Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,4,Mod(1,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, 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("1440.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.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: | \(84.9627504083\) |
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 | \(\chi\) | \(=\) | 1440.1 |
$q$-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 | ||||||||
\(7\) | −12.8680 | −0.694805 | −0.347402 | − | 0.937716i | \(-0.612936\pi\) | ||||
−0.347402 | + | 0.937716i | \(0.612936\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | \(-0.689638\pi\) | ||||
−0.561142 | + | 0.827720i | \(0.689638\pi\) | |||||||
\(14\) | 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 | \(-0.551348\pi\) | ||||
−0.160614 | + | 0.987017i | \(0.551348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −136.340 | −1.23604 | −0.618018 | − | 0.786164i | \(-0.712064\pi\) | ||||
−0.618018 | + | 0.786164i | \(0.712064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −0.0384197 | −0.0192099 | − | 0.999815i | \(-0.506115\pi\) | ||||
−0.0192099 | + | 0.999815i | \(0.506115\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.1320 | 0.273070 | 0.136535 | − | 0.990635i | \(-0.456403\pi\) | ||||
0.136535 | + | 0.990635i | \(0.456403\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 64.3398 | 0.310726 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 344.227 | 1.52948 | 0.764738 | − | 0.644341i | \(-0.222868\pi\) | ||||
0.764738 | + | 0.644341i | \(0.222868\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 43.2078 | 0.164583 | 0.0822917 | − | 0.996608i | \(-0.473776\pi\) | ||||
0.0822917 | + | 0.996608i | \(0.473776\pi\) | |||||||
\(42\) | 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 | \(-0.657536\pi\) | ||||
−0.474955 | + | 0.880010i | \(0.657536\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −177.416 | −0.517246 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 455.208 | 1.17977 | 0.589883 | − | 0.807489i | \(-0.299174\pi\) | ||||
0.589883 | + | 0.807489i | \(0.299174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 248.680 | 0.609672 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 263.019 | 0.501901 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 704.528 | 1.28465 | 0.642327 | − | 0.766431i | \(-0.277969\pi\) | ||||
0.642327 | + | 0.766431i | \(0.277969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.485291\pi\) | ||||
0.0461938 | + | 0.998932i | \(0.485291\pi\) | |||||||
\(74\) | 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 | \(-0.401016\pi\) | ||||
0.305981 | + | 0.952038i | \(0.401016\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −227.697 | −0.301120 | −0.150560 | − | 0.988601i | \(-0.548108\pi\) | ||||
−0.150560 | + | 0.988601i | \(0.548108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 423.019 | 0.539799 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1032.87 | −1.23016 | −0.615079 | − | 0.788466i | \(-0.710876\pi\) | ||||
−0.615079 | + | 0.788466i | \(0.710876\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 676.905 | 0.779768 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 133.019 | 0.143658 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −152.416 | −0.159541 | −0.0797704 | − | 0.996813i | \(-0.525419\pi\) | ||||
−0.0797704 | + | 0.996813i | \(0.525419\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 290.753 | 0.286446 | 0.143223 | − | 0.989690i | \(-0.454253\pi\) | ||||
0.143223 | + | 0.989690i | \(0.454253\pi\) | |||||||
\(102\) | 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 | \(-0.937109\pi\) | ||||
−0.980545 | + | 0.196294i | \(0.937109\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1411.58 | 1.24042 | 0.620208 | − | 0.784438i | \(-0.287048\pi\) | ||||
0.620208 | + | 0.784438i | \(0.287048\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1557.81 | 1.29687 | 0.648436 | − | 0.761269i | \(-0.275423\pi\) | ||||
0.648436 | + | 0.761269i | \(0.275423\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 681.699 | 0.552772 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1088.68 | 0.838648 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1142.66 | 0.858499 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1920.19 | −1.34165 | −0.670825 | − | 0.741616i | \(-0.734060\pi\) | ||||
−0.670825 | + | 0.741616i | \(0.734060\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | \(-0.742352\pi\) | ||||
−0.689916 | + | 0.723890i | \(0.742352\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2616.30 | 1.52997 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.0000 | 0.0171818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2938.16 | 1.61546 | 0.807728 | − | 0.589555i | \(-0.200697\pi\) | ||||
