Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2400,4,Mod(1,2400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, 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("2400.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2400.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: | \(141.604584014\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{89}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 22 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 480) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.21699\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.8680 | −0.694805 | −0.347402 | − | 0.937716i | \(-0.612936\pi\) | ||||
−0.347402 | + | 0.937716i | \(0.612936\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −49.7359 | −1.36327 | −0.681634 | − | 0.731693i | \(-0.738730\pi\) | ||||
−0.681634 | + | 0.731693i | \(0.738730\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.6039 | 1.12228 | 0.561142 | − | 0.827720i | \(-0.310362\pi\) | ||||
0.561142 | + | 0.827720i | \(0.310362\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −84.6039 | −1.20703 | −0.603513 | − | 0.797353i | \(-0.706233\pi\) | ||||
−0.603513 | + | 0.797353i | \(0.706233\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.6039 | 0.321229 | 0.160614 | − | 0.987017i | \(-0.448652\pi\) | ||||
0.160614 | + | 0.987017i | \(0.448652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −38.6039 | −0.401146 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 136.340 | 1.23604 | 0.618018 | − | 0.786164i | \(-0.287936\pi\) | ||||
0.618018 | + | 0.786164i | \(0.287936\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 0.0384197 | 0.0192099 | − | 0.999815i | \(-0.493885\pi\) | ||||
0.0192099 | + | 0.999815i | \(0.493885\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −47.1320 | −0.273070 | −0.136535 | − | 0.990635i | \(-0.543597\pi\) | ||||
−0.136535 | + | 0.990635i | \(0.543597\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −149.208 | −0.787083 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −344.227 | −1.52948 | −0.764738 | − | 0.644341i | \(-0.777132\pi\) | ||||
−0.764738 | + | 0.644341i | \(0.777132\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 157.812 | 0.647951 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −43.2078 | −0.164583 | −0.0822917 | − | 0.996608i | \(-0.526224\pi\) | ||||
−0.0822917 | + | 0.996608i | \(0.526224\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 252.000 | 0.893713 | 0.446856 | − | 0.894606i | \(-0.352544\pi\) | ||||
0.446856 | + | 0.894606i | \(0.352544\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 306.076 | 0.949909 | 0.474955 | − | 0.880010i | \(-0.342464\pi\) | ||||
0.474955 | + | 0.880010i | \(0.342464\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −177.416 | −0.517246 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −253.812 | −0.696877 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 455.208 | 1.17977 | 0.589883 | − | 0.807489i | \(-0.299174\pi\) | ||||
0.589883 | + | 0.807489i | \(0.299174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 79.8117 | 0.185462 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −708.151 | −1.56260 | −0.781301 | − | 0.624155i | \(-0.785443\pi\) | ||||
−0.781301 | + | 0.624155i | \(0.785443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −652.039 | −1.36861 | −0.684303 | − | 0.729197i | \(-0.739894\pi\) | ||||
−0.684303 | + | 0.729197i | \(0.739894\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −115.812 | −0.231602 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 704.528 | 1.28465 | 0.642327 | − | 0.766431i | \(-0.277969\pi\) | ||||
0.642327 | + | 0.766431i | \(0.277969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 409.019 | 0.713625 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 531.775 | 0.888874 | 0.444437 | − | 0.895810i | \(-0.353404\pi\) | ||||
0.444437 | + | 0.895810i | \(0.353404\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −57.6233 | −0.0923877 | −0.0461938 | − | 0.998932i | \(-0.514709\pi\) | ||||
−0.0461938 | + | 0.998932i | \(0.514709\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 640.000 | 0.947205 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −429.699 | −0.611961 | −0.305981 | − | 0.952038i | \(-0.598984\pi\) | ||||
−0.305981 | + | 0.952038i | \(0.598984\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 227.697 | 0.301120 | 0.150560 | − | 0.988601i | \(-0.451892\pi\) | ||||
0.150560 | + | 0.988601i | \(0.451892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.0000 | 0.0221816 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1032.87 | 1.23016 | 0.615079 | − | 0.788466i | \(-0.289124\pi\) | ||||
0.615079 | + | 0.788466i | \(0.289124\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −676.905 | −0.779768 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −141.396 | −0.157657 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 152.416 | 0.159541 | 0.0797704 | − | 0.996813i | \(-0.474581\pi\) | ||||
0.0797704 | + | 0.996813i | \(0.474581\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −447.623 | −0.454423 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −290.753 | −0.286446 | −0.143223 | − | 0.989690i | \(-0.545747\pi\) | ||||
−0.143223 | + | 0.989690i | \(0.545747\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.62132 | −0.00537753 | −0.00268876 | − | 0.999996i | \(-0.500856\pi\) | ||||
−0.00268876 | + | 0.999996i | \(0.500856\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2170.57 | 1.96109 | 0.980545 | − | 0.196294i | \(-0.0628908\pi\) | ||||
