Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, 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("384.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(22.6567334422\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{15}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 15 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.87298\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 | ||||||||
\(5\) | −11.4919 | −1.02787 | −0.513935 | − | 0.857829i | \(-0.671813\pi\) | ||||
−0.513935 | + | 0.857829i | \(0.671813\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.4919 | 0.728496 | 0.364248 | − | 0.931302i | \(-0.381326\pi\) | ||||
0.364248 | + | 0.931302i | \(0.381326\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.9839 | 0.301069 | 0.150535 | − | 0.988605i | \(-0.451901\pi\) | ||||
0.150535 | + | 0.988605i | \(0.451901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.0426692 | 0.0213346 | − | 0.999772i | \(-0.493208\pi\) | ||||
0.0213346 | + | 0.999772i | \(0.493208\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 34.4758 | 0.593441 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 106.952 | 1.52586 | 0.762929 | − | 0.646483i | \(-0.223761\pi\) | ||||
0.762929 | + | 0.646483i | \(0.223761\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −86.9839 | −1.05029 | −0.525144 | − | 0.851013i | \(-0.675989\pi\) | ||||
−0.525144 | + | 0.851013i | \(0.675989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −40.4758 | −0.420597 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −64.9516 | −0.588841 | −0.294421 | − | 0.955676i | \(-0.595127\pi\) | ||||
−0.294421 | + | 0.955676i | \(0.595127\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.06453 | 0.0565163 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 129.395 | 0.828554 | 0.414277 | − | 0.910151i | \(-0.364034\pi\) | ||||
0.414277 | + | 0.910151i | \(0.364034\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −246.444 | −1.42782 | −0.713912 | − | 0.700235i | \(-0.753079\pi\) | ||||
−0.713912 | + | 0.700235i | \(0.753079\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −32.9516 | −0.173822 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −155.048 | −0.748799 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −259.016 | −1.15086 | −0.575432 | − | 0.817849i | \(-0.695166\pi\) | ||||
−0.575432 | + | 0.817849i | \(0.695166\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.00000 | −0.0246351 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 324.984 | 1.23790 | 0.618951 | − | 0.785430i | \(-0.287558\pi\) | ||||
0.618951 | + | 0.785430i | \(0.287558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −292.823 | −1.03849 | −0.519244 | − | 0.854626i | \(-0.673787\pi\) | ||||
−0.519244 | + | 0.854626i | \(0.673787\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −103.427 | −0.342623 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −386.984 | −1.20101 | −0.600504 | − | 0.799622i | \(-0.705033\pi\) | ||||
−0.600504 | + | 0.799622i | \(0.705033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −160.968 | −0.469294 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −320.855 | −0.880954 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −536.508 | −1.39047 | −0.695236 | − | 0.718781i | \(-0.744700\pi\) | ||||
−0.695236 | + | 0.718781i | \(0.744700\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −126.226 | −0.309460 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 260.952 | 0.606384 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 103.806 | 0.229058 | 0.114529 | − | 0.993420i | \(-0.463464\pi\) | ||||
0.114529 | + | 0.993420i | \(0.463464\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −628.790 | −1.31981 | −0.659904 | − | 0.751350i | \(-0.729403\pi\) | ||||
−0.659904 | + | 0.751350i | \(0.729403\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 121.427 | 0.242832 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22.9839 | −0.0438584 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 719.548 | 1.31204 | 0.656021 | − | 0.754743i | \(-0.272238\pi\) | ||||
0.656021 | + | 0.754743i | \(0.272238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 194.855 | 0.339968 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −200.952 | −0.335895 | −0.167948 | − | 0.985796i | \(-0.553714\pi\) | ||||
−0.167948 | + | 0.985796i | \(0.553714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 987.581 | 1.58339 | 0.791696 | − | 0.610916i | \(-0.209199\pi\) | ||||
0.791696 | + | 0.610916i | \(0.209199\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −21.1936 | −0.0326297 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 148.194 | 0.219328 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −770.379 | −1.09714 | −0.548572 | − | 0.836103i | \(-0.684828\pi\) | ||||
−0.548572 | + | 0.836103i | \(0.684828\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1284.50 | −1.69870 | −0.849350 | − | 0.527829i | \(-0.823006\pi\) | ||||
−0.849350 | + | 0.527829i | \(0.823006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1229.08 | −1.56838 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −388.185 | −0.478366 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 844.161 | 1.00540 | 0.502702 | − | 0.864460i | \(-0.332339\pi\) | ||||
0.502702 | + | 0.864460i | \(0.332339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 26.9839 | 0.0310844 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 739.331 | 0.824355 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 999.613 | 1.07956 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1259.84 | −1.31873 | −0.659367 | − | 0.751821i | \(-0.729176\pi\) | ||||
−0.659367 | + | 0.751821i | \(0.729176\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 98.8548 | 0.100356 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −50.4113 | −0.0496644 | −0.0248322 | − | 0.999692i | \(-0.507905\pi\) | ||||
−0.0248322 | + | 0.999692i | \(0.507905\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1055.40 | −1.00962 | −0.504812 | − | 0.863230i | \(-0.668438\pi\) | ||||
−0.504812 | + | 0.863230i | \(0.668438\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 465.145 | 0.432319 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1197.39 | −1.08183 | −0.540915 | − | 0.841077i | \(-0.681922\pi\) | ||||
−0.540915 | + | 0.841077i | \(0.681922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1583.32 | 1.39133 | 0.695664 | − | 0.718367i | \(-0.255110\pi\) | ||||
0.695664 | + | 0.718367i | \(0.255110\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 777.048 | 0.664452 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −907.710 | −0.755665 | −0.377832 | − | 0.925874i | \(-0.623330\pi\) | ||||
