Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(1,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("882.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.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: | \(52.0396846251\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{193}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.44622\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −10.4462 | −0.934338 | −0.467169 | − | 0.884168i | \(-0.654726\pi\) | ||||
−0.467169 | + | 0.884168i | \(0.654726\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 20.8924 | 0.660677 | ||||||||
\(11\) | −61.1236 | −1.67540 | −0.837702 | − | 0.546128i | \(-0.816101\pi\) | ||||
−0.837702 | + | 0.546128i | \(0.816101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 59.2311 | 1.26367 | 0.631837 | − | 0.775102i | \(-0.282301\pi\) | ||||
0.631837 | + | 0.775102i | \(0.282301\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 20.4622 | 0.291930 | 0.145965 | − | 0.989290i | \(-0.453371\pi\) | ||||
0.145965 | + | 0.989290i | \(0.453371\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 80.3387 | 0.970050 | 0.485025 | − | 0.874500i | \(-0.338810\pi\) | ||||
0.485025 | + | 0.874500i | \(0.338810\pi\) | |||||||
\(20\) | −41.7849 | −0.467169 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 122.247 | 1.18469 | ||||||||
\(23\) | 158.247 | 1.43464 | 0.717322 | − | 0.696742i | \(-0.245368\pi\) | ||||
0.717322 | + | 0.696742i | \(0.245368\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15.8764 | −0.127012 | ||||||||
\(26\) | −118.462 | −0.893552 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 85.1236 | 0.545071 | 0.272535 | − | 0.962146i | \(-0.412138\pi\) | ||||
0.272535 | + | 0.962146i | \(0.412138\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −243.494 | −1.41074 | −0.705369 | − | 0.708841i | \(-0.749218\pi\) | ||||
−0.705369 | + | 0.708841i | \(0.749218\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −40.9244 | −0.206426 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 290.371 | 1.29018 | 0.645090 | − | 0.764107i | \(-0.276820\pi\) | ||||
0.645090 | + | 0.764107i | \(0.276820\pi\) | |||||||
\(38\) | −160.677 | −0.685929 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 83.5698 | 0.330339 | ||||||||
\(41\) | −168.000 | −0.639932 | −0.319966 | − | 0.947429i | \(-0.603671\pi\) | ||||
−0.319966 | + | 0.947429i | \(0.603671\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.62934 | 0.0270573 | 0.0135286 | − | 0.999908i | \(-0.495694\pi\) | ||||
0.0135286 | + | 0.999908i | \(0.495694\pi\) | |||||||
\(44\) | −244.494 | −0.837702 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −316.494 | −1.01445 | ||||||||
\(47\) | −169.291 | −0.525395 | −0.262698 | − | 0.964878i | \(-0.584612\pi\) | ||||
−0.262698 | + | 0.964878i | \(0.584612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 31.7529 | 0.0898107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 236.924 | 0.631837 | ||||||||
\(53\) | 250.112 | 0.648217 | 0.324109 | − | 0.946020i | \(-0.394936\pi\) | ||||
0.324109 | + | 0.946020i | \(0.394936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 638.510 | 1.56539 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −170.247 | −0.385423 | ||||||||
\(59\) | −805.220 | −1.77679 | −0.888395 | − | 0.459079i | \(-0.848179\pi\) | ||||
−0.888395 | + | 0.459079i | \(0.848179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −33.1715 | −0.0696259 | −0.0348130 | − | 0.999394i | \(-0.511084\pi\) | ||||
−0.0348130 | + | 0.999394i | \(0.511084\pi\) | |||||||
\(62\) | 486.988 | 0.997542 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −618.741 | −1.18070 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −277.382 | −0.505786 | −0.252893 | − | 0.967494i | \(-0.581382\pi\) | ||||
−0.252893 | + | 0.967494i | \(0.581382\pi\) | |||||||
\(68\) | 81.8489 | 0.145965 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 631.506 | 1.05558 | 0.527788 | − | 0.849376i | \(-0.323021\pi\) | ||||
0.527788 | + | 0.849376i | \(0.323021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 768.284 | 1.23179 | 0.615896 | − | 0.787828i | \(-0.288794\pi\) | ||||
0.615896 | + | 0.787828i | \(0.288794\pi\) | |||||||
\(74\) | −580.741 | −0.912295 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 321.355 | 0.485025 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −418.730 | −0.596339 | −0.298169 | − | 0.954513i | \(-0.596376\pi\) | ||||
−0.298169 | + | 0.954513i | \(0.596376\pi\) | |||||||
\(80\) | −167.140 | −0.233585 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 336.000 | 0.452500 | ||||||||
\(83\) | −761.714 | −1.00734 | −0.503668 | − | 0.863897i | \(-0.668017\pi\) | ||||
−0.503668 | + | 0.863897i | \(0.668017\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −213.753 | −0.272762 | ||||||||
\(86\) | −15.2587 | −0.0191324 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 488.988 | 0.592345 | ||||||||
\(89\) | −1572.10 | −1.87238 | −0.936190 | − | 0.351494i | \(-0.885674\pi\) | ||||
−0.936190 | + | 0.351494i | \(0.885674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 632.988 | 0.717322 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 338.581 | 0.371511 | ||||||||
\(95\) | −839.236 | −0.906355 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1045.16 | −1.09402 | −0.547012 | − | 0.837125i | \(-0.684235\pi\) | ||||
−0.547012 | + | 0.837125i | \(0.684235\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −63.5058 | −0.0635058 | ||||||||
\(101\) | 975.922 | 0.961464 | 0.480732 | − | 0.876868i | \(-0.340371\pi\) | ||||
0.480732 | + | 0.876868i | \(0.340371\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 643.144 | 0.615251 | 0.307626 | − | 0.951508i | \(-0.400466\pi\) | ||||
0.307626 | + | 0.951508i | \(0.400466\pi\) | |||||||
\(104\) | −473.849 | −0.446776 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −500.224 | −0.458359 | ||||||||
\(107\) | 311.595 | 0.281523 | 0.140762 | − | 0.990044i | \(-0.455045\pi\) | ||||
0.140762 | + | 0.990044i | \(0.455045\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1865.83 | −1.63958 | −0.819790 | − | 0.572665i | \(-0.805910\pi\) | ||||
−0.819790 | + | 0.572665i | \(0.805910\pi\) | |||||||
\(110\) | −1277.02 | −1.10690 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1720.49 | 1.43231 | 0.716153 | − | 0.697944i | \(-0.245901\pi\) | ||||