0.980545 | + | 0.196294i | \(0.0628908\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1411.58 | 1.24042 | 0.620208 | − | 0.784438i | \(-0.287048\pi\) | ||||
0.620208 | + | 0.784438i | \(0.287048\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1032.68 | −0.883043 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1557.81 | 1.29687 | 0.648436 | − | 0.761269i | \(-0.275423\pi\) | ||||
0.648436 | + | 0.761269i | \(0.275423\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 473.435 | 0.374095 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1088.68 | 0.838648 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1142.66 | 0.858499 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −129.623 | −0.0950223 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1920.19 | −1.34165 | −0.670825 | − | 0.741616i | \(-0.734060\pi\) | ||||
−0.670825 | + | 0.741616i | \(0.734060\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 756.000 | 0.515985 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −600.303 | −0.400372 | −0.200186 | − | 0.979758i | \(-0.564155\pi\) | ||||
−0.200186 | + | 0.979758i | \(0.564155\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −342.338 | −0.223191 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1953.51 | 1.21825 | 0.609124 | − | 0.793075i | \(-0.291521\pi\) | ||||
0.609124 | + | 0.793075i | \(0.291521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2261.25 | 1.37983 | 0.689916 | − | 0.723890i | \(-0.257648\pi\) | ||||
0.689916 | + | 0.723890i | \(0.257648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 918.227 | 0.548430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2616.30 | −1.52997 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −532.247 | −0.298632 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2938.16 | −1.61546 | −0.807728 | − | 0.589555i | \(-0.799303\pi\) | ||||
−0.807728 | + | 0.589555i | \(0.799303\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1053.40 | 0.567710 | 0.283855 | − | 0.958867i | \(-0.408387\pi\) | ||||
0.283855 | + | 0.958867i | \(0.408387\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −761.435 | −0.402342 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2789.43 | −1.41797 | −0.708985 | − | 0.705224i | \(-0.750846\pi\) | ||||
−0.708985 | + | 0.705224i | \(0.750846\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1365.62 | 0.681138 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1754.42 | −0.858803 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2170.35 | 1.04291 | 0.521456 | − | 0.853278i | \(-0.325389\pi\) | ||||
0.521456 | + | 0.853278i | \(0.325389\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3175.74 | 1.47153 | 0.735767 | − | 0.677234i | \(-0.236822\pi\) | ||||
0.735767 | + | 0.677234i | \(0.236822\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 570.169 | 0.259522 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 239.435 | 0.107076 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −947.740 | −0.416505 | −0.208252 | − | 0.978075i | \(-0.566778\pi\) | ||||
−0.208252 | + | 0.978075i | \(0.566778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2124.45 | −0.902168 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3003.47 | 1.25413 | 0.627067 | − | 0.778965i | \(-0.284255\pi\) | ||||
0.627067 | + | 0.778965i | \(0.284255\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1502.91 | 0.617184 | 0.308592 | − | 0.951194i | \(-0.400142\pi\) | ||||
0.308592 | + | 0.951194i | \(0.400142\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1956.12 | −0.790166 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4207.85 | 1.64550 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −347.435 | −0.133715 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3144.00 | 1.19106 | 0.595528 | − | 0.803334i | \(-0.296943\pi\) | ||||
0.595528 | + | 0.803334i | \(0.296943\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3100.87 | 1.15651 | 0.578253 | − | 0.815858i | \(-0.303735\pi\) | ||||
0.578253 | + | 0.815858i | \(0.303735\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2563.13 | 0.926982 | 0.463491 | − | 0.886102i | \(-0.346597\pi\) | ||||
0.463491 | + | 0.886102i | \(0.346597\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2929.17 | 1.04343 | 0.521717 | − | 0.853119i | \(-0.325292\pi\) | ||||
0.521717 | + | 0.853119i | \(0.325292\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2113.58 | 0.741695 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −77.2078 | −0.0266942 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1227.06 | 0.412012 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1323.17 | −0.437921 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3876.80 | 1.26488 | 0.632440 | − | 0.774609i | \(-0.282053\pi\) | ||||
0.632440 | + | 0.774609i | \(0.282053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1595.32 | 0.513192 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 606.493 | 0.189730 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −172.870 | −0.0533400 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4450.49 | −1.35463 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4268.94 | −1.28193 | −0.640963 | − | 0.767572i | \(-0.721465\pi\) | ||||
−0.640963 | + | 0.767572i | \(0.721465\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4191.03 | −1.22541 | −0.612706 | − | 0.790311i | \(-0.709919\pi\) | ||||
−0.612706 | + | 0.790311i | \(0.709919\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2036.12 | 0.587556 | 0.293778 | − | 0.955874i | \(-0.405087\pi\) | ||||