−0.377832 | + | 0.925874i | \(0.623330\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 746.419 | 0.605252 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.0000 | 0.0142231 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1442.98 | 1.11158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1210.35 | −0.909357 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −974.952 | −0.714703 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1355.31 | 0.969778 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 37.0566 | 0.0258917 | 0.0129458 | − | 0.999916i | \(-0.495879\pi\) | ||||
0.0129458 | + | 0.999916i | \(0.495879\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 878.468 | 0.599572 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 203.613 | 0.135799 | 0.0678997 | − | 0.997692i | \(-0.478370\pi\) | ||||
0.0678997 | + | 0.997692i | \(0.478370\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1173.58 | −0.765130 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 310.282 | 0.197814 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 247.403 | 0.154285 | 0.0771427 | − | 0.997020i | \(-0.475420\pi\) | ||||
0.0771427 | + | 0.997020i | \(0.475420\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1631.68 | 0.995662 | 0.497831 | − | 0.867274i | \(-0.334130\pi\) | ||||
0.497831 | + | 0.867274i | \(0.334130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1160.95 | 0.693403 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.9677 | 0.0128464 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1487.00 | −0.851646 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 482.903 | 0.270947 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −495.298 | −0.272325 | −0.136162 | − | 0.990687i | \(-0.543477\pi\) | ||||
−0.136162 | + | 0.990687i | \(0.543477\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −576.605 | −0.310751 | −0.155376 | − | 0.987855i | \(-0.549659\pi\) | ||||
−0.155376 | + | 0.987855i | \(0.549659\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 962.564 | 0.508619 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2832.11 | 1.46762 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 212.855 | 0.108202 | 0.0541008 | − | 0.998535i | \(-0.482771\pi\) | ||||
0.0541008 | + | 0.998535i | \(0.482771\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1609.52 | 0.802790 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −876.323 | −0.428968 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2991.11 | 1.43731 | 0.718657 | − | 0.695365i | \(-0.244757\pi\) | ||||
0.718657 | + | 0.695365i | \(0.244757\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 378.678 | 0.178667 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3231.23 | 1.49724 | 0.748622 | − | 0.662997i | \(-0.230716\pi\) | ||||
0.748622 | + | 0.662997i | \(0.230716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2193.00 | −0.998179 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −782.855 | −0.350096 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2815.93 | 1.23752 | 0.618760 | − | 0.785580i | \(-0.287635\pi\) | ||||
0.618760 | + | 0.785580i | \(0.287635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 95.3142 | 0.0411719 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −311.419 | −0.132247 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 630.903 | 0.263441 | 0.131720 | − | 0.991287i | \(-0.457950\pi\) | ||||
0.131720 | + | 0.991287i | \(0.457950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1748.23 | −0.717926 | −0.358963 | − | 0.933352i | \(-0.616870\pi\) | ||||
−0.358963 | + | 0.933352i | \(0.616870\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1886.37 | 0.761992 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2976.60 | 1.18294 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1174.74 | 0.459389 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −364.282 | −0.140199 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1450.52 | −0.549506 | −0.274753 | − | 0.961515i | \(-0.588596\pi\) | ||||
−0.274753 | + | 0.961515i | \(0.588596\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4302.94 | −1.60483 | −0.802415 | − | 0.596767i | \(-0.796452\pi\) | ||||
−0.802415 | + | 0.596767i | \(0.796452\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 68.9516 | 0.0253217 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4336.23 | 1.56824 | 0.784121 | − | 0.620607i | \(-0.213114\pi\) | ||||
0.784121 | + | 0.620607i | \(0.213114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4183.88 | −1.49039 | −0.745194 | − | 0.666848i | \(-0.767643\pi\) | ||||
−0.745194 | + | 0.666848i | \(0.767643\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2158.64 | −0.757508 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1745.79 | 0.603598 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3734.69 | −1.27240 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −584.564 | −0.196280 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −955.419 | −0.316209 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1476.65 | 0.481784 | 0.240892 | − | 0.970552i | \(-0.422560\pi\) | ||||
0.240892 | + | 0.970552i | \(0.422560\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 602.855 | 0.193929 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3365.10 | 1.06743 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3325.00 | −1.04016 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2962.74 | −0.914171 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 213.903 | 0.0651072 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6097.96 | 1.83116 | 0.915582 | − | 0.402131i | \(-0.131731\pi\) | ||||
0.915582 | + | 0.402131i | \(0.131731\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 63.5808 | 0.0188388 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6141.37 | −1.79567 | −0.897835 | − | 0.440332i | \(-0.854861\pi\) | ||||
−0.897835 | + | 0.440332i | \(0.854861\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2168.84 | 0.625855 | 0.312928 | − | 0.949777i | \(-0.398690\pi\) | ||||
0.312928 | + | 0.949777i | \(0.398690\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −444.581 | −0.126629 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2142.61 | −0.602434 | −0.301217 | − | 0.953556i | \(-0.597393\pi\) | ||||
−0.301217 | + | 0.953556i | \(0.597393\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4447.19 | 1.23448 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2311.14 | 0.633437 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6721.00 | −1.81902 | −0.909509 | − | 0.415684i | \(-0.863542\pi\) | ||||
