759809i | \(0.725292\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12740.4 | −0.742938 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31837.2 | −1.84819 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17233.3 | 0.991479 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24033.0 | 1.37653 | 0.688264 | − | 0.725461i | \(-0.258373\pi\) | ||||
0.688264 | + | 0.725461i | \(0.258373\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 179.638 | 0.0101980 | 0.00509901 | − | 0.999987i | \(-0.498377\pi\) | ||||
0.00509901 | + | 0.999987i | \(0.498377\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20194.9 | −1.14140 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30434.2 | 1.70502 | 0.852511 | − | 0.522709i | \(-0.175079\pi\) | ||||
0.852511 | + | 0.522709i | \(0.175079\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11500.7 | −0.641490 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20923.1 | 1.15691 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9792.73 | −0.539122 | −0.269561 | − | 0.962983i | \(-0.586879\pi\) | ||||
−0.269561 | + | 0.962983i | \(0.586879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6779.63 | −0.370023 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13359.6 | −0.726010 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8130.47 | 0.438065 | 0.219032 | − | 0.975718i | \(-0.429710\pi\) | ||||
0.219032 | + | 0.975718i | \(0.429710\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35255.0 | 1.89142 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20096.4 | −1.06903 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4859.95 | −0.257432 | −0.128716 | − | 0.991681i | \(-0.541086\pi\) | ||||
−0.128716 | + | 0.991681i | \(0.541086\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2825.17 | 0.148392 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9476.55 | 0.495669 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19463.0 | −1.00952 | −0.504762 | − | 0.863259i | \(-0.668420\pi\) | ||||
−0.504762 | + | 0.863259i | \(0.668420\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28578.6 | 1.47618 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5141.44 | −0.263377 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2432.66 | −0.124102 | −0.0620512 | − | 0.998073i | \(-0.519764\pi\) | ||||
−0.0620512 | + | 0.998073i | \(0.519764\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22829.5 | −1.15510 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17967.6 | −0.905386 | −0.452693 | − | 0.891666i | \(-0.649537\pi\) | ||||
−0.452693 | + | 0.891666i | \(0.649537\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5677.26 | −0.283751 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23473.0 | −1.16843 | −0.584214 | − | 0.811599i | \(-0.698597\pi\) | ||||
−0.584214 | + | 0.811599i | \(0.698597\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33559.2 | 1.65702 | 0.828512 | − | 0.559971i | \(-0.189188\pi\) | ||||
0.828512 | + | 0.559971i | \(0.189188\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1299.23 | −0.0638925 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24967.6 | 1.21802 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7782.75 | 0.378158 | 0.189079 | − | 0.981962i | \(-0.439450\pi\) | ||||
0.189079 | + | 0.981962i | \(0.439450\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2541.52 | −0.122510 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38154.3 | −1.83189 | −0.915946 | − | 0.401300i | \(-0.868558\pi\) | ||||
−0.915946 | + | 0.401300i | \(0.868558\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19867.1 | 0.946363 | 0.473182 | − | 0.880965i | \(-0.343105\pi\) | ||||
0.473182 | + | 0.880965i | \(0.343105\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9849.52 | 0.467335 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28158.5 | 1.32561 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15710.8 | −0.736730 | −0.368365 | − | 0.929681i | \(-0.620082\pi\) | ||||
−0.368365 | + | 0.929681i | \(0.620082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25811.9 | 1.20102 | 0.600510 | − | 0.799617i | \(-0.294964\pi\) | ||||
0.600510 | + | 0.799617i | \(0.294964\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 456.242 | 0.0211467 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20463.9 | 0.941201 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12345.8 | −0.565645 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 116.526 | 0.00529807 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29242.6 | 1.32450 | 0.662252 | − | 0.749281i | \(-0.269601\pi\) | ||||
