Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,4,Mod(1,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, 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("1600.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.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: | \(94.4030560092\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1 |
$q$-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 | ||||||||
\(3\) | −2.89898 | −0.557909 | −0.278954 | − | 0.960304i | \(-0.589988\pi\) | ||||
−0.278954 | + | 0.960304i | \(0.589988\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.6969 | −0.901550 | −0.450775 | − | 0.892638i | \(-0.648852\pi\) | ||||
−0.450775 | + | 0.892638i | \(0.648852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −18.5959 | −0.688738 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.1918 | −0.526051 | −0.263025 | − | 0.964789i | \(-0.584720\pi\) | ||||
−0.263025 | + | 0.964789i | \(0.584720\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.7980 | −1.31844 | −0.659218 | − | 0.751952i | \(-0.729113\pi\) | ||||
−0.659218 | + | 0.751952i | \(0.729113\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −30.3837 | −0.433478 | −0.216739 | − | 0.976230i | \(-0.569542\pi\) | ||||
−0.216739 | + | 0.976230i | \(0.569542\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 59.1918 | 0.714713 | 0.357356 | − | 0.933968i | \(-0.383678\pi\) | ||||
0.357356 | + | 0.933968i | \(0.383678\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 48.4041 | 0.502983 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −205.687 | −1.86472 | −0.932362 | − | 0.361526i | \(-0.882256\pi\) | ||||
−0.932362 | + | 0.361526i | \(0.882256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 132.182 | 0.942162 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.38367 | −0.0536831 | −0.0268415 | − | 0.999640i | \(-0.508545\pi\) | ||||
−0.0268415 | + | 0.999640i | \(0.508545\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −331.151 | −1.91860 | −0.959298 | − | 0.282396i | \(-0.908871\pi\) | ||||
−0.959298 | + | 0.282396i | \(0.908871\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 55.6367 | 0.293488 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −266.565 | −1.18441 | −0.592204 | − | 0.805788i | \(-0.701742\pi\) | ||||
−0.592204 | + | 0.805788i | \(0.701742\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 179.151 | 0.735567 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −320.788 | −1.22192 | −0.610959 | − | 0.791662i | \(-0.709216\pi\) | ||||
−0.610959 | + | 0.791662i | \(0.709216\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 83.1214 | 0.294788 | 0.147394 | − | 0.989078i | \(-0.452911\pi\) | ||||
0.147394 | + | 0.989078i | \(0.452911\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 276.434 | 0.857915 | 0.428957 | − | 0.903325i | \(-0.358881\pi\) | ||||
0.428957 | + | 0.903325i | \(0.358881\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −64.2122 | −0.187208 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 88.0816 | 0.241841 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −390.888 | −1.01307 | −0.506534 | − | 0.862220i | \(-0.669073\pi\) | ||||
−0.506534 | + | 0.862220i | \(0.669073\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −171.596 | −0.398744 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 779.110 | 1.71918 | 0.859589 | − | 0.510986i | \(-0.170720\pi\) | ||||
0.859589 | + | 0.510986i | \(0.170720\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 483.171 | 1.01416 | 0.507080 | − | 0.861899i | \(-0.330725\pi\) | ||||
0.507080 | + | 0.861899i | \(0.330725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 310.495 | 0.620931 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 123.707 | 0.225571 | 0.112785 | − | 0.993619i | \(-0.464023\pi\) | ||||
0.112785 | + | 0.993619i | \(0.464023\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 596.282 | 1.04035 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −187.233 | −0.312964 | −0.156482 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156482 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −778.706 | −1.24850 | −0.624251 | − | 0.781224i | \(-0.714596\pi\) | ||||
−0.624251 | + | 0.781224i | \(0.714596\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 320.445 | 0.474261 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 446.384 | 0.635723 | 0.317861 | − | 0.948137i | \(-0.397035\pi\) | ||||
0.317861 | + | 0.948137i | \(0.397035\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 118.898 | 0.163097 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1054.05 | −1.39394 | −0.696970 | − | 0.717100i | \(-0.745469\pi\) | ||||
−0.696970 | + | 0.717100i | \(0.745469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.3041 | 0.0299503 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −94.8490 | −0.112966 | −0.0564830 | − | 0.998404i | \(-0.517989\pi\) | ||||
−0.0564830 | + | 0.998404i | \(0.517989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1031.84 | 1.18864 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 960.000 | 1.07040 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 252.041 | 0.263823 | 0.131912 | − | 0.991261i | \(-0.457888\pi\) | ||||
0.131912 | + | 0.991261i | \(0.457888\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 356.890 | 0.362311 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −37.9184 | −0.0373566 | −0.0186783 | − | 0.999826i | \(-0.505946\pi\) | ||||
−0.0186783 | + | 0.999826i | \(0.505946\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −94.4133 | −0.0903186 | −0.0451593 | − | 0.998980i | \(-0.514380\pi\) | ||||
−0.0451593 | + | 0.998980i | \(0.514380\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −901.464 | −0.814466 | −0.407233 | − | 0.913324i | \(-0.633506\pi\) | ||||