−0.909509 | + | 0.415684i | \(0.863542\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −193.226 | −0.0516463 | −0.0258231 | − | 0.999667i | \(-0.508221\pi\) | ||||
−0.0258231 | + | 0.999667i | \(0.508221\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1849.83 | 0.482373 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −173.968 | −0.0448150 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3853.50 | 0.980745 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1434.98 | 0.360858 | 0.180429 | − | 0.983588i | \(-0.442251\pi\) | ||||
0.180429 | + | 0.983588i | \(0.442251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −713.420 | −0.177282 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3687.24 | 0.905506 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5333.03 | 1.29442 | 0.647209 | − | 0.762313i | \(-0.275936\pi\) | ||||
0.647209 | + | 0.762313i | \(0.275936\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3494.63 | −0.838400 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1164.56 | 0.276185 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 552.774 | 0.129603 | 0.0648014 | − | 0.997898i | \(-0.479359\pi\) | ||||
0.0648014 | + | 0.997898i | \(0.479359\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6165.51 | 1.42922 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2532.48 | −0.580470 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2364.31 | −0.535891 | −0.267946 | − | 0.963434i | \(-0.586345\pi\) | ||||
−0.267946 | + | 0.963434i | \(0.586345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7133.72 | −1.59905 | −0.799525 | − | 0.600633i | \(-0.794915\pi\) | ||||
−0.799525 | + | 0.600633i | \(0.794915\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −80.9516 | −0.0179466 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 77.5959 | 0.0170153 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2025.77 | −0.439411 | −0.219706 | − | 0.975566i | \(-0.570510\pi\) | ||||
−0.219706 | + | 0.975566i | \(0.570510\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2217.99 | −0.475942 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2068.84 | −0.439205 | −0.219602 | − | 0.975589i | \(-0.570476\pi\) | ||||
−0.219602 | + | 0.975589i | \(0.570476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3408.19 | −0.715887 | −0.357944 | − | 0.933743i | \(-0.616522\pi\) | ||||
−0.357944 | + | 0.933743i | \(0.616522\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2998.84 | −0.623284 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4384.66 | 0.901806 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6525.64 | 1.32824 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3779.52 | 0.761372 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4200.96 | −0.837620 | −0.418810 | − | 0.908074i | \(-0.637553\pi\) | ||||
−0.418810 | + | 0.908074i | \(0.637553\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1192.94 | −0.235442 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −296.564 | −0.0579408 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −129.903 | −0.0251254 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3950.74 | −0.756535 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 151.234 | 0.0286738 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7226.02 | 1.35659 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4876.19 | 0.906511 | 0.453256 | − | 0.891381i | \(-0.350262\pi\) | ||||
0.453256 | + | 0.891381i | \(0.350262\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3166.19 | 0.582906 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6881.71 | 1.25475 | 0.627373 | − | 0.778719i | \(-0.284130\pi\) | ||||
0.627373 | + | 0.778719i | \(0.284130\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7419.45 | −1.33985 | −0.669924 | − | 0.742430i | \(-0.733673\pi\) | ||||
−0.669924 | + | 0.742430i | \(0.733673\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1395.44 | −0.249600 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2675.06 | −0.473963 | −0.236981 | − | 0.971514i | \(-0.576158\pi\) | ||||
−0.236981 | + | 0.971514i | \(0.576158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1421.26 | 0.249452 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3592.16 | 0.624595 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9303.06 | −1.60259 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.1291 | 0.00241151 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4749.97 | −0.803284 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5221.16 | −0.874930 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9878.74 | −1.64044 | −0.820219 | − | 0.572050i | \(-0.806148\pi\) | ||||
−0.820219 | + | 0.572050i | \(0.806148\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2331.15 | −0.383622 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8269.00 | −1.34861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7522.81 | 1.21600 | 0.608002 | − | 0.793935i | \(-0.291971\pi\) | ||||
0.608002 | + | 0.793935i | \(0.291971\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2723.13 | 0.436283 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2706.90 | −0.429874 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6799.50 | −1.07037 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2239.26 | −0.349442 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1762.56 | −0.272678 | −0.136339 | − | 0.990662i | \(-0.543534\pi\) | ||||
−0.136339 | + | 0.990662i | \(0.543534\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3913.89 | −0.600303 | −0.300151 | − | 0.953892i | \(-0.597037\pi\) | ||||
−0.300151 | + | 0.953892i | \(0.597037\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −54.0000 | −0.00821170 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 848.742 | 0.127972 | 0.0639858 | − | 0.997951i | \(-0.479619\pi\) | ||||
0.0639858 | + | 0.997951i | \(0.479619\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2309.32 | 0.345257 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4328.95 | −0.641771 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3899.98 | −0.573352 | −0.286676 | − | 0.958028i | \(-0.592550\pi\) | ||||
−0.286676 | + | 0.958028i | \(0.592550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 707.193 | 0.103104 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3631.06 | 0.525018 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11349.2 | −1.62752 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4038.70 | −0.574437 | −0.287219 | − | 0.957865i | \(-0.592731\pi\) | ||||