0.716153 | + | 0.697944i | \(0.245901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1653.08 | −1.34044 | ||||||||
\(116\) | 340.494 | 0.272535 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1610.44 | 1.25638 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2405.09 | 1.80698 | ||||||||
\(122\) | 66.3431 | 0.0492330 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −973.977 | −0.705369 | ||||||||
\(125\) | 1471.63 | 1.05301 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 142.236 | 0.0993808 | 0.0496904 | − | 0.998765i | \(-0.484177\pi\) | ||||
0.0496904 | + | 0.998765i | \(0.484177\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1237.48 | 0.834880 | ||||||||
\(131\) | −2486.51 | −1.65838 | −0.829189 | − | 0.558969i | \(-0.811197\pi\) | ||||
−0.829189 | + | 0.558969i | \(0.811197\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 554.764 | 0.357644 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −163.698 | −0.103213 | ||||||||
\(137\) | −2597.21 | −1.61967 | −0.809835 | − | 0.586658i | \(-0.800443\pi\) | ||||
−0.809835 | + | 0.586658i | \(0.800443\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1600.52 | −0.976651 | −0.488325 | − | 0.872662i | \(-0.662392\pi\) | ||||
−0.488325 | + | 0.872662i | \(0.662392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1263.01 | −0.746405 | ||||||||
\(143\) | −3620.42 | −2.11716 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −889.220 | −0.509280 | ||||||||
\(146\) | −1536.57 | −0.871008 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1161.48 | 0.645090 | ||||||||
\(149\) | −2937.71 | −1.61521 | −0.807605 | − | 0.589724i | \(-0.799237\pi\) | ||||
−0.807605 | + | 0.589724i | \(0.799237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1823.32 | 0.982649 | 0.491325 | − | 0.870977i | \(-0.336513\pi\) | ||||
0.491325 | + | 0.870977i | \(0.336513\pi\) | |||||||
\(152\) | −642.709 | −0.342965 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2543.59 | 1.31811 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −633.648 | −0.322106 | −0.161053 | − | 0.986946i | \(-0.551489\pi\) | ||||
−0.161053 | + | 0.986946i | \(0.551489\pi\) | |||||||
\(158\) | 837.460 | 0.421675 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 334.279 | 0.165169 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1345.71 | −0.646650 | −0.323325 | − | 0.946288i | \(-0.604801\pi\) | ||||
−0.323325 | + | 0.946288i | \(0.604801\pi\) | |||||||
\(164\) | −672.000 | −0.319966 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1523.43 | 0.712295 | ||||||||
\(167\) | 387.922 | 0.179750 | 0.0898751 | − | 0.995953i | \(-0.471353\pi\) | ||||
0.0898751 | + | 0.995953i | \(0.471353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1311.32 | 0.596870 | ||||||||
\(170\) | 427.506 | 0.192872 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 30.5174 | 0.0135286 | ||||||||
\(173\) | −622.660 | −0.273641 | −0.136821 | − | 0.990596i | \(-0.543688\pi\) | ||||
−0.136821 | + | 0.990596i | \(0.543688\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −977.977 | −0.418851 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3144.19 | 1.32397 | ||||||||
\(179\) | 449.931 | 0.187874 | 0.0939368 | − | 0.995578i | \(-0.470055\pi\) | ||||
0.0939368 | + | 0.995578i | \(0.470055\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −184.353 | −0.0757063 | −0.0378532 | − | 0.999283i | \(-0.512052\pi\) | ||||
−0.0378532 | + | 0.999283i | \(0.512052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1265.98 | −0.507223 | ||||||||
\(185\) | −3033.28 | −1.20546 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1250.72 | −0.489101 | ||||||||
\(188\) | −677.163 | −0.262698 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1678.47 | 0.640890 | ||||||||
\(191\) | −350.965 | −0.132958 | −0.0664789 | − | 0.997788i | \(-0.521177\pi\) | ||||
−0.0664789 | + | 0.997788i | \(0.521177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1528.26 | 0.569982 | 0.284991 | − | 0.958530i | \(-0.408009\pi\) | ||||
0.284991 | + | 0.958530i | \(0.408009\pi\) | |||||||
\(194\) | 2090.33 | 0.773592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2874.65 | −1.03965 | −0.519823 | − | 0.854274i | \(-0.674002\pi\) | ||||
−0.519823 | + | 0.854274i | \(0.674002\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4948.70 | −1.76284 | −0.881418 | − | 0.472337i | \(-0.843410\pi\) | ||||
−0.881418 | + | 0.472337i | \(0.843410\pi\) | |||||||
\(200\) | 127.012 | 0.0449054 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1951.84 | −0.679858 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1754.97 | 0.597913 | ||||||||
\(206\) | −1286.29 | −0.435048 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 947.698 | 0.315918 | ||||||||
\(209\) | −4910.58 | −1.62523 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5280.90 | −1.72299 | −0.861497 | − | 0.507762i | \(-0.830473\pi\) | ||||
−0.861497 | + | 0.507762i | \(0.830473\pi\) | |||||||
\(212\) | 1000.45 | 0.324109 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −623.189 | −0.199067 | ||||||||
\(215\) | −79.6978 | −0.0252807 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3731.66 | 1.15936 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2554.04 | 0.782697 | ||||||||
\(221\) | 1212.00 | 0.368905 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3996.57 | −1.20013 | −0.600067 | − | 0.799950i | \(-0.704859\pi\) | ||||
−0.600067 | + | 0.799950i | \(0.704859\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3440.99 | −1.01279 | ||||||||
\(227\) | 538.592 | 0.157478 | 0.0787392 | − | 0.996895i | \(-0.474911\pi\) | ||||
0.0787392 | + | 0.996895i | \(0.474911\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4171.61 | −1.20379 | −0.601895 | − | 0.798576i | \(-0.705587\pi\) | ||||
−0.601895 | + | 0.798576i | \(0.705587\pi\) | |||||||
\(230\) | 3306.17 | 0.947836 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −680.988 | −0.192712 | ||||||||
\(233\) | 1539.73 | 0.432923 | 0.216461 | − | 0.976291i | \(-0.430548\pi\) | ||||
0.216461 | + | 0.976291i | \(0.430548\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1768.45 | 0.490897 | ||||||||
\(236\) | −3220.88 | −0.888395 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3132.67 | 0.847848 | 0.423924 | − | 0.905698i | \(-0.360652\pi\) | ||||