−0.407233 | + | 0.913324i | \(0.633506\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1415.69 | −1.24403 | −0.622013 | − | 0.783007i | \(-0.713685\pi\) | ||||
−0.622013 | + | 0.783007i | \(0.713685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 772.767 | 0.660791 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −293.576 | −0.244401 | −0.122200 | − | 0.992505i | \(-0.538995\pi\) | ||||
−0.122200 | + | 0.992505i | \(0.538995\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1149.19 | 0.908057 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 507.314 | 0.390802 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −962.673 | −0.723271 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 929.957 | 0.681719 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −774.717 | −0.541300 | −0.270650 | − | 0.962678i | \(-0.587239\pi\) | ||||
−0.270650 | + | 0.962678i | \(0.587239\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −240.967 | −0.164465 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 334.343 | 0.222990 | 0.111495 | − | 0.993765i | \(-0.464436\pi\) | ||||
0.111495 | + | 0.993765i | \(0.464436\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −988.322 | −0.644349 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 323.514 | 0.201750 | 0.100875 | − | 0.994899i | \(-0.467836\pi\) | ||||
0.100875 | + | 0.994899i | \(0.467836\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −396.482 | −0.241936 | −0.120968 | − | 0.992656i | \(-0.538600\pi\) | ||||
−0.120968 | + | 0.992656i | \(0.538600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −801.376 | −0.478638 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1186.02 | 0.693564 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 186.150 | 0.104445 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1682.89 | 0.925284 | 0.462642 | − | 0.886545i | \(-0.346901\pi\) | ||||
0.462642 | + | 0.886545i | \(0.346901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2924.52 | 1.57612 | 0.788060 | − | 0.615598i | \(-0.211085\pi\) | ||||
0.788060 | + | 0.615598i | \(0.211085\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 565.012 | 0.298553 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2768.42 | −1.40729 | −0.703644 | − | 0.710553i | \(-0.748445\pi\) | ||||
−0.703644 | + | 0.710553i | \(0.748445\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1133.18 | 0.565199 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3434.34 | 1.68114 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2816.33 | 1.35333 | 0.676663 | − | 0.736292i | \(-0.263425\pi\) | ||||
0.676663 | + | 0.736292i | \(0.263425\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1836.41 | −0.850933 | −0.425466 | − | 0.904974i | \(-0.639890\pi\) | ||||
−0.425466 | + | 0.904974i | \(0.639890\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1621.99 | 0.738274 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1100.73 | −0.492249 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1224.22 | −0.538011 | −0.269006 | − | 0.963139i | \(-0.586695\pi\) | ||||
−0.269006 | + | 0.963139i | \(0.586695\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2258.62 | −0.959145 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2729.58 | 1.13977 | 0.569883 | − | 0.821726i | \(-0.306989\pi\) | ||||
0.569883 | + | 0.821726i | \(0.306989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2642.36 | −1.08511 | −0.542555 | − | 0.840020i | \(-0.682543\pi\) | ||||
−0.542555 | + | 0.840020i | \(0.682543\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1400.70 | −0.565809 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 583.118 | 0.228031 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2207.03 | −0.849406 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2339.23 | 0.886183 | 0.443091 | − | 0.896476i | \(-0.353882\pi\) | ||||
0.443091 | + | 0.896476i | \(0.353882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4601.61 | 1.71622 | 0.858111 | − | 0.513464i | \(-0.171638\pi\) | ||||
0.858111 | + | 0.513464i | \(0.171638\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 823.941 | 0.297987 | 0.148993 | − | 0.988838i | \(-0.452397\pi\) | ||||
0.148993 | + | 0.988838i | \(0.452397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3329.70 | 1.18611 | 0.593055 | − | 0.805162i | \(-0.297922\pi\) | ||||
0.593055 | + | 0.805162i | \(0.297922\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −358.624 | −0.125848 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 139.982 | 0.0483980 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3824.93 | 1.28431 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1136.00 | −0.375975 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1018.78 | 0.332398 | 0.166199 | − | 0.986092i | \(-0.446851\pi\) | ||||
0.166199 | + | 0.986092i | \(0.446851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 542.784 | 0.174605 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5529.21 | 1.72971 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2257.45 | 0.696550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1877.65 | 0.571513 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 99.1581 | 0.0297763 | 0.0148882 | − | 0.999889i | \(-0.495261\pi\) | ||||
0.0148882 | + | 0.999889i | \(0.495261\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1197.59 | −0.350163 | −0.175081 | − | 0.984554i | \(-0.556019\pi\) | ||||
−0.175081 | + | 0.984554i | \(0.556019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 453.592 | 0.130892 | 0.0654458 | − | 0.997856i | \(-0.479153\pi\) | ||||
0.0654458 | + | 0.997856i | \(0.479153\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −928.963 | −0.264594 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3788.49 | −1.06520 | −0.532601 | − | 0.846367i | \(-0.678785\pi\) | ||||
