Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{193}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.44622\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 | ||||||||
\(5\) | −1.44622 | −0.129354 | −0.0646770 | − | 0.997906i | \(-0.520602\pi\) | ||||
−0.0646770 | + | 0.997906i | \(0.520602\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −46.1236 | −1.26425 | −0.632126 | − | 0.774866i | \(-0.717818\pi\) | ||||
−0.632126 | + | 0.774866i | \(0.717818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −32.2311 | −0.687639 | −0.343819 | − | 0.939036i | \(-0.611721\pi\) | ||||
−0.343819 | + | 0.939036i | \(0.611721\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.33867 | 0.0746826 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 77.7849 | 1.10974 | 0.554871 | − | 0.831937i | \(-0.312768\pi\) | ||||
0.554871 | + | 0.831937i | \(0.312768\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.6613 | −0.152879 | −0.0764397 | − | 0.997074i | \(-0.524355\pi\) | ||||
−0.0764397 | + | 0.997074i | \(0.524355\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 100.924 | 0.914965 | 0.457483 | − | 0.889219i | \(-0.348751\pi\) | ||||
0.457483 | + | 0.889219i | \(0.348751\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −122.908 | −0.983268 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 213.908 | 1.36972 | 0.684859 | − | 0.728676i | \(-0.259864\pi\) | ||||
0.684859 | + | 0.728676i | \(0.259864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −42.0756 | −0.243774 | −0.121887 | − | 0.992544i | \(-0.538895\pi\) | ||||
−0.121887 | + | 0.992544i | \(0.538895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 138.371 | 0.729916 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 310.080 | 1.37775 | 0.688876 | − | 0.724879i | \(-0.258104\pi\) | ||||
0.688876 | + | 0.724879i | \(0.258104\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 96.6933 | 0.397008 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 44.0320 | 0.167723 | 0.0838615 | − | 0.996477i | \(-0.473275\pi\) | ||||
0.0838615 | + | 0.996477i | \(0.473275\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −381.339 | −1.35241 | −0.676205 | − | 0.736714i | \(-0.736376\pi\) | ||||
−0.676205 | + | 0.736714i | \(0.736376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.0160 | −0.0431180 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 358.064 | 1.11126 | 0.555628 | − | 0.831431i | \(-0.312478\pi\) | ||||
0.555628 | + | 0.831431i | \(0.312478\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −233.355 | −0.640710 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 184.984 | 0.479425 | 0.239712 | − | 0.970844i | \(-0.422947\pi\) | ||||
0.239712 | + | 0.970844i | \(0.422947\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 66.7049 | 0.163536 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 37.9840 | 0.0882650 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −454.650 | −1.00323 | −0.501613 | − | 0.865092i | \(-0.667260\pi\) | ||||
−0.501613 | + | 0.865092i | \(0.667260\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8489 | 0.0248704 | 0.0124352 | − | 0.999923i | \(-0.496042\pi\) | ||||
0.0124352 | + | 0.999923i | \(0.496042\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 46.6133 | 0.0889488 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −590.359 | −1.07648 | −0.538238 | − | 0.842793i | \(-0.680910\pi\) | ||||
−0.538238 | + | 0.842793i | \(0.680910\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −302.773 | −0.528255 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −494.366 | −0.826345 | −0.413172 | − | 0.910653i | \(-0.635579\pi\) | ||||
−0.413172 | + | 0.910653i | \(0.635579\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 975.650 | 1.56426 | 0.782131 | − | 0.623114i | \(-0.214133\pi\) | ||||
0.782131 | + | 0.623114i | \(0.214133\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 368.725 | 0.567690 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −299.334 | −0.426300 | −0.213150 | − | 0.977019i | \(-0.568372\pi\) | ||||
−0.213150 | + | 0.977019i | \(0.568372\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1406.07 | 1.85947 | 0.929735 | − | 0.368229i | \(-0.120036\pi\) | ||||
0.929735 | + | 0.368229i | \(0.120036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −112.494 | −0.143550 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −641.725 | −0.790807 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −695.259 | −0.828059 | −0.414030 | − | 0.910263i | \(-0.635879\pi\) | ||||
−0.414030 | + | 0.910263i | \(0.635879\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 126.227 | 0.140743 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.3111 | 0.0197756 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 481.940 | 0.504470 | 0.252235 | − | 0.967666i | \(-0.418834\pi\) | ||||
0.252235 | + | 0.967666i | \(0.418834\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −415.112 | −0.421417 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1184.10 | −1.16656 | −0.583281 | − | 0.812270i | \(-0.698231\pi\) | ||||
−0.583281 | + | 0.812270i | \(0.698231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1283.53 | 1.22786 | 0.613932 | − | 0.789359i | \(-0.289587\pi\) | ||||
0.613932 | + | 0.789359i | \(0.289587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1613.37 | −1.45767 | −0.728833 | − | 0.684692i | \(-0.759937\pi\) | ||||
−0.728833 | + | 0.684692i | \(0.759937\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −153.833 | −0.135179 | −0.0675895 | − | 0.997713i | \(-0.521531\pi\) | ||||
−0.0675895 | + | 0.997713i | \(0.521531\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −930.240 | −0.795446 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1581.08 | 1.31625 | 0.658123 | − | 0.752910i | \(-0.271350\pi\) | ||||