−0.287219 | + | 0.957865i | \(0.592731\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2924.85 | 0.412634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7238.53 | −1.01295 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11503.2 | 1.59682 | 0.798410 | − | 0.602115i | \(-0.205675\pi\) | ||||
0.798410 | + | 0.602115i | \(0.205675\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4065.92 | −0.559902 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 258.790 | 0.0353538 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8121.63 | −1.10074 | −0.550369 | − | 0.834921i | \(-0.685513\pi\) | ||||
−0.550369 | + | 0.834921i | \(0.685513\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −111.170 | −0.0149486 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3528.45 | −0.470745 | −0.235373 | − | 0.971905i | \(-0.575631\pi\) | ||||
−0.235373 | + | 0.971905i | \(0.575631\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1703.03 | −0.225440 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2635.40 | −0.346163 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −106.234 | −0.0138465 | −0.00692324 | − | 0.999976i | \(-0.502204\pi\) | ||||
−0.00692324 | + | 0.999976i | \(0.502204\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6946.68 | −0.898487 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −610.838 | −0.0784039 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8853.14 | 1.12772 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5479.72 | 0.692744 | 0.346372 | − | 0.938097i | \(-0.387413\pi\) | ||||
0.346372 | + | 0.938097i | \(0.387413\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3520.74 | 0.441748 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4977.08 | −0.619809 | −0.309905 | − | 0.950768i | \(-0.600297\pi\) | ||||
−0.309905 | + | 0.950768i | \(0.600297\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −492.887 | −0.0609242 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −930.847 | −0.114208 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2845.00 | −0.346490 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1272.35 | 0.153824 | 0.0769119 | − | 0.997038i | \(-0.475494\pi\) | ||||
0.0769119 | + | 0.997038i | \(0.475494\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −742.210 | −0.0890767 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1400.55 | 0.166868 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14761.4 | 1.74604 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4895.03 | −0.574846 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6921.14 | 0.806969 | 0.403485 | − | 0.914986i | \(-0.367799\pi\) | ||||
0.403485 | + | 0.914986i | \(0.367799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1903.90 | −0.220405 | −0.110203 | − | 0.993909i | \(-0.535150\pi\) | ||||
−0.110203 | + | 0.993909i | \(0.535150\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3482.85 | −0.400336 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 755.563 | 0.0862358 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8483.60 | −0.961475 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −65.9032 | −0.00741687 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13752.4 | −1.53696 | −0.768482 | − | 0.639871i | \(-0.778988\pi\) | ||||
−0.768482 | + | 0.639871i | \(0.778988\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12292.7 | 1.36432 | 0.682159 | − | 0.731204i | \(-0.261041\pi\) | ||||
0.682159 | + | 0.731204i | \(0.261041\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4461.00 | 0.491698 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5649.74 | 0.618453 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16495.5 | 1.79337 | 0.896683 | − | 0.442673i | \(-0.145970\pi\) | ||||
0.896683 | + | 0.442673i | \(0.145970\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1448.71 | −0.156431 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15534.9 | 1.66610 | 0.833051 | − | 0.553196i | \(-0.186592\pi\) | ||||
0.833051 | + | 0.553196i | \(0.186592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9701.05 | −1.03342 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1485.90 | 0.157227 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2147.08 | 0.225673 | 0.112836 | − | 0.993614i | \(-0.464006\pi\) | ||||
0.112836 | + | 0.993614i | \(0.464006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3569.58 | 0.372694 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1729.81 | 0.179412 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −310.097 | −0.0319507 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8907.65 | 0.911777 | 0.455888 | − | 0.890037i | \(-0.349322\pi\) | ||||
0.455888 | + | 0.890037i | \(0.349322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2887.69 | −0.293651 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11673.7 | −1.17939 | −0.589694 | − | 0.807627i | \(-0.700752\pi\) | ||||
−0.589694 | + | 0.807627i | \(0.700752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 416.121 | 0.0417685 | 0.0208842 | − | 0.999782i | \(-0.493352\pi\) | ||||
0.0208842 | + | 0.999782i | \(0.493352\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8496.34 | −0.847330 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12272.9 | −1.21611 | −0.608055 | − | 0.793895i | \(-0.708050\pi\) | ||||
−0.608055 | + | 0.793895i | \(0.708050\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9708.10 | 0.955817 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −638.564 | −0.0624703 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3216.32 | −0.312657 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −614.500 | −0.0593583 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4828.57 | −0.463491 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19279.7 | 1.83906 | 0.919532 | − | 0.393015i | \(-0.128568\pi\) | ||||
0.919532 | + | 0.393015i | \(0.128568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −518.032 | −0.0491065 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2628.97 | 0.247665 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14478.0 | 1.35549 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14088.1 | 1.31087 | 0.655433 | − | 0.755254i | \(-0.272486\pi\) | ||||
0.655433 | + | 0.755254i | \(0.272486\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8973.34 | −0.829833 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6405.32 | 0.588734 | 0.294367 | − | 0.955693i | \(-0.404891\pi\) | ||||