−0.532601 | + | 0.846367i | \(0.678785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1294.06 | −0.354675 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6000.47 | 1.62401 | 0.812005 | − | 0.583651i | \(-0.198376\pi\) | ||||
0.812005 | + | 0.583651i | \(0.198376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1842.53 | 0.492480 | 0.246240 | − | 0.969209i | \(-0.420805\pi\) | ||||
0.246240 | + | 0.969209i | \(0.420805\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3913.59 | −1.03316 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3657.93 | −0.942303 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3055.67 | 0.777691 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1149.46 | 0.289057 | 0.144529 | − | 0.989501i | \(-0.453833\pi\) | ||||
0.144529 | + | 0.989501i | \(0.453833\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3947.51 | 0.980939 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5407.67 | −1.31253 | −0.656267 | − | 0.754528i | \(-0.727866\pi\) | ||||
−0.656267 | + | 0.754528i | \(0.727866\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4450.82 | 1.06780 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 155.902 | 0.0369735 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2067.34 | −0.484705 | −0.242352 | − | 0.970188i | \(-0.577919\pi\) | ||||
−0.242352 | + | 0.970188i | \(0.577919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 274.965 | 0.0630247 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 592.388 | 0.134270 | 0.0671348 | − | 0.997744i | \(-0.478614\pi\) | ||||
0.0671348 | + | 0.997744i | \(0.478614\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2583.27 | 0.579049 | 0.289524 | − | 0.957171i | \(-0.406503\pi\) | ||||
0.289524 | + | 0.957171i | \(0.406503\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2991.27 | −0.663151 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4488.09 | 0.973513 | 0.486756 | − | 0.873538i | \(-0.338180\pi\) | ||||
0.486756 | + | 0.873538i | \(0.338180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6158.06 | 1.32141 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6280.54 | −1.33333 | −0.666665 | − | 0.745357i | \(-0.732279\pi\) | ||||
−0.666665 | + | 0.745357i | \(0.732279\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5233.40 | −1.09927 | −0.549635 | − | 0.835405i | \(-0.685233\pi\) | ||||
−0.549635 | + | 0.835405i | \(0.685233\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5356.17 | 1.10162 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3989.83 | −0.812097 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −730.661 | −0.147189 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2438.21 | 0.486149 | 0.243074 | − | 0.970008i | \(-0.421844\pi\) | ||||
0.243074 | + | 0.970008i | \(0.421844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2536.81 | −0.495625 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12711.0 | 2.45852 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1387.87 | −0.265766 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 109.925 | 0.0208416 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7910.44 | 1.47060 | 0.735298 | − | 0.677744i | \(-0.237042\pi\) | ||||
0.735298 | + | 0.677744i | \(0.237042\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 273.702 | 0.0503895 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5419.71 | −0.988178 | −0.494089 | − | 0.869411i | \(-0.664498\pi\) | ||||
−0.494089 | + | 0.869411i | \(0.664498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5570.86 | 1.00602 | 0.503009 | − | 0.864281i | \(-0.332226\pi\) | ||||
0.503009 | + | 0.864281i | \(0.332226\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3724.09 | 0.659829 | 0.329915 | − | 0.944011i | \(-0.392980\pi\) | ||||
0.329915 | + | 0.944011i | \(0.392980\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 160.898 | 0.0282400 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2613.33 | 0.454398 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1798.47 | −0.309812 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4104.07 | 0.694053 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4615.60 | −0.773453 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3223.96 | 0.535362 | 0.267681 | − | 0.963508i | \(-0.413743\pi\) | ||||
0.267681 | + | 0.963508i | \(0.413743\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4957.03 | 0.815746 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9524.43 | 1.53955 | 0.769776 | − | 0.638314i | \(-0.220368\pi\) | ||||
0.769776 | + | 0.638314i | \(0.220368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 851.069 | 0.136353 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6355.40 | 1.00928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6799.20 | 1.07033 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6042.30 | −0.934777 | −0.467388 | − | 0.884052i | \(-0.654805\pi\) | ||||
−0.467388 | + | 0.884052i | \(0.654805\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1626.20 | 0.249422 | 0.124711 | − | 0.992193i | \(-0.460200\pi\) | ||||
0.124711 | + | 0.992193i | \(0.460200\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8168.55 | −1.24218 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 886.955 | 0.133733 | 0.0668667 | − | 0.997762i | \(-0.478700\pi\) | ||||
0.0668667 | + | 0.997762i | \(0.478700\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1470.69 | −0.218032 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1722.27 | −0.253198 | −0.126599 | − | 0.991954i | \(-0.540406\pi\) | ||||
−0.126599 | + | 0.991954i | \(0.540406\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3355.33 | −0.489186 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2790.77 | 0.403519 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9271.77 | −1.31875 | −0.659377 | − | 0.751813i | \(-0.729180\pi\) | ||||