0.293778 | + | 0.955874i | \(0.405087\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1920.00 | 0.546869 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4544.76 | 1.27784 | 0.638921 | − | 0.769273i | \(-0.279381\pi\) | ||||
0.638921 | + | 0.769273i | \(0.279381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1289.10 | −0.353316 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2068.00 | 0.559697 | 0.279848 | − | 0.960044i | \(-0.409716\pi\) | ||||
0.279848 | + | 0.960044i | \(0.409716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1901.25 | −0.508175 | −0.254087 | − | 0.967181i | \(-0.581775\pi\) | ||||
−0.254087 | + | 0.967181i | \(0.581775\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1399.47 | 0.360510 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 683.091 | 0.173852 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3794.42 | −0.954191 | −0.477095 | − | 0.878852i | \(-0.658310\pi\) | ||||
−0.477095 | + | 0.878852i | \(0.658310\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6780.99 | −1.68505 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3103.33 | −0.753231 | −0.376616 | − | 0.926370i | \(-0.622912\pi\) | ||||
−0.376616 | + | 0.926370i | \(0.622912\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4429.50 | 1.06269 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 54.0000 | 0.0128066 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4110.83 | −0.963821 | −0.481910 | − | 0.876221i | \(-0.660057\pi\) | ||||
−0.481910 | + | 0.876221i | \(0.660057\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3098.61 | 0.710232 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4272.34 | −0.968361 | −0.484180 | − | 0.874968i | \(-0.660882\pi\) | ||||
−0.484180 | + | 0.874968i | \(0.660882\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4396.64 | 0.985524 | 0.492762 | − | 0.870164i | \(-0.335987\pi\) | ||||
0.492762 | + | 0.870164i | \(0.335987\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2030.71 | −0.450199 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3068.54 | 0.665598 | 0.332799 | − | 0.942998i | \(-0.392007\pi\) | ||||
0.332799 | + | 0.942998i | \(0.392007\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −424.188 | −0.0910233 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2672.71 | 0.567405 | 0.283702 | − | 0.958912i | \(-0.408437\pi\) | ||||
0.283702 | + | 0.958912i | \(0.408437\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6135.64 | −1.28878 | −0.644392 | − | 0.764696i | \(-0.722889\pi\) | ||||
−0.644392 | + | 0.764696i | \(0.722889\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 555.996 | 0.114353 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2244.82 | 0.456914 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 457.247 | 0.0921109 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −40.7922 | −0.00813347 | −0.00406674 | − | 0.999992i | \(-0.501294\pi\) | ||||
−0.00406674 | + | 0.999992i | \(0.501294\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1342.87 | −0.262361 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7172.00 | 1.38718 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3242.73 | −0.620956 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −872.260 | −0.165380 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7126.80 | 1.32491 | 0.662456 | − | 0.749101i | \(-0.269514\pi\) | ||||
0.662456 | + | 0.749101i | \(0.269514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.8640 | −0.00310472 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1704.52 | −0.310787 | −0.155393 | − | 0.987853i | \(-0.549665\pi\) | ||||
−0.155393 | + | 0.987853i | \(0.549665\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5343.52 | −0.964963 | −0.482482 | − | 0.875906i | \(-0.660265\pi\) | ||||
−0.482482 | + | 0.875906i | \(0.660265\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5644.19 | 1.00003 | 0.500015 | − | 0.866017i | \(-0.333328\pi\) | ||||
0.500015 | + | 0.866017i | \(0.333328\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −298.416 | −0.0523764 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6511.70 | 1.13224 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2250.79 | −0.387732 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4234.75 | 0.716154 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3938.57 | −0.660001 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2361.55 | −0.392152 | −0.196076 | − | 0.980589i | \(-0.562820\pi\) | ||||
−0.196076 | + | 0.980589i | \(0.562820\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3098.04 | −0.509825 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5117.10 | −0.827141 | −0.413570 | − | 0.910472i | \(-0.635718\pi\) | ||||
−0.413570 | + | 0.910472i | \(0.635718\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4673.43 | 0.748750 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2344.16 | 0.372267 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6696.69 | 1.05419 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6087.39 | 0.941753 | 0.470876 | − | 0.882199i | \(-0.343938\pi\) | ||||
0.470876 | + | 0.882199i | \(0.343938\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7827.52 | 1.20057 | 0.600283 | − | 0.799788i | \(-0.295055\pi\) | ||||
0.600283 | + | 0.799788i | \(0.295055\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1420.30 | 0.215984 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2515.47 | −0.379278 | −0.189639 | − | 0.981854i | \(-0.560732\pi\) | ||||
−0.189639 | + | 0.981854i | \(0.560732\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3266.04 | 0.484194 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −915.914 | −0.134652 | −0.0673261 | − | 0.997731i | \(-0.521447\pi\) | ||||