0.294367 | + | 0.955693i | \(0.404891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13839.0 | 1.26426 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1136.03 | −0.103153 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2711.23 | −0.244698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4781.48 | −0.428955 | −0.214478 | − | 0.976729i | \(-0.568805\pi\) | ||||
−0.214478 | + | 0.976729i | \(0.568805\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9693.68 | −0.864434 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17222.8 | 1.52669 | 0.763346 | − | 0.645990i | \(-0.223555\pi\) | ||||
0.763346 | + | 0.645990i | \(0.223555\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 579.323 | 0.0510486 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6579.00 | 0.576299 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17597.9 | 1.53244 | 0.766220 | − | 0.642578i | \(-0.222135\pi\) | ||||
0.766220 | + | 0.642578i | \(0.222135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13324.4 | 1.15349 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2348.56 | 0.202128 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12128.5 | 1.03776 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4250.58 | −0.361587 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8447.78 | −0.714483 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6205.24 | 0.521798 | 0.260899 | − | 0.965366i | \(-0.415981\pi\) | ||||
0.260899 | + | 0.965366i | \(0.415981\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1164.66 | −0.0973749 | −0.0486874 | − | 0.998814i | \(-0.515504\pi\) | ||||
−0.0486874 | + | 0.998814i | \(0.515504\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −285.943 | −0.0237706 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26357.5 | −2.17866 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7948.29 | −0.653266 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 934.258 | 0.0763528 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 649.968 | 0.0528203 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13760.3 | 1.11198 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1892.71 | −0.152098 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1768.05 | −0.141290 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18467.1 | 1.46759 | 0.733793 | − | 0.679373i | \(-0.237748\pi\) | ||||
0.733793 | + | 0.679373i | \(0.237748\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5244.68 | 0.414495 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18195.4 | −1.43010 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4387.05 | −0.342919 | −0.171459 | − | 0.985191i | \(-0.554848\pi\) | ||||
−0.171459 | + | 0.985191i | \(0.554848\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5659.11 | −0.439936 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11255.3 | −0.870220 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10393.9 | −0.799265 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8929.79 | −0.682970 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2979.09 | 0.226621 | 0.113311 | − | 0.993560i | \(-0.463854\pi\) | ||||
0.113311 | + | 0.993560i | \(0.463854\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −585.645 | −0.0443115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3524.23 | −0.265228 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13696.2 | 1.02527 | 0.512634 | − | 0.858607i | \(-0.328670\pi\) | ||||
0.512634 | + | 0.858607i | \(0.328670\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10431.3 | 0.776725 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1092.85 | 0.0809440 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6973.98 | −0.513822 | −0.256911 | − | 0.966435i | \(-0.582705\pi\) | ||||
−0.256911 | + | 0.966435i | \(0.582705\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10571.3 | 0.774774 | 0.387387 | − | 0.921917i | \(-0.373378\pi\) | ||||
0.387387 | + | 0.921917i | \(0.373378\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4351.55 | 0.317257 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −458.853 | −0.0332791 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9195.26 | 0.663438 | 0.331719 | − | 0.943378i | \(-0.392371\pi\) | ||||
0.331719 | + | 0.943378i | \(0.392371\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12908.8 | 0.926549 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17330.4 | −1.23750 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5892.93 | −0.418628 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −206.855 | −0.0146195 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14538.3 | 1.02225 | 0.511124 | − | 0.859507i | \(-0.329229\pi\) | ||||
0.511124 | + | 0.859507i | \(0.329229\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21436.6 | 1.49963 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13008.7 | −0.905425 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10422.9 | −0.721785 | −0.360893 | − | 0.932607i | \(-0.617528\pi\) | ||||
−0.360893 | + | 0.932607i | \(0.617528\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16582.7 | −1.14256 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12551.6 | 0.860476 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7293.27 | 0.497488 | 0.248744 | − | 0.968569i | \(-0.419982\pi\) | ||||
0.248744 | + | 0.968569i | \(0.419982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16685.1 | 1.13245 | 0.566223 | − | 0.824252i | \(-0.308404\pi\) | ||||
0.566223 | + | 0.824252i | \(0.308404\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6475.93 | 0.437347 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13909.3 | 0.934701 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14554.1 | 0.973200 | 0.486600 | − | 0.873625i | \(-0.338237\pi\) | ||||
0.486600 | + | 0.873625i | \(0.338237\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5237.37 | −0.348488 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −773.968 | −0.0512461 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3335.34 | 0.219760 | 0.109880 | − | 0.993945i | \(-0.464953\pi\) | ||||
0.109880 | + | 0.993945i | \(0.464953\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11204.1 | 0.734621 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18534.0 | −1.20932 | −0.604660 | − | 0.796484i | \(-0.706691\pi\) | ||||
−0.604660 | + | 0.796484i | \(0.706691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1292.45 | 0.0839224 | 0.0419612 | − | 0.999119i | \(-0.486639\pi\) | ||||
