Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 138x^{7} + 394x^{6} + 5872x^{5} - 10822x^{4} - 85158x^{3} + 30654x^{2} + 439999x + 396802 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.95108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | 1.95108 | 0.375485 | 0.187743 | − | 0.982218i | \(-0.439883\pi\) | ||||
0.187743 | + | 0.982218i | \(0.439883\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −18.0628 | −1.61559 | −0.807793 | − | 0.589466i | \(-0.799338\pi\) | ||||
−0.807793 | + | 0.589466i | \(0.799338\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.0180 | 1.18886 | 0.594430 | − | 0.804148i | \(-0.297378\pi\) | ||||
0.594430 | + | 0.804148i | \(0.297378\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −23.1933 | −0.859011 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.1881 | −0.306667 | −0.153334 | − | 0.988174i | \(-0.549001\pi\) | ||||
−0.153334 | + | 0.988174i | \(0.549001\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.532875 | 0.0113687 | 0.00568435 | − | 0.999984i | \(-0.498191\pi\) | ||||
0.00568435 | + | 0.999984i | \(0.498191\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −35.2419 | −0.606628 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 56.2274 | 0.802185 | 0.401092 | − | 0.916038i | \(-0.368631\pi\) | ||||
0.401092 | + | 0.916038i | \(0.368631\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.5240 | −0.320264 | −0.160132 | − | 0.987096i | \(-0.551192\pi\) | ||||
−0.160132 | + | 0.987096i | \(0.551192\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 42.9588 | 0.446399 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 66.9071 | 0.606570 | 0.303285 | − | 0.952900i | \(-0.401917\pi\) | ||||
0.303285 | + | 0.952900i | \(0.401917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 201.265 | 1.61012 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −97.9310 | −0.698031 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 85.2968 | 0.494186 | 0.247093 | − | 0.968992i | \(-0.420525\pi\) | ||||
0.247093 | + | 0.968992i | \(0.420525\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −21.8288 | −0.115149 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −397.706 | −1.92070 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 180.274 | 0.800995 | 0.400498 | − | 0.916298i | \(-0.368837\pi\) | ||||
0.400498 | + | 0.916298i | \(0.368837\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.03968 | 0.00426877 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 46.4366 | 0.176882 | 0.0884412 | − | 0.996081i | \(-0.471811\pi\) | ||||
0.0884412 | + | 0.996081i | \(0.471811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −212.454 | −0.753464 | −0.376732 | − | 0.926322i | \(-0.622952\pi\) | ||||
−0.376732 | + | 0.926322i | \(0.622952\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 418.936 | 1.38781 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 108.280 | 0.336048 | 0.168024 | − | 0.985783i | \(-0.446261\pi\) | ||||
0.168024 | + | 0.985783i | \(0.446261\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 141.792 | 0.413386 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 109.704 | 0.301208 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 444.412 | 1.15179 | 0.575893 | − | 0.817525i | \(-0.304655\pi\) | ||||
0.575893 | + | 0.817525i | \(0.304655\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 202.088 | 0.495447 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −51.7503 | −0.120254 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −43.3659 | −0.0956908 | −0.0478454 | − | 0.998855i | \(-0.515235\pi\) | ||||
−0.0478454 | + | 0.998855i | \(0.515235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −33.1252 | −0.0695286 | −0.0347643 | − | 0.999396i | \(-0.511068\pi\) | ||||
−0.0347643 | + | 0.999396i | \(0.511068\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −510.670 | −1.02124 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.62522 | −0.0183671 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −988.140 | −1.80180 | −0.900899 | − | 0.434028i | \(-0.857092\pi\) | ||||
−0.900899 | + | 0.434028i | \(0.857092\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 130.541 | 0.227758 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −154.560 | −0.258350 | −0.129175 | − | 0.991622i | \(-0.541233\pi\) | ||||
−0.129175 | + | 0.991622i | \(0.541233\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1030.98 | −1.65297 | −0.826484 | − | 0.562961i | \(-0.809662\pi\) | ||||
−0.826484 | + | 0.562961i | \(0.809662\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 392.683 | 0.604575 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −246.339 | −0.364584 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −631.568 | −0.899455 | −0.449728 | − | 0.893166i | \(-0.648479\pi\) | ||||
−0.449728 | + | 0.893166i | \(0.648479\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 435.148 | 0.596911 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 145.157 | 0.191965 | 0.0959824 | − | 0.995383i | \(-0.469401\pi\) | ||||
0.0959824 | + | 0.995383i | \(0.469401\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1015.62 | −1.29600 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 56.5812 | 0.0697258 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 169.477 | 0.201849 | 0.100924 | − | 0.994894i | \(-0.467820\pi\) | ||||
0.100924 | + | 0.994894i | \(0.467820\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.7328 | 0.0135158 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 166.421 | 0.185559 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 479.097 | 0.517414 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −29.4573 | −0.0308344 | −0.0154172 | − | 0.999881i | \(-0.504908\pi\) | ||||
−0.0154172 | + | 0.999881i | \(0.504908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 259.489 | 0.263430 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −887.027 | −0.873886 | −0.436943 | − | 0.899489i | \(-0.643939\pi\) | ||||
−0.436943 | + | 0.899489i | \(0.643939\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 778.724 | 0.744951 | 0.372475 | − | 0.928042i | \(-0.378509\pi\) | ||||
0.372475 | + | 0.928042i | \(0.378509\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −775.956 | −0.721196 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1837.16 | 1.65986 | 0.829930 | − | 0.557868i | \(-0.188380\pi\) | ||||
0.829930 | + | 0.557868i | \(0.188380\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −232.609 | −0.204403 | −0.102201 | − | 0.994764i | \(-0.532589\pi\) | ||||