−0.0673261 | + | 0.997731i | \(0.521447\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6151.23 | −0.896812 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3427.99 | 0.495655 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12237.6 | 1.74060 | 0.870298 | − | 0.492525i | \(-0.163926\pi\) | ||||
0.870298 | + | 0.492525i | \(0.163926\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −388.870 | −0.0548611 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5857.60 | −0.819707 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3825.20 | −0.530996 | −0.265498 | − | 0.964111i | \(-0.585536\pi\) | ||||
−0.265498 | + | 0.964111i | \(0.585536\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 315.623 | 0.0431178 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8197.63 | 1.11104 | 0.555519 | − | 0.831504i | \(-0.312519\pi\) | ||||
0.555519 | + | 0.831504i | \(0.312519\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5760.58 | −0.774602 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 452.196 | 0.0603294 | 0.0301647 | − | 0.999545i | \(-0.490397\pi\) | ||||
0.0301647 | + | 0.999545i | \(0.490397\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2268.00 | 0.297904 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6816.13 | 0.888410 | 0.444205 | − | 0.895925i | \(-0.353486\pi\) | ||||
0.444205 | + | 0.895925i | \(0.353486\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11534.9 | −1.49193 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1800.91 | −0.231155 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13380.3 | −1.69153 | −0.845766 | − | 0.533554i | \(-0.820856\pi\) | ||||
−0.845766 | + | 0.533554i | \(0.820856\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1027.01 | −0.128860 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6130.00 | 0.763386 | 0.381693 | − | 0.924289i | \(-0.375341\pi\) | ||||
0.381693 | + | 0.924289i | \(0.375341\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2479.33 | −0.306462 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17120.5 | 2.08509 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15003.5 | −1.81387 | −0.906935 | − | 0.421270i | \(-0.861584\pi\) | ||||
−0.906935 | + | 0.421270i | \(0.861584\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5860.54 | 0.703355 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9112.47 | 1.08570 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6783.75 | 0.796646 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16300.7 | 1.90057 | 0.950287 | − | 0.311375i | \(-0.100790\pi\) | ||||
0.950287 | + | 0.311375i | \(0.100790\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7663.91 | 0.887211 | 0.443606 | − | 0.896222i | \(-0.353699\pi\) | ||||
0.443606 | + | 0.896222i | \(0.353699\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2754.68 | 0.316636 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8390.41 | 0.950914 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7848.91 | −0.883331 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3702.20 | 0.413755 | 0.206878 | − | 0.978367i | \(-0.433670\pi\) | ||||
0.206878 | + | 0.978367i | \(0.433670\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10275.8 | 1.14047 | 0.570237 | − | 0.821481i | \(-0.306852\pi\) | ||||
0.570237 | + | 0.821481i | \(0.306852\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3627.17 | 0.397050 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14178.6 | −1.54148 | −0.770738 | − | 0.637152i | \(-0.780112\pi\) | ||||
−0.770738 | + | 0.637152i | \(0.780112\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1596.74 | −0.172415 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13395.6 | 1.43666 | 0.718332 | − | 0.695700i | \(-0.244906\pi\) | ||||
0.718332 | + | 0.695700i | \(0.244906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8814.47 | −0.932684 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9490.39 | −0.997504 | −0.498752 | − | 0.866745i | \(-0.666208\pi\) | ||||
−0.498752 | + | 0.866745i | \(0.666208\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2148.98 | 0.224371 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3160.19 | 0.327767 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −587.064 | −0.0600913 | −0.0300456 | − | 0.999549i | \(-0.509565\pi\) | ||||
−0.0300456 | + | 0.999549i | \(0.509565\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2284.30 | −0.232292 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2800.42 | 0.282925 | 0.141462 | − | 0.989944i | \(-0.454820\pi\) | ||||
0.141462 | + | 0.989944i | \(0.454820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19745.6 | −1.98198 | −0.990988 | − | 0.133952i | \(-0.957233\pi\) | ||||
−0.990988 | + | 0.133952i | \(0.957233\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13552.0 | 1.34285 | 0.671427 | − | 0.741071i | \(-0.265682\pi\) | ||||
0.671427 | + | 0.741071i | \(0.265682\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9065.84 | −0.892584 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8368.30 | −0.818665 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12533.5 | −1.21837 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4096.87 | 0.393255 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14131.9 | −1.34803 | −0.674014 | − | 0.738719i | \(-0.735431\pi\) | ||||
−0.674014 | + | 0.738719i | \(0.735431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18107.7 | −1.71651 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5263.25 | −0.495830 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7958.52 | 0.740524 | 0.370262 | − | 0.928927i | \(-0.379268\pi\) | ||||