0.658123 | + | 0.752910i | \(0.271350\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −145.959 | −0.118354 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −290.080 | −0.229213 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 796.382 | 0.598334 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −132.096 | −0.0968349 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 358.531 | 0.256544 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1916.30 | −1.33893 | −0.669465 | − | 0.742844i | \(-0.733477\pi\) | ||||
−0.669465 | + | 0.742844i | \(0.733477\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1144.02 | 0.780814 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2500.48 | −1.66770 | −0.833849 | − | 0.551993i | \(-0.813867\pi\) | ||||
−0.833849 | + | 0.551993i | \(0.813867\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 39.0480 | 0.0248942 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 290.892 | 0.181406 | 0.0907030 | − | 0.995878i | \(-0.471089\pi\) | ||||
0.0907030 | + | 0.995878i | \(0.471089\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1348.77 | 0.823028 | 0.411514 | − | 0.911403i | \(-0.365000\pi\) | ||||
0.411514 | + | 0.911403i | \(0.365000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1074.19 | −0.641584 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1486.61 | 0.869349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −309.359 | −0.177178 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2848.81 | −1.56633 | −0.783165 | − | 0.621814i | \(-0.786396\pi\) | ||||
−0.783165 | + | 0.621814i | \(0.786396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1489.31 | 0.802639 | 0.401320 | − | 0.915938i | \(-0.368552\pi\) | ||||
0.401320 | + | 0.915938i | \(0.368552\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 700.064 | 0.369914 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 60.8506 | 0.0315331 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3643.38 | 1.85206 | 0.926030 | − | 0.377449i | \(-0.123199\pi\) | ||||
0.926030 | + | 0.377449i | \(0.123199\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −554.952 | −0.276796 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −769.163 | −0.369604 | −0.184802 | − | 0.982776i | \(-0.559164\pi\) | ||||
−0.184802 | + | 0.982776i | \(0.559164\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −200.115 | −0.0944176 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2399.78 | 1.11198 | 0.555991 | − | 0.831188i | \(-0.312339\pi\) | ||||
0.555991 | + | 0.831188i | \(0.312339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1158.16 | −0.527153 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −113.952 | −0.0509598 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3336.65 | −1.46636 | −0.733181 | − | 0.680033i | \(-0.761965\pi\) | ||||
−0.733181 | + | 0.680033i | \(0.761965\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1363.95 | 0.579213 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2461.77 | −1.02794 | −0.513970 | − | 0.857808i | \(-0.671826\pi\) | ||||
−0.513970 | + | 0.857808i | \(0.671826\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1316.74 | 0.540732 | 0.270366 | − | 0.962758i | \(-0.412855\pi\) | ||||
0.270366 | + | 0.962758i | \(0.412855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −35.5466 | −0.0143589 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −448.445 | −0.178218 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3587.72 | −1.40299 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3267.97 | 1.23802 | 0.619010 | − | 0.785383i | \(-0.287534\pi\) | ||||
0.619010 | + | 0.785383i | \(0.287534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 233.672 | 0.0871506 | 0.0435753 | − | 0.999050i | \(-0.486125\pi\) | ||||
0.0435753 | + | 0.999050i | \(0.486125\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −139.840 | −0.0513546 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −31.8632 | −0.0115236 | −0.00576182 | − | 0.999983i | \(-0.501834\pi\) | ||||
−0.00576182 | + | 0.999983i | \(0.501834\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1478.90 | 0.526817 | 0.263408 | − | 0.964684i | \(-0.415153\pi\) | ||||
0.263408 | + | 0.964684i | \(0.415153\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1771.08 | 0.621503 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −63.6800 | −0.0216956 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 908.320 | 0.304988 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 583.986 | 0.193278 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4498.67 | 1.46778 | 0.733889 | − | 0.679269i | \(-0.237703\pi\) | ||||
0.733889 | + | 0.679269i | \(0.237703\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1483.10 | 0.477090 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 551.500 | 0.174940 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2926.95 | −0.903127 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2507.09 | −0.763101 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5382.75 | −1.61639 | −0.808196 | − | 0.588913i | \(-0.799556\pi\) | ||||
−0.808196 | + | 0.588913i | \(0.799556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1106.18 | −0.327756 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5425.57 | 1.58638 | 0.793188 | − | 0.608977i | \(-0.208420\pi\) | ||||
0.793188 | + | 0.608977i | \(0.208420\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1989.75 | 0.574175 | 0.287088 | − | 0.957904i | \(-0.407313\pi\) | ||||
0.287088 | + | 0.957904i | \(0.407313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6297.66 | −1.77070 | −0.885351 | − | 0.464924i | \(-0.846082\pi\) | ||||
−0.885351 | + | 0.464924i | \(0.846082\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −517.840 | −0.143745 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 898.003 | 0.246125 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3395.77 | −0.919054 | −0.459527 | − | 0.888164i | \(-0.651981\pi\) | ||||
−0.459527 | + | 0.888164i | \(0.651981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6373.94 | −1.70366 | −0.851829 | − | 0.523820i | \(-0.824506\pi\) | ||||