0.807728 | + | 0.589555i | \(0.200697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1053.40 | −0.567710 | −0.283855 | − | 0.958867i | \(-0.591613\pi\) | ||||
−0.283855 | + | 0.958867i | \(0.591613\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −235.660 | −0.122121 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2789.43 | 1.41797 | 0.708985 | − | 0.705224i | \(-0.249154\pi\) | ||||
0.708985 | + | 0.705224i | \(0.249154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | \(-0.763178\pi\) | ||||
−0.735767 | + | 0.677234i | \(0.763178\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 570.169 | 0.259522 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −947.740 | −0.416505 | −0.208252 | − | 0.978075i | \(-0.566778\pi\) | ||||
−0.208252 | + | 0.978075i | \(0.566778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −321.699 | −0.138961 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 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 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1721.14 | −0.684002 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4207.85 | 1.64550 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(-0.696265\pi\) | ||||
−0.578253 | + | 0.815858i | \(0.696265\pi\) | |||||||
\(194\) | 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 | \(-0.674708\pi\) | ||||
−0.521717 | + | 0.853119i | \(0.674708\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 77.2078 | 0.0266942 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −216.039 | −0.0736039 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1323.17 | 0.437921 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3876.80 | −1.26488 | −0.632440 | − | 0.774609i | \(-0.717947\pi\) | ||||
−0.632440 | + | 0.774609i | \(0.717947\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1260.00 | −0.399680 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −606.493 | −0.189730 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | \(-0.290081\pi\) | ||||
0.612706 | + | 0.790311i | \(0.290081\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2036.12 | 0.587556 | 0.293778 | − | 0.955874i | \(-0.405087\pi\) | ||||
0.293778 | + | 0.955874i | \(0.405087\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4544.76 | 1.27784 | 0.638921 | − | 0.769273i | \(-0.279381\pi\) | ||||
0.638921 | + | 0.769273i | \(0.279381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1530.38 | 0.424812 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 887.078 | 0.231320 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1399.47 | 0.360510 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4110.83 | 0.963821 | 0.481910 | − | 0.876221i | \(-0.339943\pi\) | ||||
0.481910 | + | 0.876221i | \(0.339943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2276.04 | −0.527607 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4272.34 | 0.968361 | 0.484180 | − | 0.874968i | \(-0.339118\pi\) | ||||
0.484180 | + | 0.874968i | \(0.339118\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4396.64 | −0.985524 | −0.492762 | − | 0.870164i | \(-0.664013\pi\) | ||||
−0.492762 | + | 0.870164i | \(0.664013\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1243.40 | −0.272654 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3068.54 | −0.665598 | −0.332799 | − | 0.942998i | \(-0.607993\pi\) | ||||
−0.332799 | + | 0.942998i | \(0.607993\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2672.71 | −0.567405 | −0.283702 | − | 0.958912i | \(-0.591563\pi\) | ||||
−0.283702 | + | 0.958912i | \(0.591563\pi\) | |||||||
\(282\) | 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 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −40.7922 | −0.00813347 | −0.00406674 | − | 0.999992i | \(-0.501294\pi\) | ||||
−0.00406674 | + | 0.999992i | \(0.501294\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3540.76 | 0.698816 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7172.00 | 1.38718 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3242.73 | −0.620956 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3260.19 | 0.612060 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7126.80 | 1.32491 | 0.662456 | − | 0.749101i | \(-0.269514\pi\) | ||||
0.662456 | + | 0.749101i | \(0.269514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(-0.339735\pi\) | ||||
0.482482 | + | 0.875906i | \(0.339735\pi\) | |||||||
\(314\) | 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 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2250.79 | 0.387732 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1315.10 | −0.224457 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3938.57 | 0.660001 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2361.55 | 0.392152 | 0.196076 | − | 0.980589i | \(-0.437180\pi\) | ||||