0.423924 | + | 0.905698i | \(0.360652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2606.69 | −0.696730 | −0.348365 | − | 0.937359i | \(-0.613263\pi\) | ||||
−0.348365 | + | 0.937359i | \(0.613263\pi\) | |||||||
\(242\) | −4810.18 | −1.27773 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −132.686 | −0.0348130 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4758.55 | 1.22583 | ||||||||
\(248\) | 1947.95 | 0.498771 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2943.25 | −0.744591 | ||||||||
\(251\) | 3426.24 | 0.861603 | 0.430801 | − | 0.902447i | \(-0.358231\pi\) | ||||
0.430801 | + | 0.902447i | \(0.358231\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9672.63 | −2.40361 | ||||||||
\(254\) | −284.471 | −0.0702728 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5857.44 | −1.42170 | −0.710850 | − | 0.703343i | \(-0.751690\pi\) | ||||
−0.710850 | + | 0.703343i | \(0.751690\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2474.97 | −0.590349 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4973.02 | 1.17265 | ||||||||
\(263\) | −1085.93 | −0.254606 | −0.127303 | − | 0.991864i | \(-0.540632\pi\) | ||||
−0.127303 | + | 0.991864i | \(0.540632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2612.73 | −0.605654 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1109.53 | −0.252893 | ||||||||
\(269\) | 5579.45 | 1.26463 | 0.632315 | − | 0.774712i | \(-0.282105\pi\) | ||||
0.632315 | + | 0.774712i | \(0.282105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 560.327 | 0.125599 | 0.0627997 | − | 0.998026i | \(-0.479997\pi\) | ||||
0.0627997 | + | 0.998026i | \(0.479997\pi\) | |||||||
\(272\) | 327.396 | 0.0729826 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5194.42 | 1.14528 | ||||||||
\(275\) | 970.425 | 0.212796 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4508.08 | −0.977849 | −0.488924 | − | 0.872326i | \(-0.662611\pi\) | ||||
−0.488924 | + | 0.872326i | \(0.662611\pi\) | |||||||
\(278\) | 3201.04 | 0.690597 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4329.75 | −0.919186 | −0.459593 | − | 0.888130i | \(-0.652005\pi\) | ||||
−0.459593 | + | 0.888130i | \(0.652005\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 871.051 | 0.182963 | 0.0914817 | − | 0.995807i | \(-0.470840\pi\) | ||||
0.0914817 | + | 0.995807i | \(0.470840\pi\) | |||||||
\(284\) | 2526.02 | 0.527788 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7240.83 | 1.49706 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4494.30 | −0.914777 | ||||||||
\(290\) | 1778.44 | 0.360116 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3073.13 | 0.615896 | ||||||||
\(293\) | −1651.91 | −0.329372 | −0.164686 | − | 0.986346i | \(-0.552661\pi\) | ||||
−0.164686 | + | 0.986346i | \(0.552661\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8411.50 | 1.66012 | ||||||||
\(296\) | −2322.97 | −0.456147 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5875.41 | 1.14213 | ||||||||
\(299\) | 9373.15 | 1.81292 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3646.65 | −0.694838 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1285.42 | 0.242513 | ||||||||
\(305\) | 346.517 | 0.0650542 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1016.42 | −0.188958 | −0.0944791 | − | 0.995527i | \(-0.530119\pi\) | ||||
−0.0944791 | + | 0.995527i | \(0.530119\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5087.19 | −0.932042 | ||||||||
\(311\) | 9193.05 | 1.67617 | 0.838087 | − | 0.545536i | \(-0.183674\pi\) | ||||
0.838087 | + | 0.545536i | \(0.183674\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6692.61 | 1.20859 | 0.604295 | − | 0.796761i | \(-0.293455\pi\) | ||||
0.604295 | + | 0.796761i | \(0.293455\pi\) | |||||||
\(314\) | 1267.30 | 0.227763 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1674.92 | −0.298169 | ||||||||
\(317\) | 7052.49 | 1.24955 | 0.624775 | − | 0.780805i | \(-0.285191\pi\) | ||||
0.624775 | + | 0.780805i | \(0.285191\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5203.05 | −0.913213 | ||||||||
\(320\) | −668.558 | −0.116792 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1643.91 | 0.283187 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −940.380 | −0.160501 | ||||||||
\(326\) | 2691.41 | 0.457250 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1344.00 | 0.226250 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3140.37 | 0.521482 | 0.260741 | − | 0.965409i | \(-0.416033\pi\) | ||||
0.260741 | + | 0.965409i | \(0.416033\pi\) | |||||||
\(332\) | −3046.86 | −0.503668 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −775.843 | −0.127103 | ||||||||
\(335\) | 2897.60 | 0.472575 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2743.87 | 0.443526 | 0.221763 | − | 0.975101i | \(-0.428819\pi\) | ||||
0.221763 | + | 0.975101i | \(0.428819\pi\) | |||||||
\(338\) | −2622.65 | −0.422051 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −855.012 | −0.136381 | ||||||||
\(341\) | 14883.2 | 2.36355 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −61.0347 | −0.00956619 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1245.32 | 0.193494 | ||||||||
\(347\) | 10436.9 | 1.61465 | 0.807323 | − | 0.590110i | \(-0.200916\pi\) | ||||
0.807323 | + | 0.590110i | \(0.200916\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2257.01 | 0.346175 | 0.173087 | − | 0.984906i | \(-0.444626\pi\) | ||||
0.173087 | + | 0.984906i | \(0.444626\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1955.95 | 0.296172 | ||||||||
\(353\) | −5616.44 | −0.846835 | −0.423418 | − | 0.905935i | \(-0.639170\pi\) | ||||
−0.423418 | + | 0.905935i | \(0.639170\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6596.85 | −0.986266 | ||||||||
\(356\) | −6288.38 | −0.936190 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −899.861 | −0.132847 | ||||||||
\(359\) | −795.591 | −0.116963 | −0.0584815 | − | 0.998288i | \(-0.518626\pi\) | ||||
−0.0584815 | + | 0.998288i | \(0.518626\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −404.699 | −0.0590026 | ||||||||
\(362\) | 368.706 | 0.0535325 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8025.66 | −1.15091 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8193.97 | −1.16545 | −0.582727 | − | 0.812668i | \(-0.698014\pi\) | ||||