0.662252 | + | 0.749281i | \(0.269601\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26407.2 | −1.18702 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38880.8 | −1.74111 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32573.7 | 1.44771 | 0.723853 | − | 0.689955i | \(-0.242370\pi\) | ||||
0.723853 | + | 0.689955i | \(0.242370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 341.130 | 0.0151043 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26931.6 | 1.18356 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18887.5 | 0.826951 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34644.9 | −1.50562 | −0.752812 | − | 0.658236i | \(-0.771303\pi\) | ||||
−0.752812 | + | 0.658236i | \(0.771303\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29057.9 | 1.25815 | 0.629077 | − | 0.777343i | \(-0.283433\pi\) | ||||
0.629077 | + | 0.777343i | \(0.283433\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20160.5 | −0.866493 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34969.8 | 1.49748 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46709.5 | 1.98560 | 0.992798 | − | 0.119802i | \(-0.0382259\pi\) | ||||
0.992798 | + | 0.119802i | \(0.0382259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3468.10 | 0.146890 | 0.0734450 | − | 0.997299i | \(-0.476601\pi\) | ||||
0.0734450 | + | 0.997299i | \(0.476601\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42454.9 | −1.78513 | −0.892564 | − | 0.450920i | \(-0.851096\pi\) | ||||
−0.892564 | + | 0.450920i | \(0.851096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3933.47 | −0.164795 | −0.0823975 | − | 0.996600i | \(-0.526258\pi\) | ||||
−0.0823975 | + | 0.996600i | \(0.526258\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17208.3 | 0.715764 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3359.55 | −0.139236 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32959.6 | 1.35625 | 0.678123 | − | 0.734948i | \(-0.262794\pi\) | ||||
0.678123 | + | 0.734948i | \(0.262794\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17906.1 | 0.734188 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10395.5 | −0.423215 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11979.5 | 0.485974 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −52264.8 | −2.10530 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38845.8 | 1.55927 | 0.779634 | − | 0.626235i | \(-0.215405\pi\) | ||||
0.779634 | + | 0.626235i | \(0.215405\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29305.3 | −1.16809 | −0.584043 | − | 0.811723i | \(-0.698530\pi\) | ||||
−0.584043 | + | 0.811723i | \(0.698530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 909.659 | 0.0361318 | 0.0180659 | − | 0.999837i | \(-0.494249\pi\) | ||||
0.0180659 | + | 0.999837i | \(0.494249\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47998.0 | −1.89324 | −0.946622 | − | 0.322346i | \(-0.895529\pi\) | ||||
−0.946622 | + | 0.322346i | \(0.895529\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8167.64 | −0.321050 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −708.065 | −0.0276403 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12808.7 | 0.498286 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3050.17 | 0.117845 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3258.01 | 0.125445 | 0.0627225 | − | 0.998031i | \(-0.480022\pi\) | ||||
0.0627225 | + | 0.998031i | \(0.480022\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33380.2 | −1.27651 | −0.638256 | − | 0.769824i | \(-0.720344\pi\) | ||||
−0.638256 | + | 0.769824i | \(0.720344\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33714.6 | −1.28492 | −0.642460 | − | 0.766319i | \(-0.722086\pi\) | ||||
−0.642460 | + | 0.766319i | \(0.722086\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6218.80 | 0.235408 | 0.117704 | − | 0.993049i | \(-0.462447\pi\) | ||||
0.117704 | + | 0.993049i | \(0.462447\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18889.8 | −0.712649 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −522.537 | −0.0195812 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1706.30 | 0.0637266 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3753.19 | −0.139239 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21812.6 | −0.806529 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8479.61 | 0.311460 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22878.6 | 0.837566 | 0.418783 | − | 0.908086i | \(-0.362457\pi\) | ||||
0.418783 | + | 0.908086i | \(0.362457\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30144.8 | 1.09631 | 0.548157 | − | 0.836376i | \(-0.315330\pi\) | ||||