0.370262 | + | 0.928927i | \(0.379268\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6511.04 | 0.602125 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10984.3 | 1.00960 | 0.504799 | − | 0.863237i | \(-0.331567\pi\) | ||||
0.504799 | + | 0.863237i | \(0.331567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −507.623 | −0.0463736 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6842.86 | −0.617594 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17710.3 | 1.58882 | 0.794411 | − | 0.607381i | \(-0.207780\pi\) | ||||
0.794411 | + | 0.607381i | \(0.207780\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9527.23 | 0.849591 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2279.89 | −0.202098 | −0.101049 | − | 0.994881i | \(-0.532220\pi\) | ||||
−0.101049 | + | 0.994881i | \(0.532220\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1710.51 | 0.149835 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3254.99 | −0.283447 | −0.141724 | − | 0.989906i | \(-0.545264\pi\) | ||||
−0.141724 | + | 0.989906i | \(0.545264\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 741.495 | 0.0641914 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 718.305 | 0.0618205 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15223.0 | −1.29498 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2843.22 | −0.240469 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21591.2 | 1.81560 | 0.907799 | − | 0.419406i | \(-0.137762\pi\) | ||||
0.907799 | + | 0.419406i | \(0.137762\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16868.8 | 1.41037 | 0.705185 | − | 0.709024i | \(-0.250864\pi\) | ||||
0.705185 | + | 0.709024i | \(0.250864\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3987.55 | 0.329603 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6421.54 | 0.527784 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6373.36 | −0.520867 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2272.90 | −0.184709 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9010.42 | 0.724075 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8823.93 | 0.705145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4366.23 | −0.346985 | −0.173493 | − | 0.984835i | \(-0.555505\pi\) | ||||
−0.173493 | + | 0.984835i | \(0.555505\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4508.73 | 0.356331 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16579.7 | −1.29597 | −0.647987 | − | 0.761652i | \(-0.724389\pi\) | ||||
−0.647987 | + | 0.761652i | \(0.724389\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5868.35 | −0.456202 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 159.623 | 0.0123415 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5529.35 | 0.425193 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5971.66 | 0.454268 | 0.227134 | − | 0.973863i | \(-0.427064\pi\) | ||||
0.227134 | + | 0.973863i | \(0.427064\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13256.2 | 1.00300 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12623.6 | 0.950030 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15561.2 | −1.16488 | −0.582441 | − | 0.812873i | \(-0.697902\pi\) | ||||
−0.582441 | + | 0.812873i | \(0.697902\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1042.30 | −0.0772005 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11871.6 | 0.874662 | 0.437331 | − | 0.899301i | \(-0.355924\pi\) | ||||
0.437331 | + | 0.899301i | \(0.355924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18660.0 | −1.36759 | −0.683797 | − | 0.729672i | \(-0.739673\pi\) | ||||
−0.683797 | + | 0.729672i | \(0.739673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9432.00 | 0.687657 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7549.12 | 0.544669 | 0.272334 | − | 0.962203i | \(-0.412204\pi\) | ||||
0.272334 | + | 0.962203i | \(0.412204\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9302.61 | 0.667709 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2930.00 | −0.209220 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22640.2 | −1.60834 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4513.39 | −0.317355 | −0.158678 | − | 0.987330i | \(-0.550723\pi\) | ||||
−0.158678 | + | 0.987330i | \(0.550723\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1253.90 | −0.0877179 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7689.39 | 0.535193 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8335.46 | −0.577228 | −0.288614 | − | 0.957445i | \(-0.593194\pi\) | ||||
−0.288614 | + | 0.957445i | \(0.593194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8787.51 | 0.602427 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10806.9 | −0.737162 | −0.368581 | − | 0.929596i | \(-0.620156\pi\) | ||||
−0.368581 | + | 0.929596i | \(0.620156\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25653.1 | −1.74112 | −0.870559 | − | 0.492063i | \(-0.836243\pi\) | ||||
−0.870559 | + | 0.492063i | \(0.836243\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6340.75 | 0.428218 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8879.17 | 0.593730 | 0.296865 | − | 0.954919i | \(-0.404059\pi\) | ||||
0.296865 | + | 0.954919i | \(0.404059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −231.623 | −0.0154119 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16100.8 | 1.06607 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3846.28 | −0.253425 | −0.126713 | − | 0.991939i | \(-0.540443\pi\) | ||||
−0.126713 | + | 0.991939i | \(0.540443\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15821.2 | 1.03231 | 0.516156 | − | 0.856495i | \(-0.327363\pi\) | ||||