−0.582727 | + | 0.812668i | \(0.698014\pi\) | |||||||
\(368\) | 2531.95 | 0.358661 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6066.55 | 0.852392 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14077.4 | 1.95415 | 0.977076 | − | 0.212890i | \(-0.0682876\pi\) | ||||
0.977076 | + | 0.212890i | \(0.0682876\pi\) | |||||||
\(374\) | 2501.45 | 0.345847 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1354.33 | 0.185755 | ||||||||
\(377\) | 5041.96 | 0.688791 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6221.22 | 0.843173 | 0.421587 | − | 0.906788i | \(-0.361473\pi\) | ||||
0.421587 | + | 0.906788i | \(0.361473\pi\) | |||||||
\(380\) | −3356.94 | −0.453178 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 701.931 | 0.0940154 | ||||||||
\(383\) | 10701.4 | 1.42772 | 0.713860 | − | 0.700288i | \(-0.246945\pi\) | ||||
0.713860 | + | 0.700288i | \(0.246945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3056.52 | −0.403038 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4180.66 | −0.547012 | ||||||||
\(389\) | 4221.61 | 0.550242 | 0.275121 | − | 0.961410i | \(-0.411282\pi\) | ||||
0.275121 | + | 0.961410i | \(0.411282\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3238.09 | 0.418816 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5749.30 | 0.735141 | ||||||||
\(395\) | 4374.14 | 0.557182 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12075.7 | 1.52661 | 0.763305 | − | 0.646038i | \(-0.223575\pi\) | ||||
0.763305 | + | 0.646038i | \(0.223575\pi\) | |||||||
\(398\) | 9897.41 | 1.24651 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −254.023 | −0.0317529 | ||||||||
\(401\) | −5506.38 | −0.685724 | −0.342862 | − | 0.939386i | \(-0.611396\pi\) | ||||
−0.342862 | + | 0.939386i | \(0.611396\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14422.4 | −1.78271 | ||||||||
\(404\) | 3903.69 | 0.480732 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17748.5 | −2.16157 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1428.18 | −0.172662 | −0.0863311 | − | 0.996266i | \(-0.527514\pi\) | ||||
−0.0863311 | + | 0.996266i | \(0.527514\pi\) | |||||||
\(410\) | −3509.93 | −0.422788 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2572.58 | 0.307626 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7957.03 | 0.941193 | ||||||||
\(416\) | −1895.40 | −0.223388 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9821.17 | 1.14921 | ||||||||
\(419\) | −264.960 | −0.0308929 | −0.0154465 | − | 0.999881i | \(-0.504917\pi\) | ||||
−0.0154465 | + | 0.999881i | \(0.504917\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −281.066 | −0.0325375 | −0.0162688 | − | 0.999868i | \(-0.505179\pi\) | ||||
−0.0162688 | + | 0.999868i | \(0.505179\pi\) | |||||||
\(422\) | 10561.8 | 1.21834 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2000.90 | −0.229179 | ||||||||
\(425\) | −324.867 | −0.0370785 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1246.38 | 0.140762 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 159.396 | 0.0178761 | ||||||||
\(431\) | −1786.38 | −0.199645 | −0.0998223 | − | 0.995005i | \(-0.531827\pi\) | ||||
−0.0998223 | + | 0.995005i | \(0.531827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −184.621 | −0.0204904 | −0.0102452 | − | 0.999948i | \(-0.503261\pi\) | ||||
−0.0102452 | + | 0.999948i | \(0.503261\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7463.32 | −0.819790 | ||||||||
\(437\) | 12713.4 | 1.39168 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11274.6 | −1.22576 | −0.612881 | − | 0.790176i | \(-0.709989\pi\) | ||||
−0.612881 | + | 0.790176i | \(0.709989\pi\) | |||||||
\(440\) | −5108.08 | −0.553451 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2424.00 | −0.260855 | ||||||||
\(443\) | 7969.84 | 0.854760 | 0.427380 | − | 0.904072i | \(-0.359437\pi\) | ||||
0.427380 | + | 0.904072i | \(0.359437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16422.5 | 1.74944 | ||||||||
\(446\) | 7993.13 | 0.848623 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8850.37 | 0.930233 | 0.465117 | − | 0.885249i | \(-0.346012\pi\) | ||||
0.465117 | + | 0.885249i | \(0.346012\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10268.8 | 1.07214 | ||||||||
\(452\) | 6881.98 | 0.716153 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1077.18 | −0.111354 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13027.3 | −1.33346 | −0.666730 | − | 0.745299i | \(-0.732307\pi\) | ||||
−0.666730 | + | 0.745299i | \(0.732307\pi\) | |||||||
\(458\) | 8343.22 | 0.851207 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6612.34 | −0.670221 | ||||||||
\(461\) | −1261.05 | −0.127403 | −0.0637016 | − | 0.997969i | \(-0.520291\pi\) | ||||
−0.0637016 | + | 0.997969i | \(0.520291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4005.47 | −0.402052 | −0.201026 | − | 0.979586i | \(-0.564427\pi\) | ||||
−0.201026 | + | 0.979586i | \(0.564427\pi\) | |||||||
\(464\) | 1361.98 | 0.136268 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3079.46 | −0.306123 | ||||||||
\(467\) | −17097.8 | −1.69420 | −0.847101 | − | 0.531432i | \(-0.821654\pi\) | ||||
−0.847101 | + | 0.531432i | \(0.821654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3536.90 | −0.347117 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6441.76 | 0.628190 | ||||||||
\(473\) | −466.332 | −0.0453319 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1275.49 | −0.123208 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6265.34 | −0.599519 | ||||||||
\(479\) | −11688.5 | −1.11495 | −0.557477 | − | 0.830193i | \(-0.688230\pi\) | ||||
−0.557477 | + | 0.830193i | \(0.688230\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17199.0 | 1.63037 | ||||||||
\(482\) | 5213.39 | 0.492662 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9620.36 | 0.903489 | ||||||||
\(485\) | 10918.0 | 1.02219 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9624.79 | −0.895567 | −0.447783 | − | 0.894142i | \(-0.647786\pi\) | ||||
−0.447783 | + | 0.894142i | \(0.647786\pi\) | |||||||
\(488\) | 265.372 | 0.0246165 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6320.63 | −0.580949 | −0.290475 | − | 0.956883i | \(-0.593813\pi\) | ||||
−0.290475 | + | 0.956883i | \(0.593813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1741.82 | 0.159123 | ||||||||