0.0419612 | + | 0.999119i | \(0.486639\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1753.69 | 0.113323 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11389.4 | 0.732432 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16458.2 | −1.05332 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2866.26 | 0.182563 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27702.2 | −1.75606 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10708.0 | −0.675560 | −0.337780 | − | 0.941225i | \(-0.609676\pi\) | ||||
−0.337780 | + | 0.941225i | \(0.609676\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4429.94 | −0.278158 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −425.852 | −0.0266133 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −321.935 | −0.0200244 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1808.56 | −0.111965 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2773.50 | −0.170900 | −0.0854499 | − | 0.996342i | \(-0.527233\pi\) | ||||
−0.0854499 | + | 0.996342i | \(0.527233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5474.50 | 0.335759 | 0.167880 | − | 0.985808i | \(-0.446308\pi\) | ||||
0.167880 | + | 0.985808i | \(0.446308\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10095.3 | −0.616282 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19944.3 | 1.21189 | 0.605943 | − | 0.795508i | \(-0.292796\pi\) | ||||
0.605943 | + | 0.795508i | \(0.292796\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1140.20 | 0.0689624 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9975.00 | 0.600539 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12550.2 | −0.752111 | −0.376056 | − | 0.926597i | \(-0.622720\pi\) | ||||
−0.376056 | + | 0.926597i | \(0.622720\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2339.90 | −0.139584 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8888.22 | 0.527797 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6571.77 | −0.388467 | −0.194234 | − | 0.980955i | \(-0.562222\pi\) | ||||
−0.194234 | + | 0.980955i | \(0.562222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11166.8 | −0.657094 | −0.328547 | − | 0.944488i | \(-0.606559\pi\) | ||||
−0.328547 | + | 0.944488i | \(0.606559\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −641.710 | −0.0375896 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13486.7 | 0.786454 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8404.42 | −0.487887 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18293.9 | −1.05722 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6906.55 | −0.397354 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4712.78 | −0.269932 | −0.134966 | − | 0.990850i | \(-0.543093\pi\) | ||||
−0.134966 | + | 0.990850i | \(0.543093\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −190.742 | −0.0108766 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16444.0 | −0.933520 | −0.466760 | − | 0.884384i | \(-0.654579\pi\) | ||||
−0.466760 | + | 0.884384i | \(0.654579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16997.7 | −0.960693 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18424.1 | 1.03673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7109.18 | −0.398280 | −0.199140 | − | 0.979971i | \(-0.563815\pi\) | ||||
−0.199140 | + | 0.979971i | \(0.563815\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2843.14 | −0.158585 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6506.52 | −0.361338 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1073.02 | −0.0593304 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7879.89 | 0.433813 | 0.216907 | − | 0.976192i | \(-0.430403\pi\) | ||||
0.216907 | + | 0.976192i | \(0.430403\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1333.74 | 0.0731092 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18751.1 | −1.02341 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34757.5 | 1.88886 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6427.84 | 0.347816 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17218.0 | 0.927698 | 0.463849 | − | 0.885914i | \(-0.346468\pi\) | ||||
0.463849 | + | 0.885914i | \(0.346468\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22530.2 | 1.20874 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13341.6 | −0.712728 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −680.145 | −0.0361803 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3957.16 | −0.209611 | −0.104806 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104806 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6933.41 | −0.365715 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16006.9 | 0.840762 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −252.452 | −0.0132044 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20163.0 | 1.05021 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23531.0 | 1.22053 | 0.610263 | − | 0.792199i | \(-0.291064\pi\) | ||||
0.610263 | + | 0.792199i | \(0.291064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14239.3 | −0.735506 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 579.677 | 0.0298180 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 914.116 | 0.0468268 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2462.54 | −0.125627 | −0.0628133 | − | 0.998025i | \(-0.520007\pi\) | ||||
−0.0628133 | + | 0.998025i | \(0.520007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31317.8 | −1.58459 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7436.45 | 0.374722 | 0.187361 | − | 0.982291i | \(-0.440007\pi\) | ||||
0.187361 | + | 0.982291i | \(0.440007\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5549.49 | −0.278498 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7903.42 | 0.395015 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7969.32 | −0.396693 | −0.198347 | − | 0.980132i | \(-0.563557\pi\) | ||||
−0.198347 | + | 0.980132i | \(0.563557\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 521.903 | 0.0258739 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13701.3 | −0.676515 | −0.338257 | − | 0.941054i | \(-0.609837\pi\) | ||||
−0.338257 | + | 0.941054i | \(0.609837\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5691.94 | 0.279915 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11560.5 | −0.566234 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16155.1 | −0.788108 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13574.0 | −0.659550 | −0.329775 | − | 0.944060i | \(-0.606973\pi\) | ||||
−0.329775 | + | 0.944060i | \(0.606973\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4304.95 | −0.208342 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6626.30 | 0.319412 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19115.4 | −0.917783 | −0.458891 | − | 0.888492i | \(-0.651753\pi\) | ||||