−0.851829 | + | 0.523820i | \(0.824506\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 408.089 | 0.105126 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4218.21 | −1.07357 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2650.91 | 0.666630 | 0.333315 | − | 0.942815i | \(-0.391833\pi\) | ||||
0.333315 | + | 0.942815i | \(0.391833\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4654.99 | −1.15675 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 337.483 | 0.0828784 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1872.07 | −0.454383 | −0.227192 | − | 0.973850i | \(-0.572954\pi\) | ||||
−0.227192 | + | 0.973850i | \(0.572954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1925.18 | 0.456572 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6126.10 | −1.43632 | −0.718158 | − | 0.695880i | \(-0.755015\pi\) | ||||
−0.718158 | + | 0.695880i | \(0.755015\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −267.528 | −0.0620155 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2085.78 | 0.478080 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8504.12 | −1.92753 | −0.963764 | − | 0.266755i | \(-0.914049\pi\) | ||||
−0.963764 | + | 0.266755i | \(0.914049\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2121.54 | −0.475552 | −0.237776 | − | 0.971320i | \(-0.576418\pi\) | ||||
−0.237776 | + | 0.971320i | \(0.576418\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5668.97 | 1.24310 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8021.37 | −1.73992 | −0.869959 | − | 0.493125i | \(-0.835855\pi\) | ||||
−0.869959 | + | 0.493125i | \(0.835855\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −378.680 | −0.0812580 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8244.17 | −1.75020 | −0.875100 | − | 0.483943i | \(-0.839204\pi\) | ||||
−0.875100 | + | 0.483943i | \(0.839204\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6101.28 | −1.28157 | −0.640784 | − | 0.767722i | \(-0.721390\pi\) | ||||
−0.640784 | + | 0.767722i | \(0.721390\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −54.9333 | −0.0114174 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1137.49 | 0.231526 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1445.82 | −0.291256 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1965.98 | −0.391993 | −0.195996 | − | 0.980605i | \(-0.562794\pi\) | ||||
−0.195996 | + | 0.980605i | \(0.562794\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 657.524 | 0.129771 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1245.34 | 0.243305 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3252.91 | −0.629165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3552.31 | 0.673515 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.1361 | −0.00321708 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −997.810 | −0.185498 | −0.0927492 | − | 0.995690i | \(-0.529565\pi\) | ||||
−0.0927492 | + | 0.995690i | \(0.529565\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3850.59 | −0.708908 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6901.43 | 1.25834 | 0.629171 | − | 0.777267i | \(-0.283395\pi\) | ||||
0.629171 | + | 0.777267i | \(0.283395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6341.71 | −1.14522 | −0.572612 | − | 0.819827i | \(-0.694070\pi\) | ||||
−0.572612 | + | 0.819827i | \(0.694070\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1224.97 | 0.217039 | 0.108519 | − | 0.994094i | \(-0.465389\pi\) | ||||
0.108519 | + | 0.994094i | \(0.465389\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9866.22 | −1.73167 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4840.10 | 0.841583 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −984.860 | −0.169657 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3961.48 | 0.676133 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 461.499 | 0.0780457 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3736.30 | −0.620440 | −0.310220 | − | 0.950665i | \(-0.600403\pi\) | ||||
−0.310220 | + | 0.950665i | \(0.600403\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2790.72 | 0.459251 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 853.790 | 0.139246 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3928.18 | −0.634960 | −0.317480 | − | 0.948265i | \(-0.602837\pi\) | ||||
−0.317480 | + | 0.948265i | \(0.602837\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4743.25 | −0.759936 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1940.67 | 0.308192 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 437.877 | 0.0683320 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −542.005 | −0.0838512 | −0.0419256 | − | 0.999121i | \(-0.513349\pi\) | ||||
−0.0419256 | + | 0.999121i | \(0.513349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2331.24 | 0.357561 | 0.178780 | − | 0.983889i | \(-0.442785\pi\) | ||||
0.178780 | + | 0.983889i | \(0.442785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 870.240 | 0.132336 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2560.30 | −0.386037 | −0.193018 | − | 0.981195i | \(-0.561828\pi\) | ||||
−0.193018 | + | 0.981195i | \(0.561828\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 714.963 | 0.106891 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4568.53 | 0.671638 | 0.335819 | − | 0.941927i | \(-0.390987\pi\) | ||||
0.335819 | + | 0.941927i | \(0.390987\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6698.69 | −0.976628 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2389.15 | −0.345448 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1411.01 | −0.202344 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6381.83 | 0.907707 | 0.453854 | − | 0.891076i | \(-0.350049\pi\) | ||||
0.453854 | + | 0.891076i | \(0.350049\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 396.288 | 0.0559077 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6372.01 | −0.884532 | −0.442266 | − | 0.896884i | \(-0.645825\pi\) | ||||