−0.659377 | + | 0.751813i | \(0.729180\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5965.34 | 0.841581 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6526.63 | 0.913331 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5697.15 | −0.790850 | −0.395425 | − | 0.918498i | \(-0.629403\pi\) | ||||
−0.395425 | + | 0.918498i | \(0.629403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 518.094 | 0.0707777 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8526.24 | −1.15558 | −0.577789 | − | 0.816186i | \(-0.696084\pi\) | ||||
−0.577789 | + | 0.816186i | \(0.696084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2245.89 | 0.301996 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4069.23 | −0.542893 | −0.271447 | − | 0.962453i | \(-0.587502\pi\) | ||||
−0.271447 | + | 0.962453i | \(0.587502\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1545.72 | −0.203032 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2394.17 | 0.312054 | 0.156027 | − | 0.987753i | \(-0.450131\pi\) | ||||
0.156027 | + | 0.987753i | \(0.450131\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6249.52 | 0.808316 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −969.253 | −0.124408 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3497.79 | −0.442190 | −0.221095 | − | 0.975252i | \(-0.570963\pi\) | ||||
−0.221095 | + | 0.975252i | \(0.570963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2865.13 | 0.359488 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8608.89 | −1.07209 | −0.536044 | − | 0.844190i | \(-0.680082\pi\) | ||||
−0.536044 | + | 0.844190i | \(0.680082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20464.5 | 2.52955 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5115.88 | 0.623058 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1385.67 | 0.167523 | 0.0837615 | − | 0.996486i | \(-0.473307\pi\) | ||||
0.0837615 | + | 0.996486i | \(0.473307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −937.861 | −0.112558 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13008.8 | −1.54992 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1149.39 | 0.134978 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3738.23 | 0.435858 | 0.217929 | − | 0.975965i | \(-0.430070\pi\) | ||||
0.217929 | + | 0.975965i | \(0.430070\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8993.95 | 1.04118 | 0.520592 | − | 0.853806i | \(-0.325711\pi\) | ||||
0.520592 | + | 0.853806i | \(0.325711\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5140.54 | −0.590878 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8067.48 | −0.914316 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3438.24 | −0.386946 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −462.547 | −0.0516940 | −0.0258470 | − | 0.999666i | \(-0.508228\pi\) | ||||
−0.0258470 | + | 0.999666i | \(0.508228\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5231.82 | −0.580659 | −0.290329 | − | 0.956927i | \(-0.593765\pi\) | ||||
−0.290329 | + | 0.956927i | \(0.593765\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12175.0 | −1.33274 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8995.77 | −0.978006 | −0.489003 | − | 0.872282i | \(-0.662639\pi\) | ||||
−0.489003 | + | 0.872282i | \(0.662639\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1194.09 | 0.128937 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5549.52 | −0.595182 | −0.297591 | − | 0.954694i | \(-0.596183\pi\) | ||||
−0.297591 | + | 0.954694i | \(0.596183\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4878.65 | −0.516224 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5951.29 | −0.625521 | −0.312760 | − | 0.949832i | \(-0.601254\pi\) | ||||
−0.312760 | + | 0.949832i | \(0.601254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6156.51 | 0.642791 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8478.13 | −0.879332 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13912.7 | −1.42409 | −0.712047 | − | 0.702132i | \(-0.752232\pi\) | ||||
−0.712047 | + | 0.702132i | \(0.752232\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4016.16 | −0.408406 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17467.6 | −1.76475 | −0.882374 | − | 0.470549i | \(-0.844056\pi\) | ||||
−0.882374 | + | 0.470549i | \(0.844056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1575.36 | −0.158127 | −0.0790637 | − | 0.996870i | \(-0.525193\pi\) | ||||
−0.0790637 | + | 0.996870i | \(0.525193\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15618.3 | 1.54760 | 0.773800 | − | 0.633430i | \(-0.218354\pi\) | ||||
0.773800 | + | 0.633430i | \(0.218354\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2065.53 | −0.203363 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8025.60 | 0.785138 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1595.25 | −0.155074 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7268.92 | 0.697738 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9527.90 | −0.908854 | −0.454427 | − | 0.890784i | \(-0.650156\pi\) | ||||
−0.454427 | + | 0.890784i | \(0.650156\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16473.2 | 1.56157 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9956.08 | −0.937924 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15729.6 | −1.46361 | −0.731805 | − | 0.681514i | \(-0.761322\pi\) | ||||
−0.731805 | + | 0.681514i | \(0.761322\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8164.49 | −0.755033 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2566.49 | 0.235894 | 0.117947 | − | 0.993020i | \(-0.462369\pi\) | ||||
0.117947 | + | 0.993020i | \(0.462369\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 254.727 | 0.0232704 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3126.21 | 0.282152 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13560.4 | −1.21652 | −0.608261 | − | 0.793737i | \(-0.708133\pi\) | ||||