−0.458891 | + | 0.888492i | \(0.651753\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2140.26 | 0.102354 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 647.405 | 0.0308389 | 0.0154195 | − | 0.999881i | \(-0.495092\pi\) | ||||
0.0154195 | + | 0.999881i | \(0.495092\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21362.1 | 1.01358 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11061.7 | −0.522794 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 207.613 | 0.00977375 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13993.6 | 0.656208 | 0.328104 | − | 0.944642i | \(-0.393590\pi\) | ||||
0.328104 | + | 0.944642i | \(0.393590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15999.1 | −0.747333 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38664.6 | 1.79905 | 0.899527 | − | 0.436865i | \(-0.143911\pi\) | ||||
0.899527 | + | 0.436865i | \(0.143911\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1741.01 | −0.0806953 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10483.9 | 0.484051 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28268.4 | −1.30015 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2207.23 | −0.101128 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3493.67 | −0.159455 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2446.11 | −0.111217 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16965.4 | −0.768426 | −0.384213 | − | 0.923244i | \(-0.625527\pi\) | ||||
−0.384213 | + | 0.923244i | \(0.625527\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1658.32 | −0.0748262 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12246.8 | −0.550499 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1257.58 | −0.0563153 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18496.5 | −0.825163 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10338.1 | −0.459467 | −0.229734 | − | 0.973254i | \(-0.573786\pi\) | ||||
−0.229734 | + | 0.973254i | \(0.573786\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41388.5 | −1.83257 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7597.45 | 0.335135 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10847.5 | 0.476710 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10070.6 | 0.440924 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7092.94 | 0.309397 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28418.7 | 1.23504 | 0.617520 | − | 0.786555i | \(-0.288137\pi\) | ||||
0.617520 | + | 0.786555i | \(0.288137\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15766.2 | −0.682645 | −0.341323 | − | 0.939946i | \(-0.610875\pi\) | ||||
−0.341323 | + | 0.939946i | \(0.610875\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21401.2 | 0.923212 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34373.7 | −1.47737 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25470.8 | 1.09071 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 242.855 | 0.0103615 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32902.1 | −1.39865 | −0.699325 | − | 0.714804i | \(-0.746516\pi\) | ||||
−0.699325 | + | 0.714804i | \(0.746516\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17044.5 | 0.721912 | 0.360956 | − | 0.932583i | \(-0.382450\pi\) | ||||
0.360956 | + | 0.932583i | \(0.382450\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −232.788 | −0.00982379 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18923.1 | −0.795673 | −0.397837 | − | 0.917456i | \(-0.630239\pi\) | ||||
−0.397837 | + | 0.917456i | \(0.630239\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42319.4 | −1.77300 | −0.886498 | − | 0.462733i | \(-0.846869\pi\) | ||||
−0.886498 | + | 0.462733i | \(0.846869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6077.32 | 0.253694 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17215.8 | −0.716075 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37133.0 | −1.53897 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6653.98 | 0.274785 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18135.8 | −0.746267 | −0.373134 | − | 0.927778i | \(-0.621717\pi\) | ||||
−0.373134 | + | 0.927778i | \(0.621717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7645.90 | −0.313498 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6206.52 | 0.253575 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25201.8 | 1.02600 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16330.0 | −0.662463 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10224.6 | 0.413318 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16823.5 | 0.677676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13903.8 | −0.558097 | −0.279048 | − | 0.960277i | \(-0.590019\pi\) | ||||
−0.279048 | + | 0.960277i | \(0.590019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8996.52 | 0.359853 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2097.53 | −0.0836059 | −0.0418030 | − | 0.999126i | \(-0.513310\pi\) | ||||
−0.0418030 | + | 0.999126i | \(0.513310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19650.3 | −0.780513 | −0.390257 | − | 0.920706i | \(-0.627614\pi\) | ||||
−0.390257 | + | 0.920706i | \(0.627614\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13154.0 | −0.520658 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37574.9 | 1.48211 | 0.741057 | − | 0.671442i | \(-0.234325\pi\) | ||||
0.741057 | + | 0.671442i | \(0.234325\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32360.4 | −1.27201 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19576.9 | −0.766860 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8461.74 | −0.330316 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1439.10 | 0.0559838 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11338.5 | −0.439578 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18285.7 | 0.706480 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21977.0 | −0.846194 | −0.423097 | − | 0.906084i | \(-0.639057\pi\) | ||||
−0.423097 | + | 0.906084i | \(0.639057\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12602.9 | 0.483600 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45627.0 | 1.74485 | 0.872425 | − | 0.488747i | \(-0.162546\pi\) | ||||
0.872425 | + | 0.488747i | \(0.162546\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51068.7 | 1.94632 | 0.973158 | − | 0.230138i | \(-0.0739176\pi\) | ||||
0.973158 | + | 0.230138i | \(0.0739176\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3578.81 | 0.135933 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31208.4 | −1.18137 | −0.590685 | − | 0.806902i | \(-0.701142\pi\) | ||||