−0.442266 | + | 0.896884i | \(0.645825\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1075.59 | −0.148116 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6894.51 | −0.941870 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1494.59 | −0.202564 | −0.101282 | − | 0.994858i | \(-0.532294\pi\) | ||||
−0.101282 | + | 0.994858i | \(0.532294\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5748.90 | 0.773031 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8820.26 | −1.17675 | −0.588374 | − | 0.808589i | \(-0.700232\pi\) | ||||
−0.588374 | + | 0.808589i | \(0.700232\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3432.05 | −0.450803 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9878.47 | −1.28755 | −0.643777 | − | 0.765213i | \(-0.722634\pi\) | ||||
−0.643777 | + | 0.765213i | \(0.722634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7850.40 | 1.01537 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7501.45 | 0.962845 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 432.904 | 0.0551437 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1941.80 | 0.245481 | 0.122740 | − | 0.992439i | \(-0.460832\pi\) | ||||
0.122740 | + | 0.992439i | \(0.460832\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7584.96 | 0.944576 | 0.472288 | − | 0.881444i | \(-0.343428\pi\) | ||||
0.472288 | + | 0.881444i | \(0.343428\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1356.14 | 0.167628 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −117.144 | −0.0143727 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14302.0 | −1.74183 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8707.80 | 1.05275 | 0.526373 | − | 0.850254i | \(-0.323552\pi\) | ||||
0.526373 | + | 0.850254i | \(0.323552\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −872.677 | −0.104735 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2033.49 | −0.240530 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4046.30 | −0.475175 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6647.96 | −0.775117 | −0.387558 | − | 0.921845i | \(-0.626681\pi\) | ||||
−0.387558 | + | 0.921845i | \(0.626681\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11670.6 | 1.35105 | 0.675524 | − | 0.737338i | \(-0.263917\pi\) | ||||
0.675524 | + | 0.737338i | \(0.263917\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3222.58 | 0.370418 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9560.42 | −1.09117 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4459.84 | −0.501919 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1565.64 | 0.174975 | 0.0874876 | − | 0.996166i | \(-0.472116\pi\) | ||||
0.0874876 | + | 0.996166i | \(0.472116\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15446.4 | 1.71434 | 0.857168 | − | 0.515037i | \(-0.172222\pi\) | ||||
0.857168 | + | 0.515037i | \(0.172222\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 928.077 | 0.102294 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1277.84 | −0.139879 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10697.4 | −1.16300 | −0.581502 | − | 0.813545i | \(-0.697535\pi\) | ||||
−0.581502 | + | 0.813545i | \(0.697535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1053.96 | 0.113037 | 0.0565183 | − | 0.998402i | \(-0.482000\pi\) | ||||
0.0565183 | + | 0.998402i | \(0.482000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1005.50 | 0.107113 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8546.42 | 0.904321 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1139.33 | 0.119752 | 0.0598759 | − | 0.998206i | \(-0.480930\pi\) | ||||
0.0598759 | + | 0.998206i | \(0.480930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2030.91 | −0.212044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4467.94 | −0.463404 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5704.16 | 0.583872 | 0.291936 | − | 0.956438i | \(-0.405701\pi\) | ||||
0.291936 | + | 0.956438i | \(0.405701\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2100.19 | −0.213570 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6476.39 | −0.654307 | −0.327154 | − | 0.944971i | \(-0.606089\pi\) | ||||
−0.327154 | + | 0.944971i | \(0.606089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 232.366 | 0.0233239 | 0.0116619 | − | 0.999932i | \(-0.496288\pi\) | ||||
0.0116619 | + | 0.999932i | \(0.496288\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −182.552 | −0.0182057 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1037.17 | 0.102772 | 0.0513858 | − | 0.998679i | \(-0.483636\pi\) | ||||
0.0513858 | + | 0.998679i | \(0.483636\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10930.1 | −1.06929 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17588.7 | 1.70979 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1556.18 | 0.150321 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1664.86 | 0.159808 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10284.6 | −0.981039 | −0.490519 | − | 0.871430i | \(-0.663193\pi\) | ||||
−0.490519 | + | 0.871430i | \(0.663193\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9994.22 | −0.947396 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −696.993 | −0.0652553 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10845.8 | −1.00918 | −0.504591 | − | 0.863359i | \(-0.668357\pi\) | ||||
−0.504591 | + | 0.863359i | \(0.668357\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2307.49 | 0.213391 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8442.11 | −0.775941 | −0.387971 | − | 0.921672i | \(-0.626824\pi\) | ||||
−0.387971 | + | 0.921672i | \(0.626824\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16638.8 | 1.52003 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 600.344 | 0.0545120 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9810.85 | −0.880148 | −0.440074 | − | 0.897961i | \(-0.645048\pi\) | ||||