−0.102201 | + | 0.994764i | \(0.532589\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 351.728 | 0.300762 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1873.74 | 1.55988 | 0.779939 | − | 0.625855i | \(-0.215250\pi\) | ||||
0.779939 | + | 0.625855i | \(0.215250\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1208.53 | −0.979966 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.3591 | −0.00976583 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1238.01 | 0.953685 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1205.83 | −0.905955 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 90.6014 | 0.0664167 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1377.56 | −0.985699 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1672.06 | 1.16828 | 0.584141 | − | 0.811652i | \(-0.301432\pi\) | ||||
0.584141 | + | 0.811652i | \(0.301432\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −414.515 | −0.282915 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2611.20 | −1.74154 | −0.870769 | − | 0.491693i | \(-0.836378\pi\) | ||||
−0.870769 | + | 0.491693i | \(0.836378\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −584.004 | −0.380749 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1768.91 | 1.12773 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1506.03 | −0.939186 | −0.469593 | − | 0.882883i | \(-0.655599\pi\) | ||||
−0.469593 | + | 0.882883i | \(0.655599\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2818.87 | −1.72009 | −0.860047 | − | 0.510214i | \(-0.829566\pi\) | ||||
−0.860047 | + | 0.510214i | \(0.829566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 211.263 | 0.126181 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.96186 | −0.00348640 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −523.821 | −0.300007 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 276.646 | 0.155220 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1672.65 | −0.919658 | −0.459829 | − | 0.888007i | \(-0.652089\pi\) | ||||
−0.459829 | + | 0.888007i | \(0.652089\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1065.84 | 0.574417 | 0.287209 | − | 0.957868i | \(-0.407273\pi\) | ||||
0.287209 | + | 0.957868i | \(0.407273\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1304.10 | −0.689085 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1540.70 | −0.798400 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2554.74 | −1.29866 | −0.649332 | − | 0.760505i | \(-0.724952\pi\) | ||||
−0.649332 | + | 0.760505i | \(0.724952\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 867.081 | 0.432478 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1473.16 | 0.721126 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1345.04 | −0.646327 | −0.323164 | − | 0.946343i | \(-0.604746\pi\) | ||||
−0.323164 | + | 0.946343i | \(0.604746\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 394.290 | 0.186033 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −801.061 | −0.371185 | −0.185593 | − | 0.982627i | \(-0.559421\pi\) | ||||
−0.185593 | + | 0.982627i | \(0.559421\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2196.72 | −0.999871 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 615.178 | 0.275110 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1999.30 | −0.878635 | −0.439318 | − | 0.898332i | \(-0.644780\pi\) | ||||
−0.439318 | + | 0.898332i | \(0.644780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4431.45 | 1.91420 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −84.6102 | −0.0359305 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1183.93 | −0.494362 | −0.247181 | − | 0.968969i | \(-0.579504\pi\) | ||||
−0.247181 | + | 0.968969i | \(0.579504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1164.04 | 0.478025 | 0.239013 | − | 0.971016i | \(-0.423176\pi\) | ||||
0.239013 | + | 0.971016i | \(0.423176\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −64.6297 | −0.0261069 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3256.25 | −1.29408 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −629.077 | −0.246004 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2156.24 | −0.829860 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1613.60 | −0.611288 | −0.305644 | − | 0.952146i | \(-0.598872\pi\) | ||||
−0.305644 | + | 0.952146i | \(0.598872\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1048.74 | −0.391139 | −0.195570 | − | 0.980690i | \(-0.562656\pi\) | ||||
−0.195570 | + | 0.980690i | \(0.562656\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.7795 | −0.00689657 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1487.86 | 0.538099 | 0.269050 | − | 0.963126i | \(-0.413290\pi\) | ||||
0.269050 | + | 0.963126i | \(0.413290\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −297.754 | −0.106067 | −0.0530333 | − | 0.998593i | \(-0.516889\pi\) | ||||
−0.0530333 | + | 0.998593i | \(0.516889\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1927.94 | −0.676549 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 638.521 | 0.220766 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −838.775 | −0.285769 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1551.80 | −0.521050 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 296.753 | 0.0982145 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3947.96 | −1.28810 | −0.644049 | − | 0.764984i | \(-0.722747\pi\) | ||||
−0.644049 | + | 0.764984i | \(0.722747\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −301.558 | −0.0970065 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3837.52 | 1.21729 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1878.06 | 0.587517 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2011.51 | −0.620664 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.9622 | 0.00911979 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3790.90 | −1.13837 | −0.569187 | − | 0.822208i | \(-0.692742\pi\) | ||||
−0.569187 | + | 0.822208i | \(0.692742\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4668.00 | −1.38311 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1952.76 | 0.570966 | 0.285483 | − | 0.958384i | \(-0.407846\pi\) | ||||
0.285483 | + | 0.958384i | \(0.407846\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 878.288 | 0.253445 | 0.126723 | − | 0.991938i | \(-0.459554\pi\) | ||||