\(494\) | −9517.10 | −0.866790 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3895.91 | −0.352684 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15054.6 | −1.35057 | −0.675286 | − | 0.737556i | \(-0.735980\pi\) | ||||
−0.675286 | + | 0.737556i | \(0.735980\pi\) | |||||||
\(500\) | 5886.51 | 0.526505 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6852.48 | −0.609245 | ||||||||
\(503\) | −16559.1 | −1.46786 | −0.733930 | − | 0.679225i | \(-0.762316\pi\) | ||||
−0.733930 | + | 0.679225i | \(0.762316\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10194.7 | −0.898333 | ||||||||
\(506\) | 19345.3 | 1.69961 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 568.942 | 0.0496904 | ||||||||
\(509\) | 13339.0 | 1.16157 | 0.580785 | − | 0.814057i | \(-0.302746\pi\) | ||||
0.580785 | + | 0.814057i | \(0.302746\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11714.9 | 1.00529 | ||||||||
\(515\) | −6718.42 | −0.574853 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10347.6 | 0.880250 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4949.93 | 0.417440 | ||||||||
\(521\) | 7182.70 | 0.603992 | 0.301996 | − | 0.953309i | \(-0.402347\pi\) | ||||
0.301996 | + | 0.953309i | \(0.402347\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9630.13 | −0.805155 | −0.402578 | − | 0.915386i | \(-0.631886\pi\) | ||||
−0.402578 | + | 0.915386i | \(0.631886\pi\) | |||||||
\(524\) | −9946.04 | −0.829189 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2171.86 | 0.180034 | ||||||||
\(527\) | −4982.43 | −0.411837 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12875.1 | 1.05820 | ||||||||
\(530\) | 5225.45 | 0.428262 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9950.83 | −0.808664 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3254.99 | −0.263038 | ||||||||
\(536\) | 2219.06 | 0.178822 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11158.9 | −0.894228 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15549.5 | 1.23572 | 0.617860 | − | 0.786288i | \(-0.288000\pi\) | ||||
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(542\) | −1120.65 | −0.0888122 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −654.791 | −0.0516065 | ||||||||
\(545\) | 19490.9 | 1.53192 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5917.38 | −0.462539 | −0.231270 | − | 0.972890i | \(-0.574288\pi\) | ||||
−0.231270 | + | 0.972890i | \(0.574288\pi\) | |||||||
\(548\) | −10388.8 | −0.809835 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1940.85 | −0.150469 | ||||||||
\(551\) | 6838.71 | 0.528746 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9016.15 | 0.691444 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6402.09 | −0.488325 | ||||||||
\(557\) | 2131.86 | 0.162172 | 0.0810862 | − | 0.996707i | \(-0.474161\pi\) | ||||
0.0810862 | + | 0.996707i | \(0.474161\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 451.894 | 0.0341916 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8659.51 | 0.649963 | ||||||||
\(563\) | 7375.91 | 0.552145 | 0.276072 | − | 0.961137i | \(-0.410967\pi\) | ||||
0.276072 | + | 0.961137i | \(0.410967\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17972.7 | −1.33826 | ||||||||
\(566\) | −1742.10 | −0.129375 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5052.05 | −0.373203 | ||||||||
\(569\) | −12700.8 | −0.935759 | −0.467880 | − | 0.883792i | \(-0.654982\pi\) | ||||
−0.467880 | + | 0.883792i | \(0.654982\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7690.12 | −0.563610 | −0.281805 | − | 0.959472i | \(-0.590933\pi\) | ||||
−0.281805 | + | 0.959472i | \(0.590933\pi\) | |||||||
\(572\) | −14481.7 | −1.05858 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2512.40 | −0.182216 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3094.87 | −0.223295 | −0.111647 | − | 0.993748i | \(-0.535613\pi\) | ||||
−0.111647 | + | 0.993748i | \(0.535613\pi\) | |||||||
\(578\) | 8988.60 | 0.646845 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3556.88 | −0.254640 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15287.7 | −1.08603 | ||||||||
\(584\) | −6146.27 | −0.435504 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3303.83 | 0.232901 | ||||||||
\(587\) | 9967.83 | 0.700880 | 0.350440 | − | 0.936585i | \(-0.386032\pi\) | ||||
0.350440 | + | 0.936585i | \(0.386032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19562.0 | −1.36849 | ||||||||
\(590\) | −16823.0 | −1.17388 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4645.93 | 0.322545 | ||||||||
\(593\) | −1769.73 | −0.122553 | −0.0612766 | − | 0.998121i | \(-0.519517\pi\) | ||||
−0.0612766 | + | 0.998121i | \(0.519517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11750.8 | −0.807605 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18746.3 | −1.28193 | ||||||||
\(599\) | −6347.33 | −0.432963 | −0.216481 | − | 0.976287i | \(-0.569458\pi\) | ||||
−0.216481 | + | 0.976287i | \(0.569458\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22005.7 | −1.49356 | −0.746781 | − | 0.665070i | \(-0.768401\pi\) | ||||
−0.746781 | + | 0.665070i | \(0.768401\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7293.30 | 0.491325 | ||||||||
\(605\) | −25124.1 | −1.68833 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17707.1 | −1.18403 | −0.592017 | − | 0.805925i | \(-0.701668\pi\) | ||||
−0.592017 | + | 0.805925i | \(0.701668\pi\) | |||||||
\(608\) | −2570.84 | −0.171482 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −693.035 | −0.0460003 | ||||||||
\(611\) | −10027.3 | −0.663928 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15846.6 | 1.04411 | 0.522055 | − | 0.852912i | \(-0.325166\pi\) | ||||
0.522055 | + | 0.852912i | \(0.325166\pi\) | |||||||
\(614\) | 2032.84 | 0.133614 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29473.4 | 1.92311 | 0.961553 | − | 0.274621i | \(-0.0885524\pi\) | ||||
0.961553 | + | 0.274621i | \(0.0885524\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11527.5 | −0.748511 | −0.374255 | − | 0.927326i | \(-0.622102\pi\) | ||||
−0.374255 | + | 0.927326i | \(0.622102\pi\) | |||||||
\(620\) | 10174.4 | 0.659053 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18386.1 | −1.18523 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13388.4 | −0.856856 | ||||||||