0.516156 | + | 0.856495i | \(0.327363\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11518.7 | −0.747942 | −0.373971 | − | 0.927440i | \(-0.622004\pi\) | ||||
−0.373971 | + | 0.927440i | \(0.622004\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3681.17 | 0.237875 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13290.9 | −0.854719 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3969.51 | −0.252834 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29123.0 | 1.84612 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9053.33 | 0.571169 | 0.285584 | − | 0.958354i | \(-0.407812\pi\) | ||||
0.285584 | + | 0.958354i | \(0.407812\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11630.4 | 0.730279 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9332.75 | −0.580498 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4785.97 | 0.296291 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1700.77 | 0.104799 | 0.0523996 | − | 0.998626i | \(-0.483313\pi\) | ||||
0.0523996 | + | 0.998626i | \(0.483313\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17275.1 | 1.05951 | 0.529755 | − | 0.848151i | \(-0.322284\pi\) | ||||
0.529755 | + | 0.848151i | \(0.322284\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11182.2 | −0.679468 | −0.339734 | − | 0.940522i | \(-0.610337\pi\) | ||||
−0.339734 | + | 0.940522i | \(0.610337\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35220.6 | 2.13024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1819.48 | 0.109541 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20720.5 | −1.24174 | −0.620869 | − | 0.783915i | \(-0.713220\pi\) | ||||
−0.620869 | + | 0.783915i | \(0.713220\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −518.610 | −0.0307959 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8745.26 | 0.516945 | 0.258473 | − | 0.966019i | \(-0.416781\pi\) | ||||
0.258473 | + | 0.966019i | \(0.416781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25921.8 | −1.52533 | −0.762663 | − | 0.646796i | \(-0.776108\pi\) | ||||
−0.762663 | + | 0.646796i | \(0.776108\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13351.5 | −0.782094 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 818.039 | 0.0474881 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12806.8 | −0.740120 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32429.8 | 1.86578 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12111.4 | 0.693702 | 0.346851 | − | 0.937920i | \(-0.387251\pi\) | ||||
0.346851 | + | 0.937920i | \(0.387251\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4961.50 | −0.281663 | −0.140832 | − | 0.990034i | \(-0.544978\pi\) | ||||
−0.140832 | + | 0.990034i | \(0.544978\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1961.28 | −0.110850 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12573.1 | −0.707492 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24838.1 | 1.39151 | 0.695755 | − | 0.718279i | \(-0.255070\pi\) | ||||
0.695755 | + | 0.718279i | \(0.255070\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6108.35 | 0.339226 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23945.7 | 1.32403 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6857.65 | 0.377536 | 0.188768 | − | 0.982022i | \(-0.439551\pi\) | ||||
0.188768 | + | 0.982022i | \(0.439551\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5760.00 | 0.315735 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3655.55 | 0.198657 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13634.3 | 0.737762 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32760.0 | 1.76509 | 0.882545 | − | 0.470228i | \(-0.155828\pi\) | ||||
0.882545 | + | 0.470228i | \(0.155828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9157.78 | −0.491312 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3741.40 | 0.199024 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8678.69 | 0.459711 | 0.229855 | − | 0.973225i | \(-0.426175\pi\) | ||||
0.229855 | + | 0.973225i | \(0.426175\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3867.29 | −0.203987 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6425.97 | −0.337524 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6203.99 | 0.323141 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8160.85 | 0.423294 | 0.211647 | − | 0.977346i | \(-0.432117\pi\) | ||||
0.211647 | + | 0.977346i | \(0.432117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 72.3349 | 0.00373633 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5703.74 | −0.293395 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23907.3 | −1.21963 | −0.609816 | − | 0.792543i | \(-0.708757\pi\) | ||||
−0.609816 | + | 0.792543i | \(0.708757\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21320.2 | −1.07874 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28946.6 | 1.45862 | 0.729309 | − | 0.684185i | \(-0.239842\pi\) | ||||
0.729309 | + | 0.684185i | \(0.239842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35040.4 | −1.75133 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39038.5 | 1.94324 | 0.971620 | − | 0.236547i | \(-0.0760157\pi\) | ||||
0.971620 | + | 0.236547i | \(0.0760157\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4198.40 | 0.208141 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4175.77 | 0.206183 | 0.103092 | − | 0.994672i | \(-0.467126\pi\) | ||||
0.103092 | + | 0.994672i | \(0.467126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2049.27 | 0.100373 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27930.8 | −1.36257 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22219.1 | 1.07961 | 0.539805 | − | 0.841790i | \(-0.318498\pi\) | ||||