−0.440074 | + | 0.897961i | \(0.645048\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7199.35 | −0.642003 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6433.96 | 0.570330 | 0.285165 | − | 0.958478i | \(-0.407952\pi\) | ||||
0.285165 | + | 0.958478i | \(0.407952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1712.48 | 0.150900 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3474.47 | 0.304352 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20560.6 | −1.79044 | −0.895220 | − | 0.445624i | \(-0.852982\pi\) | ||||
−0.895220 | + | 0.445624i | \(0.852982\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 341.856 | 0.0294217 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1856.27 | −0.158829 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16515.2 | −1.40491 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10009.9 | 0.846605 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19126.1 | 1.60831 | 0.804156 | − | 0.594418i | \(-0.202617\pi\) | ||||
0.804156 | + | 0.594418i | \(0.202617\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3044.66 | 0.254558 | 0.127279 | − | 0.991867i | \(-0.459376\pi\) | ||||
0.127279 | + | 0.991867i | \(0.459376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3272.84 | −0.270526 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1981.26 | −0.162839 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4091.85 | −0.334409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1419.20 | −0.115333 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2333.29 | 0.188555 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7385.31 | 0.593482 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5895.09 | −0.468484 | −0.234242 | − | 0.972178i | \(-0.575261\pi\) | ||||
−0.234242 | + | 0.972178i | \(0.575261\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3950.22 | −0.312192 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 222.476 | 0.0174860 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11151.1 | −0.871641 | −0.435821 | − | 0.900034i | \(-0.643542\pi\) | ||||
−0.435821 | + | 0.900034i | \(0.643542\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 106.640 | 0.00829013 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2708.37 | −0.209402 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1345.33 | 0.102894 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1744.35 | 0.132694 | 0.0663468 | − | 0.997797i | \(-0.478866\pi\) | ||||
0.0663468 | + | 0.997797i | \(0.478866\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12291.0 | 0.929969 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10763.1 | 0.810019 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11524.4 | −0.862691 | −0.431345 | − | 0.902187i | \(-0.641961\pi\) | ||||
−0.431345 | + | 0.902187i | \(0.641961\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2286.60 | −0.170262 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2822.76 | 0.207973 | 0.103986 | − | 0.994579i | \(-0.466840\pi\) | ||||
0.103986 | + | 0.994579i | \(0.466840\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5167.64 | 0.378737 | 0.189369 | − | 0.981906i | \(-0.439356\pi\) | ||||
0.189369 | + | 0.981906i | \(0.439356\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9803.90 | −0.714771 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12404.5 | −0.899656 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14715.2 | −1.06170 | −0.530851 | − | 0.847465i | \(-0.678128\pi\) | ||||
−0.530851 | + | 0.847465i | \(0.678128\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −701.016 | −0.0503164 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8532.12 | −0.606114 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 419.520 | 0.0296496 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9981.64 | −0.701851 | −0.350925 | − | 0.936403i | \(-0.614133\pi\) | ||||
−0.350925 | + | 0.936403i | \(0.614133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 532.733 | 0.0372680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 95.5895 | 0.00665317 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1675.21 | −0.116008 | −0.0580039 | − | 0.998316i | \(-0.518474\pi\) | ||||
−0.0580039 | + | 0.998316i | \(0.518474\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4436.70 | −0.304158 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1039.91 | −0.0709341 | −0.0354671 | − | 0.999371i | \(-0.511292\pi\) | ||||
−0.0354671 | + | 0.999371i | \(0.511292\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4472.61 | 0.303563 | 0.151782 | − | 0.988414i | \(-0.451499\pi\) | ||||
0.151782 | + | 0.988414i | \(0.451499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5313.23 | −0.358825 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1151.75 | −0.0773969 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17790.8 | 1.18963 | 0.594814 | − | 0.803863i | \(-0.297226\pi\) | ||||
0.594814 | + | 0.803863i | \(0.297226\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11540.8 | −0.764142 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4326.74 | −0.285082 | −0.142541 | − | 0.989789i | \(-0.545527\pi\) | ||||
−0.142541 | + | 0.989789i | \(0.545527\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 191.040 | 0.0125260 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18866.2 | −1.23100 | −0.615498 | − | 0.788139i | \(-0.711045\pi\) | ||||
−0.615498 | + | 0.788139i | \(0.711045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10179.4 | 0.660975 | 0.330488 | − | 0.943810i | \(-0.392787\pi\) | ||||
0.330488 | + | 0.943810i | \(0.392787\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2724.96 | −0.176085 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14845.0 | 0.950083 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1751.96 | −0.111589 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24119.5 | 1.52895 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1661.72 | 0.104837 | 0.0524184 | − | 0.998625i | \(-0.483307\pi\) | ||||