−0.608261 | + | 0.793737i | \(0.708133\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5323.72 | 0.474743 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5222.51 | 0.462943 | 0.231471 | − | 0.972842i | \(-0.425646\pi\) | ||||
0.231471 | + | 0.972842i | \(0.425646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4702.11 | −0.411890 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11875.9 | 1.03416 | 0.517082 | − | 0.855936i | \(-0.327018\pi\) | ||||
0.517082 | + | 0.855936i | \(0.327018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13002.0 | 1.12559 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7824.07 | 0.673375 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5305.27 | −0.451307 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3549.00 | 0.300161 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2456.04 | 0.206528 | 0.103264 | − | 0.994654i | \(-0.467071\pi\) | ||||
0.103264 | + | 0.994654i | \(0.467071\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 634.460 | 0.0530459 | 0.0265229 | − | 0.999648i | \(-0.491556\pi\) | ||||
0.0265229 | + | 0.999648i | \(0.491556\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10061.6 | 0.831669 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30140.0 | 2.47720 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14488.3 | −1.18406 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19824.0 | 1.61102 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7912.98 | −0.635885 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1232.35 | 0.0984807 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18078.4 | −1.43669 | −0.718347 | − | 0.695685i | \(-0.755101\pi\) | ||||
−0.718347 | + | 0.695685i | \(0.755101\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7660.14 | 0.605393 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24815.3 | −1.93972 | −0.969860 | − | 0.243661i | \(-0.921651\pi\) | ||||
−0.969860 | + | 0.243661i | \(0.921651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8985.02 | −0.698490 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −496.245 | −0.0383680 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7453.24 | −0.573136 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10073.7 | 0.766310 | 0.383155 | − | 0.923684i | \(-0.374838\pi\) | ||||
0.383155 | + | 0.923684i | \(0.374838\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5136.73 | −0.388660 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1690.45 | −0.127221 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7505.06 | 0.561813 | 0.280906 | − | 0.959735i | \(-0.409365\pi\) | ||||
0.280906 | + | 0.959735i | \(0.409365\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1985.23 | −0.147040 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15251.4 | −1.12368 | −0.561838 | − | 0.827247i | \(-0.689906\pi\) | ||||
−0.561838 | + | 0.827247i | \(0.689906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2683.78 | −0.196695 | −0.0983474 | − | 0.995152i | \(-0.531356\pi\) | ||||
−0.0983474 | + | 0.995152i | \(0.531356\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6781.39 | −0.494409 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7369.88 | −0.531737 | −0.265868 | − | 0.964009i | \(-0.585659\pi\) | ||||
−0.265868 | + | 0.964009i | \(0.585659\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13340.0 | −0.957496 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17599.4 | 1.25671 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7501.85 | 0.532925 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20865.4 | 1.46713 | 0.733567 | − | 0.679618i | \(-0.237854\pi\) | ||||
0.733567 | + | 0.679618i | \(0.237854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19601.4 | −1.37124 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2388.59 | −0.166249 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25894.0 | −1.79316 | −0.896578 | − | 0.442886i | \(-0.853954\pi\) | ||||
−0.896578 | + | 0.442886i | \(0.853954\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9652.73 | −0.661742 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5632.42 | −0.384198 | −0.192099 | − | 0.981376i | \(-0.561529\pi\) | ||||
−0.192099 | + | 0.981376i | \(0.561529\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13079.7 | −0.887742 | −0.443871 | − | 0.896091i | \(-0.646395\pi\) | ||||
−0.443871 | + | 0.896091i | \(0.646395\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2300.45 | −0.155359 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18890.2 | 1.26314 | 0.631572 | − | 0.775317i | \(-0.282410\pi\) | ||||
0.631572 | + | 0.775317i | \(0.282410\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −405.804 | −0.0270017 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17083.0 | −1.13111 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13631.5 | 0.898155 | 0.449078 | − | 0.893493i | \(-0.351753\pi\) | ||||
0.449078 | + | 0.893493i | \(0.351753\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14982.2 | 0.977568 | 0.488784 | − | 0.872405i | \(-0.337441\pi\) | ||||
0.488784 | + | 0.872405i | \(0.337441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25049.9 | −1.62656 | −0.813279 | − | 0.581873i | \(-0.802320\pi\) | ||||
−0.813279 | + | 0.581873i | \(0.802320\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27188.0 | −1.75687 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1583.69 | 0.101844 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3293.24 | 0.209760 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8099.23 | 0.513414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18711.0 | −1.18046 | −0.590232 | − | 0.807233i | \(-0.700964\pi\) | ||||