0.539805 | + | 0.841790i | \(0.318498\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11383.3 | −0.550902 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22514.1 | −1.08096 | −0.540482 | − | 0.841355i | \(-0.681758\pi\) | ||||
−0.540482 | + | 0.841355i | \(0.681758\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20343.0 | −0.972863 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26354.3 | −1.25538 | −0.627689 | − | 0.778465i | \(-0.715999\pi\) | ||||
−0.627689 | + | 0.778465i | \(0.715999\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18164.2 | −0.861846 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37251.5 | −1.75368 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26226.3 | −1.22983 | −0.614917 | − | 0.788591i | \(-0.710811\pi\) | ||||
−0.614917 | + | 0.788591i | \(0.710811\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9309.99 | −0.434878 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28023.6 | 1.30393 | 0.651965 | − | 0.758249i | \(-0.273945\pi\) | ||||
0.651965 | + | 0.758249i | \(0.273945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13288.5 | 0.613543 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1149.49 | −0.0528690 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26448.3 | −1.21177 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 162.000 | 0.00739388 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16361.2 | −0.741061 | −0.370530 | − | 0.928820i | \(-0.620824\pi\) | ||||
−0.370530 | + | 0.928820i | \(0.620824\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12332.5 | −0.556462 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20045.9 | −0.901073 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34299.8 | −1.53597 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20999.9 | 0.933319 | 0.466660 | − | 0.884437i | \(-0.345457\pi\) | ||||
0.466660 | + | 0.884437i | \(0.345457\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25895.2 | −1.14657 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9295.83 | 0.410052 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2865.95 | 0.125949 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12817.0 | −0.559083 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29390.4 | −1.27727 | −0.638635 | − | 0.769510i | \(-0.720501\pi\) | ||||
−0.638635 | + | 0.769510i | \(0.720501\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17296.9 | −0.748924 | −0.374462 | − | 0.927242i | \(-0.622173\pi\) | ||||
−0.374462 | + | 0.927242i | \(0.622173\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13189.9 | 0.568993 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6704.18 | 0.287086 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6092.14 | −0.259923 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19989.1 | 0.849725 | 0.424862 | − | 0.905258i | \(-0.360322\pi\) | ||||
0.424862 | + | 0.905258i | \(0.360322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20226.7 | 0.856694 | 0.428347 | − | 0.903614i | \(-0.359096\pi\) | ||||
0.428347 | + | 0.903614i | \(0.359096\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24124.7 | 1.01439 | 0.507193 | − | 0.861833i | \(-0.330683\pi\) | ||||
0.507193 | + | 0.861833i | \(0.330683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43594.3 | 1.82641 | 0.913204 | − | 0.407503i | \(-0.133600\pi\) | ||||
0.913204 | + | 0.407503i | \(0.133600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9205.61 | 0.384283 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15010.0 | 0.624330 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1272.57 | −0.0525523 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29937.7 | −1.23190 | −0.615949 | − | 0.787786i | \(-0.711227\pi\) | ||||
−0.615949 | + | 0.787786i | \(0.711227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24353.0 | −0.998524 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8018.14 | 0.327591 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14703.7 | −0.596489 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18406.9 | −0.744079 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46931.9 | −1.89049 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2147.83 | 0.0862136 | 0.0431068 | − | 0.999070i | \(-0.486274\pi\) | ||||
0.0431068 | + | 0.999070i | \(0.486274\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15771.5 | −0.628638 | −0.314319 | − | 0.949317i | \(-0.601776\pi\) | ||||
−0.314319 | + | 0.949317i | \(0.601776\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29364.8 | −1.16637 | −0.583187 | − | 0.812338i | \(-0.698194\pi\) | ||||
−0.583187 | + | 0.812338i | \(0.698194\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1667.99 | 0.0660219 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44989.3 | −1.77457 | −0.887285 | − | 0.461221i | \(-0.847412\pi\) | ||||
−0.887285 | + | 0.461221i | \(0.847412\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6734.45 | 0.263799 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21371.5 | 0.834267 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37060.9 | 1.44175 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1371.74 | 0.0531803 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36547.6 | −1.40721 | −0.703606 | − | 0.710590i | \(-0.748428\pi\) | ||||
−0.703606 | + | 0.710590i | \(0.748428\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −122.377 | −0.00469586 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21146.4 | 0.808672 | 0.404336 | − | 0.914610i | \(-0.367503\pi\) | ||||
0.404336 | + | 0.914610i | \(0.367503\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39103.3 | 1.49030 | 0.745148 | − | 0.666899i | \(-0.232379\pi\) | ||||