0.196076 | + | 0.980589i | \(0.437180\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3522.64 | −0.574515 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5117.10 | 0.827141 | 0.413570 | − | 0.910472i | \(-0.364282\pi\) | ||||
0.413570 | + | 0.910472i | \(0.364282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 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 | \(-0.656062\pi\) | ||||
−0.470876 | + | 0.882199i | \(0.656062\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7827.52 | 1.20057 | 0.600283 | − | 0.799788i | \(-0.295055\pi\) | ||||
0.600283 | + | 0.799788i | \(0.295055\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2515.47 | −0.379278 | −0.189639 | − | 0.981854i | \(-0.560732\pi\) | ||||
−0.189639 | + | 0.981854i | \(0.560732\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2658.87 | −0.397517 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −288.117 | −0.0413170 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12237.6 | 1.74060 | 0.870298 | − | 0.492525i | \(-0.163926\pi\) | ||||
0.870298 | + | 0.492525i | \(0.163926\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5857.60 | −0.819707 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3825.20 | 0.530996 | 0.265498 | − | 0.964111i | \(-0.414464\pi\) | ||||
0.265498 | + | 0.964111i | \(0.414464\pi\) | |||||||
\(374\) | 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 | \(-0.687481\pi\) | ||||
−0.555519 | + | 0.831504i | \(0.687481\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −452.196 | −0.0603294 | −0.0301647 | − | 0.999545i | \(-0.509603\pi\) | ||||
−0.0301647 | + | 0.999545i | \(0.509603\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3200.00 | −0.423603 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6816.13 | −0.888410 | −0.444205 | − | 0.895925i | \(-0.646514\pi\) | ||||
−0.444205 | + | 0.895925i | \(0.646514\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11534.9 | 1.49193 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2148.50 | −0.273677 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13380.3 | 1.69153 | 0.845766 | − | 0.533554i | \(-0.179144\pi\) | ||||
0.845766 | + | 0.533554i | \(0.179144\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6130.00 | −0.763386 | −0.381693 | − | 0.924289i | \(-0.624659\pi\) | ||||
−0.381693 | + | 0.924289i | \(0.624659\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9112.47 | 1.08570 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1138.49 | 0.134665 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2115.10 | −0.241405 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8390.41 | 0.950914 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(-0.693148\pi\) | ||||
−0.570237 | + | 0.821481i | \(0.693148\pi\) | |||||||
\(434\) | 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 | \(-0.219888\pi\) | ||||
0.770738 | + | 0.637152i | \(0.219888\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13395.6 | −1.43666 | −0.718332 | − | 0.695700i | \(-0.755094\pi\) | ||||
−0.718332 | + | 0.695700i | \(0.755094\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5164.35 | 0.550143 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9490.39 | 0.997504 | 0.498752 | − | 0.866745i | \(-0.333792\pi\) | ||||
0.498752 | + | 0.866745i | \(0.333792\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2148.98 | −0.224371 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3384.52 | −0.348723 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 587.064 | 0.0600913 | 0.0300456 | − | 0.999549i | \(-0.490435\pi\) | ||||
0.0300456 | + | 0.999549i | \(0.490435\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2800.42 | −0.282925 | −0.141462 | − | 0.989944i | \(-0.545180\pi\) | ||||
−0.141462 | + | 0.989944i | \(0.545180\pi\) | |||||||
\(462\) | 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 | \(-0.734318\pi\) | ||||
−0.671427 | + | 0.741071i | \(0.734318\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9065.84 | −0.892584 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12533.5 | −1.21837 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −665.097 | −0.0642458 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 762.078 | 0.0713488 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7958.52 | 0.740524 | 0.370262 | − | 0.928927i | \(-0.379268\pi\) | ||||
0.370262 | + | 0.928927i | \(0.379268\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | \(-0.792220\pi\) | ||||
−0.794411 | + | 0.607381i | \(0.792220\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2279.89 | 0.202098 | 0.101049 | − | 0.994881i | \(-0.467780\pi\) | ||||