−0.590232 | + | 0.807233i | \(0.700964\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2953.43 | −0.185448 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3968.19 | 0.246821 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3481.76 | 0.215550 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25792.2 | 1.58929 | 0.794643 | − | 0.607077i | \(-0.207658\pi\) | ||||
0.794643 | + | 0.607077i | \(0.207658\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20256.7 | −1.24237 | −0.621186 | − | 0.783663i | \(-0.713349\pi\) | ||||
−0.621186 | + | 0.783663i | \(0.713349\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6655.43 | 0.404408 | 0.202204 | − | 0.979343i | \(-0.435190\pi\) | ||||
0.202204 | + | 0.979343i | \(0.435190\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14952.6 | −0.904375 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16029.1 | −0.965021 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8490.91 | −0.508844 | −0.254422 | − | 0.967093i | \(-0.581885\pi\) | ||||
−0.254422 | + | 0.967093i | \(0.581885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14480.8 | 0.859890 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15543.8 | 0.918816 | 0.459408 | − | 0.888225i | \(-0.348062\pi\) | ||||
0.459408 | + | 0.888225i | \(0.348062\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13519.8 | 0.795553 | 0.397777 | − | 0.917482i | \(-0.369782\pi\) | ||||
0.397777 | + | 0.917482i | \(0.369782\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5443.27 | −0.318852 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1724.41 | 0.100104 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −287.457 | −0.0166125 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9272.95 | −0.533499 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11565.3 | 0.662421 | 0.331211 | − | 0.943557i | \(-0.392543\pi\) | ||||
0.331211 | + | 0.943557i | \(0.392543\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28227.5 | 1.60247 | 0.801235 | − | 0.598350i | \(-0.204177\pi\) | ||||
0.801235 | + | 0.598350i | \(0.204177\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4208.31 | −0.237850 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3471.79 | 0.195359 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6425.99 | −0.360005 | −0.180003 | − | 0.983666i | \(-0.557611\pi\) | ||||
−0.180003 | + | 0.983666i | \(0.557611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1314.95 | −0.0730256 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24156.1 | 1.33566 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19066.9 | −1.04969 | −0.524846 | − | 0.851197i | \(-0.675877\pi\) | ||||
−0.524846 | + | 0.851197i | \(0.675877\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5958.97 | −0.326641 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9746.71 | 0.529674 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10982.7 | 0.594285 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4796.00 | −0.258406 | −0.129203 | − | 0.991618i | \(-0.541242\pi\) | ||||
−0.129203 | + | 0.991618i | \(0.541242\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15778.5 | −0.846511 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 633.121 | 0.0336789 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9805.33 | 0.519389 | 0.259695 | − | 0.965691i | \(-0.416378\pi\) | ||||
0.259695 | + | 0.965691i | \(0.416378\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8300.91 | −0.437846 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 68113.4 | 3.57765 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17395.2 | −0.906049 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27539.7 | −1.42845 | −0.714227 | − | 0.699915i | \(-0.753221\pi\) | ||||
−0.714227 | + | 0.699915i | \(0.753221\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1576.41 | 0.0814267 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5341.45 | −0.274759 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16543.8 | 0.843985 | 0.421993 | − | 0.906599i | \(-0.361331\pi\) | ||||
0.421993 | + | 0.906599i | \(0.361331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8135.16 | 0.413309 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2525.53 | −0.127784 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16718.6 | 0.842450 | 0.421225 | − | 0.906956i | \(-0.361600\pi\) | ||||
0.421225 | + | 0.906956i | \(0.361600\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2374.17 | −0.118662 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24022.6 | −1.19579 | −0.597893 | − | 0.801576i | \(-0.703995\pi\) | ||||
−0.597893 | + | 0.801576i | \(0.703995\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10604.3 | 0.525719 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26201.8 | −1.29374 | −0.646871 | − | 0.762600i | \(-0.723923\pi\) | ||||
−0.646871 | + | 0.762600i | \(0.723923\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19601.0 | 0.960059 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15051.7 | 0.734282 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24451.7 | −1.18809 | −0.594045 | − | 0.804432i | \(-0.702470\pi\) | ||||
−0.594045 | + | 0.804432i | \(0.702470\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3332.26 | −0.161268 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21403.8 | 1.02765 | 0.513827 | − | 0.857894i | \(-0.328227\pi\) | ||||
0.513827 | + | 0.857894i | \(0.328227\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11443.7 | −0.547275 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28935.9 | −1.37835 | −0.689176 | − | 0.724594i | \(-0.742027\pi\) | ||||
−0.689176 | + | 0.724594i | \(0.742027\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23637.8 | 1.12155 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −48147.4 | −2.26663 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11479.3 | −0.538301 | −0.269151 | − | 0.963098i | \(-0.586743\pi\) | ||||