0.0524184 | + | 0.998625i | \(0.483307\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13496.0 | −0.847423 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2771.39 | 0.173196 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4449.30 | −0.275448 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2277.64 | −0.140346 | −0.0701728 | − | 0.997535i | \(-0.522355\pi\) | ||||
−0.0701728 | + | 0.997535i | \(0.522355\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1217.38 | −0.0746638 | −0.0373319 | − | 0.999303i | \(-0.511886\pi\) | ||||
−0.0373319 | + | 0.999303i | \(0.511886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1654.50 | −0.101001 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10731.8 | −0.652103 | −0.326052 | − | 0.945352i | \(-0.605718\pi\) | ||||
−0.326052 | + | 0.945352i | \(0.605718\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20970.1 | 1.26833 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15228.1 | 0.912588 | 0.456294 | − | 0.889829i | \(-0.349177\pi\) | ||||
0.456294 | + | 0.889829i | \(0.349177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3616.26 | 0.215723 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8780.85 | 0.521421 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10590.8 | −0.626038 | −0.313019 | − | 0.949747i | \(-0.601340\pi\) | ||||
−0.313019 | + | 0.949747i | \(0.601340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3868.30 | −0.227624 | −0.113812 | − | 0.993502i | \(-0.536306\pi\) | ||||
−0.113812 | + | 0.993502i | \(0.536306\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7521.28 | 0.440577 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21588.6 | 1.25324 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16148.2 | 0.933225 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −546.512 | −0.0314424 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11028.7 | 0.631687 | 0.315843 | − | 0.948811i | \(-0.397713\pi\) | ||||
0.315843 | + | 0.948811i | \(0.397713\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3318.53 | 0.189230 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18792.5 | 1.06684 | 0.533422 | − | 0.845849i | \(-0.320906\pi\) | ||||
0.533422 | + | 0.845849i | \(0.320906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16276.7 | −0.915895 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20243.8 | 1.13412 | 0.567062 | − | 0.823675i | \(-0.308080\pi\) | ||||
0.567062 | + | 0.823675i | \(0.308080\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −420.695 | −0.0234656 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5969.24 | −0.331500 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5962.24 | −0.329671 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19202.9 | 1.05718 | 0.528591 | − | 0.848877i | \(-0.322721\pi\) | ||||
0.528591 | + | 0.848877i | \(0.322721\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1950.62 | −0.106462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3425.02 | 0.186129 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18893.0 | 1.02231 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22156.9 | −1.19380 | −0.596900 | − | 0.802316i | \(-0.703601\pi\) | ||||
−0.596900 | + | 0.802316i | \(0.703601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3926.03 | −0.210630 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1553.52 | 0.0829914 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27209.1 | −1.44127 | −0.720634 | − | 0.693316i | \(-0.756149\pi\) | ||||
−0.720634 | + | 0.693316i | \(0.756149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2694.01 | −0.142100 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4246.45 | −0.223045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2149.97 | −0.112454 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10187.3 | 0.530616 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21552.3 | −1.11789 | −0.558947 | − | 0.829203i | \(-0.688794\pi\) | ||||
−0.558947 | + | 0.829203i | \(0.688794\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19121.8 | 0.983607 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26291.2 | −1.34680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20599.1 | 1.05086 | 0.525431 | − | 0.850836i | \(-0.323904\pi\) | ||||
0.525431 | + | 0.850836i | \(0.323904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29662.4 | −1.50082 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19761.2 | 0.995764 | 0.497882 | − | 0.867245i | \(-0.334111\pi\) | ||||
0.497882 | + | 0.867245i | \(0.334111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27229.5 | 1.36094 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33408.9 | −1.66301 | −0.831506 | − | 0.555516i | \(-0.812521\pi\) | ||||
−0.831506 | + | 0.555516i | \(0.812521\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1224.27 | −0.0606944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36225.4 | 1.78867 | 0.894335 | − | 0.447398i | \(-0.147649\pi\) | ||||
0.894335 | + | 0.447398i | \(0.147649\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4120.00 | 0.202611 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12654.6 | 0.619824 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27320.4 | 1.32748 | 0.663740 | − | 0.747964i | \(-0.268968\pi\) | ||||
0.663740 | + | 0.747964i | \(0.268968\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7952.74 | −0.384879 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2153.88 | −0.103825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9918.43 | −0.476211 | −0.238105 | − | 0.971239i | \(-0.576526\pi\) | ||||
−0.238105 | + | 0.971239i | \(0.576526\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13965.0 | 0.667848 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5635.04 | −0.268423 | −0.134211 | − | 0.990953i | \(-0.542850\pi\) | ||||