0.126723 | + | 0.991938i | \(0.459554\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −480.627 | −0.136896 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2556.16 | −0.718711 | −0.359355 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359355 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1955.84 | −0.542914 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1232.24 | −0.337732 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.0160 | −0.00352274 | −0.00176137 | − | 0.999998i | \(-0.500561\pi\) | ||||
−0.00176137 | + | 0.999998i | \(0.500561\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1987.42 | 0.531207 | 0.265603 | − | 0.964082i | \(-0.414429\pi\) | ||||
0.265603 | + | 0.964082i | \(0.414429\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3493.14 | 0.922162 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2561.15 | −0.667861 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.1340 | −0.00364098 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 283.213 | 0.0720799 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5553.49 | 1.39655 | 0.698273 | − | 0.715831i | \(-0.253952\pi\) | ||||
0.698273 | + | 0.715831i | \(0.253952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −748.564 | −0.186015 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1981.56 | −0.486628 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1089.82 | −0.264518 | −0.132259 | − | 0.991215i | \(-0.542223\pi\) | ||||
−0.132259 | + | 0.991215i | \(0.542223\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3969.27 | 0.952271 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −672.606 | −0.159514 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6808.83 | −1.59639 | −0.798195 | − | 0.602399i | \(-0.794212\pi\) | ||||
−0.798195 | + | 0.602399i | \(0.794212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8027.32 | −1.86081 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 330.663 | 0.0757912 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4978.43 | −1.12840 | −0.564201 | − | 0.825637i | \(-0.690816\pi\) | ||||
−0.564201 | + | 0.825637i | \(0.690816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 231.445 | 0.0518793 | 0.0259397 | − | 0.999664i | \(-0.491742\pi\) | ||||
0.0259397 | + | 0.999664i | \(0.491742\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.8917 | 0.00507497 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2251.77 | −0.493771 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2395.60 | −0.519630 | −0.259815 | − | 0.965658i | \(-0.583662\pi\) | ||||
−0.259815 | + | 0.965658i | \(0.583662\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1978.31 | −0.424511 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7597.72 | 1.61296 | 0.806480 | − | 0.591261i | \(-0.201370\pi\) | ||||
0.806480 | + | 0.591261i | \(0.201370\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5203.18 | 1.09292 | 0.546461 | − | 0.837484i | \(-0.315974\pi\) | ||||
0.546461 | + | 0.837484i | \(0.315974\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 934.756 | 0.194281 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1022.44 | 0.210288 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1751.48 | −0.356500 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −57.4735 | −0.0115779 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6628.25 | 1.32159 | 0.660796 | − | 0.750566i | \(-0.270219\pi\) | ||||
0.660796 | + | 0.750566i | \(0.270219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 783.309 | 0.154597 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1095.66 | 0.214063 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 35.6532 | 0.00689590 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4677.81 | −0.895763 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1730.66 | −0.328131 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 598.333 | 0.112329 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8142.39 | −1.51371 | −0.756857 | − | 0.653580i | \(-0.773266\pi\) | ||||
−0.756857 | + | 0.653580i | \(0.773266\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1519.35 | 0.279718 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1020.13 | −0.186000 | −0.0930000 | − | 0.995666i | \(-0.529646\pi\) | ||||
−0.0930000 | + | 0.995666i | \(0.529646\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6853.77 | −1.23769 | −0.618846 | − | 0.785512i | \(-0.712400\pi\) | ||||
−0.618846 | + | 0.785512i | \(0.712400\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9224.12 | 1.64991 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7542.08 | −1.33630 | −0.668148 | − | 0.744029i | \(-0.732913\pi\) | ||||
−0.668148 | + | 0.744029i | \(0.732913\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −324.455 | −0.0569467 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3584.44 | 0.623252 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1491.37 | −0.256911 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 107.249 | 0.0183049 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −453.838 | −0.0767501 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2384.11 | 0.399514 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 849.318 | 0.141035 | 0.0705177 | − | 0.997511i | \(-0.477535\pi\) | ||||
0.0705177 | + | 0.997511i | \(0.477535\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4181.14 | −0.688064 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17848.6 | 2.91096 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8174.38 | 1.32133 | 0.660663 | − | 0.750682i | \(-0.270275\pi\) | ||||
0.660663 | + | 0.750682i | \(0.270275\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3655.81 | 0.585711 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −954.309 | −0.151551 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4430.20 | −0.697401 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2357.94 | −0.367962 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2726.57 | −0.421816 | −0.210908 | − | 0.977506i | \(-0.567642\pi\) | ||||
−0.210908 | + | 0.977506i | \(0.567642\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7409.06 | 1.13638 | 0.568191 | − | 0.822896i | \(-0.307643\pi\) | ||||
0.568191 | + | 0.822896i | \(0.307643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −52.1850 | −0.00793570 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5535.82 | −0.834679 | −0.417340 | − | 0.908751i | \(-0.637037\pi\) | ||||
−0.417340 | + | 0.908751i | \(0.637037\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2791.78 | 0.417387 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2415.46 | 0.358094 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3735.97 | 0.549239 | 0.274619 | − | 0.961553i | \(-0.411448\pi\) | ||||