−0.269151 | + | 0.963098i | \(0.586743\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15676.7 | 0.732275 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2512.27 | 0.116895 | 0.0584477 | − | 0.998290i | \(-0.481385\pi\) | ||||
0.0584477 | + | 0.998290i | \(0.481385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12902.8 | −0.595736 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18988.0 | −0.873320 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3593.34 | 0.164635 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1108.17 | −0.0505781 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2650.18 | −0.120036 | −0.0600182 | − | 0.998197i | \(-0.519116\pi\) | ||||
−0.0600182 | + | 0.998197i | \(0.519116\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5993.16 | 0.270421 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4901.81 | 0.220339 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29859.0 | −1.33711 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24516.7 | −1.08962 | −0.544810 | − | 0.838560i | \(-0.683398\pi\) | ||||
−0.544810 | + | 0.838560i | \(0.683398\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8399.07 | −0.371887 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1763.80 | 0.0778039 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14944.8 | 0.656775 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1717.32 | −0.0749102 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29725.5 | −1.29183 | −0.645917 | − | 0.763408i | \(-0.723525\pi\) | ||||
−0.645917 | + | 0.763408i | \(0.723525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2050.38 | −0.0887773 | −0.0443887 | − | 0.999014i | \(-0.514134\pi\) | ||||
−0.0443887 | + | 0.999014i | \(0.514134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7488.83 | −0.323056 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4920.11 | 0.210689 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19188.0 | −0.818658 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33863.4 | 1.43952 | 0.719758 | − | 0.694225i | \(-0.244253\pi\) | ||||
0.719758 | + | 0.694225i | \(0.244253\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1216.52 | 0.0515251 | 0.0257625 | − | 0.999668i | \(-0.491799\pi\) | ||||
0.0257625 | + | 0.999668i | \(0.491799\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25654.4 | −1.07871 | −0.539355 | − | 0.842079i | \(-0.681332\pi\) | ||||
−0.539355 | + | 0.842079i | \(0.681332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24544.6 | −1.02831 | −0.514154 | − | 0.857698i | \(-0.671894\pi\) | ||||
−0.514154 | + | 0.857698i | \(0.671894\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13010.9 | −0.543131 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1951.00 | 0.0811504 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43772.1 | −1.80763 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16548.6 | −0.680954 | −0.340477 | − | 0.940253i | \(-0.610589\pi\) | ||||
−0.340477 | + | 0.940253i | \(0.610589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24318.7 | −0.997118 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18207.2 | 0.743877 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16073.7 | 0.652065 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15171.5 | 0.613292 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54828.9 | 2.20859 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24363.5 | −0.977950 | −0.488975 | − | 0.872298i | \(-0.662629\pi\) | ||||
−0.488975 | + | 0.872298i | \(0.662629\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 575.718 | 0.0229477 | 0.0114738 | − | 0.999934i | \(-0.496348\pi\) | ||||
0.0114738 | + | 0.999934i | \(0.496348\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1531.31 | 0.0608236 | 0.0304118 | − | 0.999537i | \(-0.490318\pi\) | ||||
0.0304118 | + | 0.999537i | \(0.490318\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15527.4 | −0.614604 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7706.51 | 0.303978 | 0.151989 | − | 0.988382i | \(-0.451432\pi\) | ||||
0.151989 | + | 0.988382i | \(0.451432\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11566.4 | 0.453076 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8566.92 | −0.334422 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7644.85 | −0.297400 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4686.93 | −0.181705 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43618.9 | 1.67948 | 0.839741 | − | 0.542988i | \(-0.182707\pi\) | ||||
0.839741 | + | 0.542988i | \(0.182707\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7068.31 | −0.271227 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13416.4 | −0.513066 | −0.256533 | − | 0.966536i | \(-0.582580\pi\) | ||||
−0.256533 | + | 0.966536i | \(0.582580\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29538.2 | −1.12575 | −0.562875 | − | 0.826542i | \(-0.690305\pi\) | ||||
−0.562875 | + | 0.826542i | \(0.690305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1950.88 | −0.0738490 | −0.0369245 | − | 0.999318i | \(-0.511756\pi\) | ||||
−0.0369245 | + | 0.999318i | \(0.511756\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12935.4 | 0.488009 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2281.87 | −0.0857974 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16362.6 | 0.613162 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36849.0 | −1.37163 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2776.26 | 0.102996 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11876.6 | 0.439142 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4023.42 | 0.148273 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3507.55 | −0.128408 | −0.0642042 | − | 0.997937i | \(-0.520451\pi\) | ||||