0.101049 | + | 0.994881i | \(0.467780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1453.77 | −0.128103 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3254.99 | 0.283447 | 0.141724 | − | 0.989906i | \(-0.454736\pi\) | ||||
0.141724 | + | 0.989906i | \(0.454736\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −741.495 | −0.0641914 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.1066 | 0.00240490 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15223.0 | 1.29498 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21591.2 | −1.81560 | −0.907799 | − | 0.419406i | \(-0.862238\pi\) | ||||
−0.907799 | + | 0.419406i | \(0.862238\pi\) | |||||||
\(522\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2272.90 | −0.184709 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10852.8 | 0.877026 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7057.92 | −0.554731 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16579.7 | −1.29597 | −0.647987 | − | 0.761652i | \(-0.724389\pi\) | ||||
−0.647987 | + | 0.761652i | \(0.724389\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 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 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15561.2 | 1.16488 | 0.582441 | − | 0.812873i | \(-0.302098\pi\) | ||||
0.582441 | + | 0.812873i | \(0.302098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7789.06 | −0.579979 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11871.6 | −0.874662 | −0.437331 | − | 0.899301i | \(-0.644076\pi\) | ||||
−0.437331 | + | 0.899301i | \(0.644076\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18660.0 | 1.36759 | 0.683797 | − | 0.729672i | \(-0.260327\pi\) | ||||
0.683797 | + | 0.729672i | \(0.260327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3408.50 | −0.247207 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7549.12 | −0.544669 | −0.272334 | − | 0.962203i | \(-0.587796\pi\) | ||||
−0.272334 | + | 0.962203i | \(0.587796\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 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 | \(-0.449277\pi\) | ||||
0.158678 | + | 0.987330i | \(0.449277\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1253.90 | −0.0877179 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8335.46 | −0.577228 | −0.288614 | − | 0.957445i | \(-0.593194\pi\) | ||||
−0.288614 | + | 0.957445i | \(0.593194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5443.40 | −0.375055 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5713.31 | −0.383932 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8879.17 | 0.593730 | 0.296865 | − | 0.954919i | \(-0.404059\pi\) | ||||
0.296865 | + | 0.954919i | \(0.404059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16100.8 | 1.06607 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3846.28 | 0.253425 | 0.126713 | − | 0.991939i | \(-0.459557\pi\) | ||||
0.126713 | + | 0.991939i | \(0.459557\pi\) | |||||||
\(614\) | 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 | \(-0.377996\pi\) | ||||
0.373971 | + | 0.927440i | \(0.377996\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13290.9 | 0.854719 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29123.0 | −1.84612 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9053.33 | −0.571169 | −0.285584 | − | 0.958354i | \(-0.592188\pi\) | ||||
−0.285584 | + | 0.958354i | \(0.592188\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9600.96 | 0.600004 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9332.75 | 0.580498 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1700.77 | −0.104799 | −0.0523996 | − | 0.998626i | \(-0.516687\pi\) | ||||
−0.0523996 | + | 0.998626i | \(0.516687\pi\) | |||||||
\(642\) | 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 | \(-0.389663\pi\) | ||||
0.339734 | + | 0.940522i | \(0.389663\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35220.6 | 2.13024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20720.5 | −1.24174 | −0.620869 | − | 0.783915i | \(-0.713220\pi\) | ||||
−0.620869 | + | 0.783915i | \(0.713220\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3001.51 | 0.179052 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1711.69 | −0.0998142 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 818.039 | 0.0474881 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32429.8 | 1.86578 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12111.4 | −0.693702 | −0.346851 | − | 0.937920i | \(-0.612749\pi\) | ||||
−0.346851 | + | 0.937920i | \(0.612749\pi\) | |||||||
\(674\) | 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 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24838.1 | −1.39151 | −0.695755 | − | 0.718279i | \(-0.744930\pi\) | ||||