0.274619 | + | 0.961553i | \(0.411448\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6155.48 | −0.897431 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2352.66 | −0.340173 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18622.3 | 2.67051 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11094.8 | −1.57805 | −0.789027 | − | 0.614359i | \(-0.789415\pi\) | ||||
−0.789027 | + | 0.614359i | \(0.789415\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1077.02 | −0.151944 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9785.05 | 1.36931 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4753.81 | −0.659901 | −0.329951 | − | 0.943998i | \(-0.607032\pi\) | ||||
−0.329951 | + | 0.943998i | \(0.607032\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2687.72 | −0.370115 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.4534 | 0.00211111 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6164.88 | −0.835537 | −0.417769 | − | 0.908553i | \(-0.637188\pi\) | ||||
−0.417769 | + | 0.908553i | \(0.637188\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3262.33 | 0.438672 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2734.38 | −0.364805 | −0.182402 | − | 0.983224i | \(-0.558387\pi\) | ||||
−0.182402 | + | 0.983224i | \(0.558387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4449.58 | 0.589017 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4927.51 | 0.647234 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2349.93 | 0.306289 | 0.153144 | − | 0.988204i | \(-0.451060\pi\) | ||||
0.153144 | + | 0.988204i | \(0.451060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3762.01 | 0.486581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5094.65 | −0.653921 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11407.9 | 1.45315 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5065.74 | −0.640409 | −0.320204 | − | 0.947348i | \(-0.603752\pi\) | ||||
−0.320204 | + | 0.947348i | \(0.603752\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1139.44 | −0.142965 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5031.88 | 0.626634 | 0.313317 | − | 0.949649i | \(-0.398560\pi\) | ||||
0.313317 | + | 0.949649i | \(0.398560\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 45.4526 | 0.00561825 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7859.99 | −0.964361 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2016.92 | −0.245639 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8107.90 | −0.980220 | −0.490110 | − | 0.871661i | \(-0.663043\pi\) | ||||
−0.490110 | + | 0.871661i | \(0.663043\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2938.37 | −0.352650 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −954.829 | −0.113763 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2621.95 | −0.310136 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5499.83 | −0.645870 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12818.4 | 1.49456 | 0.747279 | − | 0.664510i | \(-0.231360\pi\) | ||||
0.747279 | + | 0.664510i | \(0.231360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6405.87 | −0.741575 | −0.370788 | − | 0.928718i | \(-0.620912\pi\) | ||||
−0.370788 | + | 0.928718i | \(0.620912\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2511.37 | −0.288669 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11316.6 | 1.29161 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −729.349 | −0.0826597 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.6321 | −0.00130909 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1873.09 | −0.209336 | −0.104668 | − | 0.994507i | \(-0.533378\pi\) | ||||
−0.104668 | + | 0.994507i | \(0.533378\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 492.001 | 0.0546052 | 0.0273026 | − | 0.999627i | \(-0.491308\pi\) | ||||
0.0273026 | + | 0.999627i | \(0.491308\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1022.02 | −0.112648 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1774.64 | −0.194262 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9655.65 | 1.04975 | 0.524874 | − | 0.851180i | \(-0.324113\pi\) | ||||
0.524874 | + | 0.851180i | \(0.324113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3288.61 | −0.355104 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3021.05 | −0.324005 | −0.162003 | − | 0.986790i | \(-0.551795\pi\) | ||||
−0.162003 | + | 0.986790i | \(0.551795\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3061.23 | −0.326104 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3263.47 | −0.345318 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1335.44 | 0.140364 | 0.0701820 | − | 0.997534i | \(-0.477642\pi\) | ||||
0.0701820 | + | 0.997534i | \(0.477642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −519.537 | −0.0542440 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2079.54 | 0.215685 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −211.928 | −0.0218359 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8984.92 | −0.919687 | −0.459843 | − | 0.888000i | \(-0.652094\pi\) | ||||
−0.459843 | + | 0.888000i | \(0.652094\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5506.40 | −0.559950 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8468.56 | 0.855575 | 0.427788 | − | 0.903879i | \(-0.359293\pi\) | ||||
0.427788 | + | 0.903879i | \(0.359293\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13946.0 | 1.39983 | 0.699917 | − | 0.714224i | \(-0.253220\pi\) | ||||
0.699917 | + | 0.714224i | \(0.253220\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3006.02 | −0.299787 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1242.51 | 0.123119 | 0.0615594 | − | 0.998103i | \(-0.480393\pi\) | ||||
0.0615594 | + | 0.998103i | \(0.480393\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21756.9 | −2.14209 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4984.49 | −0.487629 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2376.96 | 0.231063 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5338.34 | −0.515663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10307.4 | −0.989396 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1054.91 | 0.100626 | 0.0503131 | − | 0.998733i | \(-0.483978\pi\) | ||||
0.0503131 | + | 0.998733i | \(0.483978\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 96.0634 | 0.00910627 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2874.25 | 0.270772 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 532.082 | 0.0498156 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8140.23 | −0.757432 | −0.378716 | − | 0.925513i | \(-0.623634\pi\) | ||||