−0.134211 | + | 0.990953i | \(0.542850\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1012.45 | −0.0478498 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14653.9 | 0.689857 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12089.3 | 0.566907 | 0.283453 | − | 0.958986i | \(-0.408520\pi\) | ||||
0.283453 | + | 0.958986i | \(0.408520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5616.21 | 0.262338 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14171.4 | −0.659390 | −0.329695 | − | 0.944087i | \(-0.606946\pi\) | ||||
−0.329695 | + | 0.944087i | \(0.606946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5171.44 | 0.239695 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −557.504 | −0.0256414 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22801.9 | 1.04471 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5775.53 | −0.263602 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5269.14 | −0.239571 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25707.6 | 1.16439 | 0.582197 | − | 0.813047i | \(-0.302193\pi\) | ||||
0.582197 | + | 0.813047i | \(0.302193\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18378.3 | 0.829258 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −381.903 | −0.0171018 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 802.584 | 0.0358047 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6194.68 | −0.275316 | −0.137658 | − | 0.990480i | \(-0.543957\pi\) | ||||
−0.137658 | + | 0.990480i | \(0.543957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27852.0 | 1.23321 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6257.33 | −0.276020 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −45000.4 | −1.97762 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25512.4 | 1.11286 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30815.1 | 1.33919 | 0.669593 | − | 0.742729i | \(-0.266469\pi\) | ||||
0.669593 | + | 0.742729i | \(0.266469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43024.1 | −1.86286 | −0.931431 | − | 0.363917i | \(-0.881439\pi\) | ||||
−0.931431 | + | 0.363917i | \(0.881439\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6364.63 | 0.274560 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1112.38 | 0.0478098 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4828.26 | 0.206756 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11152.2 | −0.474075 | −0.237038 | − | 0.971500i | \(-0.576176\pi\) | ||||
−0.237038 | + | 0.971500i | \(0.576176\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44912.8 | 1.90226 | 0.951130 | − | 0.308790i | \(-0.0999240\pi\) | ||||
0.951130 | + | 0.308790i | \(0.0999240\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17006.9 | −0.717703 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3213.42 | 0.135117 | 0.0675584 | − | 0.997715i | \(-0.478479\pi\) | ||||
0.0675584 | + | 0.997715i | \(0.478479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8794.91 | −0.368468 | −0.184234 | − | 0.982882i | \(-0.558980\pi\) | ||||
−0.184234 | + | 0.982882i | \(0.558980\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24064.1 | 1.00454 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3470.62 | −0.143839 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1136.04 | 0.0469143 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45817.0 | −1.88532 | −0.942658 | − | 0.333761i | \(-0.891682\pi\) | ||||
−0.942658 | + | 0.333761i | \(0.891682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21367.8 | 0.876125 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24732.5 | 1.01048 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1674.95 | 0.0681894 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18303.8 | 0.739913 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31294.6 | 1.26060 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16373.6 | −0.657234 | −0.328617 | − | 0.944463i | \(-0.606583\pi\) | ||||
−0.328617 | + | 0.944463i | \(0.606583\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 164.800 | 0.00659186 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4430.20 | −0.176584 | −0.0882922 | − | 0.996095i | \(-0.528141\pi\) | ||||
−0.0882922 | + | 0.996095i | \(0.528141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4944.39 | −0.196392 | −0.0981958 | − | 0.995167i | \(-0.531307\pi\) | ||||
−0.0981958 | + | 0.995167i | \(0.531307\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13178.6 | −0.519821 | −0.259911 | − | 0.965633i | \(-0.583693\pi\) | ||||
−0.259911 | + | 0.965633i | \(0.583693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4825.53 | 0.189680 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3412.47 | −0.133672 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13806.4 | 0.538951 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19027.9 | 0.740226 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4337.46 | 0.168157 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12985.9 | −0.500003 | −0.250001 | − | 0.968245i | \(-0.580431\pi\) | ||||
−0.250001 | + | 0.968245i | \(0.580431\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5897.94 | 0.226317 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36877.4 | 1.41025 | 0.705126 | − | 0.709082i | \(-0.250890\pi\) | ||||
0.705126 | + | 0.709082i | \(0.250890\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24874.5 | 0.948012 | 0.474006 | − | 0.880522i | \(-0.342808\pi\) | ||||
0.474006 | + | 0.880522i | \(0.342808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1972.57 | −0.0749235 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4410.64 | −0.166961 | −0.0834806 | − | 0.996509i | \(-0.526604\pi\) | ||||
−0.0834806 | + | 0.996509i | \(0.526604\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3736.01 | −0.140472 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4533.57 | −0.169888 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3560.27 | 0.132968 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9758.72 | 0.363249 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9000.32 | −0.333901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14389.0 | 0.532037 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1904.30 | −0.0699459 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7273.99 | 0.266294 | 0.133147 | − | 0.991096i | \(-0.457492\pi\) | ||||