−0.695755 | + | 0.718279i | \(0.744930\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9767.56 | −0.544817 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23945.7 | −1.32403 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6857.65 | −0.377536 | −0.188768 | − | 0.982022i | \(-0.560449\pi\) | ||||
−0.188768 | + | 0.982022i | \(0.560449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11306.2 | 0.617079 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3655.55 | −0.198657 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32760.0 | −1.76509 | −0.882545 | − | 0.470228i | \(-0.844172\pi\) | ||||
−0.882545 | + | 0.470228i | \(0.844172\pi\) | |||||||
\(702\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6425.97 | −0.337524 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13081.5 | −0.684225 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −150.000 | −0.00768395 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23907.3 | −1.21963 | −0.609816 | − | 0.792543i | \(-0.708757\pi\) | ||||
−0.609816 | + | 0.792543i | \(0.708757\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21320.2 | −1.07874 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28946.6 | −1.45862 | −0.729309 | − | 0.684185i | \(-0.760158\pi\) | ||||
−0.729309 | + | 0.684185i | \(0.760158\pi\) | |||||||
\(734\) | 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 | \(-0.923984\pi\) | ||||
−0.971620 | + | 0.236547i | \(0.923984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4175.77 | −0.206183 | −0.103092 | − | 0.994672i | \(-0.532874\pi\) | ||||
−0.103092 | + | 0.994672i | \(0.532874\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14690.8 | −0.722454 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27930.8 | 1.36257 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22219.1 | −1.07961 | −0.539805 | − | 0.841790i | \(-0.681502\pi\) | ||||
−0.539805 | + | 0.841790i | \(0.681502\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5266.98 | 0.253887 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22514.1 | 1.08096 | 0.540482 | − | 0.841355i | \(-0.318242\pi\) | ||||
0.540482 | + | 0.841355i | \(0.318242\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26354.3 | 1.25538 | 0.627689 | − | 0.778465i | \(-0.284001\pi\) | ||||
0.627689 | + | 0.778465i | \(0.284001\pi\) | |||||||
\(762\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28023.6 | 1.30393 | 0.651965 | − | 0.758249i | \(-0.273945\pi\) | ||||
0.651965 | + | 0.758249i | \(0.273945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1178.30 | 0.0546140 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1149.49 | −0.0528690 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26448.3 | −1.21177 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13947.2 | −0.634135 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16361.2 | −0.741061 | −0.370530 | − | 0.928820i | \(-0.620824\pi\) | ||||
−0.370530 | + | 0.928820i | \(0.620824\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2865.95 | −0.125949 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8772.08 | −0.384068 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29390.4 | 1.27727 | 0.638635 | − | 0.769510i | \(-0.279499\pi\) | ||||
0.638635 | + | 0.769510i | \(0.279499\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17296.9 | 0.748924 | 0.374462 | − | 0.927242i | \(-0.377827\pi\) | ||||
0.374462 | + | 0.927242i | \(0.377827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10851.7 | −0.466404 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6704.18 | −0.287086 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19989.1 | −0.849725 | −0.424862 | − | 0.905258i | \(-0.639678\pi\) | ||||
−0.424862 | + | 0.905258i | \(0.639678\pi\) | |||||||
\(822\) | 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 | \(-0.669317\pi\) | ||||
−0.507193 | + | 0.861833i | \(0.669317\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43594.3 | 1.82641 | 0.913204 | − | 0.407503i | \(-0.133600\pi\) | ||||
0.913204 | + | 0.407503i | \(0.133600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15010.0 | 0.624330 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15878.7 | 0.658090 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2850.84 | −0.116062 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14703.7 | −0.596489 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46931.9 | −1.89049 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2147.83 | −0.0862136 | −0.0431068 | − | 0.999070i | \(-0.513726\pi\) | ||||
−0.0431068 | + | 0.999070i | \(0.513726\pi\) | |||||||
\(854\) | 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 | \(-0.301806\pi\) | ||||
0.583187 | + | 0.812338i | \(0.301806\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44989.3 | 1.77457 | 0.887285 | − | 0.461221i | \(-0.152588\pi\) | ||||