−0.378716 | + | 0.925513i | \(0.623634\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2624.27 | −0.242686 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19696.4 | 1.81035 | 0.905177 | − | 0.425034i | \(-0.139738\pi\) | ||||
0.905177 | + | 0.425034i | \(0.139738\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1630.59 | 0.148962 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4687.10 | −0.425595 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3403.09 | −0.307142 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3554.81 | 0.318908 | 0.159454 | − | 0.987205i | \(-0.449027\pi\) | ||||
0.159454 | + | 0.987205i | \(0.449027\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1562.93 | −0.139375 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21333.8 | −1.89111 | −0.945555 | − | 0.325463i | \(-0.894480\pi\) | ||||
−0.945555 | + | 0.325463i | \(0.894480\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16022.2 | 1.41184 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4285.96 | −0.375436 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11816.7 | −1.02901 | −0.514506 | − | 0.857487i | \(-0.672025\pi\) | ||||
−0.514506 | + | 0.857487i | \(0.672025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22700.0 | −1.96515 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2597.52 | 0.223554 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14065.9 | −1.20353 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1211.45 | −0.103055 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3900.79 | −0.329914 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12945.2 | 1.08856 | 0.544278 | − | 0.838905i | \(-0.316804\pi\) | ||||
0.544278 | + | 0.838905i | \(0.316804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2842.92 | −0.237690 | −0.118845 | − | 0.992913i | \(-0.537919\pi\) | ||||
−0.118845 | + | 0.992913i | \(0.537919\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8646.09 | 0.718755 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4796.01 | 0.396428 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7690.44 | −0.632073 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1005.80 | 0.0821994 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.7449 | 0.00201092 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33184.3 | −2.68165 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2309.93 | −0.185625 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1586.38 | −0.126772 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −564.312 | −0.0448459 | −0.0224230 | − | 0.999749i | \(-0.507138\pi\) | ||||
−0.0224230 | + | 0.999749i | \(0.507138\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2271.14 | 0.179491 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4201.57 | 0.330230 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21063.9 | 1.64648 | 0.823241 | − | 0.567692i | \(-0.192164\pi\) | ||||
0.823241 | + | 0.567692i | \(0.192164\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 768.282 | 0.0597258 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −769.195 | −0.0594715 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13905.9 | −1.06933 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6353.20 | −0.485907 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23042.5 | 1.75286 | 0.876430 | − | 0.481530i | \(-0.159919\pi\) | ||||
0.876430 | + | 0.481530i | \(0.159919\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −113.212 | −0.00856590 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1227.38 | −0.0923707 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9753.28 | −0.730109 | −0.365055 | − | 0.930986i | \(-0.618950\pi\) | ||||
−0.365055 | + | 0.930986i | \(0.618950\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33844.9 | −2.52012 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9581.08 | 0.709643 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11380.6 | −0.838485 | −0.419242 | − | 0.907874i | \(-0.637704\pi\) | ||||
−0.419242 | + | 0.907874i | \(0.637704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12977.3 | 0.951109 | 0.475555 | − | 0.879686i | \(-0.342247\pi\) | ||||
0.475555 | + | 0.879686i | \(0.342247\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3148.26 | −0.229529 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13466.1 | 0.976649 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12229.5 | 0.882359 | 0.441180 | − | 0.897419i | \(-0.354560\pi\) | ||||
0.441180 | + | 0.897419i | \(0.354560\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2046.17 | −0.146867 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3196.07 | 0.228219 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4972.12 | −0.353215 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 223.241 | 0.0157775 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13884.3 | −0.976263 | −0.488132 | − | 0.872770i | \(-0.662321\pi\) | ||||
−0.488132 | + | 0.872770i | \(0.662321\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2262.41 | −0.158270 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2902.93 | 0.202048 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22356.1 | −1.54815 | −0.774077 | − | 0.633092i | \(-0.781786\pi\) | ||||
−0.774077 | + | 0.633092i | \(0.781786\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22362.0 | −1.54076 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −580.942 | −0.0398264 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3966.27 | −0.270546 | −0.135273 | − | 0.990808i | \(-0.543191\pi\) | ||||
−0.135273 | + | 0.990808i | \(0.543191\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17343.0 | −1.17710 | −0.588550 | − | 0.808461i | \(-0.700301\pi\) | ||||
−0.588550 | + | 0.808461i | \(0.700301\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22918.2 | 1.54777 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21780.6 | 1.46365 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17468.7 | −1.16810 | −0.584048 | − | 0.811719i | \(-0.698532\pi\) | ||||
−0.584048 | + | 0.811719i | \(0.698532\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1245.80 | 0.0828942 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 57.6997 | 0.00382042 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5605.90 | 0.369364 | 0.184682 | − | 0.982798i | \(-0.440875\pi\) | ||||