\(626\) | −13385.2 | −0.854602 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2534.59 | −0.161053 | ||||||||
\(629\) | 5941.63 | 0.376643 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25846.1 | 1.63062 | 0.815308 | − | 0.579027i | \(-0.196568\pi\) | ||||
0.815308 | + | 0.579027i | \(0.196568\pi\) | |||||||
\(632\) | 3349.84 | 0.210838 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14105.0 | −0.883565 | ||||||||
\(635\) | −1485.82 | −0.0928553 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10406.1 | 0.645739 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1337.12 | 0.0825846 | ||||||||
\(641\) | 5534.78 | 0.341046 | 0.170523 | − | 0.985354i | \(-0.445454\pi\) | ||||
0.170523 | + | 0.985354i | \(0.445454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1634.56 | −0.100250 | −0.0501251 | − | 0.998743i | \(-0.515962\pi\) | ||||
−0.0501251 | + | 0.998743i | \(0.515962\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3287.81 | −0.200244 | ||||||||
\(647\) | −7538.01 | −0.458036 | −0.229018 | − | 0.973422i | \(-0.573552\pi\) | ||||
−0.229018 | + | 0.973422i | \(0.573552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 49217.9 | 2.97684 | ||||||||
\(650\) | 1880.76 | 0.113491 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5382.83 | −0.323325 | ||||||||
\(653\) | −13312.2 | −0.797773 | −0.398887 | − | 0.917000i | \(-0.630603\pi\) | ||||
−0.398887 | + | 0.917000i | \(0.630603\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25974.6 | 1.54949 | ||||||||
\(656\) | −2688.00 | −0.159983 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10962.0 | 0.647981 | 0.323991 | − | 0.946060i | \(-0.394975\pi\) | ||||
0.323991 | + | 0.946060i | \(0.394975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23632.5 | 1.39062 | 0.695309 | − | 0.718711i | \(-0.255267\pi\) | ||||
0.695309 | + | 0.718711i | \(0.255267\pi\) | |||||||
\(662\) | −6280.74 | −0.368743 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6093.71 | 0.356147 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13470.6 | 0.781982 | ||||||||
\(668\) | 1551.69 | 0.0898751 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5795.19 | −0.334161 | ||||||||
\(671\) | 2027.56 | 0.116652 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23483.0 | 1.34503 | 0.672513 | − | 0.740085i | \(-0.265215\pi\) | ||||
0.672513 | + | 0.740085i | \(0.265215\pi\) | |||||||
\(674\) | −5487.75 | −0.313620 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5245.30 | 0.298435 | ||||||||
\(677\) | −24672.5 | −1.40065 | −0.700325 | − | 0.713824i | \(-0.746961\pi\) | ||||
−0.700325 | + | 0.713824i | \(0.746961\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1710.02 | 0.0964359 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −29766.5 | −1.67129 | ||||||||
\(683\) | 8939.46 | 0.500818 | 0.250409 | − | 0.968140i | \(-0.419435\pi\) | ||||
0.250409 | + | 0.968140i | \(0.419435\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27131.1 | 1.51332 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 122.069 | 0.00676432 | ||||||||
\(689\) | 14814.4 | 0.819135 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15110.1 | −0.831858 | −0.415929 | − | 0.909397i | \(-0.636543\pi\) | ||||
−0.415929 | + | 0.909397i | \(0.636543\pi\) | |||||||
\(692\) | −2490.64 | −0.136821 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20873.8 | −1.14173 | ||||||||
\(695\) | 16719.4 | 0.912523 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3437.65 | −0.186815 | ||||||||
\(698\) | −4514.02 | −0.244783 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18353.3 | 0.988865 | 0.494432 | − | 0.869216i | \(-0.335376\pi\) | ||||
0.494432 | + | 0.869216i | \(0.335376\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23328.0 | 1.25154 | ||||||||
\(704\) | −3911.91 | −0.209426 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11232.9 | 0.598803 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10073.7 | −0.533604 | −0.266802 | − | 0.963751i | \(-0.585967\pi\) | ||||
−0.266802 | + | 0.963751i | \(0.585967\pi\) | |||||||
\(710\) | 13193.7 | 0.697395 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12576.8 | 0.661986 | ||||||||
\(713\) | −38532.3 | −2.02391 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37819.7 | 1.97815 | ||||||||
\(716\) | 1799.72 | 0.0939368 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1591.18 | 0.0827053 | ||||||||
\(719\) | −19889.3 | −1.03163 | −0.515817 | − | 0.856699i | \(-0.672511\pi\) | ||||
−0.515817 | + | 0.856699i | \(0.672511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 809.397 | 0.0417211 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −737.412 | −0.0378532 | ||||||||
\(725\) | −1351.46 | −0.0692303 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13403.5 | −0.683780 | −0.341890 | − | 0.939740i | \(-0.611067\pi\) | ||||
−0.341890 | + | 0.939740i | \(0.611067\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16051.3 | 0.813816 | ||||||||
\(731\) | 156.113 | 0.00789884 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13255.0 | −0.667919 | −0.333960 | − | 0.942587i | \(-0.608385\pi\) | ||||
−0.333960 | + | 0.942587i | \(0.608385\pi\) | |||||||
\(734\) | 16387.9 | 0.824101 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5063.91 | −0.253612 | ||||||||
\(737\) | 16954.6 | 0.847395 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15420.4 | 0.767588 | 0.383794 | − | 0.923419i | \(-0.374617\pi\) | ||||
0.383794 | + | 0.923419i | \(0.374617\pi\) | |||||||
\(740\) | −12133.1 | −0.602732 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 943.019 | 0.0465626 | 0.0232813 | − | 0.999729i | \(-0.492589\pi\) | ||||
0.0232813 | + | 0.999729i | \(0.492589\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30687.9 | 1.50915 | ||||||||
\(746\) | −28154.7 | −1.38179 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5002.89 | −0.244551 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28595.9 | −1.38945 | −0.694726 | − | 0.719275i | \(-0.744474\pi\) | ||||
−0.694726 | + | 0.719275i | \(0.744474\pi\) | |||||||
\(752\) | −2708.65 | −0.131349 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10083.9 | −0.487049 | ||||||||
\(755\) | −19046.9 | −0.918127 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28984.4 | −1.39162 | −0.695810 | − | 0.718226i | \(-0.744955\pi\) | ||||