0.548157 | + | 0.836376i | \(0.315330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15821.1 | 0.573496 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29624.1 | −1.06682 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3803.52 | −0.136525 | −0.0682625 | − | 0.997667i | \(-0.521746\pi\) | ||||
−0.0682625 | + | 0.997667i | \(0.521746\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27854.0 | 0.993312 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8440.33 | −0.300018 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 125.985 | 0.00444934 | 0.00222467 | − | 0.999998i | \(-0.499292\pi\) | ||||
0.00222467 | + | 0.999998i | \(0.499292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26359.3 | −0.927918 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9879.41 | −0.345552 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28107.9 | 0.979984 | 0.489992 | − | 0.871727i | \(-0.337000\pi\) | ||||
0.489992 | + | 0.871727i | \(0.337000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49194.9 | −1.70426 | −0.852130 | − | 0.523330i | \(-0.824689\pi\) | ||||
−0.852130 | + | 0.523330i | \(0.824689\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30337.3 | −1.04763 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14498.0 | 0.497490 | 0.248745 | − | 0.968569i | \(-0.419982\pi\) | ||||
0.248745 | + | 0.968569i | \(0.419982\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60761.7 | −2.07841 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3201.79 | 0.108831 | 0.0544155 | − | 0.998518i | \(-0.482670\pi\) | ||||
0.0544155 | + | 0.998518i | \(0.482670\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3632.26 | −0.123075 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −56126.7 | −1.88991 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29457.9 | −0.988820 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21236.3 | −0.708415 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57781.9 | −1.92155 | −0.960776 | − | 0.277326i | \(-0.910552\pi\) | ||||
−0.960776 | + | 0.277326i | \(0.910552\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2611.60 | −0.0863133 | −0.0431566 | − | 0.999068i | \(-0.513741\pi\) | ||||
−0.0431566 | + | 0.999068i | \(0.513741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33086.4 | −1.09013 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33598.3 | −1.10021 | −0.550104 | − | 0.835096i | \(-0.685412\pi\) | ||||
−0.550104 | + | 0.835096i | \(0.685412\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2438.51 | −0.0796067 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39484.8 | 1.28115 | 0.640575 | − | 0.767895i | \(-0.278696\pi\) | ||||
0.640575 | + | 0.767895i | \(0.278696\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13392.6 | −0.433222 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51841.9 | −1.66681 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39918.6 | −1.27957 | −0.639786 | − | 0.768553i | \(-0.720977\pi\) | ||||
−0.639786 | + | 0.768553i | \(0.720977\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7432.41 | 0.236807 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25670.3 | −0.815432 | −0.407716 | − | 0.913109i | \(-0.633675\pi\) | ||||
−0.407716 | + | 0.913109i | \(0.633675\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2160.4.a.be.1.1 | 3 | ||
3.2 | odd | 2 | 2160.4.a.bm.1.1 | 3 | |||
4.3 | odd | 2 | 135.4.a.g.1.3 | yes | 3 | ||
12.11 | even | 2 | 135.4.a.f.1.1 | ✓ | 3 | ||
20.3 | even | 4 | 675.4.b.k.649.1 | 6 | |||
20.7 | even | 4 | 675.4.b.k.649.6 | 6 | |||
20.19 | odd | 2 | 675.4.a.q.1.1 | 3 | |||
36.7 | odd | 6 | 405.4.e.r.271.1 | 6 | |||
36.11 | even | 6 | 405.4.e.t.271.3 | 6 | |||
36.23 | even | 6 | 405.4.e.t.136.3 | 6 | |||
36.31 | odd | 6 | 405.4.e.r.136.1 | 6 | |||
60.23 | odd | 4 | 675.4.b.l.649.6 | 6 | |||
60.47 | odd | 4 | 675.4.b.l.649.1 | 6 | |||
60.59 | even | 2 | 675.4.a.r.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.f.1.1 | ✓ | 3 | 12.11 | even | 2 | ||
135.4.a.g.1.3 | yes | 3 | 4.3 | odd | 2 | ||
405.4.e.r.136.1 | 6 | 36.31 | odd | 6 | |||
405.4.e.r.271.1 | 6 | 36.7 | odd | 6 | |||
405.4.e.t.136.3 | 6 | 36.23 | even | 6 | |||
405.4.e.t.271.3 | 6 | 36.11 | even | 6 | |||
675.4.a.q.1.1 | 3 | 20.19 | odd | 2 | |||
675.4.a.r.1.3 | 3 | 60.59 | even | 2 | |||
675.4.b.k.649.1 | 6 | 20.3 | even | 4 | |||
675.4.b.k.649.6 | 6 | 20.7 | even | 4 | |||
675.4.b.l.649.1 | 6 | 60.47 | odd | 4 | |||
675.4.b.l.649.6 | 6 | 60.23 | odd | 4 | |||
2160.4.a.be.1.1 | 3 | 1.1 | even | 1 | trivial | ||
2160.4.a.bm.1.1 | 3 | 3.2 | odd | 2 |