0.184682 | + | 0.982798i | \(0.440875\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1636.52 | −0.107302 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12413.8 | 0.809987 | 0.404993 | − | 0.914320i | \(-0.367274\pi\) | ||||
0.404993 | + | 0.914320i | \(0.367274\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24588.8 | 1.59662 | 0.798310 | − | 0.602247i | \(-0.205728\pi\) | ||||
0.798310 | + | 0.602247i | \(0.205728\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6552.28 | −0.423404 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3731.54 | 0.239970 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −275.570 | −0.0176365 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 578.988 | 0.0368781 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10136.3 | 0.642546 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15144.9 | −0.955481 | −0.477740 | − | 0.878501i | \(-0.658544\pi\) | ||||
−0.477740 | + | 0.878501i | \(0.658544\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7702.78 | −0.483662 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30202.2 | −1.88746 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 75.5572 | 0.00469966 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3584.75 | 0.221925 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1087.26 | −0.0669957 | −0.0334979 | − | 0.999439i | \(-0.510665\pi\) | ||||
−0.0334979 | + | 0.999439i | \(0.510665\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14014.7 | 0.859541 | 0.429771 | − | 0.902938i | \(-0.358594\pi\) | ||||
0.429771 | + | 0.902938i | \(0.358594\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7487.30 | 0.457073 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9390.59 | 0.570606 | 0.285303 | − | 0.958437i | \(-0.407906\pi\) | ||||
0.285303 | + | 0.958437i | \(0.407906\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 485.182 | 0.0293452 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3664.25 | 0.220604 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8357.09 | 0.500824 | 0.250412 | − | 0.968139i | \(-0.419434\pi\) | ||||
0.250412 | + | 0.968139i | \(0.419434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 47165.5 | 2.81360 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23911.7 | 1.41992 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13965.0 | −0.825489 | −0.412745 | − | 0.910847i | \(-0.635430\pi\) | ||||
−0.412745 | + | 0.910847i | \(0.635430\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10501.3 | −0.617934 | −0.308967 | − | 0.951073i | \(-0.599983\pi\) | ||||
−0.308967 | + | 0.951073i | \(0.599983\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 58.4585 | 0.00342434 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10548.8 | 0.615133 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1940.31 | 0.112637 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7396.34 | −0.427443 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 370.608 | 0.0213221 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30084.5 | −1.72314 | −0.861569 | − | 0.507641i | \(-0.830518\pi\) | ||||
−0.861569 | + | 0.507641i | \(0.830518\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19710.1 | −1.12391 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14825.2 | −0.841621 | −0.420810 | − | 0.907149i | \(-0.638254\pi\) | ||||
−0.420810 | + | 0.907149i | \(0.638254\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −648.591 | −0.0366578 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3809.99 | 0.214389 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30850.4 | −1.72834 | −0.864171 | − | 0.503199i | \(-0.832156\pi\) | ||||
−0.864171 | + | 0.503199i | \(0.832156\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27203.1 | 1.51734 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1713.61 | 0.0951648 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 236.816 | 0.0130943 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27669.0 | 1.52327 | 0.761635 | − | 0.648006i | \(-0.224397\pi\) | ||||
0.761635 | + | 0.648006i | \(0.224397\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5713.42 | 0.313182 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 50916.6 | 2.77896 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2611.01 | 0.141892 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4987.26 | −0.269865 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18155.9 | 0.978229 | 0.489115 | − | 0.872220i | \(-0.337320\pi\) | ||||
0.489115 | + | 0.872220i | \(0.337320\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4781.58 | −0.256530 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3815.99 | −0.203856 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19530.5 | −1.03893 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12971.8 | 0.687118 | 0.343559 | − | 0.939131i | \(-0.388367\pi\) | ||||
0.343559 | + | 0.939131i | \(0.388367\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14648.1 | 0.772642 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5706.97 | 0.299758 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 107.688 | 0.00563259 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.3952 | −0.00132274 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11163.6 | −0.579044 | −0.289522 | − | 0.957171i | \(-0.593496\pi\) | ||||
−0.289522 | + | 0.957171i | \(0.593496\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17145.9 | 0.885642 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3877.60 | 0.199460 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5836.68 | 0.298992 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23149.5 | −1.18097 | −0.590487 | − | 0.807047i | \(-0.701064\pi\) | ||||
−0.590487 | + | 0.807047i | \(0.701064\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4933.60 | −0.250653 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11945.7 | −0.604418 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30271.8 | 1.52539 | 0.762697 | − | 0.646756i | \(-0.223875\pi\) | ||||
0.762697 | + | 0.646756i | \(0.223875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4997.01 | −0.250772 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11055.4 | 0.552553 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31154.1 | −1.55077 | −0.775387 | − | 0.631487i | \(-0.782445\pi\) | ||||
−0.775387 | + | 0.631487i | \(0.782445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.5765 | −0.00136713 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32817.8 | 1.62041 | 0.810207 | − | 0.586144i | \(-0.199355\pi\) | ||||