0.133147 | + | 0.991096i | \(0.457492\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10656.9 | −0.388854 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49491.9 | 1.79993 | 0.899967 | − | 0.435957i | \(-0.143590\pi\) | ||||
0.899967 | + | 0.435957i | \(0.143590\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −64852.9 | −2.35084 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 51.4083 | 0.00185738 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5015.90 | 0.180043 | 0.0900213 | − | 0.995940i | \(-0.471306\pi\) | ||||
0.0900213 | + | 0.995940i | \(0.471306\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2993.43 | 0.107098 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15934.0 | 0.568227 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38111.4 | −1.35470 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11551.8 | 0.409288 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −52158.2 | −1.84204 | −0.921021 | − | 0.389514i | \(-0.872643\pi\) | ||||
−0.921021 | + | 0.389514i | \(0.872643\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20704.3 | −0.726504 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5188.63 | 0.181483 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14821.9 | −0.516766 | −0.258383 | − | 0.966042i | \(-0.583190\pi\) | ||||
−0.258383 | + | 0.966042i | \(0.583190\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19025.1 | 0.661195 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26492.3 | 0.917772 | 0.458886 | − | 0.888495i | \(-0.348249\pi\) | ||||
0.458886 | + | 0.888495i | \(0.348249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4443.90 | 0.153461 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6410.25 | −0.219963 | −0.109982 | − | 0.993934i | \(-0.535079\pi\) | ||||
−0.109982 | + | 0.993934i | \(0.535079\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31446.3 | −1.07565 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3674.92 | −0.125307 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25108.5 | −0.853458 | −0.426729 | − | 0.904380i | \(-0.640334\pi\) | ||||
−0.426729 | + | 0.904380i | \(0.640334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4726.21 | −0.160143 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29598.7 | 0.999779 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28020.6 | −0.940574 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14520.3 | −0.485888 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −337.941 | −0.0112733 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32928.1 | −1.09503 | −0.547516 | − | 0.836795i | \(-0.684426\pi\) | ||||
−0.547516 | + | 0.836795i | \(0.684426\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2954.58 | 0.0979513 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31543.2 | 1.04250 | 0.521251 | − | 0.853403i | \(-0.325465\pi\) | ||||
0.521251 | + | 0.853403i | \(0.325465\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11884.4 | −0.390365 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53881.8 | 1.76441 | 0.882206 | − | 0.470864i | \(-0.156058\pi\) | ||||
0.882206 | + | 0.470864i | \(0.156058\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32067.8 | 1.04688 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1384.50 | −0.0450597 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35688.6 | −1.15798 | −0.578988 | − | 0.815336i | \(-0.696552\pi\) | ||||
−0.578988 | + | 0.815336i | \(0.696552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.0812 | 0.00149063 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38486.4 | −1.23741 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14839.7 | −0.475681 | −0.237840 | − | 0.971304i | \(-0.576439\pi\) | ||||
−0.237840 | + | 0.971304i | \(0.576439\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11208.9 | 0.358211 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2138.82 | −0.0681459 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17372.1 | 0.551834 | 0.275917 | − | 0.961181i | \(-0.411018\pi\) | ||||
0.275917 | + | 0.961181i | \(0.411018\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8372.16 | −0.265149 |
(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 | 2352.4.a.bt.1.1 | 2 | ||
4.3 | odd | 2 | 588.4.a.i.1.1 | 2 | |||
7.2 | even | 3 | 336.4.q.i.193.2 | 4 | |||
7.4 | even | 3 | 336.4.q.i.289.2 | 4 | |||
7.6 | odd | 2 | 2352.4.a.bx.1.2 | 2 | |||
12.11 | even | 2 | 1764.4.a.o.1.2 | 2 | |||
28.3 | even | 6 | 588.4.i.j.373.1 | 4 | |||
28.11 | odd | 6 | 84.4.i.a.37.2 | yes | 4 | ||
28.19 | even | 6 | 588.4.i.j.361.1 | 4 | |||
28.23 | odd | 6 | 84.4.i.a.25.2 | ✓ | 4 | ||
28.27 | even | 2 | 588.4.a.f.1.2 | 2 | |||
84.11 | even | 6 | 252.4.k.f.37.1 | 4 | |||
84.23 | even | 6 | 252.4.k.f.109.1 | 4 | |||
84.47 | odd | 6 | 1764.4.k.q.361.2 | 4 | |||
84.59 | odd | 6 | 1764.4.k.q.1549.2 | 4 | |||
84.83 | odd | 2 | 1764.4.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.a.25.2 | ✓ | 4 | 28.23 | odd | 6 | ||
84.4.i.a.37.2 | yes | 4 | 28.11 | odd | 6 | ||
252.4.k.f.37.1 | 4 | 84.11 | even | 6 | |||
252.4.k.f.109.1 | 4 | 84.23 | even | 6 | |||
336.4.q.i.193.2 | 4 | 7.2 | even | 3 | |||
336.4.q.i.289.2 | 4 | 7.4 | even | 3 | |||
588.4.a.f.1.2 | 2 | 28.27 | even | 2 | |||
588.4.a.i.1.1 | 2 | 4.3 | odd | 2 | |||
588.4.i.j.361.1 | 4 | 28.19 | even | 6 | |||
588.4.i.j.373.1 | 4 | 28.3 | even | 6 | |||
1764.4.a.o.1.2 | 2 | 12.11 | even | 2 | |||
1764.4.a.y.1.1 | 2 | 84.83 | odd | 2 | |||
1764.4.k.q.361.2 | 4 | 84.47 | odd | 6 | |||
1764.4.k.q.1549.2 | 4 | 84.59 | odd | 6 | |||
2352.4.a.bt.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2352.4.a.bx.1.2 | 2 | 7.6 | odd | 2 |