0.887285 | + | 0.461221i | \(0.152588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4738.70 | 0.186267 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21371.5 | −0.834267 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37060.9 | −1.44175 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1608.50 | 0.0621452 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36547.6 | 1.40721 | 0.703606 | − | 0.710590i | \(-0.251572\pi\) | ||||
0.703606 | + | 0.710590i | \(0.251572\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21146.4 | −0.808672 | −0.404336 | − | 0.914610i | \(-0.632497\pi\) | ||||
−0.404336 | + | 0.914610i | \(0.632497\pi\) | |||||||
\(882\) | 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 | \(-0.291622\pi\) | ||||
0.608873 | + | 0.793268i | \(0.291622\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24709.0 | 0.932184 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8142.80 | 0.305138 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15017.4 | −0.560866 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −282.792 | −0.0104913 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38512.3 | −1.42401 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7514.54 | −0.276013 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10810.4 | 0.395759 | 0.197880 | − | 0.980226i | \(-0.436595\pi\) | ||||
0.197880 | + | 0.980226i | \(0.436595\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | \(-0.289902\pi\) | ||||
0.613151 | + | 0.789966i | \(0.289902\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27973.4 | −0.997569 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8605.68 | 0.305895 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35758.6 | 1.26287 | 0.631433 | − | 0.775431i | \(-0.282467\pi\) | ||||
0.631433 | + | 0.775431i | \(0.282467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4719.94 | 0.166155 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21039.3 | −0.735890 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40301.0 | 1.40510 | 0.702549 | − | 0.711635i | \(-0.252045\pi\) | ||||
0.702549 | + | 0.711635i | \(0.252045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48866.6 | −1.69289 | −0.846443 | − | 0.532480i | \(-0.821260\pi\) | ||||
−0.846443 | + | 0.532480i | \(0.821260\pi\) | |||||||
\(942\) | 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 | \(-0.238548\pi\) | ||||
0.732084 | + | 0.681214i | \(0.238548\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3031.21 | −0.103685 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42523.5 | 1.44541 | 0.722703 | − | 0.691158i | \(-0.242899\pi\) | ||||
0.722703 | + | 0.691158i | \(0.242899\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15720.0 | −0.532657 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25137.7 | −0.846444 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27569.6 | −0.925433 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15504.3 | 0.517205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13205.1 | −0.439138 | −0.219569 | − | 0.975597i | \(-0.570465\pi\) | ||||
−0.219569 | + | 0.975597i | \(0.570465\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12342.3 | 0.400467 | 0.200234 | − | 0.979748i | \(-0.435830\pi\) | ||||
0.200234 | + | 0.979748i | \(0.435830\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12815.7 | −0.414559 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34357.6 | −1.10466 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35095.4 | 1.12497 | 0.562484 | − | 0.826808i | \(-0.309846\pi\) | ||||
0.562484 | + | 0.826808i | \(0.309846\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14645.9 | 0.466638 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46486.0 | −1.47666 | −0.738328 | − | 0.674442i | \(-0.764384\pi\) | ||||
−0.738328 | + | 0.674442i | \(0.764384\pi\) | |||||||
\(998\) | 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 | 1440.4.a.y.1.1 | 2 | ||
3.2 | odd | 2 | 480.4.a.r.1.1 | yes | 2 | ||
4.3 | odd | 2 | 1440.4.a.s.1.2 | 2 | |||
12.11 | even | 2 | 480.4.a.o.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 2400.4.a.y.1.2 | 2 | |||
24.5 | odd | 2 | 960.4.a.bk.1.1 | 2 | |||
24.11 | even | 2 | 960.4.a.bn.1.2 | 2 | |||
60.59 | even | 2 | 2400.4.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.4.a.o.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
480.4.a.r.1.1 | yes | 2 | 3.2 | odd | 2 | ||
960.4.a.bk.1.1 | 2 | 24.5 | odd | 2 | |||
960.4.a.bn.1.2 | 2 | 24.11 | even | 2 | |||
1440.4.a.s.1.2 | 2 | 4.3 | odd | 2 | |||
1440.4.a.y.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2400.4.a.y.1.2 | 2 | 15.14 | odd | 2 | |||
2400.4.a.bb.1.1 | 2 | 60.59 | even | 2 |