−0.695810 | + | 0.718226i | \(0.744955\pi\) | |||||||
\(758\) | −12442.4 | −0.596213 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6713.88 | 0.320445 | ||||||||
\(761\) | −8930.11 | −0.425383 | −0.212691 | − | 0.977119i | \(-0.568223\pi\) | ||||
−0.212691 | + | 0.977119i | \(0.568223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1403.86 | −0.0664789 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21402.8 | −1.00955 | ||||||||
\(767\) | −47694.0 | −2.24528 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2373.15 | −0.111285 | −0.0556424 | − | 0.998451i | \(-0.517721\pi\) | ||||
−0.0556424 | + | 0.998451i | \(0.517721\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6113.03 | 0.284991 | ||||||||
\(773\) | −27977.0 | −1.30176 | −0.650881 | − | 0.759180i | \(-0.725600\pi\) | ||||
−0.650881 | + | 0.759180i | \(0.725600\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3865.82 | 0.179180 | ||||||||
\(776\) | 8361.32 | 0.386796 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8443.23 | −0.389080 | ||||||||
\(779\) | −13496.9 | −0.620766 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38599.9 | −1.76852 | ||||||||
\(782\) | −6476.17 | −0.296148 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6619.23 | 0.300956 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34360.9 | −1.55633 | −0.778167 | − | 0.628058i | \(-0.783850\pi\) | ||||
−0.778167 | + | 0.628058i | \(0.783850\pi\) | |||||||
\(788\) | −11498.6 | −0.519823 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8748.29 | −0.393987 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1964.79 | −0.0879844 | ||||||||
\(794\) | −24151.5 | −1.07948 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19794.8 | −0.881418 | ||||||||
\(797\) | 10399.5 | 0.462196 | 0.231098 | − | 0.972930i | \(-0.425768\pi\) | ||||
0.231098 | + | 0.972930i | \(0.425768\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3464.06 | −0.153379 | ||||||||
\(800\) | 508.046 | 0.0224527 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11012.8 | 0.484880 | ||||||||
\(803\) | −46960.2 | −2.06375 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28844.9 | 1.26057 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7807.37 | −0.339929 | ||||||||
\(809\) | −17943.1 | −0.779783 | −0.389891 | − | 0.920861i | \(-0.627487\pi\) | ||||
−0.389891 | + | 0.920861i | \(0.627487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 571.663 | 0.0247519 | 0.0123760 | − | 0.999923i | \(-0.496061\pi\) | ||||
0.0123760 | + | 0.999923i | \(0.496061\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 35497.0 | 1.52846 | ||||||||
\(815\) | 14057.6 | 0.604190 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 612.931 | 0.0262469 | ||||||||
\(818\) | 2856.36 | 0.122091 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7019.86 | 0.298956 | ||||||||
\(821\) | 13895.7 | 0.590698 | 0.295349 | − | 0.955389i | \(-0.404564\pi\) | ||||
0.295349 | + | 0.955389i | \(0.404564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21629.3 | −0.916098 | −0.458049 | − | 0.888927i | \(-0.651452\pi\) | ||||
−0.458049 | + | 0.888927i | \(0.651452\pi\) | |||||||
\(824\) | −5145.15 | −0.217524 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4700.10 | 0.197628 | 0.0988140 | − | 0.995106i | \(-0.468495\pi\) | ||||
0.0988140 | + | 0.995106i | \(0.468495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38110.8 | 1.59667 | 0.798337 | − | 0.602211i | \(-0.205713\pi\) | ||||
0.798337 | + | 0.602211i | \(0.205713\pi\) | |||||||
\(830\) | −15914.1 | −0.665524 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3790.79 | 0.157959 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4052.32 | −0.167948 | ||||||||
\(836\) | −19642.3 | −0.812613 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 529.920 | 0.0218446 | ||||||||
\(839\) | −20080.2 | −0.826277 | −0.413138 | − | 0.910668i | \(-0.635567\pi\) | ||||
−0.413138 | + | 0.910668i | \(0.635567\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17143.0 | −0.702898 | ||||||||
\(842\) | 562.131 | 0.0230075 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21123.6 | −0.861497 | ||||||||
\(845\) | −13698.4 | −0.557679 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4001.79 | 0.162054 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 649.735 | 0.0262185 | ||||||||
\(851\) | 45950.3 | 1.85095 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34906.8 | 1.40116 | 0.700578 | − | 0.713576i | \(-0.252926\pi\) | ||||
0.700578 | + | 0.713576i | \(0.252926\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2492.76 | −0.0995335 | ||||||||
\(857\) | −48046.8 | −1.91511 | −0.957553 | − | 0.288257i | \(-0.906924\pi\) | ||||
−0.957553 | + | 0.288257i | \(0.906924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35206.2 | 1.39840 | 0.699198 | − | 0.714928i | \(-0.253541\pi\) | ||||
0.699198 | + | 0.714928i | \(0.253541\pi\) | |||||||
\(860\) | −318.791 | −0.0126403 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3572.76 | 0.141170 | ||||||||
\(863\) | −35857.7 | −1.41438 | −0.707190 | − | 0.707024i | \(-0.750037\pi\) | ||||
−0.707190 | + | 0.707024i | \(0.750037\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6504.44 | 0.255674 | ||||||||
\(866\) | 369.242 | 0.0144889 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25594.3 | 0.999109 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16429.7 | −0.639148 | ||||||||
\(872\) | 14926.6 | 0.579679 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −25426.7 | −0.984064 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7366.18 | 0.283624 | 0.141812 | − | 0.989894i | \(-0.454707\pi\) | ||||
0.141812 | + | 0.989894i | \(0.454707\pi\) | |||||||
\(878\) | 22549.3 | 0.866744 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10216.2 | 0.391349 | ||||||||
\(881\) | −3628.00 | −0.138741 | −0.0693703 | − | 0.997591i | \(-0.522099\pi\) | ||||
−0.0693703 | + | 0.997591i | \(0.522099\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25123.0 | 0.957483 | 0.478741 | − | 0.877956i | \(-0.341093\pi\) | ||||
0.478741 | + | 0.877956i | \(0.341093\pi\) | |||||||
\(884\) | 4848.00 | 0.184452 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15939.7 | −0.604406 | ||||||||