−0.590685 | + | 0.806902i | \(0.701142\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 499.965 | 0.0188620 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 889.693 | 0.0334521 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33661.4 | 1.26140 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7250.29 | −0.270783 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 389.710 | 0.0145062 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31888.6 | −1.18303 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −57380.4 | −2.12166 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11852.2 | 0.436786 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20090.5 | 0.737934 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46768.6 | 1.71216 | 0.856078 | − | 0.516847i | \(-0.172895\pi\) | ||||
0.856078 | + | 0.516847i | \(0.172895\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −453.701 | −0.0165548 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21752.7 | 0.791107 | 0.395553 | − | 0.918443i | \(-0.370553\pi\) | ||||
0.395553 | + | 0.918443i | \(0.370553\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14108.8 | −0.511426 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21678.0 | −0.783229 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2747.13 | 0.0989294 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3529.71 | −0.126697 | −0.0633483 | − | 0.997991i | \(-0.520178\pi\) | ||||
−0.0633483 | + | 0.997991i | \(0.520178\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14628.6 | −0.523375 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −401.903 | −0.0143324 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1829.83 | −0.0650426 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9498.56 | −0.336541 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29473.1 | 1.04088 | 0.520442 | − | 0.853897i | \(-0.325767\pi\) | ||||
0.520442 | + | 0.853897i | \(0.325767\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14001.6 | 0.492893 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20645.1 | −0.724428 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13500.1 | −0.472192 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43332.6 | −1.51079 | −0.755397 | − | 0.655268i | \(-0.772556\pi\) | ||||
−0.755397 | + | 0.655268i | \(0.772556\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22258.4 | 0.773561 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48873.8 | −1.69314 | −0.846568 | − | 0.532281i | \(-0.821335\pi\) | ||||
−0.846568 | + | 0.532281i | \(0.821335\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21108.2 | −0.728927 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4186.31 | 0.144106 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2596.71 | 0.0891043 | 0.0445521 | − | 0.999007i | \(-0.485814\pi\) | ||||
0.0445521 | + | 0.999007i | \(0.485814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1975.16 | 0.0675621 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8025.17 | 0.273642 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6101.34 | −0.207389 | −0.103695 | − | 0.994609i | \(-0.533066\pi\) | ||||
−0.103695 | + | 0.994609i | \(0.533066\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16669.2 | 0.564821 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4263.78 | −0.144021 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3337.95 | 0.112396 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30943.4 | 1.03868 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10776.5 | −0.360610 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 49449.0 | 1.64956 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7375.86 | 0.245286 | 0.122643 | − | 0.992451i | \(-0.460863\pi\) | ||||
0.122643 | + | 0.992451i | \(0.460863\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27909.2 | 0.925255 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34152.0 | −1.12872 | −0.564361 | − | 0.825528i | \(-0.690877\pi\) | ||||
−0.564361 | + | 0.825528i | \(0.690877\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22014.5 | 0.725336 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −42.3872 | −0.00139228 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1170.76 | −0.0383377 | −0.0191689 | − | 0.999816i | \(-0.506102\pi\) | ||||
−0.0191689 | + | 0.999816i | \(0.506102\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9272.16 | 0.302696 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14249.9 | 0.463776 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31786.9 | 1.03138 | 0.515689 | − | 0.856776i | \(-0.327536\pi\) | ||||
0.515689 | + | 0.856776i | \(0.327536\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49831.7 | −1.61195 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15663.5 | 0.505141 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19019.3 | 0.611505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47078.3 | −1.50907 | −0.754537 | − | 0.656258i | \(-0.772138\pi\) | ||||
−0.754537 | + | 0.656258i | \(0.772138\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29636.2 | 0.947107 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48080.9 | 1.53193 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40091.9 | 1.27354 | 0.636771 | − | 0.771053i | \(-0.280270\pi\) | ||||
0.636771 | + | 0.771053i | \(0.280270\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6993.44 | 0.221484 |
(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 | 384.4.a.k.1.1 | yes | 2 | |
3.2 | odd | 2 | 1152.4.a.o.1.2 | 2 | |||
4.3 | odd | 2 | 384.4.a.o.1.1 | yes | 2 | ||
8.3 | odd | 2 | 384.4.a.j.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 384.4.a.n.1.2 | yes | 2 | ||
12.11 | even | 2 | 1152.4.a.p.1.2 | 2 | |||
16.3 | odd | 4 | 768.4.d.q.385.4 | 4 | |||
16.5 | even | 4 | 768.4.d.t.385.3 | 4 | |||
16.11 | odd | 4 | 768.4.d.q.385.1 | 4 | |||
16.13 | even | 4 | 768.4.d.t.385.2 | 4 | |||
24.5 | odd | 2 | 1152.4.a.u.1.1 | 2 | |||
24.11 | even | 2 | 1152.4.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.a.j.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
384.4.a.k.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
384.4.a.n.1.2 | yes | 2 | 8.5 | even | 2 | ||
384.4.a.o.1.1 | yes | 2 | 4.3 | odd | 2 | ||
768.4.d.q.385.1 | 4 | 16.11 | odd | 4 | |||
768.4.d.q.385.4 | 4 | 16.3 | odd | 4 | |||
768.4.d.t.385.2 | 4 | 16.13 | even | 4 | |||
768.4.d.t.385.3 | 4 | 16.5 | even | 4 | |||
1152.4.a.o.1.2 | 2 | 3.2 | odd | 2 | |||
1152.4.a.p.1.2 | 2 | 12.11 | even | 2 | |||
1152.4.a.u.1.1 | 2 | 24.5 | odd | 2 | |||
1152.4.a.v.1.1 | 2 | 24.11 | even | 2 |