0.810207 | + | 0.586144i | \(0.199355\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30212.8 | 1.48579 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3366.68 | −0.164900 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40450.6 | 1.97334 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26390.0 | 1.28227 | 0.641135 | − | 0.767428i | \(-0.278464\pi\) | ||||
0.641135 | + | 0.767428i | \(0.278464\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10835.3 | 0.524382 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19252.1 | −0.928021 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2340.44 | −0.112371 | −0.0561853 | − | 0.998420i | \(-0.517894\pi\) | ||||
−0.0561853 | + | 0.998420i | \(0.517894\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1460.51 | −0.0698458 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34510.4 | 1.64389 | 0.821946 | − | 0.569565i | \(-0.192888\pi\) | ||||
0.821946 | + | 0.569565i | \(0.192888\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5121.58 | −0.243006 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 23555.7 | 1.11328 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.1086 | −0.00108788 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24619.2 | 1.15447 | 0.577237 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577237 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2126.32 | −0.0993225 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4506.63 | −0.209692 | −0.104846 | − | 0.994488i | \(-0.533435\pi\) | ||||
−0.104846 | + | 0.994488i | \(0.533435\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17167.2 | 0.795698 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7744.34 | 0.357563 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1231.68 | −0.0566491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1729.23 | 0.0792274 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2840.00 | −0.129621 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46145.7 | 2.09810 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12917.4 | 0.585076 | 0.292538 | − | 0.956254i | \(-0.405500\pi\) | ||||
0.292538 | + | 0.956254i | \(0.405500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13284.6 | −0.599421 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41255.9 | 1.85448 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.6516 | −0.000790449 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15661.9 | −0.698706 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14608.1 | 0.649243 | 0.324621 | − | 0.945844i | \(-0.394763\pi\) | ||||
0.324621 | + | 0.945844i | \(0.394763\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6088.29 | 0.269572 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3930.73 | −0.173390 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11534.7 | 0.506911 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26609.4 | −1.16504 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9713.31 | −0.423698 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16506.3 | 0.717342 | 0.358671 | − | 0.933464i | \(-0.383230\pi\) | ||||
0.358671 | + | 0.933464i | \(0.383230\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43809.7 | 1.89688 | 0.948438 | − | 0.316964i | \(-0.102663\pi\) | ||||
0.948438 | + | 0.316964i | \(0.102663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 451.568 | 0.0194799 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24295.1 | 1.04420 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5635.13 | 0.241308 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −272.123 | −0.0116102 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17285.6 | −0.734802 | −0.367401 | − | 0.930063i | \(-0.619752\pi\) | ||||
−0.367401 | + | 0.930063i | \(0.619752\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39612.1 | 1.67775 | 0.838876 | − | 0.544323i | \(-0.183213\pi\) | ||||
0.838876 | + | 0.544323i | \(0.183213\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4393.38 | −0.185403 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23037.5 | −0.968674 | −0.484337 | − | 0.874882i | \(-0.660939\pi\) | ||||
−0.484337 | + | 0.874882i | \(0.660939\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32090.7 | 1.34446 | 0.672228 | − | 0.740344i | \(-0.265337\pi\) | ||||
0.672228 | + | 0.740344i | \(0.265337\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4674.00 | −0.195113 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7972.57 | 0.331612 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14469.4 | 0.599682 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8353.20 | −0.344957 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19295.2 | 0.793973 | 0.396987 | − | 0.917824i | \(-0.370056\pi\) | ||||
0.396987 | + | 0.917824i | \(0.370056\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14823.7 | 0.605643 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39678.8 | 1.61538 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26549.9 | −1.07705 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10151.8 | 0.410376 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12061.6 | 0.485860 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19213.6 | −0.771234 | −0.385617 | − | 0.922659i | \(-0.626011\pi\) | ||||
−0.385617 | + | 0.922659i | \(0.626011\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11111.8 | −0.444464 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38335.0 | −1.52800 | −0.764001 | − | 0.645214i | \(-0.776768\pi\) | ||||
−0.764001 | + | 0.645214i | \(0.776768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34344.3 | 1.36416 | 0.682080 | − | 0.731278i | \(-0.261076\pi\) | ||||
0.682080 | + | 0.731278i | \(0.261076\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1994.86 | 0.0789601 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39162.2 | −1.54472 | −0.772362 | − | 0.635183i | \(-0.780925\pi\) | ||||
−0.772362 | + | 0.635183i | \(0.780925\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36112.9 | 1.41951 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3417.28 | −0.133860 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7066.05 | 0.275833 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −526.555 | −0.0204841 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 683.212 | 0.0264871 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30331.0 | −1.17186 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15235.0 | 0.586601 | 0.293301 | − | 0.956020i | \(-0.405246\pi\) | ||||