0.745148 | + | 0.666899i | \(0.232379\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32169.3 | −1.21775 | −0.608873 | − | 0.793268i | \(-0.708378\pi\) | ||||
−0.608873 | + | 0.793268i | \(0.708378\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24709.0 | 0.932184 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4028.61 | −0.151474 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8142.80 | 0.305138 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21516.0 | 0.800890 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −282.792 | −0.0104913 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38512.3 | −1.42401 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9728.18 | −0.358509 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10810.4 | 0.395759 | 0.197880 | − | 0.980226i | \(-0.436595\pi\) | ||||
0.197880 | + | 0.980226i | \(0.436595\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2616.78 | −0.0954820 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −244.183 | −0.00888053 | −0.00444026 | − | 0.999990i | \(-0.501413\pi\) | ||||
−0.00444026 | + | 0.999990i | \(0.501413\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11324.7 | −0.410508 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7724.68 | 0.278180 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34164.1 | −1.22630 | −0.613151 | − | 0.789966i | \(-0.710098\pi\) | ||||
−0.613151 | + | 0.789966i | \(0.710098\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21380.4 | 0.764938 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27973.4 | 0.997569 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −50.5919 | −0.00179251 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35758.6 | −1.26287 | −0.631433 | − | 0.775431i | \(-0.717533\pi\) | ||||
−0.631433 | + | 0.775431i | \(0.717533\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4719.94 | −0.166155 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5113.57 | −0.179433 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40301.0 | −1.40510 | −0.702549 | − | 0.711635i | \(-0.747955\pi\) | ||||
−0.702549 | + | 0.711635i | \(0.747955\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16030.6 | −0.557122 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48866.6 | 1.69289 | 0.846443 | − | 0.532480i | \(-0.178740\pi\) | ||||
0.846443 | + | 0.532480i | \(0.178740\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5890.94 | −0.203431 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42669.4 | −1.46417 | −0.732084 | − | 0.681214i | \(-0.761452\pi\) | ||||
−0.732084 | + | 0.681214i | \(0.761452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3031.21 | −0.103685 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16932.6 | 0.577368 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42523.5 | 1.44541 | 0.722703 | − | 0.691158i | \(-0.242899\pi\) | ||||
0.722703 | + | 0.691158i | \(0.242899\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −895.247 | −0.0302395 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25137.7 | −0.846444 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27569.6 | −0.925433 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19535.1 | 0.653697 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13205.1 | −0.439138 | −0.219569 | − | 0.975597i | \(-0.570465\pi\) | ||||
−0.219569 | + | 0.975597i | \(0.570465\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6752.38 | −0.223857 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3545.55 | 0.117180 | 0.0585901 | − | 0.998282i | \(-0.481339\pi\) | ||||
0.0585901 | + | 0.998282i | \(0.481339\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29097.7 | −0.958713 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13070.8 | 0.428015 | 0.214008 | − | 0.976832i | \(-0.431348\pi\) | ||||
0.214008 | + | 0.976832i | \(0.431348\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51370.7 | −1.67703 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12704.3 | 0.413472 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12342.3 | −0.400467 | −0.200234 | − | 0.979748i | \(-0.564170\pi\) | ||||
−0.200234 | + | 0.979748i | \(0.564170\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11815.7 | −0.381052 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34357.6 | 1.10466 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35095.4 | −1.12497 | −0.562484 | − | 0.826808i | \(-0.690154\pi\) | ||||
−0.562484 | + | 0.826808i | \(0.690154\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7084.64 | −0.226409 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46486.0 | 1.47666 | 0.738328 | − | 0.674442i | \(-0.235616\pi\) | ||||
0.738328 | + | 0.674442i | \(0.235616\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9294.13 | −0.294348 |
(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 | 2400.4.a.bb.1.1 | 2 | ||
4.3 | odd | 2 | 2400.4.a.y.1.2 | 2 | |||
5.4 | even | 2 | 480.4.a.o.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 1440.4.a.s.1.2 | 2 | |||
20.19 | odd | 2 | 480.4.a.r.1.1 | yes | 2 | ||
40.19 | odd | 2 | 960.4.a.bk.1.1 | 2 | |||
40.29 | even | 2 | 960.4.a.bn.1.2 | 2 | |||
60.59 | even | 2 | 1440.4.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.4.a.o.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
480.4.a.r.1.1 | yes | 2 | 20.19 | odd | 2 | ||
960.4.a.bk.1.1 | 2 | 40.19 | odd | 2 | |||
960.4.a.bn.1.2 | 2 | 40.29 | even | 2 | |||
1440.4.a.s.1.2 | 2 | 15.14 | odd | 2 | |||
1440.4.a.y.1.1 | 2 | 60.59 | even | 2 | |||
2400.4.a.y.1.2 | 2 | 4.3 | odd | 2 | |||
2400.4.a.bb.1.1 | 2 | 1.1 | even | 1 | trivial |