\(887\) | 15774.8 | 0.597142 | 0.298571 | − | 0.954387i | \(-0.403490\pi\) | ||||
0.298571 | + | 0.954387i | \(0.403490\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −32844.9 | −1.23704 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15986.3 | −0.600067 | ||||||||
\(893\) | −13600.6 | −0.509660 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4700.07 | −0.175538 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17700.7 | −0.657774 | ||||||||
\(899\) | −20727.1 | −0.768951 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5117.85 | 0.189234 | ||||||||
\(902\) | −20537.5 | −0.758120 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13764.0 | −0.506396 | ||||||||
\(905\) | 1925.79 | 0.0707353 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5113.98 | −0.187218 | −0.0936092 | − | 0.995609i | \(-0.529840\pi\) | ||||
−0.0936092 | + | 0.995609i | \(0.529840\pi\) | |||||||
\(908\) | 2154.37 | 0.0787392 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10279.1 | 0.373834 | 0.186917 | − | 0.982376i | \(-0.440150\pi\) | ||||
0.186917 | + | 0.982376i | \(0.440150\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46558.7 | 1.68770 | ||||||||
\(914\) | 26054.6 | 0.942899 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16686.4 | −0.601895 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38921.9 | −1.39708 | −0.698540 | − | 0.715571i | \(-0.746167\pi\) | ||||
−0.698540 | + | 0.715571i | \(0.746167\pi\) | |||||||
\(920\) | 13224.7 | 0.473918 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2522.10 | 0.0900877 | ||||||||
\(923\) | 37404.8 | 1.33390 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4610.05 | −0.163868 | ||||||||
\(926\) | 8010.93 | 0.284293 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2723.95 | −0.0963558 | ||||||||
\(929\) | 14967.6 | 0.528603 | 0.264302 | − | 0.964440i | \(-0.414859\pi\) | ||||
0.264302 | + | 0.964440i | \(0.414859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6158.92 | 0.216461 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34195.6 | 1.19798 | ||||||||
\(935\) | 13065.3 | 0.456986 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22353.0 | 0.779339 | 0.389669 | − | 0.920955i | \(-0.372589\pi\) | ||||
0.389669 | + | 0.920955i | \(0.372589\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7073.79 | 0.245449 | ||||||||
\(941\) | 13381.5 | 0.463577 | 0.231788 | − | 0.972766i | \(-0.425542\pi\) | ||||
0.231788 | + | 0.972766i | \(0.425542\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26585.5 | −0.918074 | ||||||||
\(944\) | −12883.5 | −0.444198 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 932.665 | 0.0320545 | ||||||||
\(947\) | −633.777 | −0.0217476 | −0.0108738 | − | 0.999941i | \(-0.503461\pi\) | ||||
−0.0108738 | + | 0.999941i | \(0.503461\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45506.3 | 1.55658 | ||||||||
\(950\) | 2550.98 | 0.0871209 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49340.0 | −1.67710 | −0.838551 | − | 0.544823i | \(-0.816597\pi\) | ||||
−0.838551 | + | 0.544823i | \(0.816597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3666.26 | 0.124228 | ||||||||
\(956\) | 12530.7 | 0.423924 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23377.1 | 0.788391 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29498.4 | 0.990179 | ||||||||
\(962\) | −34398.0 | −1.15284 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10426.8 | −0.348365 | ||||||||
\(965\) | −15964.5 | −0.532556 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3340.71 | −0.111096 | −0.0555480 | − | 0.998456i | \(-0.517691\pi\) | ||||
−0.0555480 | + | 0.998456i | \(0.517691\pi\) | |||||||
\(968\) | −19240.7 | −0.638863 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21836.0 | −0.722797 | ||||||||
\(971\) | 4870.40 | 0.160967 | 0.0804833 | − | 0.996756i | \(-0.474354\pi\) | ||||
0.0804833 | + | 0.996756i | \(0.474354\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19249.6 | 0.633261 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −530.745 | −0.0174065 | ||||||||
\(977\) | −6841.34 | −0.224027 | −0.112013 | − | 0.993707i | \(-0.535730\pi\) | ||||
−0.112013 | + | 0.993707i | \(0.535730\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 96092.1 | 3.13699 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12641.3 | 0.410793 | ||||||||
\(983\) | −10689.9 | −0.346851 | −0.173425 | − | 0.984847i | \(-0.555484\pi\) | ||||
−0.173425 | + | 0.984847i | \(0.555484\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30029.2 | 0.971381 | ||||||||
\(986\) | −3483.63 | −0.112517 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19034.2 | 0.612913 | ||||||||
\(989\) | 1207.32 | 0.0388176 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7465.69 | 0.239309 | 0.119655 | − | 0.992816i | \(-0.461821\pi\) | ||||
0.119655 | + | 0.992816i | \(0.461821\pi\) | |||||||
\(992\) | 7791.81 | 0.249385 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 51695.3 | 1.64709 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17354.8 | 0.551286 | 0.275643 | − | 0.961260i | \(-0.411109\pi\) | ||||
0.275643 | + | 0.961260i | \(0.411109\pi\) | |||||||
\(998\) | 30109.1 | 0.954998 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.4.a.u.1.1 | 2 | ||
3.2 | odd | 2 | 882.4.a.bh.1.2 | 2 | |||
7.2 | even | 3 | 882.4.g.bj.361.2 | 4 | |||
7.3 | odd | 6 | 126.4.g.f.37.1 | yes | 4 | ||
7.4 | even | 3 | 882.4.g.bj.667.2 | 4 | |||
7.5 | odd | 6 | 126.4.g.f.109.1 | yes | 4 | ||
7.6 | odd | 2 | 882.4.a.ba.1.2 | 2 | |||
21.2 | odd | 6 | 882.4.g.z.361.1 | 4 | |||
21.5 | even | 6 | 126.4.g.e.109.2 | yes | 4 | ||
21.11 | odd | 6 | 882.4.g.z.667.1 | 4 | |||
21.17 | even | 6 | 126.4.g.e.37.2 | ✓ | 4 | ||
21.20 | even | 2 | 882.4.a.bd.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.g.e.37.2 | ✓ | 4 | 21.17 | even | 6 | ||
126.4.g.e.109.2 | yes | 4 | 21.5 | even | 6 | ||
126.4.g.f.37.1 | yes | 4 | 7.3 | odd | 6 | ||
126.4.g.f.109.1 | yes | 4 | 7.5 | odd | 6 | ||
882.4.a.u.1.1 | 2 | 1.1 | even | 1 | trivial | ||
882.4.a.ba.1.2 | 2 | 7.6 | odd | 2 | |||
882.4.a.bd.1.1 | 2 | 21.20 | even | 2 | |||
882.4.a.bh.1.2 | 2 | 3.2 | odd | 2 | |||
882.4.g.z.361.1 | 4 | 21.2 | odd | 6 | |||
882.4.g.z.667.1 | 4 | 21.11 | odd | 6 | |||
882.4.g.bj.361.2 | 4 | 7.2 | even | 3 | |||
882.4.g.bj.667.2 | 4 | 7.4 | even | 3 |