0.293301 | + | 0.956020i | \(0.405246\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12932.2 | 0.496238 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29455.1 | 1.12641 | 0.563206 | − | 0.826317i | \(-0.309568\pi\) | ||||
0.563206 | + | 0.826317i | \(0.309568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37608.0 | 1.43331 | 0.716653 | − | 0.697430i | \(-0.245673\pi\) | ||||
0.716653 | + | 0.697430i | \(0.245673\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1528.30 | 0.0580487 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20517.3 | 0.776666 | 0.388333 | − | 0.921519i | \(-0.373051\pi\) | ||||
0.388333 | + | 0.921519i | \(0.373051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36815.5 | 1.38892 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4868.48 | −0.183053 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2872.01 | −0.107624 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21385.0 | 0.798684 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 69.5621 | 0.00258931 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2473.61 | 0.0917680 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24988.1 | 0.923944 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9126.78 | −0.336346 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21025.9 | −0.772291 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49117.1 | −1.79813 | −0.899067 | − | 0.437811i | \(-0.855754\pi\) | ||||
−0.899067 | + | 0.437811i | \(0.855754\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20573.1 | 0.750678 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23792.4 | −0.865289 | −0.432645 | − | 0.901564i | \(-0.642420\pi\) | ||||
−0.432645 | + | 0.901564i | \(0.642420\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1624.03 | −0.0588693 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1167.39 | 0.0421780 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −57493.3 | −2.07044 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43361.1 | −1.55642 | −0.778211 | − | 0.628003i | \(-0.783873\pi\) | ||||
−0.778211 | + | 0.628003i | \(0.783873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15886.4 | −0.568377 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −82.3610 | −0.00293710 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36282.8 | 1.28970 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18061.2 | −0.639921 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24782.7 | −0.875235 | −0.437617 | − | 0.899161i | \(-0.644178\pi\) | ||||
−0.437617 | + | 0.899161i | \(0.644178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3760.88 | −0.132393 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1990.34 | −0.0698402 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11362.9 | 0.397440 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31441.0 | −1.09619 | −0.548097 | − | 0.836415i | \(-0.684647\pi\) | ||||
−0.548097 | + | 0.836415i | \(0.684647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13372.2 | −0.464735 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2094.24 | 0.0725509 | 0.0362754 | − | 0.999342i | \(-0.488451\pi\) | ||||
0.0362754 | + | 0.999342i | \(0.488451\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3106.94 | 0.107292 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 38947.8 | 1.34071 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29337.6 | −1.00670 | −0.503350 | − | 0.864083i | \(-0.667899\pi\) | ||||
−0.503350 | + | 0.864083i | \(0.667899\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −549.381 | −0.0187921 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14715.2 | −0.501759 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13702.6 | −0.465763 | −0.232881 | − | 0.972505i | \(-0.574815\pi\) | ||||
−0.232881 | + | 0.972505i | \(0.574815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29146.1 | 0.987588 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −633.037 | −0.0213826 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33159.7 | −1.11656 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22515.5 | −0.755780 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42609.8 | −1.42584 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18943.2 | 0.631919 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15477.4 | −0.514706 | −0.257353 | − | 0.966318i | \(-0.582850\pi\) | ||||
−0.257353 | + | 0.966318i | \(0.582850\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2909.78 | −0.0964662 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −943.820 | −0.0311932 | −0.0155966 | − | 0.999878i | \(-0.504965\pi\) | ||||
−0.0155966 | + | 0.999878i | \(0.504965\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62065.8 | −2.04495 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 209.251 | 0.00687323 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41392.6 | 1.35544 | 0.677720 | − | 0.735320i | \(-0.262968\pi\) | ||||
0.677720 | + | 0.735320i | \(0.262968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1896.13 | −0.0619004 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5394.96 | 0.175584 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9580.92 | −0.310869 | −0.155434 | − | 0.987846i | \(-0.549678\pi\) | ||||
−0.155434 | + | 0.987846i | \(0.549678\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26874.9 | −0.869346 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4651.57 | 0.150011 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14214.7 | −0.457029 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25374.3 | 0.813361 | 0.406680 | − | 0.913570i | \(-0.366686\pi\) | ||||
0.406680 | + | 0.913570i | \(0.366686\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1657.08 | 0.0529567 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5378.28 | 0.171360 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51564.5 | 1.63798 | 0.818989 | − | 0.573810i | \(-0.194535\pi\) | ||||
0.818989 | + | 0.573810i | \(0.194535\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17654.4 | −0.559119 |
(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 | 1856.4.a.bf.1.6 | 9 | ||
4.3 | odd | 2 | 1856.4.a.bg.1.4 | 9 | |||
8.3 | odd | 2 | 928.4.a.d.1.6 | ✓ | 9 | ||
8.5 | even | 2 | 928.4.a.e.1.4 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.d.1.6 | ✓ | 9 | 8.3 | odd | 2 | ||
928.4.a.e.1.4 | yes | 9 | 8.5 | even | 2 | ||
1856.4.a.bf.1.6 | 9 | 1.1 | even | 1 | trivial | ||
1856.4.a.bg.1.4 | 9 | 4.3 | odd | 2 |