−0.0642042 | + | 0.997937i | \(0.520451\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 705.127 | 0.0257289 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33841.4 | 1.23075 | 0.615377 | − | 0.788233i | \(-0.289004\pi\) | ||||
0.615377 | + | 0.788233i | \(0.289004\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20229.2 | 0.733283 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5582.50 | −0.201036 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25440.7 | −0.913178 | −0.456589 | − | 0.889678i | \(-0.650929\pi\) | ||||
−0.456589 | + | 0.889678i | \(0.650929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22932.2 | −0.820458 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11570.6 | 0.412623 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1755.70 | 0.0622058 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26416.7 | −0.932941 | −0.466471 | − | 0.884537i | \(-0.654475\pi\) | ||||
−0.466471 | + | 0.884537i | \(0.654475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3800.84 | −0.133800 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15711.6 | 0.551313 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1936.70 | 0.0675231 | 0.0337616 | − | 0.999430i | \(-0.489251\pi\) | ||||
0.0337616 | + | 0.999430i | \(0.489251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16149.8 | −0.561266 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23459.1 | −0.812694 | −0.406347 | − | 0.913719i | \(-0.633198\pi\) | ||||
−0.406347 | + | 0.913719i | \(0.633198\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 65981.8 | 2.27854 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23606.8 | −0.810049 | −0.405025 | − | 0.914306i | \(-0.632737\pi\) | ||||
−0.405025 | + | 0.914306i | \(0.632737\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48122.4 | 1.64607 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10796.1 | −0.368125 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30164.2 | −1.02530 | −0.512652 | − | 0.858596i | \(-0.671337\pi\) | ||||
−0.512652 | + | 0.858596i | \(0.671337\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −466.440 | −0.0157553 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5401.70 | −0.181887 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 79870.0 | 2.68101 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16763.6 | 0.560953 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9034.04 | 0.300429 | 0.150215 | − | 0.988653i | \(-0.452004\pi\) | ||||
0.150215 | + | 0.988653i | \(0.452004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5213.71 | 0.172847 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36159.0 | 1.19506 | 0.597528 | − | 0.801848i | \(-0.296150\pi\) | ||||
0.597528 | + | 0.801848i | \(0.296150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6620.03 | 0.218118 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38584.0 | 1.26347 | 0.631736 | − | 0.775184i | \(-0.282343\pi\) | ||||
0.631736 | + | 0.775184i | \(0.282343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1820.33 | 0.0594258 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26326.1 | 0.856808 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53046.3 | 1.72117 | 0.860587 | − | 0.509303i | \(-0.170097\pi\) | ||||
0.860587 | + | 0.509303i | \(0.170097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13380.5 | 0.431516 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17097.0 | −0.549699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16425.7 | 0.526517 | 0.263259 | − | 0.964725i | \(-0.415203\pi\) | ||||
0.263259 | + | 0.964725i | \(0.415203\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9346.19 | −0.298683 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20024.6 | 0.636092 | 0.318046 | − | 0.948075i | \(-0.396973\pi\) | ||||
0.318046 | + | 0.948075i | \(0.396973\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35235.0 | −1.11590 |
(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 | 1600.4.a.cm.1.1 | 2 | ||
4.3 | odd | 2 | 1600.4.a.ce.1.2 | 2 | |||
5.2 | odd | 4 | 320.4.c.h.129.3 | 4 | |||
5.3 | odd | 4 | 320.4.c.h.129.2 | 4 | |||
5.4 | even | 2 | 1600.4.a.cf.1.2 | 2 | |||
8.3 | odd | 2 | 200.4.a.l.1.1 | 2 | |||
8.5 | even | 2 | 400.4.a.v.1.2 | 2 | |||
20.3 | even | 4 | 320.4.c.g.129.3 | 4 | |||
20.7 | even | 4 | 320.4.c.g.129.2 | 4 | |||
20.19 | odd | 2 | 1600.4.a.cl.1.1 | 2 | |||
24.11 | even | 2 | 1800.4.a.bp.1.2 | 2 | |||
40.3 | even | 4 | 40.4.c.a.9.2 | ✓ | 4 | ||
40.13 | odd | 4 | 80.4.c.c.49.3 | 4 | |||
40.19 | odd | 2 | 200.4.a.k.1.2 | 2 | |||
40.27 | even | 4 | 40.4.c.a.9.3 | yes | 4 | ||
40.29 | even | 2 | 400.4.a.x.1.1 | 2 | |||
40.37 | odd | 4 | 80.4.c.c.49.2 | 4 | |||
120.53 | even | 4 | 720.4.f.m.289.2 | 4 | |||
120.59 | even | 2 | 1800.4.a.bk.1.1 | 2 | |||
120.77 | even | 4 | 720.4.f.m.289.1 | 4 | |||
120.83 | odd | 4 | 360.4.f.e.289.2 | 4 | |||
120.107 | odd | 4 | 360.4.f.e.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.c.a.9.2 | ✓ | 4 | 40.3 | even | 4 | ||
40.4.c.a.9.3 | yes | 4 | 40.27 | even | 4 | ||
80.4.c.c.49.2 | 4 | 40.37 | odd | 4 | |||
80.4.c.c.49.3 | 4 | 40.13 | odd | 4 | |||
200.4.a.k.1.2 | 2 | 40.19 | odd | 2 | |||
200.4.a.l.1.1 | 2 | 8.3 | odd | 2 | |||
320.4.c.g.129.2 | 4 | 20.7 | even | 4 | |||
320.4.c.g.129.3 | 4 | 20.3 | even | 4 | |||
320.4.c.h.129.2 | 4 | 5.3 | odd | 4 | |||
320.4.c.h.129.3 | 4 | 5.2 | odd | 4 | |||
360.4.f.e.289.1 | 4 | 120.107 | odd | 4 | |||
360.4.f.e.289.2 | 4 | 120.83 | odd | 4 | |||
400.4.a.v.1.2 | 2 | 8.5 | even | 2 | |||
400.4.a.x.1.1 | 2 | 40.29 | even | 2 | |||
720.4.f.m.289.1 | 4 | 120.77 | even | 4 | |||
720.4.f.m.289.2 | 4 | 120.53 | even | 4 | |||
1600.4.a.ce.1.2 | 2 | 4.3 | odd | 2 | |||
1600.4.a.cf.1.2 | 2 | 5.4 | even | 2 | |||
1600.4.a.cl.1.1 | 2 | 20.19 | odd | 2 | |||
1600.4.a.cm.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1800.4.a.bk.1.1 | 2 | 120.59 | even | 2 | |||
1800.4.a.bp.1.2 | 2 | 24.11 | even | 2 |